a dynamic model for automotive engine control analysis

5/28/2018 A Dynamic Model for Automotive Engine Control Analysis

1/7

A JXNAWC MODEL FOR AUTOMOTIVE ENGINE CONTROL ANALYSISbYB. K. Powell

Engineering and Research StaffFord Motor CompanyDearborn, Michigan

INTRODUCTIONThe automotive manufacturers a r e confronted with theproblem of developing vehicles that maximize h e 1 economy,yield minimum engine exhaust emissions, provide eatiefac-tory driveability characteristics, and e a t i e increasinglyrigid coat cowtrainte. The overa ll dynamic performance ofa vehicle engine drivetrain system is limited by the anglnecontrol policy and ultimatelyby the hardware implementationof that policy.Engine mapping techniques incorporating output vari-able-control variable regreseionl'3 combined with power-train simulation tools4 and various optimization technique&-9have been employed by a number of automotive companies as

fuel ratio, and exhaust gas recirculation (EGR) that wffl op-a means of estimating control values for p a r k advance, air-timize vehicle performance overa specified drivlng cycle.A general information flow of the complete process is shownin F@re 1. Generally, limited dynamic effects a r e con-sidered in the optimization processused to obtain the con-tro l variables. The control variables are often given aa afunction of maasureable quanti ties suchas pressure orspeedlo-13 and are implemented into a control computer forengine regulation. The complete system is then tested todetermine the affect of hardware and control policy imple-mentation on an actual vehicle system. Judicious controlalgorithm adjustment is often necessary to compensate forvarious unforseen system transients that may influence fue l ,emissions, and driveability. A technique for optimizing thecontrol variable trajectory for a given driving cyclehas beendeveloped by Dohner9. This technique is applicable to thecomplete system resplendent with transients . However, theapproach requires a prio ri hardware efinition and completesystem qnthesis.The engine vehicle control problem is complex enough torequire formulation as a mathematical model suitable for in-corporation of transient behavior into optimal engine controldevelopment. This paper contafne the development and sim-ulation results of a basic dynamic nonlinear mathematicalrepresentat ion of an internal combustion engine system.The model contains descr iptions of the induction proces sincluding characterizations of the throttle body manifoldplenum, and fuel injection system, a sonic EGR valve as wellas characterizations of the engine pumping charac teris ticsand torque output. The nonlinear dynamic system model is aclosed loop characterizationwith "driver" supplied thrott leangle and computer dictated EGR, spark and fuel commands.

A schematic block diagram of the major system model ele-ments is shown in Figure 2. A simplified diagram focusingon the major elements discussed in this paper is shown inFigure 3.variables are employed to represent the system. Changesin control mechanism represeatations could easily add orsubtract ataie variables, The detai ls of the system modelar e presented in the main body of the text

For the assumed control mechanism dynamics, ten state

A simple fuel/spark/EGR control policy14 was imple-mented to allow multivariable engine control while simulat-ing a CVS eat or step type hrottle disturbances that r e d tin large torque variation and hence poor driveability. Var-

i ous numerically simulated experiments were performednumerous engine operating conditionewing reaeonable asumptions fo r control actuator charaeteriatics. These rsults a re presented in the formof time hletoriee of the kengine state variables (e.g. torque, speed, maas flow afuel ratio, spark advance and EGR).The mathematical model developed in the paper presa simulation tool for an engne eystem that forms the foution for engineering systems analysis. The &ate variabdescription facilitates substitution of various hardwarerresentations, incorporation of tran6mission-driveline ch

the analysis, simulation and eynthesis of engine controlacterletice, and finally, provides a systematic approachteme.

ENGINE ACCELERATTONThe rotational motionof the engine crankshaft is givte rm s of the enginepolar moment of inertia, angular acceration, and the difference between then d torque generaby the w e nd the load torque of the shaft. Cylinder tcylinder torque variations are not included in t h i s modelCrankshaft acceleration is given byJ e = Tet) - TL (t)

whereJe = engine inertia, t-lb-sec2/radBe = crankanglevalve, adTe = engine net torque output, t-lbTL = engine external torque load, ft-lbt = time, sec.

