research article fxlms method for suppressing in...

Research ArticleFxLMS Method for Suppressing In-Wheel Switched ReluctanceMotor Vertical Force Based on Vehicle Active Suspension System

Yan-yang Wang Yi-nong Li Wei Sun Chao Yang and Guang-hui Xu

The State Key Laboratory of Mechanical Transmission Chongqing University Chongqing 400044 China

Correspondence should be addressed to Yi-nong Li ynlicqueducn

Received 27 January 2014 Revised 27 April 2014 Accepted 16 May 2014 Published 4 June 2014

Academic Editor Yang Shi

Copyright copy 2014 Yan-yang Wang et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The vibration of SRM obtains less attention for in-wheel motor applications according to the present research works In this paperthe vertical component of SRM unbalanced radial force which is named as SRM vertical force is taken into account in suspensionperformance for in-wheel motor driven electric vehicles (IWM-EV)The analysis results suggest that SRM vertical force has a greateffect on suspension performanceThe direct cause for this phenomenon is that SRM vertical force is directly exerted on the wheelwhich will result in great variation in tyre dynamic load and the tyre will easily jump off the ground Furthermore the frequencyof SRM vertical force is broad which covers the suspension resonance frequencies So it is easy to arouse suspension resonance andgreatly damage suspension performance Aiming at the new problem FxLMS (filtered-X least mean square) controller is proposedto improve suspension performanceTheFxLMS controller is based on active suspension systemwhich can generate the controllableforce to suppress the vibration caused by SRM vertical force The conclusion shows that it is effective to take advantage of activesuspensions to reduce the effect of SRM vertical force on suspension performance

1 Introduction

Electric vehicles have achieved sufficient driving perfor-mance due to the great improvements inmotors and batteriesDue to the remarkable advantages for example highlyefficient transfer of power driving force to be distributedfreely and space saving and packaging the in-wheel motortechnology has become the focus of electric vehicle inves-tigation [1ndash3] As the key component of propulsion systemelectric motors play an important role in in-wheel motordriven electric vehicles (IWM-EV) dynamics It is desiredthat electric motors of electric vehicles have a wide operatingspeed range high torque density a high starting torque forinitial acceleration and high efficiency to extend the batteryserve-life [4 5] And the switched reluctance motor (SRM)exactly satisfied the above requirements [6ndash8] Howeverthese advantages of SRM are overshadowed by its inherenthigh torque ripple and vibration which seriously hinderedthe development of SRM for in-wheel motor applications [9ndash12] To reduce or eliminate the insufficiency of SRM muchattention has been focused on SRM structure and control

To improve the performance of SRM the commonsolution is to increase SRM power density starting torqueand efficiency by optimal control method or multiobjec-tive systematic optimization design [13ndash16] These existingresearchesmainly focus on the SRMrsquos power or torque charac-teristics which leave other factors such as torque ripple thevibration and noise out of consideration However torqueripple and the vibration will greatly limit the performance ofSRM and further reduce the stability and comfort of electricvehicle [9ndash11]

To suppress SRM vibration some structures and con-trollers are investigated Inagaki et al [17] proposed a two-degree-of-freedom119867

infincontrol to suppress vehicle drive train

vibration which was caused by SRM torque ripple and radialforce By controlling the current waveform the radial force ofSRM is reducedMarques dos Santos et al [10 18] presented amultiphysics analysis to predict acoustic radiation propertiesof SRM for an electric vehicle Li and Cho [19] proposed amethod to reduce the unbalanced radial force and vibrationof SRM by introducing parallel paths in windings Theseresults revealed that the currents could be balanced in parallel

Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2014 Article ID 486140 16 pageshttpdxdoiorg1011552014486140

2 Journal of Control Science and Engineering

paths and unbalanced radial force could be reduced Theseexisting researches contribute to suppress SRM vibrationhowever the SRM vibration effect on vehicle stability andcomfort is seldom considered The role and effect of IWM-EV suspension performance need to be considered further

