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Research ArticleOptimization of Fuel Injection Control System of Two-StrokeAeroengine of UAV
Yixuan Wang1 Yan Shi 12 Maolin Cai1 Weiqing Xu 1 Jian Zhang1 Wei Zhong23
and Na Wang 1
1School of Automation Science and Electrical Engineering Beihang University Beijing 100191 China2Jiangsu Provincial Key Laboratory of Advanced Manufacture and Process for Marine Mechanical EquipmentZhenjiang 212003 China3School of Mechanical Engineering Jiangsu University of Science and Technology Zhenjiang 212003 China
Correspondence should be addressed to Yan Shi yesoyougmailcom and Na Wang lion_na987buaaeducn
Received 1 May 2020 Accepted 8 June 2020 Published 9 July 2020
Guest Editor Juan Sandoval
Copyright copy 2020 YixuanWang et alis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Power efficiency of two-stroke spark-ignition engine is generally low because improper amount of fuel injection leads to a lot ofunburned fuel loss during the engine working process However parameters of the fuel injection system are hard to confirm byaviation experiments due to expensive test costs is paper proposes a method of calibrating injection parameters of two-strokespark-ignition engine based on thermodynamic simulation and parameter optimum algorithm Firstly the one-dimensionalthermodynamic model is built according to the internal structure and thermodynamic process of the engine then the modelparameters are corrected according to the operating principle of the injector after experimental verification of the modelconsidering both the engine power sufficiency and fuel economy Analytic Hierarchy Process method is applied to look for theoptimal injection amount and fuel injection advance angle at different engine working speeds finally an aeroengine experimentstation with an electronic fuel injector system is built rough simulation and experiment studies it can be seen that when theengine speed changes from 3000 to 3500 RPM the oil consumption rate of the optimal results is higher than that of the previousones when the aeroengine speed is higher than 4000 RPM the oil consumption rate results of the optimal method are 10 to 27higher than the original results is paper can be a reference in the optimization of UAV aircraft engine
1 Introduction
Two-stroke engine has been widely applied in the powersystem of small aerial equipment fuel-powered UAV becauseof the advantages of strong explosive and small size [1]However model selection of engine is always difficult for thedesign of fuel-powered UAVrsquos power system at is be-cause in the flight simulation environment of UAV theoutput characteristics of the engine are hard to accuratelypredict especially it is hard to find a matching fuel supplysystem Traditional fuel supply method for two-stroke en-gine is using carburetor which canmechanically atomize fuelduring the engine working process [2] Nevertheless au-tomatic control cannot be achieved in engine with a car-buretor and the engine can hardly automatically adapt to
the flight condition variation of UAV Electronic fuel in-jector (EFI) has been widely developed in the area of enginefuel supply due to its superiorities of controllability andfavourable characteristics [3] Performance of the enginewith the EFI system has been generally studied by setting upexperimental stations which can test the output speedtorque air-fuel ratio (AFR) cylinder pressure and exhaustcontents and the researchers do a lot of experiments tooptimize the engine structure or control method [4 5]
Although the engine experiments are designed more andmore realistic in recent time there is still some distancebetween test results to the real application In addition thetraditional two-stroke engine test stations are alwaysdesigned more suitable for the ground vehicles because thetest torque is always added by means of electromagnetism
HindawiComplexityVolume 2020 Article ID 8921320 12 pageshttpsdoiorg10115520208921320
which is hard to test the output power of an aeroengine witha propeller Furthermore in order to get accurate results theexperiment conditions have to be prepared strictly such ashigh precision sensors and stable environment which willgreatly increase the research cost Last but not the least it isdangerous and inaccurate to simulate extreme workingconditions by engine station tests
erefore research studies have paid more and more at-tention to the engine working process simulation by mathe-matical models In order to estimate engine performance suchas cylinder pressure heat release rate and fuel consumptionVenkatraman and Devaradjane [6] build the working math-ematical model of a 4-stroke engine e simulation modelincludes cylinder state equation heat transfer process ignitiondelay combustion duration and NOx formation In additionbased on the mathematical model Venkatraman and Devar-adjane [7] design engine experiments for demonstration Intheir works the heat release rate brake thermal efficiencycarbon monoxide hydrocarbon and so on are predictedthrough the model and the experiments verify that the rec-tification model coincides with the reality Furthermore in thecombustion model Wiebe heat release function is appliedbased on the exponential rate of the chemical reactions Wiebeequations have been implemented by Miyamoto et al [8] andone of the equation factors is considered to be important whichis called ldquorate of heat releaserdquo Ganapathy et al [9] haveemployed a thermodynamic model based on two-zone Wiebeheat release function to simulate the performance of new fuelengine Raut [10] also use an exponential rate-basedWiebe heatrelease model and the Pflaum formula is applied in the esti-mation of empirical coefficient of the heat transfer processFrom these works it can be seen that engine performance studyby using the mathematical model method is effective
GT-Power is the leading engine simulation softwarebased on one-dimensional gas dynamic which represents theflow and transfer in the components of the engine systemandmore andmore scientists and engineers have applied thecomputing tool in engine prediction in order to improve thecontrol performance or reduce the emission Kassa et al [11]have leveraged experimental data from a 6-cylinder engineto a GT-Power model to better understand the distributionof the port-injected fuel across cylinders under severaloperating conditions Rahimi-Gorji et al [12] have opti-mized the performance and fuel consumption according tothe weather conditions by combining the artificial neuralnetwork and GT-Power model and pressure temperatureand humidity of the incoming air are considered in thenetwork to obtain a better engine performance Alves et al[13] apply GT-Power in the engine intake system design andthe best intake runner length and diameter configuration ofeach speed for a four-stroke and single cylinder engine isfound to get the optimum volume efficiency Trajkovic et al[14] build the GT-Power model of a 2-stroke engine to studythe effect of different parameters and their effect onpneumatic hybrid performance From the works above themathematical model built by GT-Power is proved to beeffective to predict and improve the engine characteristicsHowever these papers mainly focus on the engine structurerather than the control strategy of the EFI system
In order to match the power system of a kind ofdownsized fuel-powered UAV the characteristics of theaeroengine including output speed and output powershould be analyzed based on the GT-Power model with afixed structure Furthermore key control parameters of thematched EFI system should be confirmed for the aeroengineapplication Calculations of the engine power based on theGT-Power module have been researched Yang and Zhu [15]have developed a mixed valve and crank-based engine modelfor a dual-stage turbocharged engine Under differentloading states the output torque and released AFR of theengine are simulated and values of the fuel pulse width arecalculated for a reference for the engine control unit (ECU)design Menacer and Bouchetara [16] have applied the GT-Power model to study the effect of the inject fuel mass flowon the brake power and indicate power under the certainignition advanced angle compression ratio and outputspeed In their work the maximum power and economycorresponding to the optimal speed are determined Weiet al [17] have adopted a serial of experiment data in a GT-Power model of a water-cooled four-stroke engine andlengths of the opening and closing delay times are optimizedand an optimal inject fuel mass flow is optimized MoreoverYang et al [18] have designed the controlled fuel process andstudied the different intake air parameters to improve theengine dynamic performances However in these works theengine confirmatory experiments are far away from the realapplication of the aeroengine because the torque propellermainly comes from the propeller air resistance In additionsome of the works are short of detailed experiment de-scription and relative theory basis so it is important for us toprovide a theoretical model reference for the aeroengine fuelsupply system in order to avoid multiple engine parametertests which can cause huge development costs FurthermoreECU controls the injector of the EFI system of the aero-engine and the electrified injector is opened and atomizesthe input high pressure gasoline into the engine manifold[19] However because of the electromagnetic force char-acteristic of the injector the dynamic response of the in-jected fuel mass flow will affect the precision of the suppliedfuel erefore based on the model results of the theory fuelflow it is necessary to analyze the dynamic response of theinjector and compensate the fuel spray and then we can get aconfirmed EFI control parameter which can provide opti-mum performance for the aeroengine
In this paper we firstly analyze the structure of theaeroengine and one-dimensional GT-Power mode of theengine is established Furthermore several parameter cor-rection methods are proposed Based on the simulationresults of the correctedmodel the analytic hierarchy methodis applied to optimize the fuel injection control systemEngine experiment results which use the optimize injectionMAP demonstrate that the oil consumption rate can beimproved differently
2 Methodology of Model
21 Subject Introduction In this paper the studied two-stroke aeroengine with the model of DLE170 has two
2 Complexity
opposing twin cylinders and mainly includes two air cyl-inders chambers two pistons one crankcase and onecrankshaft As shown in Figure 1 each of the cylinders has ascavenging channel and an exhaust vent and all the ports arewithout valves at means that opening and closing of theholes on the cylinder chambers depend on the movement ofthe pistons In addition main parameters of the aeroengineare shown in Table 1
When the two-stroke aeroengine starts to work duringthe first stroke firstly the air-fuel mixture is sucked into thecrankcase and the scavenging port is opened when thepistons move from the bottom dead center (BDC) until thecrankshaft rotates to the intake valve closed (IVC) anglewhich can be seen in Figure 2 e exhaust port is openedfrom BDC until the crankshaft rotates to the emission valveclosed (EVC) angle then the air-fuel mixture is compressedand at the ignition advance angle before the top dead center(TDC) the engine is sparked During the piston powerprocess before the exhaust valve opened (EVO) angle boththe exhaust and scavenging ports are closed and the cylinderchambers are hermetic which can ensure that the piston getsthe maximum power e ignition advanced angle (θ) isusually set to 5sim15 degrees ahead of TDC Because thecompressed ratio of the engine is relatively high and therated engine speed is fast the ignition advanced angle is setat 15 degrees e fuel in the crankcase comes from theelectronic injector as a certain air-fuel ratio (λ) and the ratiois determined by the average intake fuel flow ( _mf ) and airflow into the manifold ( _mman) which is controlled by injectfuel pulse width (Pw) inject fuel pressure (pf ) and throttleopening degree (α) e relative parameters can also be seenin Table 1
e engine working process is designed as shown inFigure 3 according to the working principle of the one-dimensional simulation software GT-Power In this pictureit can be seen that connected to the inlet port there are twosymmetrical crankcase chambers with numbers 1 and 2When the air-fuel mixture is flows into the crankcase it isgenerally assumed that two homogeneous mounts of oil andgas are divided by the crankshaft and then flow into the twocylinders Furthermore there are also symmetrical scav-enging passages intake ports cylinder chambers exhaustports and exhaust passages e opening and closing de-grees of the two kinds of ports determine the intake time ofthe air-fuel mixture and the exhaust time of the emissionsAccording to the actual measurement results the openingareas with the crankshaft angles are as shown in Figures 4(a)and 4(b) It should be noted that in these figures range ofthe x-coordinates is 0 to 180 degrees which is in the firstworking stroke e changing area with the shaft angle issymmetrical in the second working stroke
22 Modeling Method en the one-dimensional GT-Power model of the two-stroke aeroengine can be set asshown in Figure 5 according to the aeroengine workingprocess Structure of the aeroengine is based on the actualmeasure results
Main setting parameters of the fuel injector are ṁf andthe set air-fuel ratio (λset) In practice ECU controls theinjector work and breaks through pulse signal with a certain
TDC (0deg)
BDC (180deg)
EVOEVC
IVOIVC
Exhaust port opens
Scavenging port opens
Crankshaft anglephase
Compress Power
Spark
Exhaust port closes
Scavenging port closes
Ignition advanceangle
Figure 1 Main parts of the two-stroke aeroengine
Table 1 Specifications of DLE170 engine
Parameter ValueCylinder bore (mm) 52Engine stroke (mm) 40Connecting rod length (mm) 175Compression ratio 95TDC clearance height (mm) 2Displacement (cc) 85X2Intake fuel pressure (MPa) 03EVO (degrees) 65IVO (degrees) 123Intake pressure (bar) 1Intake temperature (K) 298Exhaust temperature (K) 700Exhaust pressure (bar) 12
Maximum performance 13 kw7500RPM
Minimum idle (RPM) 1000Range of the throttle opening degree (degrees) 10sim90EVC (degrees) minus65IVC (degrees) minus123
TDC (0deg)
BDC (180deg)
EVOEVC
IVOIVC
Exhaust port opens
Scavenging port opens
Crankshaft anglephase
Compress Power
Spark
Exhaust port closes
Scavenging port closes
Ignitionadvance
angle
Figure 2 Working schematic diagram of the two-strokeaeroengine
Complexity 3
width Relationship between _mf λset and the inject fuel pulsewidth (Pw) is shown in the following equation
_mf ηvρrefVDλset(CYL)Pw
(1)
where ηv is volumetric efficiency ρref is reference air densityused to calculate volumetric efficiency VD is the enginedisplacement and CYL is the number of cylinders Fromthis equation we can see that Pw directly determines theinjected fuel flow In order to improve the comprehensiveperformance of the aeroengine the inject fuel flow rates arecalibrated under different working conditions So as tomake the setup more intuitive in this paper the calibratingstandard is based on the expected air-fuel ratio and then theECU can calculate the output Pw in the real practiceHowever because the injector is driven by electromagnetic
Env Filter Throttleplate Manifold
Injector
Inlet port
Crankcase system
Scavenging passage 1
Cylinderchamber 2
Exhaust passage 2Exhaust passage 1
EnvEnv
Cylinderchamber 1
Scavenging passage 2
Crankcasechamber 1
Crankcasechamber 2
Load ofthe propeller
Intake port 2Intake port 1
Exhaust port 2Exhaust port 1
055 06 065 07 075 08
10002000
30004000
50006000
05
10152025
ndash1000ndash1500ndash2000
ndash2500ndash3000
ndash3500ndash4000
ndash4500
UAV propeller rotor diameter (m)
ndash5000
ndash5500ndash6000
Engine speed (rpm)
Load
torq
ue (N
m)
Figure 3 Working process of the two-stroke aeroengine
Port
area
(mm
2 )
0
300
600
900
1200
1500
120 140 160 180100Cranksha angle (degree)
(a)
Port
area
(mm
2 )
0
50
100
150
200
80 100 120 140 160 18060Cranksha angle (degree)
(b)
Figure 4 Working process of the two-stroke aeroengine (a) Intake port area (b) Exhaust port area
Intakeports
Exhaustports
Cylinderchambers
Fuelinjector
Propellerload
Throttleplate
Env-1 cranktrain-1
Env-4
Env-2Exhrunner-1
Exhrunner-2
Propeller_N_T-1
exhport-1
exhport-2
Exvalve-1
Exvalve-2
Cylinder-1
Cylinder-2
Invalve-1
Invalve-2
PipeRound-1
PipeRound-2
EngCrankcase-1
EngCrankcase-2
Man-fs-1
ValveCheckConn-2
Intport-1Intrunner-1
ThrottleConn-1
Intrunner-2
AirFilter
Si-inject-1
ValveCheckConn-1
Figure 5 One-dimensional GT-Power model of the two-strokeaeroengine
4 Complexity
force the dynamic action of the needle valve should beconsidered in the compensation of the set pulse width
Fuel injector working progress mainly includes threesteps the injector receives the pulse signal from ECU theelectromagnetic coil is gradually energized and the needlevalve starts to move when overcoming the spring preloadwhen the magnetized solenoid coil is saturated the needlevalve stops at the mechanical limit position when the pulsesignal becomes zero the magnetic flux of the solenoid coilreduces gradually and the needle valve will return to thenormal position Basically all the nozzles of the electro-magnetic type work in this way and the response delayimpact on the dynamic inject fuel flow caused by mechanicalfactors cannot be ignored In order to deeply analyze thedynamic injection and formulate the calibration strategy thedynamic model of the injector is built as follows
U0 Ri + NdΦbdt
when electrified
0 R + R0( 1113857 i + NdΦbdt
when not electrified
(2)
ese equations are magnetic flux when the injector iselectrified and not electrified where R is the basic resistanceof the electrified coil loop R0 is the protective resistance Vbrepresents total magnetic circuitN is the number of the coili is the current in the loop and U0 is the driving voltage eelectromagnetic force (Fm) on the needle valve when the coilis electrified is as follows
Fm μ0(iN)2S
2δ2 (3)
where μ0 represents permeability of vacuum S is cross-section of the air gap and δ means length of the working airgap Kinetic equation of the magnetic needle valve is
Fm minus F0 minus kx + Ffuel mvd2xdt2
(4)
where F0 is the initial tension of spring k is the springstiffness x is the displacement of the needle valve mv is themass of needle valve and Ffuel is fuel pressure force on theneedle valve When the needle valve is opened the highpressure fuel erupts and produces spray into the manifolde equation of the fuel flow is as follows according to orificecompensation principle
_mfi CdA0
2 ρf pf minus pm( 1113857
1113969
(5)
where _mfi is the instantaneous inject fuel mass flow Cd isdischarge coefficient A0 is aperture area ρf is the fueldensity and Pm is the atmosphere pressure Based on theequations the dynamic displacement of the needle valve iscalculated under different spring stiffness values As shownin Figure 6(a) when the initial spring tension force F0 is setat 55N the response of the valve displacement will not keeppace with the control signal However when F0 is set at95N pulse width of the needle displacement is muchshorter than the control signal which can be shown inFigure 6(b) and that will lead to insufficient of the inject fuel
erefore the pulse width of the valve displacement can beadjusted to be the same with that of the control signal bysetting the spring tension force F0 As shown in Figure 6(c)pulse width of the dynamic displacement of the needle valveis approximate to the control signal except at the beginningof the period where there is a rise process which causesinjection control error
is paper proposes a compensation method for theinjection control error As shown in Figure 7 it can be seenthat the displacement compensation time is equal to thecurrent delay time Compensation area of the rise process isapproximate as a triangle erefore the compensationwidth (Pc) is shown in the following equation
Pc Di
2 (6)
where Di is the current time delay Equation (1) can beamended as follows
_mf ηvρ refVDλset
(CYL) Pw + Pc( 1113857 (7)
Propeller load can be calculated according to differentworking conditions based on standard strip analysis Asknown from the calculation load torque of the propellermainly depends on engine speed (n) and propeller rotordiameter (rp) Main formula of the torque is as follows
MR 1113944(ΔD cos β + ΔL sin β)rp (8)
where MR is the propeller torque ΔD is differential form ofthe drag force ΔL is differential form of the lift force β is theintake air flow angle and rp is the propeller radius en theparameters are confirmed according to a blade materialthen we can get the torque MAP in horizontal directionunder different working conditions which is shown inFigure 8 From Figure 8 we can see that the load torque doesnot increase linearly with increasing engine speed and theUAV propeller rotor diameter However we can substitutethe torque MAP into the one-dimensional model by thelinear interpolation method
3 Experiments and Optimization
31ExperimentalVerification Numerical simulation cannotcompletely replace experiment analysis and if we want tomake the simulation results reflect the engine mechanism asprecisely as possible the mathematical simulation and ex-periment analysis should be combined e mathematicalmodel needs to be verified by experiment results whichmainly includes two parts the engine structure and thecombustion model e engine structure can be verified byintake air flow experiments at is because the engine isdriven by the oil and gas combustion and if the detected airflow is consistent with the simulation result in differentconditions we can see that the built engine model structurecan provide an equal inlet air mass flow In addition thecombustion model should be demonstrated by the cylinderpressure test e reason is that the output power of theinternal combustion engine mainly comes from the in-
Complexity 5
0 001 002 003 004 0050
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(a)
0 001 002 003 004 005
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(b)
0005 001 0015 002
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(c)
Figure 6 Dynamic displacement of the needle valve with different spring initial tension F0 (a) F0 55N (b) F0 95N (c) F0 80N
Control signalCurrent signalNeedle valve displacement
0
12
Nee
dle v
alve
disp
lace
men
t (m
m)
0
1