overall driveability characteristics, the detailed descripAlthough drivetra in interac tion is important in term

of a drivetrain system is beyond the scope of thispaper.Simplified drivetrain characteriza tions are defined byPra bhakar s and may be employed in place of more rigo romodels. The model formulation does not preclude the adtion of detai led drivetra in dynamics if 8 desired. A simfied constituitive relation waa used to represent the enginshaft coupling torque as the primary purpose was to detedrivetrain interaction dynamics. For the reported studymine the engine dynamic characteriatics rather than engwas assumed that the load torque waa proportional to thetwist in the cylindrical shaft. That is,

whereK, = shaft stiffness constant for a hollow steel ehaf

ft-lb/radA more practical representation is obtained by def inengine speed in revolutions per minute. With the additio

120CHl486-0/79/0000-0120 00.75@ 1979 IEEE


2/7

a damping term the f inal form of the ine rtia-sha ft relat iongiven previously isJ e i ( t ) = Te(t) - 30 TL (t) 3)

k H

whereS (t) = engine peed,RPM

andt-0 TL(t) = Ks [E Be (t)- S(0)t- s g t )dt (4)H H 0

- 2t- [s(t)- Sd(0)- g(t)]where

g(t) = desired peedvariation,RPMS 0 ) = initialdynamometerspeed,RPMPowerplant demands, in the form of s peed and load , ar eobtainable from drivetrain type models suchas developed byBlumberg4 and may be used a s a forcing function input to themodel. The two state variables at this point in the develop-ment may be chosen as; (1) he produc t of s haft gain andtwist and 2 ) the engine speed. The order of the variable swill be defined in a later section. The other primary torqueaffecting engine acceleration is the net torque developed bythe engine. A discuss ion of that variable follows.

d

ENGINE NET TORQUEAn esti mate for chara cteri zati on of the engine torque isobtainable by employing analytical curve fitting techniques(regression) to dynamometer obtained experimental data.The choice of regression variables will yi eld engine torquebehavior as an implicit function of both contr ol va ria ble s andinduction proce ss variab les. In order to ultimately obtain aneffective dynamic (representat ion, the engine torque shouldbe defined in the most basic term s possibl e. For example,intake port mass flow rates a re prefe rable t o thrott le angledue to the l arg e nu mbe r of dynamic elements between thethrottle and intake ports.

based on the quadratic representati on of Pra bhak ar, et a18The for m of the engine torque employed in this paper iswhich is the res ult of a study by Keranen and Werthe im er ls .More recent higher order regression analyses have beenperform ed on conventional engines as r ep or te d by Mencik andBlumbergl. These techniqu es could be adapted for applica-tion to the present problem.An augmented fo rm of t he engine net torque14 i s given inte rm s of five explicit and implicit system variables by theequationTe = -115.0 + ,411 (M ) 22 (A /F) - 82 (A/F)2

+ .927 ( 6 - .0227( 6 )2 .00092 6 ) S)- 0179(S) - . 00029(S) - 779(E)

whereTe =

=

6 =s =

A / F =

engine net torque output, ft-lbengine intake speed density mass flow(SDMF) lb /h rspark advance, degengine speed, RPMair mass rate to fuel mass rate ratio

The engine mas s c harg e o r speed density mass flow (SDMFdefined herein consi sts of the produ ct of volu metr ic effi-ciency,enginedisplacement, and speed. It represen ts heintake mass charge excluding fuel. An equation for SDMFis given in the next section. The quantity E in Equation (5)is defined in t er ms of exhaust g as recirc ulation m ass flowrate and the throt tle body air ma ss flow rat e by the relat ionE = / A + I % )e a e

wherehe = exhaust gas recirculation (EGR) mass flow rat e,lb/hrha = throttle body air mas s flow rate, lb/hr

In this paper, the percent (f raction) of EGR is defined as thratio of EGR mass ra te to the air plus fuel ma ss rat e asEg = he/(ha hf)

whereThe independent variables in the engine torque equatio(Equation 5) cons ist of the spark adv ance, which is generalldirectly regulatable; the engine speed, which is direct ly mea-sureable; the A / F ra ti o and EGR, both of which a r e not di-rectly measurea ble; and finally, SDMF M, which is strictlyand internal system variable (an implici t variable). That ispark advance is the only directly regulatable variable in thengine torque equation while the remaining variables used ithe equation are the res ult of manipulation and int eract ion oother variables. The interrelationships among these vari-ables will become apparent in the subsequent sections f thpaper,The fresh mass charge used in the power strokef agiven cylinder (SDMF) i s inducted one cycle previously.Thus, a time constant related to the engine speed could beassigned to the engine torque generation. A simple modelobtained by defining an engine torque t ime constant inverselproportional to engine speed, and applying this to Equat ion5 ) to yield7e - ( T ~ ) + T~ = F~ M, A / F , 6 , s, E)dt

Other torque models, including isolation of engine frictiontorque, and inclusion of cyli nder by cylind er mass samplin gare de scri bed by Garofalol6. Mass charge mixing phenom-ena are discussedby Wu and Blumbergl7.Model systhesis continues in the next sectionwith thedevelopment of the equation s represent ing the induction process.