Unbalanced radial force caused by rotor eccentricity maydegrade the performance of SRM increasing vibration andacoustic noise [12 19ndash23] In practice some degree of rotoreccentricity is always present due to the tolerances introducedduring the manufacturing process wear of bearings andstatic friction especially when the rotor is sitting idle as wellas other reasons [9 12 24]The air gap of the SRM is generallybetween 02 and 1mm which is much smaller than any othertype of motor and is more sensitive to rotor eccentricity Arelative eccentricity between the stator and rotor of 10 iscommon [24 25] On the other hand SRMunbalanced radialforce will be magnified by the vehicle continuously idlingroad excitation and unbalanced load This phenomenon isparticularly serious to IWM-EV because the vertical compo-nent of SRM unbalanced radial force namely SRM verticalforce applies directly on vehicle wheels and will change thetyre load Although SRMunbalanced radial force is inevitableand serious the contributions of SRM unbalanced radialforce to IWM-EV stability and comfort have not been studiedthoroughly yet

After a review of the past studies on in-wheel motorand SRM it is found that one key problem needs to beconsidered for example the effect of SRM vertical force onvehicle suspension performance needs to be discovered areasonable method to solve this new problem needs to bedeveloped and such work is consequently investigated in thisresearch

This paper is organized as follows first of all the quarter-car suspension model of a IWM-EV is given followed bythe development of SRM model and vertical force modelThen the effect of SRM vertical force on suspension perfor-mance is investigated under wheel resonance in Section 3To reduce the effect of SRM vertical force and improvesuspension performance the FxLMS (filtered-X least meansquare) controller is developed based on active suspensionin Section 4 Computer simulations and discussions of theresults are provided in Section 5 And finally the conclusionsdrawn from this research are presented

2 Vehicle Modeling

The vehicle model consists of three submodels the suspen-sion model that emphasizes the effect of SRM vertical forcewhich is a new vertical excitement of vehicle suspension theSRMmodel that provides the desired torque for vehicle SRMvertical force model which works out the vertical force thatSRM exerts on wheel

21 Suspension Model A two-degree-of-freedom (2DOF)vehicle suspension system is used as shown in Figure 1 Thissuspension model is widely used to study the conflictingdynamic performances of a vehicle suspension such as ridequality and road holding [26ndash29] The vehicle suspension

ms

mu

q

dp Fc

F

Car

Suspension

Wheel

Tyre

zs

zu

ks

Figure 1 Quarter-car suspension

system mainly includes three components sprung masssuspension actuator and unsprung mass which is shownin Figure 1 of the paper The sprung mass represents thevehicle body of which the vibration will reduce vehiclecomfort performance The unsprung mass represents thewheel and tyre The vibration of unsprung mass is related tovehicle stability Due to the road and external excitation beingtime-varying the desired force which is used to suppressvehicle vibration is expected to be adjustable So the activesuspension actuator is used to suppress the vibration whichcan generate the controllable force SRM is a new type ofin-wheel motor which is mounted in wheel as a part ofvehicle unsprung mass SRM vertical force is directly exertedon the wheel What is important in this study is that SRMvertical force is brought into the in-wheel motored vehiclesuspensionThe governing equations of suspension dynamicscan be described as

119898119904119904= minus 119889

119901(119904minus 119906) minus 119896119904(119911119904minus 119911119906) minus 119865119888

119898119906119906= 119889119901(119904minus 119906) + 119896119904(119911119904minus 119911119906) minus 119896119905(119911119906minus 119902) + 119865

119888+ 119865V

(1)

where 119898119904is the sprung mass which represents the vehicle

body 119898119906is the unsprung mass which represents the wheel

assembly 119911119904and 119911

119906are the displacement of sprung and

unsprung mass respectively and 119896119905serves to model the

compressibility of the pneumatic tyre 119902 is the road displace-ment input 119865V is the vertical force generated by SRM 119865

119888

means the controllable force of active suspension 119889119901and 119896

119904

are damping and stiffness of the passive suspension systemrespectively Note that if the controllable force 119865

119888= 0

and without considering SRM vertical force then the activesuspension system becomes a passive suspension systemAnd the parameters of the suspension of IWM-EV are listedin Table 3