Current time delayDisplacement compensation
Approximatetriangle
Cont
rol s
igna
l (V
)
0
1
Curr
ent s
igna
l (A
)
1 2 3 4 5 6 7 8 9 100Time (ms)
Figure 7 Schematic diagram of needle valve displacementcompensation
05506
06507
07508
10002000
30004000
50006000 1000
15002000
25003000
35004000
4500
UAV propeller rotor diameter (m)
5000
5500
6000
Engine speed (rpm)
0
5
10
15
20
25
Load
torq
ue (N
middotm)
Figure 8 Horizontal torque of the propeller under differentworking conditions
6 Complexity
cylinder pressure and if the detected pressure fits well withthe simulation result it can be seen that the combustionprediction model in the simulation is effective erefore anengine intake air flowmeter is connected with the intakemanifold and a high frequency pressure sensor is setup onthe engine cylinder en we can get the air mass flow andcylinder pressure compare curves as shown in Figures 9(a)and 9(b) From these two pictures we can see that the resulterrors are no more than 5 and can demonstrate themathematic model to be effective
Injection fuel compensation can be demonstrated byECU experiments ECU gets trigger signal and outputs pulsesignal with a certain pulse width According to above re-search result the inject fuel pulse is compensated by thedelay time of the current through the electrified coil loopAccording to Figure 10 an ECU with the above function isdesigned and tested e current signal as well as the controlvoltage through the fuel injector is tested According toFigure 11 we can obtain that the current delay time is about4ms erefore in the model we compensate for the injectpulse by 2ms Repetitive experiments with different controlsignal widths are conducted and according to the real ap-plication the signal width is controlled within the range of35ms to 50ms and we obtain that the current delay time isthe same at is because their lowering processes of thecurrent are the same So in the simulation model we can setthe current delay time as constant 2ms
rough the simulation based on the model above therelative working parameters can be calculated e basicsimulation setting parameters are throttle opening degree(α) and the set air-fuel ratio (λset) Generally the mostconcerned characteristics and evaluation indicators of theengine mainly include engine speed (n) output power (Po)power efficiency (η) and rotational fuel consumption (c) ηand c can be calculated as follows
η Po
Pi
nTo
9550 _mfHu
c n
_mf
(9)
where Pi is the input power of the engine To is the outputtorque of the engine andHu is the gas calorific value which isabout 46000KJkg By changing the setting parameters α andλset a group of output parameters are obtained
32 Simulation Results As shown in Tables 2ndash4 there areseveral arrays of input and output parameters In additionall the parameters are recorded when the engine simulationstend to be stable
Tables 2ndash4 represent a part of simulation results In thispaper the throttle opening degree (α) is changed from 10deg to90deg and the engine speed is from 2500 RPM to 6000RPMaccording to the real application What needs illustration isthat according to our a large number of experiment resultsthe output AFR of the engine can only be controlled within aprecision of 05 and the general range of AFR during theengine working process is from 12 to 155 erefore in the
simulation the input AFR value is set to every 05 from 12 to155
As shown in the three tables To reflects the load-carryingcapacity and generally it is considered as the main indicatorof grade ability in the area of ground gasoline However inthe application of the rotorcraft UAV field the lift force ofthe UAV is primarily determined by the engine speed Sothe parameter To is mainly considered in the start and ac-celeration processes Po is the output power of the engineand in the case of the same displacement output powershould be bigger However in this paper the fuel economy istreated as a priority so in the engine fuel injection controlweight of η should be put more Considering that the enginespeed directly influences the lift of the UAV the rotationalfuel consumption c reflects the fuel consumption rate atconstant speed In addition Pc is the maximum cylinderpressure of one crankshaft rotate cycle
Since these output characteristics affect each other theinfluence rules of the injection parameter should be analyzedin order to assist in the formulation of the optimizationstrategies e set AFR directly affects the oil injection flowrate and its value always combines with that of the throttleopening degree (α) Here α is controlled stably as 40deg be-cause the single opening degrees value can reflect the wholeprinciple Engine speed (n) which is as the final controlquantity of the UAV power system should be simulated bystages According to the application requirement the in-terval is set as 500 RPM from 2500RPM to 6000 RPMenthe tendency charts which show the relationships betweenthe input parameters and the output characteristics areobtained as shown in Figures 12ndash15
As shown in Figures 12 and 13 it can be seen that whenthe throttle opening degree is constant the output torquecurves and output power curves will have a peak at a samespeed However it is difficult to find a regular rule betweenthe set AFR and these two output characteristics at isbecause when the throttle opening degree is set constantlythere must be a primal AFR setting value with differentworking conditions which is in accordance with the engineexternal characteristics According to the settled weight theoptimization should be comprehensively considered Inaddition from the two figures the curve trends are almostthe same so only one of the items can be considered whensetting weights in order to reduce the amount of calculation
It is a bit of mess in Figure 14 which represents theefficiency of the engine system Curves in Figure 14 almosthave peak values and the peak values basically independentof the output torque and powererefore the characteristicof power efficiency can be considered independently Powerefficiency is significant for the fuel economy improvementNevertheless it should be secondary to the torque and powerin the startup and acceleration processes in order to ensurethe safety of the UAV flight
Since the engine speed is kept steady during the flightthe oil consumption of rotation speed (c) is the most im-portant characteristic for fuel saving and flight enduranceextension As shown in Figure 15 the curves have troughs atthe same speed point with the torque and power curvesHowever in Figure 15 the arrange regular way of the curves
Complexity 7
of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV
Simulation resultsExperiment results
202224262830323436
Air
mas
s flo
w (K
gh)
3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)
(a)
Simulation resultsExperiment results
0
5
10
15
20
25
Cylin
der p
ress
ure (
bar)
ndash50 0 50 100 150 200ndash100Crank angle (degree)
(b)
Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM
ECUWiringharness
OscilloscopeFuel injector
Figure 10 Injector test picture
Current signalPulse signal
Current delay time
0
002
004
006
008
01
012
014
Curr
ent s
igna
l (A
)
0
05
1
15
2
25
3
Vol
tage
pul
se (V
)
20 40 60 800Time (ms)
Figure 11 Results of the current delay time test
Table 2 Results of the GT-power simulation when α 10deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMhKg)Pc
(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687
Table 3 Results of the GT-power simulation when α 40deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128
Table 4 Results of the GT-power simulation when α 80deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391
8 Complexity
33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations
n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857
(10)
where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)
f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c
(11)
where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
8
10
12
14
16
18
20
Out
put t
orqu
e (N
middotm)
3000 4000 5000 60002000Engine speed (RPM)
Figure 12 Output torque at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
2
3
4
5
6
7
8
9
10
Oup
ut p
ower
(Kw
)
Figure 13 Output power at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
01
012
014
016
018
02
022
024
026
028
Pow
er e
ffici
ency
Figure 14 Power efficiency at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000O
il co
nsum
ptio
n ra
te o
f rot
atio
n sp
eed
(RPM
middothK
g)
Figure 15 Oil consumption rate of rotation speed
Complexity 9
matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16
e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5
According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows
(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping
(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed
(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered
(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced
rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17
From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows
(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator
calculate the weight matrixesW1W2W3 and W4
obtain the simulation results
calculate the evaluation function results f (θn)
derive the evaluation function matrix F (θn)
data normalization preprocessing determine the relationship
between throttle openingdegree and engine speedaccording to A and equ(12)
obtain the engine set AFR optimization curve
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Final
determine the set AFRmatrix A according to theevaluation function matrix
Figure 16 Optimization process
Table 5 Definition and explanation of preference weights based onSaatyrsquos theory
Preferenceweights Definition Explanation
1 Equally preferable Two factors contributeequally to the objective
3 Moderate preferredExperience and judgementslightly favour one over
other
5 Strongly preferredExperience and judgementstrongly favour one over the
other
7 Very stronglypreferred
Experience and judgementvery strongly favour one
over the other
9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity
2 4 6 8 Intermediates valuesUsed to represent
compromise between thepreferences listed
Reciprocals Reciprocals forinverse comparison mdash
Table 6 Optimize calibration data of fuel injection parameter
α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135
10 Complexity
(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10
34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded
From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results
4 Conclusion
is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system
Data Availability
e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article
10 20 30 40 50 60 70 80 90
2500300035004000450050005500600012
13
14
15
16larrlarr6000
Throttle opening degree (deg)Engine speed (RPM)
Targ
et A
FR
Figure 17 Fuel injection MAP
020
4060
80100
20003000
40005000
6000ndash01
ndash005
0
005
01
2500
Throttle opening degree (deg)
300035004000
50004500
55006000
Engine speed (RPM)
Effic
ienc
y er
ror
Figure 18 Efficiency error MAP
Fuel tank
Weightingsensor
Testaeroengine
Analysiscomputer
Remotecontroller
Figure 19 Aeroengine test station
Optimal resultsPrevious results
1800
2000
2200
2400
2600
2800
Oil
cons
umpt
ion
rate
of r
otat
ion
spee
d (R
PMmiddoth
Kg)
3000 3500 4000 4500 5000 5500 60002500
Engine speed (RPM)
Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed
Complexity 11
Acknowledgments
is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment
References
[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017
[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015
[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014
[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014
[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016
[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011
[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011
[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985
[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009
[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013
[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016
[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017
[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three
stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017
[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009
[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010
[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014
[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017
[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012
[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992
[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980
[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018
[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018
[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014
[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019
[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020
[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020
12 Complexity
which is hard to test the output power of an aeroengine witha propeller Furthermore in order to get accurate results theexperiment conditions have to be prepared strictly such ashigh precision sensors and stable environment which willgreatly increase the research cost Last but not the least it isdangerous and inaccurate to simulate extreme workingconditions by engine station tests
erefore research studies have paid more and more at-tention to the engine working process simulation by mathe-matical models In order to estimate engine performance suchas cylinder pressure heat release rate and fuel consumptionVenkatraman and Devaradjane [6] build the working math-ematical model of a 4-stroke engine e simulation modelincludes cylinder state equation heat transfer process ignitiondelay combustion duration and NOx formation In additionbased on the mathematical model Venkatraman and Devar-adjane [7] design engine experiments for demonstration Intheir works the heat release rate brake thermal efficiencycarbon monoxide hydrocarbon and so on are predictedthrough the model and the experiments verify that the rec-tification model coincides with the reality Furthermore in thecombustion model Wiebe heat release function is appliedbased on the exponential rate of the chemical reactions Wiebeequations have been implemented by Miyamoto et al [8] andone of the equation factors is considered to be important whichis called ldquorate of heat releaserdquo Ganapathy et al [9] haveemployed a thermodynamic model based on two-zone Wiebeheat release function to simulate the performance of new fuelengine Raut [10] also use an exponential rate-basedWiebe heatrelease model and the Pflaum formula is applied in the esti-mation of empirical coefficient of the heat transfer processFrom these works it can be seen that engine performance studyby using the mathematical model method is effective
GT-Power is the leading engine simulation softwarebased on one-dimensional gas dynamic which represents theflow and transfer in the components of the engine systemandmore andmore scientists and engineers have applied thecomputing tool in engine prediction in order to improve thecontrol performance or reduce the emission Kassa et al [11]have leveraged experimental data from a 6-cylinder engineto a GT-Power model to better understand the distributionof the port-injected fuel across cylinders under severaloperating conditions Rahimi-Gorji et al [12] have opti-mized the performance and fuel consumption according tothe weather conditions by combining the artificial neuralnetwork and GT-Power model and pressure temperatureand humidity of the incoming air are considered in thenetwork to obtain a better engine performance Alves et al[13] apply GT-Power in the engine intake system design andthe best intake runner length and diameter configuration ofeach speed for a four-stroke and single cylinder engine isfound to get the optimum volume efficiency Trajkovic et al[14] build the GT-Power model of a 2-stroke engine to studythe effect of different parameters and their effect onpneumatic hybrid performance From the works above themathematical model built by GT-Power is proved to beeffective to predict and improve the engine characteristicsHowever these papers mainly focus on the engine structurerather than the control strategy of the EFI system
In order to match the power system of a kind ofdownsized fuel-powered UAV the characteristics of theaeroengine including output speed and output powershould be analyzed based on the GT-Power model with afixed structure Furthermore key control parameters of thematched EFI system should be confirmed for the aeroengineapplication Calculations of the engine power based on theGT-Power module have been researched Yang and Zhu [15]have developed a mixed valve and crank-based engine modelfor a dual-stage turbocharged engine Under differentloading states the output torque and released AFR of theengine are simulated and values of the fuel pulse width arecalculated for a reference for the engine control unit (ECU)design Menacer and Bouchetara [16] have applied the GT-Power model to study the effect of the inject fuel mass flowon the brake power and indicate power under the certainignition advanced angle compression ratio and outputspeed In their work the maximum power and economycorresponding to the optimal speed are determined Weiet al [17] have adopted a serial of experiment data in a GT-Power model of a water-cooled four-stroke engine andlengths of the opening and closing delay times are optimizedand an optimal inject fuel mass flow is optimized MoreoverYang et al [18] have designed the controlled fuel process andstudied the different intake air parameters to improve theengine dynamic performances However in these works theengine confirmatory experiments are far away from the realapplication of the aeroengine because the torque propellermainly comes from the propeller air resistance In additionsome of the works are short of detailed experiment de-scription and relative theory basis so it is important for us toprovide a theoretical model reference for the aeroengine fuelsupply system in order to avoid multiple engine parametertests which can cause huge development costs FurthermoreECU controls the injector of the EFI system of the aero-engine and the electrified injector is opened and atomizesthe input high pressure gasoline into the engine manifold[19] However because of the electromagnetic force char-acteristic of the injector the dynamic response of the in-jected fuel mass flow will affect the precision of the suppliedfuel erefore based on the model results of the theory fuelflow it is necessary to analyze the dynamic response of theinjector and compensate the fuel spray and then we can get aconfirmed EFI control parameter which can provide opti-mum performance for the aeroengine
In this paper we firstly analyze the structure of theaeroengine and one-dimensional GT-Power mode of theengine is established Furthermore several parameter cor-rection methods are proposed Based on the simulationresults of the correctedmodel the analytic hierarchy methodis applied to optimize the fuel injection control systemEngine experiment results which use the optimize injectionMAP demonstrate that the oil consumption rate can beimproved differently
2 Methodology of Model
21 Subject Introduction In this paper the studied two-stroke aeroengine with the model of DLE170 has two
2 Complexity
opposing twin cylinders and mainly includes two air cyl-inders chambers two pistons one crankcase and onecrankshaft As shown in Figure 1 each of the cylinders has ascavenging channel and an exhaust vent and all the ports arewithout valves at means that opening and closing of theholes on the cylinder chambers depend on the movement ofthe pistons In addition main parameters of the aeroengineare shown in Table 1
When the two-stroke aeroengine starts to work duringthe first stroke firstly the air-fuel mixture is sucked into thecrankcase and the scavenging port is opened when thepistons move from the bottom dead center (BDC) until thecrankshaft rotates to the intake valve closed (IVC) anglewhich can be seen in Figure 2 e exhaust port is openedfrom BDC until the crankshaft rotates to the emission valveclosed (EVC) angle then the air-fuel mixture is compressedand at the ignition advance angle before the top dead center(TDC) the engine is sparked During the piston powerprocess before the exhaust valve opened (EVO) angle boththe exhaust and scavenging ports are closed and the cylinderchambers are hermetic which can ensure that the piston getsthe maximum power e ignition advanced angle (θ) isusually set to 5sim15 degrees ahead of TDC Because thecompressed ratio of the engine is relatively high and therated engine speed is fast the ignition advanced angle is setat 15 degrees e fuel in the crankcase comes from theelectronic injector as a certain air-fuel ratio (λ) and the ratiois determined by the average intake fuel flow ( _mf ) and airflow into the manifold ( _mman) which is controlled by injectfuel pulse width (Pw) inject fuel pressure (pf ) and throttleopening degree (α) e relative parameters can also be seenin Table 1
e engine working process is designed as shown inFigure 3 according to the working principle of the one-dimensional simulation software GT-Power In this pictureit can be seen that connected to the inlet port there are twosymmetrical crankcase chambers with numbers 1 and 2When the air-fuel mixture is flows into the crankcase it isgenerally assumed that two homogeneous mounts of oil andgas are divided by the crankshaft and then flow into the twocylinders Furthermore there are also symmetrical scav-enging passages intake ports cylinder chambers exhaustports and exhaust passages e opening and closing de-grees of the two kinds of ports determine the intake time ofthe air-fuel mixture and the exhaust time of the emissionsAccording to the actual measurement results the openingareas with the crankshaft angles are as shown in Figures 4(a)and 4(b) It should be noted that in these figures range ofthe x-coordinates is 0 to 180 degrees which is in the firstworking stroke e changing area with the shaft angle issymmetrical in the second working stroke
22 Modeling Method en the one-dimensional GT-Power model of the two-stroke aeroengine can be set asshown in Figure 5 according to the aeroengine workingprocess Structure of the aeroengine is based on the actualmeasure results