INDUCTION PROCESS DYNAMICS

tl e body and manifold plenum. The dynamic vari ables in-volved in these element s include air mas s rate, throttle an-gle, EGR mass rate manifold pressure, SDMF, and enginespeed. Fuel mass flow rat e is not considered part of the inbeen assumed. That is, the fuel is injecte d in the form of aduction process in this model as a fuel injection system hapulse at the i ntake p ort of each cylinder.

Included in the elements shown in Fi gur e 3 ar e the thro

charge from the plenum maybe repr ese nte d by an engineThe effect of the cycling engin e on the m ass ra te dis -pumping element. The "Engine Pump" element is alsoshown in Fig ure 3. The pump u se s manifold plenum pre s-su re and engine speed to generate an engine charge massra te (SDMF). In the static situation this mass rate must beexactly equal to the throttle body air ma ss ra te pl us he EGmass rate. A Difference in the mass rates results in achange of manifold pres sure. Thus, the pumping capabilityof the engine not only directly depends on the pressurendspeed, but indirectly on throttl e angle and EGR mass,


3/7

In an Engine modeling study conducted by Garofalo16 theengine pumping effect was represented in terms of enginespeed and volumetric efficiency. Volumetric efficiency wasin tur obtained from regressed engine data and was givenas a cubic polynomial of engine speed and manifold pressure .The product of volumetric efficiency, Engine displacementand engine speed yields a polynomial characterization ofSDMF as a function of speed and pressure.The engine pumping effect, in the form of steady s tate

mass flow data , may be presented in the form of an induc-tion process mass rate map. The map provides the rela-tionships between manifold pre ssure , engine speed, thrott leEGR is shown in Figure 4.angle and mass flow rate. An example of such a map for no

This particular map was obtained from a physical modelof the Ford 400 CID induction process as developed by Wu18.The Wu model employs the equilibration of mass and pres-sure balance equations in an induction system designed oapproximate the manifold geometry and engine pumping char-acteristi cs. The general behavior reflected in the map isimportant for the approximation to mass flow rat e and throt-tle influence used in the paper. An approximation to theSDMF data from the induction map shown in Figure 4 yieldsM = .01925 (S) (P) + .0006875 S ) (P)2 9)

whereP = manifold pressure psiIn a static equilibrium state SDMF equals the sum of airmass and EGR mass rates. In a dynamic situation a differ-

variation. Although the stati c relat ion in SDMF may be ade-ence between SDMF and intake mass rates causes a pressurequate to represent mass flow rate through the plenum, themass flow in actuality takes a certain period of time. Forexample, with no change in manifold press ure the plenumresidence time for the mass charge is approximately equalto the ratio of plenum volume to volume flow rate. The ple-num volume for the assumed characterization is about 40percent of the displacement and the volume flow ra te is pro-portional to speed. Thus, a reasonable period of time formas s flow through the plenum is assumed to be on he orderof 1/4 to 1/2 of an engine cycle. Therefore, an additionaltime constant, T "60/(2S) sec. may be assumed for SDMF.Thus,'M -& M)+ M = FMS,P) (10)

where F S,P) in the polynomial given by Equation (9).It is possible to descr ibe the influence of the throttleangle on the air mass flow rate as a function of manifoldpressure and various physical conetants aswas done byGarofalol6, or Hamburg and Hylandlg, and Harrington20.The basic throttle hody model is developed from assumingthat the flow is one dimensional, steady compressible flowof an ideal gas Initial pressure and temperature losses