The tyre dynamic load is

119878119911= 119896119905(119911119906minus 119902) (2)

Journal of Control Science and Engineering 3

Tref Torquedirect

controllerCurrent

controllerMechanical

section

120579 120579120579120579

ΨΨ(t)

i

i

T

T

SpeedTorquePosition

ix iy Vx Vyi(Ψ 120579) T(i 120579)

Figure 2 SRMmodel configuration

1

4

3

2

5

6

y

x120579998400

Fr F

Fto

(a) The eccentric rotor overlap stators 2 and 5

1

4

y

x

F

3

2

5

6

o

(b) The eccentric rotor overlap stators 1 and 4

Figure 3 SRM vertical force

For the passive suspension system the sprung andunsprung natural frequency is

1205961=

1

2120587radic119896119904

119898119904

1205962=

1

2120587radic119896119905+ 119896119904

119898119906

(3)

According to (3) the sprung and unsprung naturalfrequency of passive suspension system are 13Hz and 75Hzrespectively And it is easy to cause suspension resonancewhen the frequency of excitation for example SRM verticalforce is near the natural frequency

22 SRM Model The SRM model is used to generate thedrive torque for vehicle The magnetization characteristictorque characteristic mechanical section of the plant anddirect torque control of SRM are shown in Figure 2 Thelook-up table method is used to simulate the characteristic ofSRM and design SRM controller The table values of 119894(120595 120579)and 119879(119894 120579) are obtained by analytical formulations whichare easy to implement and convenient by discrete method[30ndash32] The reference torque 119879ref is determined by in-wheelmotor operation states According to torque direct controllerthe control current of conducting-phase 119894

119909 119894119910is determined

which can be translated to control voltage 119881119909 119881119910by current

controller [33] Control voltage 119881119909 119881119910is used to generate

the flux of SRM Looking-up table 119894(120595 120579) and 119879(119894 120579) can getmotor torque The torques produced by all stator phases arethen summedup to provide the total torque on the rotor shaft

In the electrical circuit of SRM the magnetic flux linkagein the windings is obtained as follows

120595 (119905) = int

119905

0

(119881 minus 119877119894) 119889119905 (4)

where 119881 is the stator voltage vector 119877 is the stator windingresistance This equation is used to calculate SRM flux valueswhich are supplied to table 119894(120595 120579) as shown in Figure 2

According to SRManalyticalmodel the inductance119871 andmagnetization characteristic 120595 of SRM can be expressed as afunction of stator current and rotor position

119871 (119894 120579) = 119871119902+ [119871119889sat +

119860 (1 minus 119890minus119861119894

)

119894minus 119871119902]119891 (120579)

120595 (119894 120579) = 119871 (119894 120579) 119894

(5)

where 119860 = Ψ119898minus 119871 sat119868119898 119861 = (119871

119889minus 119871119889sat)119860 119891(120579) = (2 lowast

1198733

1199031205873

)1205793

minus(3lowast1198732

1199031205872

)1205792

+1 119871119902is minimum inductance 119871

119889

is themaximum inductance119871119889sat is the saturated inductance

120595119898is the maximum flux linkage 119868

119898is the maximum current


003

002

001

0

100

50

00

50

100

Indu

ctan

ce (H

)

Position (deg) Current (A)

(a) Inductance characteristic

0

100

50

00

50

100

Angle (deg) Current (A)

1

05

Flux

(Wb)

(b) Flux characteristic

100

50

00

50

100


100

0

minus100

Torq

ue (N

m)

(c) Torque characteristic

Figure 4 Characteristics of SRM

626

624

622

62

618

6160 1 2 3 4 5

DesiredActual

Roto

r spe

ed (r

ads

)

Time (s)

(a) Speed of SRM

0 1 2 3 4 5

DesiredActual

Time (s)

60

40

20

0

Torq

ue (N

m)

(b) Torque of SRM

Figure 5 Comparison of actual and desired value of SRM response at velocity 60 kmh