Main setting parameters of the fuel injector are ṁf andthe set air-fuel ratio (λset) In practice ECU controls theinjector work and breaks through pulse signal with a certain
TDC (0deg)
BDC (180deg)
EVOEVC
IVOIVC
Exhaust port opens
Scavenging port opens
Crankshaft anglephase
Compress Power
Spark
Exhaust port closes
Scavenging port closes
Ignition advanceangle
Figure 1 Main parts of the two-stroke aeroengine
Table 1 Specifications of DLE170 engine
Parameter ValueCylinder bore (mm) 52Engine stroke (mm) 40Connecting rod length (mm) 175Compression ratio 95TDC clearance height (mm) 2Displacement (cc) 85X2Intake fuel pressure (MPa) 03EVO (degrees) 65IVO (degrees) 123Intake pressure (bar) 1Intake temperature (K) 298Exhaust temperature (K) 700Exhaust pressure (bar) 12
Maximum performance 13 kw7500RPM
Minimum idle (RPM) 1000Range of the throttle opening degree (degrees) 10sim90EVC (degrees) minus65IVC (degrees) minus123
TDC (0deg)
BDC (180deg)
EVOEVC
IVOIVC
Exhaust port opens
Scavenging port opens
Crankshaft anglephase
Compress Power
Spark
Exhaust port closes
Scavenging port closes
Ignitionadvance
angle
Figure 2 Working schematic diagram of the two-strokeaeroengine
Complexity 3
width Relationship between _mf λset and the inject fuel pulsewidth (Pw) is shown in the following equation
_mf ηvρrefVDλset(CYL)Pw
(1)
where ηv is volumetric efficiency ρref is reference air densityused to calculate volumetric efficiency VD is the enginedisplacement and CYL is the number of cylinders Fromthis equation we can see that Pw directly determines theinjected fuel flow In order to improve the comprehensiveperformance of the aeroengine the inject fuel flow rates arecalibrated under different working conditions So as tomake the setup more intuitive in this paper the calibratingstandard is based on the expected air-fuel ratio and then theECU can calculate the output Pw in the real practiceHowever because the injector is driven by electromagnetic
Env Filter Throttleplate Manifold
Injector
Inlet port
Crankcase system
Scavenging passage 1
Cylinderchamber 2
Exhaust passage 2Exhaust passage 1
EnvEnv
Cylinderchamber 1
Scavenging passage 2
Crankcasechamber 1
Crankcasechamber 2
Load ofthe propeller
Intake port 2Intake port 1
Exhaust port 2Exhaust port 1
055 06 065 07 075 08
10002000
30004000
50006000
05
10152025
ndash1000ndash1500ndash2000
ndash2500ndash3000
ndash3500ndash4000
ndash4500
UAV propeller rotor diameter (m)
ndash5000
ndash5500ndash6000
Engine speed (rpm)
Load
torq
ue (N
m)
Figure 3 Working process of the two-stroke aeroengine
Port
area
(mm
2 )
0
300
600
900
1200
1500
120 140 160 180100Cranksha angle (degree)
(a)
Port
area
(mm
2 )
0
50
100
150
200
80 100 120 140 160 18060Cranksha angle (degree)
(b)
Figure 4 Working process of the two-stroke aeroengine (a) Intake port area (b) Exhaust port area
Intakeports
Exhaustports
Cylinderchambers
Fuelinjector
Propellerload
Throttleplate
Env-1 cranktrain-1
Env-4
Env-2Exhrunner-1
Exhrunner-2
Propeller_N_T-1
exhport-1
exhport-2
Exvalve-1
Exvalve-2
Cylinder-1
Cylinder-2
Invalve-1
Invalve-2
PipeRound-1
PipeRound-2
EngCrankcase-1
EngCrankcase-2
Man-fs-1
ValveCheckConn-2
Intport-1Intrunner-1
ThrottleConn-1
Intrunner-2
AirFilter
Si-inject-1
ValveCheckConn-1
Figure 5 One-dimensional GT-Power model of the two-strokeaeroengine
4 Complexity
force the dynamic action of the needle valve should beconsidered in the compensation of the set pulse width
Fuel injector working progress mainly includes threesteps the injector receives the pulse signal from ECU theelectromagnetic coil is gradually energized and the needlevalve starts to move when overcoming the spring preloadwhen the magnetized solenoid coil is saturated the needlevalve stops at the mechanical limit position when the pulsesignal becomes zero the magnetic flux of the solenoid coilreduces gradually and the needle valve will return to thenormal position Basically all the nozzles of the electro-magnetic type work in this way and the response delayimpact on the dynamic inject fuel flow caused by mechanicalfactors cannot be ignored In order to deeply analyze thedynamic injection and formulate the calibration strategy thedynamic model of the injector is built as follows
U0 Ri + NdΦbdt
when electrified
0 R + R0( 1113857 i + NdΦbdt
when not electrified
(2)
ese equations are magnetic flux when the injector iselectrified and not electrified where R is the basic resistanceof the electrified coil loop R0 is the protective resistance Vbrepresents total magnetic circuitN is the number of the coili is the current in the loop and U0 is the driving voltage eelectromagnetic force (Fm) on the needle valve when the coilis electrified is as follows
Fm μ0(iN)2S
2δ2 (3)
where μ0 represents permeability of vacuum S is cross-section of the air gap and δ means length of the working airgap Kinetic equation of the magnetic needle valve is
Fm minus F0 minus kx + Ffuel mvd2xdt2
(4)
where F0 is the initial tension of spring k is the springstiffness x is the displacement of the needle valve mv is themass of needle valve and Ffuel is fuel pressure force on theneedle valve When the needle valve is opened the highpressure fuel erupts and produces spray into the manifolde equation of the fuel flow is as follows according to orificecompensation principle
_mfi CdA0
2 ρf pf minus pm( 1113857
1113969
(5)
where _mfi is the instantaneous inject fuel mass flow Cd isdischarge coefficient A0 is aperture area ρf is the fueldensity and Pm is the atmosphere pressure Based on theequations the dynamic displacement of the needle valve iscalculated under different spring stiffness values As shownin Figure 6(a) when the initial spring tension force F0 is setat 55N the response of the valve displacement will not keeppace with the control signal However when F0 is set at95N pulse width of the needle displacement is muchshorter than the control signal which can be shown inFigure 6(b) and that will lead to insufficient of the inject fuel
erefore the pulse width of the valve displacement can beadjusted to be the same with that of the control signal bysetting the spring tension force F0 As shown in Figure 6(c)pulse width of the dynamic displacement of the needle valveis approximate to the control signal except at the beginningof the period where there is a rise process which causesinjection control error
is paper proposes a compensation method for theinjection control error As shown in Figure 7 it can be seenthat the displacement compensation time is equal to thecurrent delay time Compensation area of the rise process isapproximate as a triangle erefore the compensationwidth (Pc) is shown in the following equation
Pc Di
2 (6)
where Di is the current time delay Equation (1) can beamended as follows
_mf ηvρ refVDλset
(CYL) Pw + Pc( 1113857 (7)
Propeller load can be calculated according to differentworking conditions based on standard strip analysis Asknown from the calculation load torque of the propellermainly depends on engine speed (n) and propeller rotordiameter (rp) Main formula of the torque is as follows
MR 1113944(ΔD cos β + ΔL sin β)rp (8)
where MR is the propeller torque ΔD is differential form ofthe drag force ΔL is differential form of the lift force β is theintake air flow angle and rp is the propeller radius en theparameters are confirmed according to a blade materialthen we can get the torque MAP in horizontal directionunder different working conditions which is shown inFigure 8 From Figure 8 we can see that the load torque doesnot increase linearly with increasing engine speed and theUAV propeller rotor diameter However we can substitutethe torque MAP into the one-dimensional model by thelinear interpolation method
3 Experiments and Optimization
31ExperimentalVerification Numerical simulation cannotcompletely replace experiment analysis and if we want tomake the simulation results reflect the engine mechanism asprecisely as possible the mathematical simulation and ex-periment analysis should be combined e mathematicalmodel needs to be verified by experiment results whichmainly includes two parts the engine structure and thecombustion model e engine structure can be verified byintake air flow experiments at is because the engine isdriven by the oil and gas combustion and if the detected airflow is consistent with the simulation result in differentconditions we can see that the built engine model structurecan provide an equal inlet air mass flow In addition thecombustion model should be demonstrated by the cylinderpressure test e reason is that the output power of theinternal combustion engine mainly comes from the in-
Complexity 5
0 001 002 003 004 0050
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(a)
0 001 002 003 004 005
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(b)
0005 001 0015 002
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(c)
Figure 6 Dynamic displacement of the needle valve with different spring initial tension F0 (a) F0 55N (b) F0 95N (c) F0 80N
Control signalCurrent signalNeedle valve displacement
0
12
Nee
dle v
alve
disp
lace
men
t (m
m)
0
1
Current time delayDisplacement compensation
Approximatetriangle
Cont
rol s
igna
l (V
)
0
1
Curr
ent s
igna
l (A
)
1 2 3 4 5 6 7 8 9 100Time (ms)
Figure 7 Schematic diagram of needle valve displacementcompensation
05506
06507
07508
10002000
30004000
50006000 1000
15002000
25003000
35004000
4500
UAV propeller rotor diameter (m)
5000
5500
6000
Engine speed (rpm)
0
5
10
15
20
25
Load
torq
ue (N
middotm)
Figure 8 Horizontal torque of the propeller under differentworking conditions
6 Complexity
cylinder pressure and if the detected pressure fits well withthe simulation result it can be seen that the combustionprediction model in the simulation is effective erefore anengine intake air flowmeter is connected with the intakemanifold and a high frequency pressure sensor is setup onthe engine cylinder en we can get the air mass flow andcylinder pressure compare curves as shown in Figures 9(a)and 9(b) From these two pictures we can see that the resulterrors are no more than 5 and can demonstrate themathematic model to be effective
Injection fuel compensation can be demonstrated byECU experiments ECU gets trigger signal and outputs pulsesignal with a certain pulse width According to above re-search result the inject fuel pulse is compensated by thedelay time of the current through the electrified coil loopAccording to Figure 10 an ECU with the above function isdesigned and tested e current signal as well as the controlvoltage through the fuel injector is tested According toFigure 11 we can obtain that the current delay time is about4ms erefore in the model we compensate for the injectpulse by 2ms Repetitive experiments with different controlsignal widths are conducted and according to the real ap-plication the signal width is controlled within the range of35ms to 50ms and we obtain that the current delay time isthe same at is because their lowering processes of thecurrent are the same So in the simulation model we can setthe current delay time as constant 2ms
rough the simulation based on the model above therelative working parameters can be calculated e basicsimulation setting parameters are throttle opening degree(α) and the set air-fuel ratio (λset) Generally the mostconcerned characteristics and evaluation indicators of theengine mainly include engine speed (n) output power (Po)power efficiency (η) and rotational fuel consumption (c) ηand c can be calculated as follows
η Po
Pi
nTo
9550 _mfHu
c n
_mf
(9)
where Pi is the input power of the engine To is the outputtorque of the engine andHu is the gas calorific value which isabout 46000KJkg By changing the setting parameters α andλset a group of output parameters are obtained
32 Simulation Results As shown in Tables 2ndash4 there areseveral arrays of input and output parameters In additionall the parameters are recorded when the engine simulationstend to be stable
Tables 2ndash4 represent a part of simulation results In thispaper the throttle opening degree (α) is changed from 10deg to90deg and the engine speed is from 2500 RPM to 6000RPMaccording to the real application What needs illustration isthat according to our a large number of experiment resultsthe output AFR of the engine can only be controlled within aprecision of 05 and the general range of AFR during theengine working process is from 12 to 155 erefore in the
simulation the input AFR value is set to every 05 from 12 to155
As shown in the three tables To reflects the load-carryingcapacity and generally it is considered as the main indicatorof grade ability in the area of ground gasoline However inthe application of the rotorcraft UAV field the lift force ofthe UAV is primarily determined by the engine speed Sothe parameter To is mainly considered in the start and ac-celeration processes Po is the output power of the engineand in the case of the same displacement output powershould be bigger However in this paper the fuel economy istreated as a priority so in the engine fuel injection controlweight of η should be put more Considering that the enginespeed directly influences the lift of the UAV the rotationalfuel consumption c reflects the fuel consumption rate atconstant speed In addition Pc is the maximum cylinderpressure of one crankshaft rotate cycle
Since these output characteristics affect each other theinfluence rules of the injection parameter should be analyzedin order to assist in the formulation of the optimizationstrategies e set AFR directly affects the oil injection flowrate and its value always combines with that of the throttleopening degree (α) Here α is controlled stably as 40deg be-cause the single opening degrees value can reflect the wholeprinciple Engine speed (n) which is as the final controlquantity of the UAV power system should be simulated bystages According to the application requirement the in-terval is set as 500 RPM from 2500RPM to 6000 RPMenthe tendency charts which show the relationships betweenthe input parameters and the output characteristics areobtained as shown in Figures 12ndash15
As shown in Figures 12 and 13 it can be seen that whenthe throttle opening degree is constant the output torquecurves and output power curves will have a peak at a samespeed However it is difficult to find a regular rule betweenthe set AFR and these two output characteristics at isbecause when the throttle opening degree is set constantlythere must be a primal AFR setting value with differentworking conditions which is in accordance with the engineexternal characteristics According to the settled weight theoptimization should be comprehensively considered Inaddition from the two figures the curve trends are almostthe same so only one of the items can be considered whensetting weights in order to reduce the amount of calculation
It is a bit of mess in Figure 14 which represents theefficiency of the engine system Curves in Figure 14 almosthave peak values and the peak values basically independentof the output torque and powererefore the characteristicof power efficiency can be considered independently Powerefficiency is significant for the fuel economy improvementNevertheless it should be secondary to the torque and powerin the startup and acceleration processes in order to ensurethe safety of the UAV flight
Since the engine speed is kept steady during the flightthe oil consumption of rotation speed (c) is the most im-portant characteristic for fuel saving and flight enduranceextension As shown in Figure 15 the curves have troughs atthe same speed point with the torque and power curvesHowever in Figure 15 the arrange regular way of the curves
Complexity 7
of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV
Simulation resultsExperiment results
202224262830323436
Air
mas
s flo
w (K
gh)
3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)
(a)
Simulation resultsExperiment results
0
5
10
15
20
25
Cylin
der p
ress
ure (
bar)
ndash50 0 50 100 150 200ndash100Crank angle (degree)
(b)
Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM
ECUWiringharness
OscilloscopeFuel injector
Figure 10 Injector test picture
Current signalPulse signal
Current delay time
0
002
004
006
008
01
012
014
Curr
ent s
igna
l (A
)
0
05
1
15
2
25
3
Vol
tage
pul
se (V
)
20 40 60 800Time (ms)
Figure 11 Results of the current delay time test
Table 2 Results of the GT-power simulation when α 10deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMhKg)Pc
(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687
Table 3 Results of the GT-power simulation when α 40deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128
Table 4 Results of the GT-power simulation when α 80deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391
8 Complexity
33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations
n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857
(10)
where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)
f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c
(11)
where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
8
10
12
14
16
18
20
Out
put t
orqu
e (N
middotm)
3000 4000 5000 60002000Engine speed (RPM)
Figure 12 Output torque at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
2
3
4
5
6
7
8
9
10
Oup
ut p
ower
(Kw
)
Figure 13 Output power at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
01
012
014
016
018
02
022
024
026
028
Pow
er e
ffici
ency
Figure 14 Power efficiency at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000O
il co
nsum
ptio
n ra
te o
f rot
atio
n sp
eed
(RPM
middothK
g)
Figure 15 Oil consumption rate of rotation speed
Complexity 9
matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16
e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5
According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows
(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping
(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed
(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered
(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced
rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17
From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows
(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator
calculate the weight matrixesW1W2W3 and W4
obtain the simulation results
calculate the evaluation function results f (θn)
derive the evaluation function matrix F (θn)
data normalization preprocessing determine the relationship
between throttle openingdegree and engine speedaccording to A and equ(12)
obtain the engine set AFR optimization curve
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Final
determine the set AFRmatrix A according to theevaluation function matrix
Figure 16 Optimization process
Table 5 Definition and explanation of preference weights based onSaatyrsquos theory
Preferenceweights Definition Explanation
1 Equally preferable Two factors contributeequally to the objective
3 Moderate preferredExperience and judgementslightly favour one over
other
5 Strongly preferredExperience and judgementstrongly favour one over the
other
7 Very stronglypreferred
Experience and judgementvery strongly favour one
over the other
9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity
2 4 6 8 Intermediates valuesUsed to represent
compromise between thepreferences listed
Reciprocals Reciprocals forinverse comparison mdash
Table 6 Optimize calibration data of fuel injection parameter
α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135
10 Complexity
(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10
34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded
From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results
4 Conclusion
is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system
Data Availability
e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article
10 20 30 40 50 60 70 80 90
2500300035004000450050005500600012
13
14
15
16larrlarr6000
Throttle opening degree (deg)Engine speed (RPM)
Targ
et A
FR
Figure 17 Fuel injection MAP
020
4060
80100
20003000
40005000
6000ndash01
ndash005
0
005
01
2500
Throttle opening degree (deg)
300035004000
50004500
55006000
Engine speed (RPM)
Effic
ienc
y er
ror
Figure 18 Efficiency error MAP
Fuel tank
Weightingsensor
Testaeroengine
Analysiscomputer
Remotecontroller
Figure 19 Aeroengine test station
Optimal resultsPrevious results
1800
2000
2200
2400
2600
2800
Oil
cons
umpt
ion
rate
of r
otat
ion
spee
d (R
PMmiddoth
Kg)
3000 3500 4000 4500 5000 5500 60002500
Engine speed (RPM)
Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed
Complexity 11
Acknowledgments
is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment
References
[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017
[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015
[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014
[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014
[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016
[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011
[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011
[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985
[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009
[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013
[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016
[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017
[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three
stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017
[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009
[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010
[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014
[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017
[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012
[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992
[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980
[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018
[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018
[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014
[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019
[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020
[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020
12 Complexity
opposing twin cylinders and mainly includes two air cyl-inders chambers two pistons one crankcase and onecrankshaft As shown in Figure 1 each of the cylinders has ascavenging channel and an exhaust vent and all the ports arewithout valves at means that opening and closing of theholes on the cylinder chambers depend on the movement ofthe pistons In addition main parameters of the aeroengineare shown in Table 1