before the throttle plate are accounted fo r by assuming isen-tropic flow.The throttle angle behavior can be separated into twomodes. From Figure 4 it is evident that when manifold pres-sure is less than about half of atmospheric pressure, achoked or sonic condition exists and mass flow rate is afunction only of throttle angle. In the operating region wheremanjfold press ure is greater than aboutone half atmosphericpres sure , the choked mass flow is moddated with the rootof the pr ess ure relation. Thus, air mass flow rate throughthe throttle body may be approximated by a nonlinear separ-able function of manifold pre ssu re and thrott le angle asAa = K a f ( B ) g ( P ) (11)

whereKa =

f ( e ) =

characteristic coefficient for a particularthrottle body Ib/hrnonlinear (elliptic) function of coefficient odischarge and throat geometrymot of the throttle body (manifold) press urand atmospheric pressure

ma = .96 e - 25) (&a ) 2 1/2The previous equation was u s e d to represent the air maflow rate as a function of throttle angle and press ure foresults presented in h i s paper.

The description of the induction process is completdeveloping an expression for the ate of change of manifpressu re. An expression for pressu re change is develousing the fi rs t law of thermo cs and the ideal gas by Garofa ldG, or Prabha-nerally, the equationdting from these developments defines the rate of chanof manifold press ure as being proportional to the differein manifold i n g r e s s and egress mass low rates.

Thus,= K ( m + m e - & )P a

. .The proportionality constant K is a function of the

constant, gas molecular weight, specific heat parametermanifold temperature, and manifold volume. Fo r the enopera- conditions simulated herein, the value of Kobtained from FJrabakar8, wassed.hus, P'

P'

K = .572PA definition if the induction process, including the ttle body, manifold plenum, and engine pump char acteri sas depicted in Figure 3, is thus given by Equations (S),(l l) , and 12).

CONTROL MECHANISM EQUATIONSfunctional forms were assumed for the throttle. fue l conFor the purpose of synthesizing a system model, simloop, and exhaust gas rec irculation valve. More fundamedescriptions of these devices may be developed.Throttle Dynamics

sent the behavior of the throttle angle to a commanded vFor simplicity a first order relation was usedo reThat is,T e + e = e

mechanical stop behavior compatible with a practical thA limit was placed on the throttle angle range to yiemechanism. The range employed was1 2 5 B 7 5 Degrees

could be formulated where estimateswould be needed foparameter values and important nonlinear character isticA given throttle mecaanism could haverate and positionMore general representations for the throttle mecha

1 2 2


4/7

limits aswell as Tdeadband,ll hysteresis nd other nonlineareffects. N ENGINE CONTBOL POLICY

Fuel Injection SystemThe fuel system may be designed such that the flow rateis proportional to an injection pulse width commsnd A

In order to maintain the simplicity of the present overalldynamic modal of such a system is given by Rachel, et al21.system model, the actual flow rate was described by a firstorder relation to the commanded fuel rate as,

r f -& if)kf = mfcwhere

T~ = fuel loop timeconstant,sec.kfc = external fuel loop command

fold fuel holdup effects resulting in much more complicatedFuel system characterizations could ale0 include mani-relationehips as well as various enrichment and other com-pensation methods.EGR System

A similar first order relation may be developed for theEGR mass rate control. A sonic EGR value was assumedfor the study. For such a valve, Kaufman22 has shown thatstatic mass flow rate obeys the following relationie Ke Pex Cm Ae/(Tex)1 / 2

wherePex = exhaust gas pressure, psiTex = absolute exhaust gas temperat ure, ORCDe = coefficient of dischargeAe = flow area of the throat of the valve, square in.

The cross sectional area Ae, as given in Kaufmanz, is pro-portional to the position of the sonic valve plug, which is re-ferred to as he pintle position. huswith proper calibra-tion Equation (15) gives the proportional relation betweenpintle position and EGR mass flow rate. Conversely, if acertain mass rate is desired, the necessary pintle positionmay be obtained from the valve calibration. In other words,statically there is no error in the EGR mass flow rate. Thus,me = SIec

In the actual system implementation the EGR valve re-here, the exhaust temperature and press ure ariat ti one areceives a pintle position command. Fo r the work presentedassumed to be small compared with the change in mass flowrate due to a change in the pintle posit ion of the valve.