120579 is the rotor position 119894 is the phase current and 119873119903is the

number of rotor poles The table value of 120595(119894 120579) is calculatedfrom the analytical equation (5) by discrete method Usingcubic spline interpolation the table 119894(120595 120579) is produced fromthe flux table 120595(119894 120579)

The analytical expression for the torque can be describedas

119879 (119894 120579) = minus1198942

2

120597119871

120597120579 (6)


3000

2000

1000

0

Vert

ical

forc

e (N

)

0 1 2 3 4 5

Time (s)

4 42 44 46 48 5

Time (s)

3000

2000

1000

0

Vert

ical

forc

e (N

)

4000

3000

2000

1000

0

45 46 47 48 49 5

Time (s)

Vert

ical

forc

e (N

)105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Figure 6 SRM vertical force (a1) Time history of vertical force at vehicle 2 kmh (a2) PSD of vertical force at vehicle 2 kmh (b1) Timehistory of vertical force at vehicle 11 kmh (b2) PSD of vertical force at vehicle 11 kmh (c1) Time history of vertical force at vehicle 60 kmh(c2) PSD of vertical force at vehicle 60 kmh

The table values of 119879(119894 120579) are calculated from the analyticalequation (6)

The mechanical dynamics of the motor and load aregoverned by the motion equation

119879 = 119869119889Ω

119889119905+ 119861Ω + 119879

119871 (7)

whereΩ is the rotor speed 119869 is themoment of inertia 119861 is thetorque friction coefficient and 119879

119871is the load toque which is

determined by IWM-EV operation statesThe control method of SRM is a commonly used direct

torque controlmethod [33 34]Themain advantages of directtorque control are fast torque response and lower torqueripple which meet the requirements of IWM-EV

23 SRM Vertical Force Model The primary purpose of SRMvertical forcemodel is towork out SRMvertical forcewhich isaccompanied by the forming of torque The electromagneticforce of SRM can be separated into a tangential and a radialforce The tangential force converts to the rotational torquewhich will drive IWM-EVThe radial force has no attributionto the rotation of SRM however it is the dominant noisesource which could excite stator vibrations and emit acousticnoise The net radial force is ideally zero because of thegeometrical balance motor structure However due to thefabrication tolerances the wheel motor often sits idle invehicle common manoeuvre unbalanced loads and roadexcitations the actual net radial force is usually not zeroand results in the unbalanced radical force as described inSection 1 What is important in this study is that the SRM


7000

4000

100080

40

0 5

10

15

Vert

ical

forc

e (N

)

Velocity (kmh) Displacement ()

Figure 7 SRM vertical force (unit N)

unbalanced radial force is taken into account as the wheelvertical excitation

The unbalanced radial force is the radial force differencebetween a pair of opposite stator poles Manymethods can beused to calculate SRM radial force [23 33 35] In this paperthe method of [33] is used The benefit of this method is thatonly four parameters are needed According to [33] the radialforce of opposite stator poles can be described as follows

1198651= minus

119903 sin (120579119900)

119892119898minus Δ119892

119865119905

1198652= minus

119903 sin (120579119900)

119892119898+ Δ119892

119865119905

(8)

The unbalanced radical force is

119865119903= 1198651minus 1198652 (9)

And SRM vertical force on the wheel is

119865V = 119865119903 sin (1205791015840

) (10)

where 119903 is the outer radius of the rotor 119892119898is air gap of SRM

and 120579119900is stator and rotor pole overlap position which will be

changed with rotor position 120579 For 64 SRM the range of 120579119900

is [0 30] degree [33] 1205791015840 is the angle between stator and wheellongitudinal axis 119865

119905means the tangential force of SRM It is

obtained by dividing the tangential torque by the radius ofthe rotor pole AndΔ119892means the rotor relative displacementwhich will directly affect the unbalanced radical force value

The 64 outside-rotor SRM is used in this study Themain advantage of the outside-rotor structure is the gearlessoperation which will reduce the drive line componentsthus improving the overall reliability and efficiency [36] Thesimilar structure is already validated in [37 38] The airgap eccentricity includes two types static eccentricity anddynamics eccentricity [22 39 40] For the convenience of thepresentation we focus on the static type in our research Forstatic eccentricity the relative eccentricity 120576 is