When the two-stroke aeroengine starts to work duringthe first stroke firstly the air-fuel mixture is sucked into thecrankcase and the scavenging port is opened when thepistons move from the bottom dead center (BDC) until thecrankshaft rotates to the intake valve closed (IVC) anglewhich can be seen in Figure 2 e exhaust port is openedfrom BDC until the crankshaft rotates to the emission valveclosed (EVC) angle then the air-fuel mixture is compressedand at the ignition advance angle before the top dead center(TDC) the engine is sparked During the piston powerprocess before the exhaust valve opened (EVO) angle boththe exhaust and scavenging ports are closed and the cylinderchambers are hermetic which can ensure that the piston getsthe maximum power e ignition advanced angle (θ) isusually set to 5sim15 degrees ahead of TDC Because thecompressed ratio of the engine is relatively high and therated engine speed is fast the ignition advanced angle is setat 15 degrees e fuel in the crankcase comes from theelectronic injector as a certain air-fuel ratio (λ) and the ratiois determined by the average intake fuel flow ( _mf ) and airflow into the manifold ( _mman) which is controlled by injectfuel pulse width (Pw) inject fuel pressure (pf ) and throttleopening degree (α) e relative parameters can also be seenin Table 1
e engine working process is designed as shown inFigure 3 according to the working principle of the one-dimensional simulation software GT-Power In this pictureit can be seen that connected to the inlet port there are twosymmetrical crankcase chambers with numbers 1 and 2When the air-fuel mixture is flows into the crankcase it isgenerally assumed that two homogeneous mounts of oil andgas are divided by the crankshaft and then flow into the twocylinders Furthermore there are also symmetrical scav-enging passages intake ports cylinder chambers exhaustports and exhaust passages e opening and closing de-grees of the two kinds of ports determine the intake time ofthe air-fuel mixture and the exhaust time of the emissionsAccording to the actual measurement results the openingareas with the crankshaft angles are as shown in Figures 4(a)and 4(b) It should be noted that in these figures range ofthe x-coordinates is 0 to 180 degrees which is in the firstworking stroke e changing area with the shaft angle issymmetrical in the second working stroke
22 Modeling Method en the one-dimensional GT-Power model of the two-stroke aeroengine can be set asshown in Figure 5 according to the aeroengine workingprocess Structure of the aeroengine is based on the actualmeasure results
Main setting parameters of the fuel injector are ṁf andthe set air-fuel ratio (λset) In practice ECU controls theinjector work and breaks through pulse signal with a certain
TDC (0deg)
BDC (180deg)
EVOEVC
IVOIVC
Exhaust port opens
Scavenging port opens
Crankshaft anglephase
Compress Power
Spark
Exhaust port closes
Scavenging port closes
Ignition advanceangle
Figure 1 Main parts of the two-stroke aeroengine
Table 1 Specifications of DLE170 engine
Parameter ValueCylinder bore (mm) 52Engine stroke (mm) 40Connecting rod length (mm) 175Compression ratio 95TDC clearance height (mm) 2Displacement (cc) 85X2Intake fuel pressure (MPa) 03EVO (degrees) 65IVO (degrees) 123Intake pressure (bar) 1Intake temperature (K) 298Exhaust temperature (K) 700Exhaust pressure (bar) 12
Maximum performance 13 kw7500RPM
Minimum idle (RPM) 1000Range of the throttle opening degree (degrees) 10sim90EVC (degrees) minus65IVC (degrees) minus123
TDC (0deg)
BDC (180deg)
EVOEVC
IVOIVC
Exhaust port opens
Scavenging port opens
Crankshaft anglephase
Compress Power
Spark
Exhaust port closes
Scavenging port closes
Ignitionadvance
angle
Figure 2 Working schematic diagram of the two-strokeaeroengine
Complexity 3
width Relationship between _mf λset and the inject fuel pulsewidth (Pw) is shown in the following equation
_mf ηvρrefVDλset(CYL)Pw
(1)
where ηv is volumetric efficiency ρref is reference air densityused to calculate volumetric efficiency VD is the enginedisplacement and CYL is the number of cylinders Fromthis equation we can see that Pw directly determines theinjected fuel flow In order to improve the comprehensiveperformance of the aeroengine the inject fuel flow rates arecalibrated under different working conditions So as tomake the setup more intuitive in this paper the calibratingstandard is based on the expected air-fuel ratio and then theECU can calculate the output Pw in the real practiceHowever because the injector is driven by electromagnetic
Env Filter Throttleplate Manifold
Injector
Inlet port
Crankcase system
Scavenging passage 1
Cylinderchamber 2
Exhaust passage 2Exhaust passage 1
EnvEnv
Cylinderchamber 1
Scavenging passage 2
Crankcasechamber 1
Crankcasechamber 2
Load ofthe propeller
Intake port 2Intake port 1
Exhaust port 2Exhaust port 1
055 06 065 07 075 08
10002000
30004000
50006000
05
10152025
ndash1000ndash1500ndash2000
ndash2500ndash3000
ndash3500ndash4000
ndash4500
UAV propeller rotor diameter (m)
ndash5000
ndash5500ndash6000
Engine speed (rpm)
Load
torq
ue (N
m)
Figure 3 Working process of the two-stroke aeroengine
Port
area
(mm
2 )
0
300
600
900
1200
1500
120 140 160 180100Cranksha angle (degree)
(a)
Port
area
(mm
2 )
0
50
100
150
200
80 100 120 140 160 18060Cranksha angle (degree)
(b)
Figure 4 Working process of the two-stroke aeroengine (a) Intake port area (b) Exhaust port area
Intakeports
Exhaustports
Cylinderchambers
Fuelinjector
Propellerload
Throttleplate
Env-1 cranktrain-1
Env-4
Env-2Exhrunner-1
Exhrunner-2
Propeller_N_T-1
exhport-1
exhport-2
Exvalve-1
Exvalve-2
Cylinder-1
Cylinder-2
Invalve-1
Invalve-2
PipeRound-1
PipeRound-2
EngCrankcase-1
EngCrankcase-2
Man-fs-1
ValveCheckConn-2
Intport-1Intrunner-1
ThrottleConn-1
Intrunner-2
AirFilter
Si-inject-1
ValveCheckConn-1
Figure 5 One-dimensional GT-Power model of the two-strokeaeroengine
4 Complexity
force the dynamic action of the needle valve should beconsidered in the compensation of the set pulse width
Fuel injector working progress mainly includes threesteps the injector receives the pulse signal from ECU theelectromagnetic coil is gradually energized and the needlevalve starts to move when overcoming the spring preloadwhen the magnetized solenoid coil is saturated the needlevalve stops at the mechanical limit position when the pulsesignal becomes zero the magnetic flux of the solenoid coilreduces gradually and the needle valve will return to thenormal position Basically all the nozzles of the electro-magnetic type work in this way and the response delayimpact on the dynamic inject fuel flow caused by mechanicalfactors cannot be ignored In order to deeply analyze thedynamic injection and formulate the calibration strategy thedynamic model of the injector is built as follows
U0 Ri + NdΦbdt
when electrified
0 R + R0( 1113857 i + NdΦbdt
when not electrified
(2)
ese equations are magnetic flux when the injector iselectrified and not electrified where R is the basic resistanceof the electrified coil loop R0 is the protective resistance Vbrepresents total magnetic circuitN is the number of the coili is the current in the loop and U0 is the driving voltage eelectromagnetic force (Fm) on the needle valve when the coilis electrified is as follows
Fm μ0(iN)2S
2δ2 (3)
where μ0 represents permeability of vacuum S is cross-section of the air gap and δ means length of the working airgap Kinetic equation of the magnetic needle valve is
Fm minus F0 minus kx + Ffuel mvd2xdt2
(4)
where F0 is the initial tension of spring k is the springstiffness x is the displacement of the needle valve mv is themass of needle valve and Ffuel is fuel pressure force on theneedle valve When the needle valve is opened the highpressure fuel erupts and produces spray into the manifolde equation of the fuel flow is as follows according to orificecompensation principle
_mfi CdA0
2 ρf pf minus pm( 1113857
1113969
(5)
where _mfi is the instantaneous inject fuel mass flow Cd isdischarge coefficient A0 is aperture area ρf is the fueldensity and Pm is the atmosphere pressure Based on theequations the dynamic displacement of the needle valve iscalculated under different spring stiffness values As shownin Figure 6(a) when the initial spring tension force F0 is setat 55N the response of the valve displacement will not keeppace with the control signal However when F0 is set at95N pulse width of the needle displacement is muchshorter than the control signal which can be shown inFigure 6(b) and that will lead to insufficient of the inject fuel
erefore the pulse width of the valve displacement can beadjusted to be the same with that of the control signal bysetting the spring tension force F0 As shown in Figure 6(c)pulse width of the dynamic displacement of the needle valveis approximate to the control signal except at the beginningof the period where there is a rise process which causesinjection control error
is paper proposes a compensation method for theinjection control error As shown in Figure 7 it can be seenthat the displacement compensation time is equal to thecurrent delay time Compensation area of the rise process isapproximate as a triangle erefore the compensationwidth (Pc) is shown in the following equation
Pc Di
2 (6)
where Di is the current time delay Equation (1) can beamended as follows
_mf ηvρ refVDλset
(CYL) Pw + Pc( 1113857 (7)
Propeller load can be calculated according to differentworking conditions based on standard strip analysis Asknown from the calculation load torque of the propellermainly depends on engine speed (n) and propeller rotordiameter (rp) Main formula of the torque is as follows
MR 1113944(ΔD cos β + ΔL sin β)rp (8)
where MR is the propeller torque ΔD is differential form ofthe drag force ΔL is differential form of the lift force β is theintake air flow angle and rp is the propeller radius en theparameters are confirmed according to a blade materialthen we can get the torque MAP in horizontal directionunder different working conditions which is shown inFigure 8 From Figure 8 we can see that the load torque doesnot increase linearly with increasing engine speed and theUAV propeller rotor diameter However we can substitutethe torque MAP into the one-dimensional model by thelinear interpolation method
3 Experiments and Optimization
31ExperimentalVerification Numerical simulation cannotcompletely replace experiment analysis and if we want tomake the simulation results reflect the engine mechanism asprecisely as possible the mathematical simulation and ex-periment analysis should be combined e mathematicalmodel needs to be verified by experiment results whichmainly includes two parts the engine structure and thecombustion model e engine structure can be verified byintake air flow experiments at is because the engine isdriven by the oil and gas combustion and if the detected airflow is consistent with the simulation result in differentconditions we can see that the built engine model structurecan provide an equal inlet air mass flow In addition thecombustion model should be demonstrated by the cylinderpressure test e reason is that the output power of theinternal combustion engine mainly comes from the in-
Complexity 5
0 001 002 003 004 0050
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(a)
0 001 002 003 004 005
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(b)
0005 001 0015 002
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(c)
Figure 6 Dynamic displacement of the needle valve with different spring initial tension F0 (a) F0 55N (b) F0 95N (c) F0 80N
Control signalCurrent signalNeedle valve displacement
0
12
Nee
dle v
alve
disp
lace
men
t (m
m)
0
1
Current time delayDisplacement compensation
Approximatetriangle
Cont
rol s
igna
l (V
)
0
1
Curr
ent s
igna
l (A
)
1 2 3 4 5 6 7 8 9 100Time (ms)
Figure 7 Schematic diagram of needle valve displacementcompensation
05506
06507
07508
10002000
30004000
50006000 1000
15002000
25003000
35004000
4500
UAV propeller rotor diameter (m)
5000
5500
6000
Engine speed (rpm)
0
5
10
15
20
25
Load
torq
ue (N
middotm)
Figure 8 Horizontal torque of the propeller under differentworking conditions
6 Complexity
cylinder pressure and if the detected pressure fits well withthe simulation result it can be seen that the combustionprediction model in the simulation is effective erefore anengine intake air flowmeter is connected with the intakemanifold and a high frequency pressure sensor is setup onthe engine cylinder en we can get the air mass flow andcylinder pressure compare curves as shown in Figures 9(a)and 9(b) From these two pictures we can see that the resulterrors are no more than 5 and can demonstrate themathematic model to be effective
Injection fuel compensation can be demonstrated byECU experiments ECU gets trigger signal and outputs pulsesignal with a certain pulse width According to above re-search result the inject fuel pulse is compensated by thedelay time of the current through the electrified coil loopAccording to Figure 10 an ECU with the above function isdesigned and tested e current signal as well as the controlvoltage through the fuel injector is tested According toFigure 11 we can obtain that the current delay time is about4ms erefore in the model we compensate for the injectpulse by 2ms Repetitive experiments with different controlsignal widths are conducted and according to the real ap-plication the signal width is controlled within the range of35ms to 50ms and we obtain that the current delay time isthe same at is because their lowering processes of thecurrent are the same So in the simulation model we can setthe current delay time as constant 2ms
rough the simulation based on the model above therelative working parameters can be calculated e basicsimulation setting parameters are throttle opening degree(α) and the set air-fuel ratio (λset) Generally the mostconcerned characteristics and evaluation indicators of theengine mainly include engine speed (n) output power (Po)power efficiency (η) and rotational fuel consumption (c) ηand c can be calculated as follows
η Po
Pi
nTo
9550 _mfHu
c n
_mf
(9)
where Pi is the input power of the engine To is the outputtorque of the engine andHu is the gas calorific value which isabout 46000KJkg By changing the setting parameters α andλset a group of output parameters are obtained
32 Simulation Results As shown in Tables 2ndash4 there areseveral arrays of input and output parameters In additionall the parameters are recorded when the engine simulationstend to be stable
Tables 2ndash4 represent a part of simulation results In thispaper the throttle opening degree (α) is changed from 10deg to90deg and the engine speed is from 2500 RPM to 6000RPMaccording to the real application What needs illustration isthat according to our a large number of experiment resultsthe output AFR of the engine can only be controlled within aprecision of 05 and the general range of AFR during theengine working process is from 12 to 155 erefore in the
simulation the input AFR value is set to every 05 from 12 to155
As shown in the three tables To reflects the load-carryingcapacity and generally it is considered as the main indicatorof grade ability in the area of ground gasoline However inthe application of the rotorcraft UAV field the lift force ofthe UAV is primarily determined by the engine speed Sothe parameter To is mainly considered in the start and ac-celeration processes Po is the output power of the engineand in the case of the same displacement output powershould be bigger However in this paper the fuel economy istreated as a priority so in the engine fuel injection controlweight of η should be put more Considering that the enginespeed directly influences the lift of the UAV the rotationalfuel consumption c reflects the fuel consumption rate atconstant speed In addition Pc is the maximum cylinderpressure of one crankshaft rotate cycle
Since these output characteristics affect each other theinfluence rules of the injection parameter should be analyzedin order to assist in the formulation of the optimizationstrategies e set AFR directly affects the oil injection flowrate and its value always combines with that of the throttleopening degree (α) Here α is controlled stably as 40deg be-cause the single opening degrees value can reflect the wholeprinciple Engine speed (n) which is as the final controlquantity of the UAV power system should be simulated bystages According to the application requirement the in-terval is set as 500 RPM from 2500RPM to 6000 RPMenthe tendency charts which show the relationships betweenthe input parameters and the output characteristics areobtained as shown in Figures 12ndash15
As shown in Figures 12 and 13 it can be seen that whenthe throttle opening degree is constant the output torquecurves and output power curves will have a peak at a samespeed However it is difficult to find a regular rule betweenthe set AFR and these two output characteristics at isbecause when the throttle opening degree is set constantlythere must be a primal AFR setting value with differentworking conditions which is in accordance with the engineexternal characteristics According to the settled weight theoptimization should be comprehensively considered Inaddition from the two figures the curve trends are almostthe same so only one of the items can be considered whensetting weights in order to reduce the amount of calculation
It is a bit of mess in Figure 14 which represents theefficiency of the engine system Curves in Figure 14 almosthave peak values and the peak values basically independentof the output torque and powererefore the characteristicof power efficiency can be considered independently Powerefficiency is significant for the fuel economy improvementNevertheless it should be secondary to the torque and powerin the startup and acceleration processes in order to ensurethe safety of the UAV flight
Since the engine speed is kept steady during the flightthe oil consumption of rotation speed (c) is the most im-portant characteristic for fuel saving and flight enduranceextension As shown in Figure 15 the curves have troughs atthe same speed point with the torque and power curvesHowever in Figure 15 the arrange regular way of the curves
Complexity 7
of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV
Simulation resultsExperiment results
202224262830323436
Air
mas
s flo
w (K
gh)
3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)
(a)
Simulation resultsExperiment results
0
5
10
15
20
25
Cylin
der p
ress
ure (
bar)
ndash50 0 50 100 150 200ndash100Crank angle (degree)
(b)
Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM
ECUWiringharness
OscilloscopeFuel injector
Figure 10 Injector test picture
Current signalPulse signal
Current delay time
0
002
004
006
008
01
012
014
Curr
ent s
igna
l (A
)
0
05
1
15
2
25
3
Vol
tage
pul
se (V
)
20 40 60 800Time (ms)
Figure 11 Results of the current delay time test
Table 2 Results of the GT-power simulation when α 10deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMhKg)Pc
(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687
Table 3 Results of the GT-power simulation when α 40deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128
Table 4 Results of the GT-power simulation when α 80deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391
8 Complexity
33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations
n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857
(10)
where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)
f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c
(11)
where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
8
10
12
14
16
18
20
Out
put t
orqu
e (N
middotm)
3000 4000 5000 60002000Engine speed (RPM)
Figure 12 Output torque at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
2
3
4
5
6
7
8
9
10
Oup
ut p
ower
(Kw
)
Figure 13 Output power at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
01
012
014
016
018
02
022
024
026
028
Pow
er e
ffici
ency
Figure 14 Power efficiency at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000O
il co
nsum
ptio
n ra
te o
f rot
atio
n sp
eed
(RPM
middothK
g)
Figure 15 Oil consumption rate of rotation speed
Complexity 9
matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16
e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5
According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows
(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping
(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed
(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered
(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced
rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17
From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows
(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator
calculate the weight matrixesW1W2W3 and W4
obtain the simulation results
calculate the evaluation function results f (θn)
derive the evaluation function matrix F (θn)
data normalization preprocessing determine the relationship
between throttle openingdegree and engine speedaccording to A and equ(12)
obtain the engine set AFR optimization curve
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Final
determine the set AFRmatrix A according to theevaluation function matrix
Figure 16 Optimization process
Table 5 Definition and explanation of preference weights based onSaatyrsquos theory
Preferenceweights Definition Explanation
1 Equally preferable Two factors contributeequally to the objective
3 Moderate preferredExperience and judgementslightly favour one over
other
5 Strongly preferredExperience and judgementstrongly favour one over the
other
7 Very stronglypreferred
Experience and judgementvery strongly favour one
over the other
9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity
2 4 6 8 Intermediates valuesUsed to represent
compromise between thepreferences listed
Reciprocals Reciprocals forinverse comparison mdash
Table 6 Optimize calibration data of fuel injection parameter
α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135
10 Complexity
(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10
34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded
From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results
4 Conclusion
is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system
Data Availability