In a dynamic mode, there exist valve lags between com-manded and achieved mass rates due to the pintle inertia,viscous and possibly static friction, exhaust back pressurevariation, and mas s flow rate interaction with the pintle.Again for simplicity, a firs t orde r behavior was assumedto describe the relationahip between commanded and achievedEGR mass flaw rate. Thus,

where

It is desirable to formulate a simple control policy thatr e q u i r e s minimal system parameter estima tion and minimaldependent variable measurement. That is, it is desirable tohave one set of control gains for a l l engine operating points(se t points) with very few measurements or computations re-quired in the control policy.A simple fuel control may be developed assuming thatthe air flow rate is meas ured or computed during system

operation. Of course the dynamic and static fidel ity of suchmeamuements should be accounted for in the model. If thedesired A/F is defined as (A/F)D then a reasonable fuel loopcommand is given simply asif, I ~ ~ / ( A / F ) ~

With this relation, there will always be a residual commandto the fuel loop unlessA/F = h a = ( A / F ) ~

Fuel control policy formulation odd include the effectsof A/F s e m r behavior e.g. ~a ss id yl 3, s well as possiblefuel transients induced by driver/t hrot tle input.The EGR mass rate command must ultimately be reeolv-ed into a desired pintle position by using the appropria teeonic EGR calibration. It wi l l be treated as an EGR massrate command here. A simple control command is readilyobtained from Equation 7) y factoring the EGR mass rateto obtain

* = if g 1 A / F ) (18)The calculated fuel flow rate command from Equation (17)may be used in (18) to complete the command calculations.Using this EGR command yields EGR m ass rates compatiblewith the fuel and air mass rates.

The remaining variable necessary to control is the enginetorque. It is desirable to have the engine achieve a specifiedtorque T, while controlling speed, A/F, Eg and spark. Atorque e r ro r throffle position command lawwill generallyyield a residual error in torque for a specific commandedvalue. Good fidelity in torque control can be achieved byusing torque error and the integral of that e r ro r to form thethroffle command. In addition, a predictive capability o rrate control may be added to enhance stability and improvetrol isthe overall system response. The form of the throttle con-

= K (Td - Te) + KO d(Td - Te)C P dimeSome difficulty may result in control gain choice if it isdesirable to operate the model over all conditions rep resenta-tive of the CVS cycle. This is to be expected as a real driverdoes not control with invariant gains for nonuniform drivingdemands.

INITIAL ENGINE EQUILIBRIUM

plicitly specified by the set point values where a set point isThe equilibrium values a t a given engine state are im-defined by a desired speed, load (torque), A/F, percent EGR,and spark. Once these quantities a re specified it is news-sary to ascertain the initial manifold pressu re, throffle an-gle, and mas s flow ratea that would yield engine equilibri-um.Realistic torque and speed values may be obtained froma vehicle simulation model such as that of Blumbed. Thate = dynamic EGR lag, 88c.

123


5/7

modelives thentire speed-load profileornssumed SIMULATIONESULTSdrive trai n for the CVS cycle or any other driving cycle. Ofcourse, arbitary values of speed and torque may be assumed. The program was ested at speed and load values repInitial values for A/F,Eg and s p a r k may be chosen to be senta tive of the engine operating range A t each of thesecompatible with the particular problem being investigated. points a r nge of A/F, percent EGR and spark advance cbe simulated.

NONLINEAR STATE VARIABLE FORMIn many instances a state variable formulation L easily

dynamic effects due to the control mechanism or sensorargumented in the event that t was necessary to add othercharact eris tics . The complete engine mathematical descrip-tion may be represented in a statevariable fo rm by definingnew variables X.(t) in te rms of the previous engine systemequations. Furthermore, a state variable form L amenableto multivariable analytical methods. Following is the de-velopment of a state variable formulation.Defining X,(t) as he product of the shaft gain and twist,XZ(t) s the engine speed, and X5(t) as he net engine torque,Equabon (e) becomes

X1 = % X 2 - K Ss dkz = - 30/Je r ) X1 (30/Je ) X5

where S s.the desired speed RPM). The pressure P, massflow rate M, and EGR mass rate , are defined by X3(t) ,X4(t) and X8(t), respectively. Thus, Equation (12) becomesk 3 = - K X + K X + K 61P 4 P a P a

Using X6(t) to define the throttle angle, results in I,s afunction of X3 and X6 and Equation (11)becomes'a = Ka (x61 g x31

Using the above definitions, Equation (10) fo r SDMF becomesx4 = x2i . 1925 (x,) .0006875

Defining X (t) as the s p a r k advance, Equation (5) for enginenet torque&omesx5 = -. 179

e x2 - 000029'e + e x 4 X5'e 'e

where E is given in Eq;ation (6). Finally, defining X (t)asthe throttle angle rate 0 , and Xg(t) as he fuel mass howrate r h f , Equations (13) and (14), and a second order rela-tion in the thrott le, yieldX6 = x7x7 = (LO x 6 - ~ x 7 +, e c4 2 2kg * + me,

'eig g + fc

f 'fkl0 = i

where i L a spark advance command rate, in deg/sec.