120576 =119909

119892100 (11)

where 119892 is the radial air gap length in the case of uniformair gap or no eccentricity and 119909 is the eccentricity in thehorizontal (or vertical) directionThe eccentric positioning ofthe SRM creates unbalanced electromechanical radial forcesdue to asymmetrical magnetic pull as shown in Figure 3For 64 outside-rotor SRM the degree between adjacentstator is 60 degrees and adjacent rotor is 90 degrees Whenthe eccentric rotor overlap stators are 2 and 5 the 1205791015840 is 30degrees Similarly when the eccentric rotor overlap statorsare 1 and 4 the 1205791015840 is 90 degrees as shown in Figure 3(b)So the longitudinal force component of SRM vertical force iszero under this condition It means that the SRM unbalancedradial force is equal to SRM vertical force and (10) issimplified to 119865V = 119865

119903 In the actual working condition

the unbalanced radial force is distributed along the statorradius And each pair of opposite rotors with eccentricitycan generate unbalanced radial force For the convenience ofpresentation we take a situation where the eccentric rotoroverlap stators are 1 and 4 as an example to investigate SRMvertical force effect on vehicle dynamics As the discussionabove the relative eccentricity between the stator and rotorof 10 is common So in the following study we mainlydiscuss the effect of SRMvertical force under 10 eccentricityconditions

3 Effect of SRM Vertical Force onSuspension Performance

Resonance vibration of vehicle is very common and severeso it is necessary to look at the effect of this kind of vibrationinduced by SRMvertical forceThe extreme case is when SRMvertical force excitation frequency is inducing resonance ofvehicle suspension that is the frequency is about sprungmass natural frequency of passive suspension system 13Hzand wheel natural frequency 75Hz The rotor pole numberof SRM is 4 which means the vertical force frequency is fourtimes of the wheel rotation frequency So when the frequencyof SRM vertical force is 13Hz and 75Hz the vehicle velocityis about 2 kmh (13Hz4times2timespitimes0269 is 2 kmh) and 11 kmh(75Hz4times2timespitimes0269 is 11 kmh) respectively Although thevehicle speed is too low for daily drive under the two severecases it is valuable to study it because the human body issensitive to vertical vibration at low frequencies (lt10Hz) Inanother aspect the vehicle is often sitting idle stops or startsup and the speed is very low under congested urban drivingconditions Next we will look into the effect of suspensionvibration induced by SRM vertical force

31 Preliminary Analysis on SRM Vertical Force In this sec-tion the effect of SRM vertical force at vehicle speed 2 kmh11 kmh and 60 kmh is analysed Computer simulations areperformed to verify the effectiveness of SRM controller andanalyse the vibration phenomenon The specifications of the64 outside-rotor SRM are listed in Table 4 From the look-uptables the flux and torque characteristics of SRM are shownin Figure 4 And the response of the SRM speed and torqueat vehicle speed 60 kmh is shown in Figure 5 It shows thatthe actual rotor speed and torque of the motor dynamics


15

1

05

0

minus05

minus1

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)

Figure 8 Suspension response to SRM vertical force at velocity 2 kmh (a1) Time history of sprung mass acceleration (a2) PSD of sprungmass acceleration (b1) Time history of tyre dynamic load (b2) PSD of tyre dynamic load

follow the desired references The torque pulsations in SRMare relatively higher compared to sinusoidal machines due tothe doubly salient structure of the motor Many studies focuson torque ripple [41 42] so we will not repeat it here

SRM vertical force under rotor displacement 10 isshown in Figure 6 Figure 6(a1) shows the time response ofSRM vertical force at vehicle speed 2 kmh The peak valueof SRM vertical force is nearly up to 2542N Figure 6(a2)shows the power spectral density (PSD) of SRM vertical forceat velocity 2 kmh in the low frequency band 0sim100Hz whichis concerned by vehicle suspension system It can be seen thatwith the increase of excitation frequency the PSD of SRMvertical force is decreased dramatically SRM vertical forceis the mixed harmonic disturbance with the basis frequencyof about 13Hz Similarly Figures 6(b) and 6(c) show thetime history and PSD of SRM vertical force at 11 kmh and60 kmh respectively It can be seen that the fundamentalfrequency of SRM vertical force is about 75Hz and 39Hz