e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article
10 20 30 40 50 60 70 80 90
2500300035004000450050005500600012
13
14
15
16larrlarr6000
Throttle opening degree (deg)Engine speed (RPM)
Targ
et A
FR
Figure 17 Fuel injection MAP
020
4060
80100
20003000
40005000
6000ndash01
ndash005
0
005
01
2500
Throttle opening degree (deg)
300035004000
50004500
55006000
Engine speed (RPM)
Effic
ienc
y er
ror
Figure 18 Efficiency error MAP
Fuel tank
Weightingsensor
Testaeroengine
Analysiscomputer
Remotecontroller
Figure 19 Aeroengine test station
Optimal resultsPrevious results
1800
2000
2200
2400
2600
2800
Oil
cons
umpt
ion
rate
of r
otat
ion
spee
d (R
PMmiddoth
Kg)
3000 3500 4000 4500 5000 5500 60002500
Engine speed (RPM)
Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed
Complexity 11
Acknowledgments
is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment
References
[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017
[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015
[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014
[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014
[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016
[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011
[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011
[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985
[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009
[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013
[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016
[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017
[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three
stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017
[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009
[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010
[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014
[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017
[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012
[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992
[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980
[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018
[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018
[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014
[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019
[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020
[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020
12 Complexity
width Relationship between _mf λset and the inject fuel pulsewidth (Pw) is shown in the following equation
_mf ηvρrefVDλset(CYL)Pw
(1)
where ηv is volumetric efficiency ρref is reference air densityused to calculate volumetric efficiency VD is the enginedisplacement and CYL is the number of cylinders Fromthis equation we can see that Pw directly determines theinjected fuel flow In order to improve the comprehensiveperformance of the aeroengine the inject fuel flow rates arecalibrated under different working conditions So as tomake the setup more intuitive in this paper the calibratingstandard is based on the expected air-fuel ratio and then theECU can calculate the output Pw in the real practiceHowever because the injector is driven by electromagnetic
Env Filter Throttleplate Manifold
Injector
Inlet port
Crankcase system
Scavenging passage 1
Cylinderchamber 2
Exhaust passage 2Exhaust passage 1
EnvEnv
Cylinderchamber 1
Scavenging passage 2
Crankcasechamber 1
Crankcasechamber 2
Load ofthe propeller
Intake port 2Intake port 1
Exhaust port 2Exhaust port 1
055 06 065 07 075 08
10002000
30004000
50006000
05
10152025
ndash1000ndash1500ndash2000
ndash2500ndash3000
ndash3500ndash4000
ndash4500
UAV propeller rotor diameter (m)
ndash5000
ndash5500ndash6000
Engine speed (rpm)
Load
torq
ue (N
m)
Figure 3 Working process of the two-stroke aeroengine
Port
area
(mm
2 )
0
300
600
900
1200
1500
120 140 160 180100Cranksha angle (degree)
(a)
Port
area
(mm
2 )
0
50
100
150
200
80 100 120 140 160 18060Cranksha angle (degree)
(b)
Figure 4 Working process of the two-stroke aeroengine (a) Intake port area (b) Exhaust port area
Intakeports
Exhaustports
Cylinderchambers
Fuelinjector
Propellerload
Throttleplate
Env-1 cranktrain-1
Env-4
Env-2Exhrunner-1
Exhrunner-2
Propeller_N_T-1
exhport-1
exhport-2
Exvalve-1
Exvalve-2
Cylinder-1
Cylinder-2
Invalve-1
Invalve-2
PipeRound-1
PipeRound-2
EngCrankcase-1
EngCrankcase-2
Man-fs-1
ValveCheckConn-2
Intport-1Intrunner-1
ThrottleConn-1
Intrunner-2
AirFilter
Si-inject-1
ValveCheckConn-1
Figure 5 One-dimensional GT-Power model of the two-strokeaeroengine
4 Complexity
force the dynamic action of the needle valve should beconsidered in the compensation of the set pulse width
Fuel injector working progress mainly includes threesteps the injector receives the pulse signal from ECU theelectromagnetic coil is gradually energized and the needlevalve starts to move when overcoming the spring preloadwhen the magnetized solenoid coil is saturated the needlevalve stops at the mechanical limit position when the pulsesignal becomes zero the magnetic flux of the solenoid coilreduces gradually and the needle valve will return to thenormal position Basically all the nozzles of the electro-magnetic type work in this way and the response delayimpact on the dynamic inject fuel flow caused by mechanicalfactors cannot be ignored In order to deeply analyze thedynamic injection and formulate the calibration strategy thedynamic model of the injector is built as follows
U0 Ri + NdΦbdt
when electrified
0 R + R0( 1113857 i + NdΦbdt
when not electrified
(2)
ese equations are magnetic flux when the injector iselectrified and not electrified where R is the basic resistanceof the electrified coil loop R0 is the protective resistance Vbrepresents total magnetic circuitN is the number of the coili is the current in the loop and U0 is the driving voltage eelectromagnetic force (Fm) on the needle valve when the coilis electrified is as follows
Fm μ0(iN)2S
2δ2 (3)
where μ0 represents permeability of vacuum S is cross-section of the air gap and δ means length of the working airgap Kinetic equation of the magnetic needle valve is
Fm minus F0 minus kx + Ffuel mvd2xdt2
(4)
where F0 is the initial tension of spring k is the springstiffness x is the displacement of the needle valve mv is themass of needle valve and Ffuel is fuel pressure force on theneedle valve When the needle valve is opened the highpressure fuel erupts and produces spray into the manifolde equation of the fuel flow is as follows according to orificecompensation principle
_mfi CdA0
2 ρf pf minus pm( 1113857
1113969
(5)
where _mfi is the instantaneous inject fuel mass flow Cd isdischarge coefficient A0 is aperture area ρf is the fueldensity and Pm is the atmosphere pressure Based on theequations the dynamic displacement of the needle valve iscalculated under different spring stiffness values As shownin Figure 6(a) when the initial spring tension force F0 is setat 55N the response of the valve displacement will not keeppace with the control signal However when F0 is set at95N pulse width of the needle displacement is muchshorter than the control signal which can be shown inFigure 6(b) and that will lead to insufficient of the inject fuel
erefore the pulse width of the valve displacement can beadjusted to be the same with that of the control signal bysetting the spring tension force F0 As shown in Figure 6(c)pulse width of the dynamic displacement of the needle valveis approximate to the control signal except at the beginningof the period where there is a rise process which causesinjection control error
is paper proposes a compensation method for theinjection control error As shown in Figure 7 it can be seenthat the displacement compensation time is equal to thecurrent delay time Compensation area of the rise process isapproximate as a triangle erefore the compensationwidth (Pc) is shown in the following equation
Pc Di
2 (6)
where Di is the current time delay Equation (1) can beamended as follows
_mf ηvρ refVDλset
(CYL) Pw + Pc( 1113857 (7)
Propeller load can be calculated according to differentworking conditions based on standard strip analysis Asknown from the calculation load torque of the propellermainly depends on engine speed (n) and propeller rotordiameter (rp) Main formula of the torque is as follows
MR 1113944(ΔD cos β + ΔL sin β)rp (8)
where MR is the propeller torque ΔD is differential form ofthe drag force ΔL is differential form of the lift force β is theintake air flow angle and rp is the propeller radius en theparameters are confirmed according to a blade materialthen we can get the torque MAP in horizontal directionunder different working conditions which is shown inFigure 8 From Figure 8 we can see that the load torque doesnot increase linearly with increasing engine speed and theUAV propeller rotor diameter However we can substitutethe torque MAP into the one-dimensional model by thelinear interpolation method
3 Experiments and Optimization
31ExperimentalVerification Numerical simulation cannotcompletely replace experiment analysis and if we want tomake the simulation results reflect the engine mechanism asprecisely as possible the mathematical simulation and ex-periment analysis should be combined e mathematicalmodel needs to be verified by experiment results whichmainly includes two parts the engine structure and thecombustion model e engine structure can be verified byintake air flow experiments at is because the engine isdriven by the oil and gas combustion and if the detected airflow is consistent with the simulation result in differentconditions we can see that the built engine model structurecan provide an equal inlet air mass flow In addition thecombustion model should be demonstrated by the cylinderpressure test e reason is that the output power of theinternal combustion engine mainly comes from the in-
Complexity 5
0 001 002 003 004 0050
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(a)
0 001 002 003 004 005
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(b)
0005 001 0015 002
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(c)
Figure 6 Dynamic displacement of the needle valve with different spring initial tension F0 (a) F0 55N (b) F0 95N (c) F0 80N
Control signalCurrent signalNeedle valve displacement
0
12
Nee
dle v
alve
disp
lace
men
t (m
m)
0
1
Current time delayDisplacement compensation
Approximatetriangle
Cont
rol s
igna
l (V
)
0
1
Curr
ent s
igna
l (A
)
1 2 3 4 5 6 7 8 9 100Time (ms)
Figure 7 Schematic diagram of needle valve displacementcompensation
05506
06507
07508
10002000
30004000
50006000 1000
15002000
25003000
35004000
4500
UAV propeller rotor diameter (m)
5000
5500
6000
Engine speed (rpm)
0
5
10
15
20
25
Load
torq
ue (N
middotm)
Figure 8 Horizontal torque of the propeller under differentworking conditions
6 Complexity
cylinder pressure and if the detected pressure fits well withthe simulation result it can be seen that the combustionprediction model in the simulation is effective erefore anengine intake air flowmeter is connected with the intakemanifold and a high frequency pressure sensor is setup onthe engine cylinder en we can get the air mass flow andcylinder pressure compare curves as shown in Figures 9(a)and 9(b) From these two pictures we can see that the resulterrors are no more than 5 and can demonstrate themathematic model to be effective
Injection fuel compensation can be demonstrated byECU experiments ECU gets trigger signal and outputs pulsesignal with a certain pulse width According to above re-search result the inject fuel pulse is compensated by thedelay time of the current through the electrified coil loopAccording to Figure 10 an ECU with the above function isdesigned and tested e current signal as well as the controlvoltage through the fuel injector is tested According toFigure 11 we can obtain that the current delay time is about4ms erefore in the model we compensate for the injectpulse by 2ms Repetitive experiments with different controlsignal widths are conducted and according to the real ap-plication the signal width is controlled within the range of35ms to 50ms and we obtain that the current delay time isthe same at is because their lowering processes of thecurrent are the same So in the simulation model we can setthe current delay time as constant 2ms
rough the simulation based on the model above therelative working parameters can be calculated e basicsimulation setting parameters are throttle opening degree(α) and the set air-fuel ratio (λset) Generally the mostconcerned characteristics and evaluation indicators of theengine mainly include engine speed (n) output power (Po)power efficiency (η) and rotational fuel consumption (c) ηand c can be calculated as follows
η Po
Pi
nTo
9550 _mfHu
c n
_mf
(9)
where Pi is the input power of the engine To is the outputtorque of the engine andHu is the gas calorific value which isabout 46000KJkg By changing the setting parameters α andλset a group of output parameters are obtained
32 Simulation Results As shown in Tables 2ndash4 there areseveral arrays of input and output parameters In additionall the parameters are recorded when the engine simulationstend to be stable
Tables 2ndash4 represent a part of simulation results In thispaper the throttle opening degree (α) is changed from 10deg to90deg and the engine speed is from 2500 RPM to 6000RPMaccording to the real application What needs illustration isthat according to our a large number of experiment resultsthe output AFR of the engine can only be controlled within aprecision of 05 and the general range of AFR during theengine working process is from 12 to 155 erefore in the
simulation the input AFR value is set to every 05 from 12 to155
As shown in the three tables To reflects the load-carryingcapacity and generally it is considered as the main indicatorof grade ability in the area of ground gasoline However inthe application of the rotorcraft UAV field the lift force ofthe UAV is primarily determined by the engine speed Sothe parameter To is mainly considered in the start and ac-celeration processes Po is the output power of the engineand in the case of the same displacement output powershould be bigger However in this paper the fuel economy istreated as a priority so in the engine fuel injection controlweight of η should be put more Considering that the enginespeed directly influences the lift of the UAV the rotationalfuel consumption c reflects the fuel consumption rate atconstant speed In addition Pc is the maximum cylinderpressure of one crankshaft rotate cycle
Since these output characteristics affect each other theinfluence rules of the injection parameter should be analyzedin order to assist in the formulation of the optimizationstrategies e set AFR directly affects the oil injection flowrate and its value always combines with that of the throttleopening degree (α) Here α is controlled stably as 40deg be-cause the single opening degrees value can reflect the wholeprinciple Engine speed (n) which is as the final controlquantity of the UAV power system should be simulated bystages According to the application requirement the in-terval is set as 500 RPM from 2500RPM to 6000 RPMenthe tendency charts which show the relationships betweenthe input parameters and the output characteristics areobtained as shown in Figures 12ndash15
As shown in Figures 12 and 13 it can be seen that whenthe throttle opening degree is constant the output torquecurves and output power curves will have a peak at a samespeed However it is difficult to find a regular rule betweenthe set AFR and these two output characteristics at isbecause when the throttle opening degree is set constantlythere must be a primal AFR setting value with differentworking conditions which is in accordance with the engineexternal characteristics According to the settled weight theoptimization should be comprehensively considered Inaddition from the two figures the curve trends are almostthe same so only one of the items can be considered whensetting weights in order to reduce the amount of calculation
It is a bit of mess in Figure 14 which represents theefficiency of the engine system Curves in Figure 14 almosthave peak values and the peak values basically independentof the output torque and powererefore the characteristicof power efficiency can be considered independently Powerefficiency is significant for the fuel economy improvementNevertheless it should be secondary to the torque and powerin the startup and acceleration processes in order to ensurethe safety of the UAV flight
Since the engine speed is kept steady during the flightthe oil consumption of rotation speed (c) is the most im-portant characteristic for fuel saving and flight enduranceextension As shown in Figure 15 the curves have troughs atthe same speed point with the torque and power curvesHowever in Figure 15 the arrange regular way of the curves
Complexity 7
of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV
Simulation resultsExperiment results
202224262830323436
Air
mas
s flo
w (K
gh)
3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)
(a)
Simulation resultsExperiment results
0
5
10
15
20
25
Cylin
der p
ress
ure (
bar)
ndash50 0 50 100 150 200ndash100Crank angle (degree)
(b)
Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM
ECUWiringharness
OscilloscopeFuel injector
Figure 10 Injector test picture
Current signalPulse signal
Current delay time
0
002
004
006
008
01
012
014
Curr
ent s
igna
l (A
)
0
05
1
15
2
25
3
Vol
tage
pul
se (V
)
20 40 60 800Time (ms)
Figure 11 Results of the current delay time test
Table 2 Results of the GT-power simulation when α 10deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMhKg)Pc
(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687
Table 3 Results of the GT-power simulation when α 40deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128
Table 4 Results of the GT-power simulation when α 80deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391
8 Complexity
33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations
n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857
(10)
where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)
f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c
(11)
where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
8
10
12
14
16
18
20
Out
put t
orqu
e (N
middotm)
3000 4000 5000 60002000Engine speed (RPM)
Figure 12 Output torque at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
2
3
4
5
6
7
8
9
10
Oup
ut p
ower
(Kw
)
Figure 13 Output power at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
01
012
014
016
018
02
022
024
026
028
Pow
er e
ffici
ency
Figure 14 Power efficiency at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000O
il co
nsum
ptio
n ra
te o
f rot
atio
n sp
eed
(RPM
middothK
g)
Figure 15 Oil consumption rate of rotation speed
Complexity 9
matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16
e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5
According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows
(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping
(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed
(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered
(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced
rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17
From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows
(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator
calculate the weight matrixesW1W2W3 and W4
obtain the simulation results
calculate the evaluation function results f (θn)
derive the evaluation function matrix F (θn)
data normalization preprocessing determine the relationship
between throttle openingdegree and engine speedaccording to A and equ(12)
obtain the engine set AFR optimization curve
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Final
determine the set AFRmatrix A according to theevaluation function matrix
Figure 16 Optimization process
Table 5 Definition and explanation of preference weights based onSaatyrsquos theory
Preferenceweights Definition Explanation
1 Equally preferable Two factors contributeequally to the objective
3 Moderate preferredExperience and judgementslightly favour one over
other
5 Strongly preferredExperience and judgementstrongly favour one over the
other
7 Very stronglypreferred
Experience and judgementvery strongly favour one
over the other
9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity
2 4 6 8 Intermediates valuesUsed to represent
compromise between thepreferences listed
Reciprocals Reciprocals forinverse comparison mdash
Table 6 Optimize calibration data of fuel injection parameter
α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135
10 Complexity
(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10
34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded
From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results
4 Conclusion
is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system
Data Availability
e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article
10 20 30 40 50 60 70 80 90
2500300035004000450050005500600012
13
14
15
16larrlarr6000
Throttle opening degree (deg)Engine speed (RPM)
Targ
et A
FR
Figure 17 Fuel injection MAP
020
4060
80100
20003000
40005000
6000ndash01
ndash005
0
005
01
2500
Throttle opening degree (deg)
300035004000
50004500
55006000
Engine speed (RPM)
Effic
ienc
y er
ror
Figure 18 Efficiency error MAP
Fuel tank
Weightingsensor
Testaeroengine
Analysiscomputer
Remotecontroller
Figure 19 Aeroengine test station
Optimal resultsPrevious results
1800
2000
2200
2400
2600
2800
Oil
cons
umpt
ion
rate
of r
otat
ion
spee
d (R
PMmiddoth
Kg)
3000 3500 4000 4500 5000 5500 60002500
Engine speed (RPM)
Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed
Complexity 11
Acknowledgments
is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment
References
[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017
[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015
[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014
[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014
[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016
[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011
[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011
[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985
[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009
[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013
[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016