An ncrease in throttle angle results in an instantanincrease in air flow while both the fuel and EGR control and mass flow lag behind the increased air flow. This rsults in a rapid lean A/F excursion and a temporary decin percent EGR. An example of s imulated A/F for an increa se and d e c r e a s e in throttle angle is shown in FigureTwo different throttle rates are simulated to illustrate tgeneral nonlinear relationship between throttle angle andA/F .

Additional time hist orie s are shown in Figures 6 andfor a simulation of the first few seconds of the CVS drivicycle. The desired speed/torque profi le is obtained direfrom the drivetrain simulationmodel (Eilwnbe&) and increasing s p a r k and EGR calibration values are assumedbe ramp functions between 20 and 21 seconds. The "DriThrottle I n p u r r is obtained simply by using a PID controon orque. The assumed Wesir ed Torque" shown in Fig6 causes a arge throttle command which in turn resultsan initially lean A/F and resul ting %mque droop.TT Fornately the throttle is rate limited in the model o r the in-creased driver demand based on torque er ror would ultimately result in an engine s ta l l . A t about 0.4 seconds thdriver senses a change in torque err or and begins to de-crease the throttle angle. The A/F and EGR mass ratesociated with this numerical experiment are shown n Fi7. The point is, that the various time delays present inphysical process prevent direct control to simple conventional trajectories, due to transients th t are both systemand driver induced,Numerical experiments were initiated o examine thaffects of various system element time delayson the ovresponse. Fo r example, increasing the fuel loop time dfrom ,1 sec. to .5 sec. and rapeating the numerical exp

ure a. The results illustrate what can happen in a multiment previously discussed, yie ld8 the results shown in Fvariable interacting dynamic system with a variation of oone parameter. In this instance, the variation of the fueparameter resulting in increased ue l lag, caused an incin A/F leaning and decrease in achieved torque. The drthe form of increased throt tle angle. Thus, transients cresponded to this by placing more demand on the systemdirectly influence system torque o r driveability behaviorof course, fuel and emissions behavior.

CONCLUSIONSThe development of a basic nonlinear representationan engine dynamic system has been presented. The mod

power system aswell as dynamic characterization of thecontains descriptions for the nduction process and engithrottle mechanism, a sonic EGR valve, and a fuel injecsystem.The completed nonlinear system model is an open locharacterization of the engine with throttle angle, EGR, loop and s p a r k advance control variables . A control pothat properly manipulates the control variableso achievdesired set point has been developed.The mathematical model developed in the paper pran analysis and simulation tool of the engine dynamic sythat forms the oundation for furth erengineering systemanalysis. The modular form given by a state variable dcription of he system facilitates substitution of var iousware representations, substitution of the tranamissbn/dline characteris tics and finally, provides the basis for asystematic approach to the analysis, simulation and synof vehicle engine control systems.

124


6/7

ACKNOWLEDGEMENTS 11. Hubbard, M. , ftApplications f Automatic Control to In-ternal Combustion Enzines.qf Ph.D. Thesis. W o r dTheuthor is gr teful to Drs. P. N. Blumberg, and H. University, June 1975: ~Wu of Ford Motor Company for their techni cal suggestions intion. In addition, the author aclmcrwledges he analytical andthe cour~ef the model developmeat and manusc ript prepara- 12. Rivard, J. G. , fClosed-Loop Electronic Fuel InjectionControl of the Internal Combustion Engine,1t SAE Paperprogramming ssis tance of Mr. A. Chung and Ms. G. C 730005, January 1973.1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