Figure 7 and Table 1 show SRM vertical force characteris-tics under different velocity and rotor displacement It can beseen that SRM vertical force quickly increases as the vehiclevelocity and rotor displacement increase The effect of rotorrelative displacement is more serious than vehicle speed And

Table 1 SRM vertical force (unit N)

Velocity (kmh) Rotor displacements ()5 10 15

20 1321 2666 404340 1523 3070 457260 1800 3573 542880 2168 4410 6636

SRM vertical force reaches approximately 7000N at vehicle80 kmh and rotor relative displacement 15 which implythat SRM effect on suspension performance is considerableSo it is essential to study the effects of SRM vertical force onIWM-EV suspension performance

32 SRM Vertical Force Effect on Suspension PerformanceThe response of sprung mass acceleration and tyre dynamicload subject to SRM vertical force is selected to evaluatesuspension performance The vehicle speeds are 2 kmh11 kmh and 60 kmh respectively The original reference


4

2

0

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)


suspension does not take SRM vertical force into consider-ation Computer simulations are performed to analyse SRMvertical force effect on vehicle suspension system

According to the statistical characteristic of a real unevenroad the road velocity input can bemodeled as a white noisethe power spectral density (PSD) of which is denoted as

119866119908(119891) = 4120587

2

119866 (1198990) 1198992

0V (12)

where 119866(1198990) is road roughness coefficient 119899

0is reference

spatial frequency V is vehicle forward velocity and 119891 is time-domain frequency In the studied case 119899

0= 01 For level B

road 119866(1198990) is set at 64 times 10minus6m3 which represents a smooth

road surface And for level C road119866(1198990) is set at 256times10minus6m3

which represents a terrible road surfaceUnder level B road the suspension response to SRM

vertical force at vehicle speeds 2 kmh 11 kmh and 60 kmhis shown in Figures 8ndash9 Figure 8 shows vehicle suspensionunder speed 2 kmh From the time-domain results it canbe seen that SRM vertical force arouse a higher sprung massacceleration And the sprung mass resonance is nearly at thefrequency 13Hz Similarly the vibration of wheel is severedue to sprung mass resonance

Figure 9 shows the suspension response under speed11 kmh It can be seen that the wheel resonance is atfrequency 75Hz which increases the sprung mass vibrationAnd SRMvertical force generates sprungmass vibration peakat the fundamental frequency and multiple frequency whichmeans the vehicle comfort is greatly decreased at the vibrationpeak

Figure 10 shows the suspension response under speed60 kmh It shows that SRM vertical force generates sprungmass vibration peak at the fundamental frequency 39Hz andthe multiple frequency Although SRM vertical force effecton tyre dynamics is small in the frequencies above 10Hz theeffect is obvious in the frequencies below 1Hz as shown inFigure 10(b2)

According to the above analysis it can be seen thatSRM vertical force greatly increases the vibration of vehiclesuspension system So it is an important factor that cannot beneglected in IWM-EV suspension system research

4 FxLMS Controller Design

FxLMS controller is employed to suppress the vibrationcaused by SRM vertical force excitation Due to its simplicity


3

2

1

0

minus1

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)


x(k) Reference d(k) e(k)+

minusPrimary path

y(k)W(z) S(z)

yf(k)

Secondly pathS(z)

x(k) FxLMSalgorithm

P(z)

Figure 11 The structure of FxLMS algorithm

and stable reliable operation the FxLMS is one of the mostoften applied strategies in active noise control [43ndash45] Itis adjusting an adaptive filter in a feedforward structuretherefore it is especially suited for the damping of periodicdisturbances And the analysis above shows that SRM verticalforce is periodic excitation so the FxLMS algorithms areadopted to improve suspension performance