[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017
[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three
stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017
[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009
[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010
[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014
[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017
[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012
[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992
[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980
[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018
[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018
[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014
[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019
[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020
[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020
12 Complexity
force the dynamic action of the needle valve should beconsidered in the compensation of the set pulse width
Fuel injector working progress mainly includes threesteps the injector receives the pulse signal from ECU theelectromagnetic coil is gradually energized and the needlevalve starts to move when overcoming the spring preloadwhen the magnetized solenoid coil is saturated the needlevalve stops at the mechanical limit position when the pulsesignal becomes zero the magnetic flux of the solenoid coilreduces gradually and the needle valve will return to thenormal position Basically all the nozzles of the electro-magnetic type work in this way and the response delayimpact on the dynamic inject fuel flow caused by mechanicalfactors cannot be ignored In order to deeply analyze thedynamic injection and formulate the calibration strategy thedynamic model of the injector is built as follows
U0 Ri + NdΦbdt
when electrified
0 R + R0( 1113857 i + NdΦbdt
when not electrified
(2)
ese equations are magnetic flux when the injector iselectrified and not electrified where R is the basic resistanceof the electrified coil loop R0 is the protective resistance Vbrepresents total magnetic circuitN is the number of the coili is the current in the loop and U0 is the driving voltage eelectromagnetic force (Fm) on the needle valve when the coilis electrified is as follows
Fm μ0(iN)2S
2δ2 (3)
where μ0 represents permeability of vacuum S is cross-section of the air gap and δ means length of the working airgap Kinetic equation of the magnetic needle valve is
Fm minus F0 minus kx + Ffuel mvd2xdt2
(4)
where F0 is the initial tension of spring k is the springstiffness x is the displacement of the needle valve mv is themass of needle valve and Ffuel is fuel pressure force on theneedle valve When the needle valve is opened the highpressure fuel erupts and produces spray into the manifolde equation of the fuel flow is as follows according to orificecompensation principle
_mfi CdA0
2 ρf pf minus pm( 1113857
1113969
(5)
where _mfi is the instantaneous inject fuel mass flow Cd isdischarge coefficient A0 is aperture area ρf is the fueldensity and Pm is the atmosphere pressure Based on theequations the dynamic displacement of the needle valve iscalculated under different spring stiffness values As shownin Figure 6(a) when the initial spring tension force F0 is setat 55N the response of the valve displacement will not keeppace with the control signal However when F0 is set at95N pulse width of the needle displacement is muchshorter than the control signal which can be shown inFigure 6(b) and that will lead to insufficient of the inject fuel
erefore the pulse width of the valve displacement can beadjusted to be the same with that of the control signal bysetting the spring tension force F0 As shown in Figure 6(c)pulse width of the dynamic displacement of the needle valveis approximate to the control signal except at the beginningof the period where there is a rise process which causesinjection control error
is paper proposes a compensation method for theinjection control error As shown in Figure 7 it can be seenthat the displacement compensation time is equal to thecurrent delay time Compensation area of the rise process isapproximate as a triangle erefore the compensationwidth (Pc) is shown in the following equation
Pc Di
2 (6)
where Di is the current time delay Equation (1) can beamended as follows
_mf ηvρ refVDλset
(CYL) Pw + Pc( 1113857 (7)
Propeller load can be calculated according to differentworking conditions based on standard strip analysis Asknown from the calculation load torque of the propellermainly depends on engine speed (n) and propeller rotordiameter (rp) Main formula of the torque is as follows
MR 1113944(ΔD cos β + ΔL sin β)rp (8)
where MR is the propeller torque ΔD is differential form ofthe drag force ΔL is differential form of the lift force β is theintake air flow angle and rp is the propeller radius en theparameters are confirmed according to a blade materialthen we can get the torque MAP in horizontal directionunder different working conditions which is shown inFigure 8 From Figure 8 we can see that the load torque doesnot increase linearly with increasing engine speed and theUAV propeller rotor diameter However we can substitutethe torque MAP into the one-dimensional model by thelinear interpolation method
3 Experiments and Optimization
31ExperimentalVerification Numerical simulation cannotcompletely replace experiment analysis and if we want tomake the simulation results reflect the engine mechanism asprecisely as possible the mathematical simulation and ex-periment analysis should be combined e mathematicalmodel needs to be verified by experiment results whichmainly includes two parts the engine structure and thecombustion model e engine structure can be verified byintake air flow experiments at is because the engine isdriven by the oil and gas combustion and if the detected airflow is consistent with the simulation result in differentconditions we can see that the built engine model structurecan provide an equal inlet air mass flow In addition thecombustion model should be demonstrated by the cylinderpressure test e reason is that the output power of theinternal combustion engine mainly comes from the in-
Complexity 5
0 001 002 003 004 0050
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(a)
0 001 002 003 004 005
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(b)
0005 001 0015 002
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(c)
Figure 6 Dynamic displacement of the needle valve with different spring initial tension F0 (a) F0 55N (b) F0 95N (c) F0 80N
Control signalCurrent signalNeedle valve displacement
0
12
Nee
dle v
alve
disp
lace
men
t (m
m)
0
1
Current time delayDisplacement compensation
Approximatetriangle
Cont
rol s
igna
l (V
)
0
1
Curr
ent s
igna
l (A
)
1 2 3 4 5 6 7 8 9 100Time (ms)
Figure 7 Schematic diagram of needle valve displacementcompensation
05506
06507
07508
10002000
30004000
50006000 1000
15002000
25003000
35004000
4500
UAV propeller rotor diameter (m)
5000
5500
6000
Engine speed (rpm)
0
5
10
15
20
25
Load
torq
ue (N
middotm)
Figure 8 Horizontal torque of the propeller under differentworking conditions
6 Complexity
cylinder pressure and if the detected pressure fits well withthe simulation result it can be seen that the combustionprediction model in the simulation is effective erefore anengine intake air flowmeter is connected with the intakemanifold and a high frequency pressure sensor is setup onthe engine cylinder en we can get the air mass flow andcylinder pressure compare curves as shown in Figures 9(a)and 9(b) From these two pictures we can see that the resulterrors are no more than 5 and can demonstrate themathematic model to be effective
Injection fuel compensation can be demonstrated byECU experiments ECU gets trigger signal and outputs pulsesignal with a certain pulse width According to above re-search result the inject fuel pulse is compensated by thedelay time of the current through the electrified coil loopAccording to Figure 10 an ECU with the above function isdesigned and tested e current signal as well as the controlvoltage through the fuel injector is tested According toFigure 11 we can obtain that the current delay time is about4ms erefore in the model we compensate for the injectpulse by 2ms Repetitive experiments with different controlsignal widths are conducted and according to the real ap-plication the signal width is controlled within the range of35ms to 50ms and we obtain that the current delay time isthe same at is because their lowering processes of thecurrent are the same So in the simulation model we can setthe current delay time as constant 2ms
rough the simulation based on the model above therelative working parameters can be calculated e basicsimulation setting parameters are throttle opening degree(α) and the set air-fuel ratio (λset) Generally the mostconcerned characteristics and evaluation indicators of theengine mainly include engine speed (n) output power (Po)power efficiency (η) and rotational fuel consumption (c) ηand c can be calculated as follows
η Po
Pi
nTo
9550 _mfHu
c n
_mf
(9)
where Pi is the input power of the engine To is the outputtorque of the engine andHu is the gas calorific value which isabout 46000KJkg By changing the setting parameters α andλset a group of output parameters are obtained
32 Simulation Results As shown in Tables 2ndash4 there areseveral arrays of input and output parameters In additionall the parameters are recorded when the engine simulationstend to be stable
Tables 2ndash4 represent a part of simulation results In thispaper the throttle opening degree (α) is changed from 10deg to90deg and the engine speed is from 2500 RPM to 6000RPMaccording to the real application What needs illustration isthat according to our a large number of experiment resultsthe output AFR of the engine can only be controlled within aprecision of 05 and the general range of AFR during theengine working process is from 12 to 155 erefore in the
simulation the input AFR value is set to every 05 from 12 to155
As shown in the three tables To reflects the load-carryingcapacity and generally it is considered as the main indicatorof grade ability in the area of ground gasoline However inthe application of the rotorcraft UAV field the lift force ofthe UAV is primarily determined by the engine speed Sothe parameter To is mainly considered in the start and ac-celeration processes Po is the output power of the engineand in the case of the same displacement output powershould be bigger However in this paper the fuel economy istreated as a priority so in the engine fuel injection controlweight of η should be put more Considering that the enginespeed directly influences the lift of the UAV the rotationalfuel consumption c reflects the fuel consumption rate atconstant speed In addition Pc is the maximum cylinderpressure of one crankshaft rotate cycle
Since these output characteristics affect each other theinfluence rules of the injection parameter should be analyzedin order to assist in the formulation of the optimizationstrategies e set AFR directly affects the oil injection flowrate and its value always combines with that of the throttleopening degree (α) Here α is controlled stably as 40deg be-cause the single opening degrees value can reflect the wholeprinciple Engine speed (n) which is as the final controlquantity of the UAV power system should be simulated bystages According to the application requirement the in-terval is set as 500 RPM from 2500RPM to 6000 RPMenthe tendency charts which show the relationships betweenthe input parameters and the output characteristics areobtained as shown in Figures 12ndash15
As shown in Figures 12 and 13 it can be seen that whenthe throttle opening degree is constant the output torquecurves and output power curves will have a peak at a samespeed However it is difficult to find a regular rule betweenthe set AFR and these two output characteristics at isbecause when the throttle opening degree is set constantlythere must be a primal AFR setting value with differentworking conditions which is in accordance with the engineexternal characteristics According to the settled weight theoptimization should be comprehensively considered Inaddition from the two figures the curve trends are almostthe same so only one of the items can be considered whensetting weights in order to reduce the amount of calculation
It is a bit of mess in Figure 14 which represents theefficiency of the engine system Curves in Figure 14 almosthave peak values and the peak values basically independentof the output torque and powererefore the characteristicof power efficiency can be considered independently Powerefficiency is significant for the fuel economy improvementNevertheless it should be secondary to the torque and powerin the startup and acceleration processes in order to ensurethe safety of the UAV flight
Since the engine speed is kept steady during the flightthe oil consumption of rotation speed (c) is the most im-portant characteristic for fuel saving and flight enduranceextension As shown in Figure 15 the curves have troughs atthe same speed point with the torque and power curvesHowever in Figure 15 the arrange regular way of the curves
Complexity 7
of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV
Simulation resultsExperiment results
202224262830323436
Air
mas
s flo
w (K
gh)
3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)
(a)
Simulation resultsExperiment results
0
5
10
15
20
25
Cylin
der p
ress
ure (
bar)
ndash50 0 50 100 150 200ndash100Crank angle (degree)
(b)
Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM
ECUWiringharness
OscilloscopeFuel injector
Figure 10 Injector test picture
Current signalPulse signal
Current delay time
0
002
004
006
008
01
012
014
Curr
ent s
igna
l (A
)
0
05
1
15
2
25
3
Vol
tage
pul
se (V
)
20 40 60 800Time (ms)
Figure 11 Results of the current delay time test
Table 2 Results of the GT-power simulation when α 10deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMhKg)Pc
(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687
Table 3 Results of the GT-power simulation when α 40deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128
Table 4 Results of the GT-power simulation when α 80deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391
8 Complexity
33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations
n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857
(10)
where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)
f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c
(11)
where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
8
10
12
14
16
18
20
Out
put t
orqu
e (N
middotm)
3000 4000 5000 60002000Engine speed (RPM)
Figure 12 Output torque at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
2
3
4
5
6
7
8
9
10
Oup
ut p
ower
(Kw
)
Figure 13 Output power at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
01
012
014
016
018
02
022
024
026
028
Pow
er e
ffici
ency
Figure 14 Power efficiency at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000O
il co
nsum
ptio
n ra
te o
f rot
atio
n sp
eed
(RPM
middothK
g)
Figure 15 Oil consumption rate of rotation speed
Complexity 9
matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16
e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5
According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows
(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping
(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed
(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered
(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced
rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17
From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows
(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator
calculate the weight matrixesW1W2W3 and W4
obtain the simulation results
calculate the evaluation function results f (θn)
derive the evaluation function matrix F (θn)
data normalization preprocessing determine the relationship
between throttle openingdegree and engine speedaccording to A and equ(12)
obtain the engine set AFR optimization curve
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Final
determine the set AFRmatrix A according to theevaluation function matrix
Figure 16 Optimization process
Table 5 Definition and explanation of preference weights based onSaatyrsquos theory
Preferenceweights Definition Explanation
1 Equally preferable Two factors contributeequally to the objective
3 Moderate preferredExperience and judgementslightly favour one over
other
5 Strongly preferredExperience and judgementstrongly favour one over the
other
7 Very stronglypreferred
Experience and judgementvery strongly favour one
over the other
9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity
2 4 6 8 Intermediates valuesUsed to represent
compromise between thepreferences listed
Reciprocals Reciprocals forinverse comparison mdash
Table 6 Optimize calibration data of fuel injection parameter
α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135
10 Complexity
(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10
34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded
From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results
4 Conclusion
is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system
Data Availability
e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article
10 20 30 40 50 60 70 80 90
2500300035004000450050005500600012
13
14
15
16larrlarr6000
Throttle opening degree (deg)Engine speed (RPM)
Targ
et A
FR
Figure 17 Fuel injection MAP
020
4060
80100
20003000
40005000
6000ndash01
ndash005
0
005
01
2500
Throttle opening degree (deg)
300035004000
50004500
55006000
Engine speed (RPM)
Effic
ienc
y er
ror
Figure 18 Efficiency error MAP
Fuel tank
Weightingsensor
Testaeroengine
Analysiscomputer
Remotecontroller
Figure 19 Aeroengine test station
Optimal resultsPrevious results
1800
2000
2200
2400
2600
2800
Oil
cons
umpt
ion
rate
of r
otat
ion
spee
d (R
PMmiddoth
Kg)
3000 3500 4000 4500 5000 5500 60002500
Engine speed (RPM)
Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed
Complexity 11
Acknowledgments
is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment
References
[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017
[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015
[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014
[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014
[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016
[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011
[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011
[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985
[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009
[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013
[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016
[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017
[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three
stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017
[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009
[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010
[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014
[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017
[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012
[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992
[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980
[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018
[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018
[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014
[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019
[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020
[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020
12 Complexity
0 001 002 003 004 0050
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(a)
0 001 002 003 004 005
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(b)
0005 001 0015 002
3
6
9
12
15
Time (s)
Con
trol s
igna
l (V
)
0
05
1
15
2
25
3 times10ndash4
Nee
dle d
ispla
cem
ent (
m)
Control signalNeedle displacement
(c)
Figure 6 Dynamic displacement of the needle valve with different spring initial tension F0 (a) F0 55N (b) F0 95N (c) F0 80N
Control signalCurrent signalNeedle valve displacement
0
12
Nee
dle v
alve
disp
lace
men
t (m
m)
0
1
Current time delayDisplacement compensation
Approximatetriangle
Cont
rol s
igna
l (V
)
0
1
Curr
ent s
igna
l (A
)
1 2 3 4 5 6 7 8 9 100Time (ms)
Figure 7 Schematic diagram of needle valve displacementcompensation
05506
06507
07508
10002000
30004000
50006000 1000
15002000
25003000
35004000
4500
UAV propeller rotor diameter (m)
5000
5500
6000
Engine speed (rpm)
0
5
10
15
20
25
Load
torq
ue (N
middotm)
Figure 8 Horizontal torque of the propeller under differentworking conditions
6 Complexity
cylinder pressure and if the detected pressure fits well withthe simulation result it can be seen that the combustionprediction model in the simulation is effective erefore anengine intake air flowmeter is connected with the intakemanifold and a high frequency pressure sensor is setup onthe engine cylinder en we can get the air mass flow andcylinder pressure compare curves as shown in Figures 9(a)and 9(b) From these two pictures we can see that the resulterrors are no more than 5 and can demonstrate themathematic model to be effective
Injection fuel compensation can be demonstrated byECU experiments ECU gets trigger signal and outputs pulsesignal with a certain pulse width According to above re-search result the inject fuel pulse is compensated by thedelay time of the current through the electrified coil loopAccording to Figure 10 an ECU with the above function isdesigned and tested e current signal as well as the controlvoltage through the fuel injector is tested According toFigure 11 we can obtain that the current delay time is about4ms erefore in the model we compensate for the injectpulse by 2ms Repetitive experiments with different controlsignal widths are conducted and according to the real ap-plication the signal width is controlled within the range of35ms to 50ms and we obtain that the current delay time isthe same at is because their lowering processes of thecurrent are the same So in the simulation model we can setthe current delay time as constant 2ms