REFERENCESMencik, Z. and Blumberg, P. N. ; fRepresentation fEngine Data by Multi-Variate Least-Square8 Reg res -sion," Society of Automotive Englueere, Paper No.780288, February 1978.Vora, L. S. , Vomputerized Five Parameter EngineMapping, I AE Paper No. 770079.Baker, R. E. , and Daby, E. E., v7Engine Mapping Me-tho do log^,^^ SAE Paper 770079.Blumberg, P. N., "Powert rain Simulation: A Tool fo rthe Design and Evaluation of Engine Control Strategiesin Vehicl es,TT AE P aper 760158.Auiler, J. E., Zbrozek, J. D. , and Blumberg, P: N.,"Optimization of Automotive Engine Cal ibra tion forBetter Fuel Economy - Methods and Applications,'I SAEPaper 770076, February 28, 1977.Cassidy, J. F. , "A Computerized On-Line Approach toCalcu lating Optimum Engine calibration^,^^ SAE Paper770078, February 28, 1977.Rishavy, E. A., Hamilton, S. C., Ayers, J. A . , andKeane, M. A., 'fEngine ControlOptimization for Bes tFuel Economy With Emiss ion Const raints,T1 AE Paper770075, February 28, 1977.Prabhakar, R., Citron, S. J., and Goodaon, R. E.,TIOptimizationf Automotive Engine Fuel Economy andEmissions,'TASME Paper 75-WA/AUT-19, December2, 1975.Dohner, A. R., "Transient System Optimization of anExperimental Engine Control System over the FederalEmissions Driving Schedule," SAE Paper 780286,February 1978.Hubbard, M., Dobson, P. D., Powell, J. D., VlosedLoop Control of Spark Advance Using a Cylinder Pres-sure Sens or," ASME Paper 75-WA/AUT-17.

t

Figure 1. Vehicle System InfornutionF lo w

13. Cassidy, J. F., "Electronic Closed-Loop Controls forthe Automobile," SAE Paper 740014.14. Powell, B. K., "A Simulation Model of an Internal Com-bustion Engine-Dynamometer System," 1978 SummerComputer Simulation Conference, Newport Beach Cali-fornia, July 24, 1978.15. Keranen T. W.,and Werthemeimer, I. ., "A Studyof spark-Ignition-Engine Control Variables,TtBendixTechnical Journal, Vol. 4, NO. 3, pp 40-50,1971.16. Garofalo. F. J. , "Performance Capabilitiea of VariouaAir Measurement Techniques for Air/Fuel Ratio Feed-forward Control Strategieson Electronic Fuel MeteredEngines," The University of Michigan, June 30, 1975.17. Wu., H., and Blumberg, P. N., "An Attenuation andTransport Delay Model for Single Point Closed-LoopFuel Metering Sys tems," SAE Paper No. 790172,February, 1979.18. Wu,H. , %duction System M o d e l i n g , Progress Re-ports R3550, Ford Motor Company, Engineering andResearch Staff October, 1977.19. Hamburg, D. R., and Hyland, J. E. , "A VaporizedGasoline Metering System for Internal Combustion En-gines,' SAE Paper No.760288, February, 1976.20. Harringo n, D. L. , fAnalysis and Digital Simulation fo rCarburetor Metering,tTPh.D. Thesis, The Universityof Michigan, AM Arbor, Michigan, 1968.21. Rachel, T. L., Sauer, R.G., and Slimak, L. E.,"Analysis Of Electronic Fuel Inject ion,1f endix Tech-nical Journal, Vol. 2, NO. 3, pp 36-45, 1969.22. Kaufman, W F., Sonic EGR Valve Design Report,Advanced Engine Engineering, Ford Motor CompanyFeb.2,1976.

I - I IFigure 2. Vehicle Poremain System Schematic Block Diagram


7/7

N L Lo I u D c Q y y D

Figure3. EngineSystem Element Schematic BlockDm

I200am Wdp oaas 6003L 4 0 0a= a01u

00 2 4 6 8 IO I2 14

NANIFOLD PRESSURE-PSIFigure4. Induction Rocest?hi as Flow Map

I I

\ /Lev*I 1 . 0 0 I I J I I

o LOO ax 300 4m SJO am zooFigure 5. AIF Thnsient for ThrottleDamp Input

TlYE -sEt

20 0 205 21.o 20 0 20.5TlYE -SEC n E -SEC

Fiqun 6. Toque lad Throttle from Engine Idle

1

17.00

0t5 15.00Y

14.00

12.000 0 0s aan y - s a

0 a guTY-SEcFigure 7. AIF and EGR h h s Flow Tnnrienb from Engine I

I4 Y mt

126

a dynamic model for automotive engine control analysis

Documents