rough the simulation based on the model above therelative working parameters can be calculated e basicsimulation setting parameters are throttle opening degree(α) and the set air-fuel ratio (λset) Generally the mostconcerned characteristics and evaluation indicators of theengine mainly include engine speed (n) output power (Po)power efficiency (η) and rotational fuel consumption (c) ηand c can be calculated as follows
η Po
Pi
nTo
9550 _mfHu
c n
_mf
(9)
where Pi is the input power of the engine To is the outputtorque of the engine andHu is the gas calorific value which isabout 46000KJkg By changing the setting parameters α andλset a group of output parameters are obtained
32 Simulation Results As shown in Tables 2ndash4 there areseveral arrays of input and output parameters In additionall the parameters are recorded when the engine simulationstend to be stable
Tables 2ndash4 represent a part of simulation results In thispaper the throttle opening degree (α) is changed from 10deg to90deg and the engine speed is from 2500 RPM to 6000RPMaccording to the real application What needs illustration isthat according to our a large number of experiment resultsthe output AFR of the engine can only be controlled within aprecision of 05 and the general range of AFR during theengine working process is from 12 to 155 erefore in the
simulation the input AFR value is set to every 05 from 12 to155
As shown in the three tables To reflects the load-carryingcapacity and generally it is considered as the main indicatorof grade ability in the area of ground gasoline However inthe application of the rotorcraft UAV field the lift force ofthe UAV is primarily determined by the engine speed Sothe parameter To is mainly considered in the start and ac-celeration processes Po is the output power of the engineand in the case of the same displacement output powershould be bigger However in this paper the fuel economy istreated as a priority so in the engine fuel injection controlweight of η should be put more Considering that the enginespeed directly influences the lift of the UAV the rotationalfuel consumption c reflects the fuel consumption rate atconstant speed In addition Pc is the maximum cylinderpressure of one crankshaft rotate cycle
Since these output characteristics affect each other theinfluence rules of the injection parameter should be analyzedin order to assist in the formulation of the optimizationstrategies e set AFR directly affects the oil injection flowrate and its value always combines with that of the throttleopening degree (α) Here α is controlled stably as 40deg be-cause the single opening degrees value can reflect the wholeprinciple Engine speed (n) which is as the final controlquantity of the UAV power system should be simulated bystages According to the application requirement the in-terval is set as 500 RPM from 2500RPM to 6000 RPMenthe tendency charts which show the relationships betweenthe input parameters and the output characteristics areobtained as shown in Figures 12ndash15
As shown in Figures 12 and 13 it can be seen that whenthe throttle opening degree is constant the output torquecurves and output power curves will have a peak at a samespeed However it is difficult to find a regular rule betweenthe set AFR and these two output characteristics at isbecause when the throttle opening degree is set constantlythere must be a primal AFR setting value with differentworking conditions which is in accordance with the engineexternal characteristics According to the settled weight theoptimization should be comprehensively considered Inaddition from the two figures the curve trends are almostthe same so only one of the items can be considered whensetting weights in order to reduce the amount of calculation
It is a bit of mess in Figure 14 which represents theefficiency of the engine system Curves in Figure 14 almosthave peak values and the peak values basically independentof the output torque and powererefore the characteristicof power efficiency can be considered independently Powerefficiency is significant for the fuel economy improvementNevertheless it should be secondary to the torque and powerin the startup and acceleration processes in order to ensurethe safety of the UAV flight
Since the engine speed is kept steady during the flightthe oil consumption of rotation speed (c) is the most im-portant characteristic for fuel saving and flight enduranceextension As shown in Figure 15 the curves have troughs atthe same speed point with the torque and power curvesHowever in Figure 15 the arrange regular way of the curves
Complexity 7
of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV
Simulation resultsExperiment results
202224262830323436
Air
mas
s flo
w (K
gh)
3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)
(a)
Simulation resultsExperiment results
0
5
10
15
20
25
Cylin
der p
ress
ure (
bar)
ndash50 0 50 100 150 200ndash100Crank angle (degree)
(b)
Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM
ECUWiringharness
OscilloscopeFuel injector
Figure 10 Injector test picture
Current signalPulse signal
Current delay time
0
002
004
006
008
01
012
014
Curr
ent s
igna
l (A
)
0
05
1
15
2
25
3
Vol
tage
pul
se (V
)
20 40 60 800Time (ms)
Figure 11 Results of the current delay time test
Table 2 Results of the GT-power simulation when α 10deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMhKg)Pc
(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687
Table 3 Results of the GT-power simulation when α 40deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128
Table 4 Results of the GT-power simulation when α 80deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391
8 Complexity
33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations
n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857
(10)
where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)
f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c
(11)
where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
8
10
12
14
16
18
20
Out
put t
orqu
e (N
middotm)
3000 4000 5000 60002000Engine speed (RPM)
Figure 12 Output torque at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
2
3
4
5
6
7
8
9
10
Oup
ut p
ower
(Kw
)
Figure 13 Output power at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
01
012
014
016
018
02
022
024
026
028
Pow
er e
ffici
ency
Figure 14 Power efficiency at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000O
il co
nsum
ptio
n ra
te o
f rot
atio
n sp
eed
(RPM
middothK
g)
Figure 15 Oil consumption rate of rotation speed
Complexity 9
matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16
e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5
According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows
(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping
(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed
(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered
(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced
rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17
From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows
(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator
calculate the weight matrixesW1W2W3 and W4
obtain the simulation results
calculate the evaluation function results f (θn)
derive the evaluation function matrix F (θn)
data normalization preprocessing determine the relationship
between throttle openingdegree and engine speedaccording to A and equ(12)
obtain the engine set AFR optimization curve
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Final
determine the set AFRmatrix A according to theevaluation function matrix
Figure 16 Optimization process
Table 5 Definition and explanation of preference weights based onSaatyrsquos theory
Preferenceweights Definition Explanation
1 Equally preferable Two factors contributeequally to the objective
3 Moderate preferredExperience and judgementslightly favour one over
other
5 Strongly preferredExperience and judgementstrongly favour one over the
other
7 Very stronglypreferred
Experience and judgementvery strongly favour one
over the other
9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity
2 4 6 8 Intermediates valuesUsed to represent
compromise between thepreferences listed
Reciprocals Reciprocals forinverse comparison mdash
Table 6 Optimize calibration data of fuel injection parameter
α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135
10 Complexity
(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10
34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded
From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results
4 Conclusion
is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system
Data Availability
e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article
10 20 30 40 50 60 70 80 90
2500300035004000450050005500600012
13
14
15
16larrlarr6000
Throttle opening degree (deg)Engine speed (RPM)
Targ
et A
FR
Figure 17 Fuel injection MAP
020
4060
80100
20003000
40005000
6000ndash01
ndash005
0
005
01
2500
Throttle opening degree (deg)
300035004000
50004500
55006000
Engine speed (RPM)
Effic
ienc
y er
ror
Figure 18 Efficiency error MAP
Fuel tank
Weightingsensor
Testaeroengine
Analysiscomputer
Remotecontroller
Figure 19 Aeroengine test station
Optimal resultsPrevious results
1800
2000
2200
2400
2600
2800
Oil
cons
umpt
ion
rate
of r
otat
ion
spee
d (R
PMmiddoth
Kg)
3000 3500 4000 4500 5000 5500 60002500
Engine speed (RPM)
Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed
Complexity 11
Acknowledgments
is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment
References
[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017
[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015
[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014
[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014
[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016
[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011
[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011
[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985
[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009
[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013
[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016
[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017
[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three
stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017
[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009
[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010
[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014
[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017
[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012
[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992
[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980
[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018
[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018
[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014
[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019
[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020
[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020
12 Complexity
cylinder pressure and if the detected pressure fits well withthe simulation result it can be seen that the combustionprediction model in the simulation is effective erefore anengine intake air flowmeter is connected with the intakemanifold and a high frequency pressure sensor is setup onthe engine cylinder en we can get the air mass flow andcylinder pressure compare curves as shown in Figures 9(a)and 9(b) From these two pictures we can see that the resulterrors are no more than 5 and can demonstrate themathematic model to be effective
Injection fuel compensation can be demonstrated byECU experiments ECU gets trigger signal and outputs pulsesignal with a certain pulse width According to above re-search result the inject fuel pulse is compensated by thedelay time of the current through the electrified coil loopAccording to Figure 10 an ECU with the above function isdesigned and tested e current signal as well as the controlvoltage through the fuel injector is tested According toFigure 11 we can obtain that the current delay time is about4ms erefore in the model we compensate for the injectpulse by 2ms Repetitive experiments with different controlsignal widths are conducted and according to the real ap-plication the signal width is controlled within the range of35ms to 50ms and we obtain that the current delay time isthe same at is because their lowering processes of thecurrent are the same So in the simulation model we can setthe current delay time as constant 2ms
rough the simulation based on the model above therelative working parameters can be calculated e basicsimulation setting parameters are throttle opening degree(α) and the set air-fuel ratio (λset) Generally the mostconcerned characteristics and evaluation indicators of theengine mainly include engine speed (n) output power (Po)power efficiency (η) and rotational fuel consumption (c) ηand c can be calculated as follows
η Po
Pi
nTo
9550 _mfHu
c n
_mf
(9)
where Pi is the input power of the engine To is the outputtorque of the engine andHu is the gas calorific value which isabout 46000KJkg By changing the setting parameters α andλset a group of output parameters are obtained
32 Simulation Results As shown in Tables 2ndash4 there areseveral arrays of input and output parameters In additionall the parameters are recorded when the engine simulationstend to be stable
Tables 2ndash4 represent a part of simulation results In thispaper the throttle opening degree (α) is changed from 10deg to90deg and the engine speed is from 2500 RPM to 6000RPMaccording to the real application What needs illustration isthat according to our a large number of experiment resultsthe output AFR of the engine can only be controlled within aprecision of 05 and the general range of AFR during theengine working process is from 12 to 155 erefore in the
simulation the input AFR value is set to every 05 from 12 to155
As shown in the three tables To reflects the load-carryingcapacity and generally it is considered as the main indicatorof grade ability in the area of ground gasoline However inthe application of the rotorcraft UAV field the lift force ofthe UAV is primarily determined by the engine speed Sothe parameter To is mainly considered in the start and ac-celeration processes Po is the output power of the engineand in the case of the same displacement output powershould be bigger However in this paper the fuel economy istreated as a priority so in the engine fuel injection controlweight of η should be put more Considering that the enginespeed directly influences the lift of the UAV the rotationalfuel consumption c reflects the fuel consumption rate atconstant speed In addition Pc is the maximum cylinderpressure of one crankshaft rotate cycle
Since these output characteristics affect each other theinfluence rules of the injection parameter should be analyzedin order to assist in the formulation of the optimizationstrategies e set AFR directly affects the oil injection flowrate and its value always combines with that of the throttleopening degree (α) Here α is controlled stably as 40deg be-cause the single opening degrees value can reflect the wholeprinciple Engine speed (n) which is as the final controlquantity of the UAV power system should be simulated bystages According to the application requirement the in-terval is set as 500 RPM from 2500RPM to 6000 RPMenthe tendency charts which show the relationships betweenthe input parameters and the output characteristics areobtained as shown in Figures 12ndash15
As shown in Figures 12 and 13 it can be seen that whenthe throttle opening degree is constant the output torquecurves and output power curves will have a peak at a samespeed However it is difficult to find a regular rule betweenthe set AFR and these two output characteristics at isbecause when the throttle opening degree is set constantlythere must be a primal AFR setting value with differentworking conditions which is in accordance with the engineexternal characteristics According to the settled weight theoptimization should be comprehensively considered Inaddition from the two figures the curve trends are almostthe same so only one of the items can be considered whensetting weights in order to reduce the amount of calculation
It is a bit of mess in Figure 14 which represents theefficiency of the engine system Curves in Figure 14 almosthave peak values and the peak values basically independentof the output torque and powererefore the characteristicof power efficiency can be considered independently Powerefficiency is significant for the fuel economy improvementNevertheless it should be secondary to the torque and powerin the startup and acceleration processes in order to ensurethe safety of the UAV flight
Since the engine speed is kept steady during the flightthe oil consumption of rotation speed (c) is the most im-portant characteristic for fuel saving and flight enduranceextension As shown in Figure 15 the curves have troughs atthe same speed point with the torque and power curvesHowever in Figure 15 the arrange regular way of the curves
Complexity 7
of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV
Simulation resultsExperiment results
202224262830323436
Air
mas
s flo
w (K
gh)
3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)
(a)
Simulation resultsExperiment results
0
5
10
15
20
25
Cylin
der p
ress
ure (
bar)
ndash50 0 50 100 150 200ndash100Crank angle (degree)
(b)
Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM
ECUWiringharness
OscilloscopeFuel injector
Figure 10 Injector test picture
Current signalPulse signal
Current delay time
0
002
004
006
008
01
012
014
Curr
ent s
igna
l (A
)
0
05
1
15
2
25
3
Vol
tage
pul
se (V
)
20 40 60 800Time (ms)
Figure 11 Results of the current delay time test
Table 2 Results of the GT-power simulation when α 10deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMhKg)Pc
(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687
Table 3 Results of the GT-power simulation when α 40deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128
Table 4 Results of the GT-power simulation when α 80deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391
8 Complexity
33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations
n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857
(10)
where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)
f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c
(11)
where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
8
10
12
14
16
18
20
Out
put t
orqu
e (N
middotm)
3000 4000 5000 60002000Engine speed (RPM)
Figure 12 Output torque at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
2
3
4
5
6
7
8
9
10
Oup
ut p
ower
(Kw
)
Figure 13 Output power at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
01
012
014
016
018
02
022
024
026
028
Pow
er e
ffici
ency
Figure 14 Power efficiency at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000O
il co
nsum
ptio
n ra
te o
f rot
atio
n sp
eed
(RPM
middothK
g)
Figure 15 Oil consumption rate of rotation speed
Complexity 9
matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16
e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5
According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows
(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping
(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed
(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered
(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced
rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17
From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows
(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator
calculate the weight matrixesW1W2W3 and W4
obtain the simulation results
calculate the evaluation function results f (θn)
derive the evaluation function matrix F (θn)
data normalization preprocessing determine the relationship
between throttle openingdegree and engine speedaccording to A and equ(12)
obtain the engine set AFR optimization curve
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Final
determine the set AFRmatrix A according to theevaluation function matrix
Figure 16 Optimization process
Table 5 Definition and explanation of preference weights based onSaatyrsquos theory
Preferenceweights Definition Explanation
1 Equally preferable Two factors contributeequally to the objective
3 Moderate preferredExperience and judgementslightly favour one over
other
5 Strongly preferredExperience and judgementstrongly favour one over the
other
7 Very stronglypreferred
Experience and judgementvery strongly favour one
over the other
9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity
2 4 6 8 Intermediates valuesUsed to represent
compromise between thepreferences listed
Reciprocals Reciprocals forinverse comparison mdash
Table 6 Optimize calibration data of fuel injection parameter
α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135
10 Complexity
(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10
34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded
From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results
4 Conclusion
is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system
Data Availability
e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article
10 20 30 40 50 60 70 80 90
2500300035004000450050005500600012
13
14
15
16larrlarr6000
Throttle opening degree (deg)Engine speed (RPM)
Targ
et A
FR
Figure 17 Fuel injection MAP
020
4060
80100
20003000
40005000
6000ndash01
ndash005
0
005
01
2500
Throttle opening degree (deg)
300035004000
50004500
55006000
Engine speed (RPM)
Effic
ienc
y er
ror
Figure 18 Efficiency error MAP
Fuel tank
Weightingsensor
Testaeroengine
Analysiscomputer
Remotecontroller
Figure 19 Aeroengine test station
Optimal resultsPrevious results
1800
2000
2200
2400
2600
2800
Oil
cons
umpt
ion
rate
of r
otat
ion
spee
d (R
PMmiddoth
Kg)
3000 3500 4000 4500 5000 5500 60002500
Engine speed (RPM)
Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed
Complexity 11
Acknowledgments
is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment
References
[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017
[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015
[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014
[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014
[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016
[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011
[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011
[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985
[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009
[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013
[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016
[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017
[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three
stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017
[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009
[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010
[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014
[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017
[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012
[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992
[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980
[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018
[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018
[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014
[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019
[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020
[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020
12 Complexity
of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV
Simulation resultsExperiment results
202224262830323436
Air
mas
s flo
w (K
gh)
3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)
(a)
Simulation resultsExperiment results
0
5
10
15
20
25
Cylin
der p
ress
ure (
bar)
ndash50 0 50 100 150 200ndash100Crank angle (degree)
(b)
Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM
ECUWiringharness
OscilloscopeFuel injector
Figure 10 Injector test picture
Current signalPulse signal
Current delay time
0
002
004
006
008
01
012
014
Curr
ent s
igna
l (A
)
0
05
1
15
2
25
3
Vol
tage
pul
se (V
)
20 40 60 800Time (ms)
Figure 11 Results of the current delay time test
Table 2 Results of the GT-power simulation when α 10deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMhKg)Pc
(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687
Table 3 Results of the GT-power simulation when α 40deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128
Table 4 Results of the GT-power simulation when α 80deg
α(deg)
n(RPM) λset
To(Nm)
Po(kw) η c
(RPMmiddothKg)Pc
(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391
8 Complexity
33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations
n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857
(10)
where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)
f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c
(11)
where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
8
10
12
14
16
18
20
Out
put t
orqu
e (N
middotm)
3000 4000 5000 60002000Engine speed (RPM)
Figure 12 Output torque at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
2
3
4
5
6
7
8
9
10
Oup
ut p
ower
(Kw
)
Figure 13 Output power at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
01
012
014
016
018
02
022
024
026
028
Pow
er e
ffici
ency
Figure 14 Power efficiency at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000O
il co
nsum
ptio
n ra
te o
f rot
atio
n sp
eed
(RPM
middothK
g)
Figure 15 Oil consumption rate of rotation speed
Complexity 9
matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16
e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5
According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows
(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping
(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed
(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered
(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced
rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17
From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows
(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator
calculate the weight matrixesW1W2W3 and W4
obtain the simulation results
calculate the evaluation function results f (θn)
derive the evaluation function matrix F (θn)
data normalization preprocessing determine the relationship
between throttle openingdegree and engine speedaccording to A and equ(12)
obtain the engine set AFR optimization curve
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Final
determine the set AFRmatrix A according to theevaluation function matrix
Figure 16 Optimization process
Table 5 Definition and explanation of preference weights based onSaatyrsquos theory
Preferenceweights Definition Explanation
1 Equally preferable Two factors contributeequally to the objective
3 Moderate preferredExperience and judgementslightly favour one over
other
5 Strongly preferredExperience and judgementstrongly favour one over the
other
7 Very stronglypreferred
Experience and judgementvery strongly favour one
over the other
9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity
2 4 6 8 Intermediates valuesUsed to represent
compromise between thepreferences listed
Reciprocals Reciprocals forinverse comparison mdash
Table 6 Optimize calibration data of fuel injection parameter
α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135
10 Complexity
(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10
34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded
From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results
4 Conclusion
is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system
Data Availability
e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article
10 20 30 40 50 60 70 80 90
2500300035004000450050005500600012
13
14
15
16larrlarr6000
Throttle opening degree (deg)Engine speed (RPM)
Targ
et A
FR
Figure 17 Fuel injection MAP
020
4060
80100
20003000
40005000
6000ndash01
ndash005
0
005
01
2500
Throttle opening degree (deg)
300035004000
50004500
55006000
Engine speed (RPM)
Effic
ienc
y er
ror
Figure 18 Efficiency error MAP
Fuel tank
Weightingsensor
Testaeroengine
Analysiscomputer
Remotecontroller
Figure 19 Aeroengine test station
Optimal resultsPrevious results
1800
2000
2200
2400
2600
2800
Oil
cons
umpt
ion
rate
of r
otat
ion
spee
d (R
PMmiddoth
Kg)
3000 3500 4000 4500 5000 5500 60002500
Engine speed (RPM)
Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed
Complexity 11
Acknowledgments
is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment
References
[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017
[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015
[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014
[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014
[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016
[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011
[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011
[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985
[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009
[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013
[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016
[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017
[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three
stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017
[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009
[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010
[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014
[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017
[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012
[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992
[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980
[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018
[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018
[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014
[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019
[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020
[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020
12 Complexity
33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations
n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857
(10)
where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)
f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c
(11)
where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
8
10
12
14
16
18
20
Out
put t
orqu
e (N
middotm)
3000 4000 5000 60002000Engine speed (RPM)
Figure 12 Output torque at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
2
3
4
5
6
7
8
9
10
Oup
ut p
ower
(Kw
)
Figure 13 Output power at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
01
012
014
016
018
02
022
024
026
028
Pow
er e
ffici
ency
Figure 14 Power efficiency at different engine speeds
AFR = 12AFR = 125AFR = 13AFR = 135
AFR = 14AFR = 145AFR = 15AFR = 155
3000 4000 5000 60002000Engine speed (RPM)
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000O
il co
nsum
ptio
n ra
te o
f rot
atio
n sp
eed
(RPM
middothK
g)
Figure 15 Oil consumption rate of rotation speed
Complexity 9
matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16
e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5
According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows
(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping
(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed
(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered
(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced
rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17
From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows
(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator
calculate the weight matrixesW1W2W3 and W4
obtain the simulation results
calculate the evaluation function results f (θn)
derive the evaluation function matrix F (θn)
data normalization preprocessing determine the relationship
between throttle openingdegree and engine speedaccording to A and equ(12)
obtain the engine set AFR optimization curve
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Final
determine the set AFRmatrix A according to theevaluation function matrix
Figure 16 Optimization process
Table 5 Definition and explanation of preference weights based onSaatyrsquos theory
Preferenceweights Definition Explanation
1 Equally preferable Two factors contributeequally to the objective
3 Moderate preferredExperience and judgementslightly favour one over
other
5 Strongly preferredExperience and judgementstrongly favour one over the
other
7 Very stronglypreferred
Experience and judgementvery strongly favour one
over the other
9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity
2 4 6 8 Intermediates valuesUsed to represent
compromise between thepreferences listed
Reciprocals Reciprocals forinverse comparison mdash
Table 6 Optimize calibration data of fuel injection parameter
α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135
10 Complexity
(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10
34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded
From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results
4 Conclusion
is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system
Data Availability
e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article
10 20 30 40 50 60 70 80 90
2500300035004000450050005500600012
13
14
15
16larrlarr6000
Throttle opening degree (deg)Engine speed (RPM)
Targ
et A
FR
Figure 17 Fuel injection MAP
020
4060
80100
20003000
40005000
6000ndash01
ndash005
0
005
01
2500
Throttle opening degree (deg)
300035004000
50004500
55006000
Engine speed (RPM)
Effic
ienc
y er
ror
Figure 18 Efficiency error MAP
Fuel tank
Weightingsensor
Testaeroengine
Analysiscomputer
Remotecontroller
Figure 19 Aeroengine test station
Optimal resultsPrevious results
1800
2000
2200
2400
2600
2800
Oil
cons
umpt
ion
rate
of r
otat
ion
spee
d (R
PMmiddoth
Kg)
3000 3500 4000 4500 5000 5500 60002500
Engine speed (RPM)
Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed
Complexity 11
Acknowledgments
is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment
References
[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017
[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015
[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014
[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014
[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016
[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011
[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011
[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985
[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009
[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013
[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016
[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017
[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three
stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017
[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009
[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010
[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014
[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017
[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012
[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992
[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980
[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018
[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018
[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014
[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019
[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020
[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020
12 Complexity
matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16
e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5
According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows
(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping
(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed
(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered
(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced
rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17
From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows
(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator
calculate the weight matrixesW1W2W3 and W4
obtain the simulation results
calculate the evaluation function results f (θn)
derive the evaluation function matrix F (θn)
data normalization preprocessing determine the relationship
between throttle openingdegree and engine speedaccording to A and equ(12)
obtain the engine set AFR optimization curve
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Final
determine the set AFRmatrix A according to theevaluation function matrix
Figure 16 Optimization process
Table 5 Definition and explanation of preference weights based onSaatyrsquos theory
Preferenceweights Definition Explanation
1 Equally preferable Two factors contributeequally to the objective
3 Moderate preferredExperience and judgementslightly favour one over
other
5 Strongly preferredExperience and judgementstrongly favour one over the
other
7 Very stronglypreferred
Experience and judgementvery strongly favour one
over the other
9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity
2 4 6 8 Intermediates valuesUsed to represent
compromise between thepreferences listed
Reciprocals Reciprocals forinverse comparison mdash
Table 6 Optimize calibration data of fuel injection parameter
α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135
10 Complexity
(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10
34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded
From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results
4 Conclusion
is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system
Data Availability
e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article
10 20 30 40 50 60 70 80 90
2500300035004000450050005500600012
13
14
15
16larrlarr6000
Throttle opening degree (deg)Engine speed (RPM)
Targ
et A
FR
Figure 17 Fuel injection MAP
020
4060
80100
20003000
40005000
6000ndash01
ndash005
0
005
01
2500
Throttle opening degree (deg)
300035004000
50004500
55006000
Engine speed (RPM)
Effic
ienc
y er
ror
Figure 18 Efficiency error MAP
Fuel tank
Weightingsensor
Testaeroengine
Analysiscomputer
Remotecontroller
Figure 19 Aeroengine test station
Optimal resultsPrevious results
1800
2000
2200
2400
2600
2800
Oil
cons
umpt
ion
rate
of r
otat
ion
spee
d (R
PMmiddoth
Kg)
3000 3500 4000 4500 5000 5500 60002500
Engine speed (RPM)
Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed
Complexity 11
Acknowledgments
is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment
References
[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017
[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015
[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014
[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014
[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016
[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011
[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011
[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985
[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009
[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013
[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016
[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017
[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three
stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017
[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009
[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010
[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014
[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017
[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012
[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992
[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980
[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018
[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018
[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014
[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019
[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020
[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020
12 Complexity
(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10
34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded
From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results
4 Conclusion
is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system
Data Availability
e data used to support the findings of this study are in-cluded within the article
Conflicts of Interest
e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article
10 20 30 40 50 60 70 80 90
2500300035004000450050005500600012
13
14
15
16larrlarr6000
Throttle opening degree (deg)Engine speed (RPM)
Targ
et A
FR
Figure 17 Fuel injection MAP
020
4060
80100
20003000
40005000
6000ndash01
ndash005
0
005
01
2500
Throttle opening degree (deg)
300035004000
50004500
55006000
Engine speed (RPM)
Effic
ienc
y er
ror
Figure 18 Efficiency error MAP
Fuel tank
Weightingsensor
Testaeroengine
Analysiscomputer
Remotecontroller
Figure 19 Aeroengine test station
Optimal resultsPrevious results
1800
2000
2200
2400
2600
2800
Oil
cons
umpt
ion
rate
of r
otat
ion
spee
d (R
PMmiddoth
Kg)
3000 3500 4000 4500 5000 5500 60002500
Engine speed (RPM)
Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed
Complexity 11
Acknowledgments
is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment
References
[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017
[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015
[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014
[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014
[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016
[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011
[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011
[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985
[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009
[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013
[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016
[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017
[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three
stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017
[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009
[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010
[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014
[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017
[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012
[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992
[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980
[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018
[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018
[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014
[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019
[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020
[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020
12 Complexity
Acknowledgments
is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment
References
[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017
[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015
[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014
[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014
[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016
[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011
[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011
[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985
[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009
[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013
[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016
[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017
[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three
stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017
[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009
[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010
[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014
[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017
[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012
[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992
[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980
[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018
[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018
[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014
[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019
[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020
[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020
12 Complexity
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