The structure of the FxLMS algorithm is shown in Fig-ure 11 following the notation of [43] The cancellation of the

disturbance signal 119889(119896) is achieved by subtracting the signal119910119891(119896) The cancellation of the disturbance signal is achieved

by subtracting the signal generated by the secondary path(119911) In typical active noise control applications the secondarypath includes an actuator driven by the output signal 119910(119896) ofthe adaptive filter119882(119911)Themodel 119878(119911) of the secondary pathis applied to compensate for the negative effects of 119878(119911) on thestability of the algorithm In the following it is assumed that119878(119911) = 119878(119911) Since the input signal of 119882(119911) is the referencesignal119909(119896)measured at the source of the disturbing vibrationa feedforward configuration is realized

The adaptation of119882(119911) is performed by an algorithm ofFxLMS structure which adjusts the coefficients by applyingthe recursive formula

119908 (119896 + 1) = 119908 (119896) + 120583119909 (119896) 119890 (119896) (13)

where 119909(119896) = [119909(0) 119909(1) sdot sdot sdot 119909(119896 minus 119897)]119879and 120583 denotes a

step size which influences the convergence speed of thealgorithm

The basic formula of the error signal is given by

119890 (119896) = 119889 (119896) + 119908119879

(119896) 119909 (119896) (14)


Primary path

Secondly path (a)FxLMS controllerSecondly path (b)

[Road]

[Road]

[Road]

0

00

[F]

[F]

+

+

+

dudt

dudt

dudt

FxLMS

Weight

Errorminus

Fck lowast u

k lowast ux998400 = Ax + Buy = Cx + Du

x998400 = Ax + Buy = Cx + Du

x998400 = Ax + Buy = Cx + Du

Figure 12 The Simulink model for FxLMS controller

The output vector is

119910 (119896) = 119908119879

(119896) 119909 (119896) (15)

According to (13)ndash(15) the FxLMS does not include thecalculations of square mean and differential values So thealgorithm is simple and efficient FxLMS adaptive methodwith adjusting the weight coefficient can adapt the output tothe input The algorithm has been applied in the study of theactive control of the engine vibration and the effect is verygood [42]

In order to design the FxLMS controller based on vehicleactive suspension system the state space equations of suspen-sion dynamics equations (1) in matrix form are given by

= 119860119883 + 119861119880

119884 = 119862119883 + 119863119880

(16)

where the state vector 119883 is defined as 119883 = [119911119904119904119911119906119906]119879

the input vector 119906 is defined as 119906 = [119865119888119902 119865V]

119879 the outputvector 119884 is equal to 119883 the parameter matrices 119860 and 119861 aredefined as

119860 =

[[[[[[[

[

0 1 0 0

minus119896119904

119898119904

minus119888119904

119898119904

119896119904

119898119904

119888119904

119898119904

0 0 0 1

119896119904

119898119906

119888119904

119898119906

minus119896119904+ 119896119905

119898119906

minus119888119904

119898119906

]]]]]]]

]

119861 =

[[[[[[[

[

0 0 0

minus1

119898119904

0 0

0 0 0

1

119898119906

119896119905

119898119906

minus1

119898119906

]]]]]]]

]

(17)

the parameter matrix 119862 is the four by four identity matrixand matrix119863 is a four by three matrix of zeros

Design the FxLMS controller based on vehicle activesuspension systemas followsThe reference signal119909 is definedas the sum of SRM vertical force and road excitement 119909(119896) =119865V(119896) + 119902(119896) The cancellation of the disturbance signal 119889(119896)is the acceleration of unsprung mass

119906(119896) The primary

path model 119875(119911) is equal to the secondary path 119878(119911) whichis the state space equations of vehicle suspension systemas described by (16) According to (13)ndash(15) the FxLMScontroller based on active suspension can be described as

119908 (119896 + 1) = 119908 (119896) + 120583 [119865V (119896) + 119902 (119896)] 119890 (119896)

119890 (119896) = 119906(119896) + 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

119865119888(119896) = 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

(18)

The Simulink model for FxLMS controller is illustratedby Figure 12The input reference signal of the primary path isroad excitation 119902 and SRM vertical force 119865V which is achievedby SRM controller And the output is the acceleration ofvehicle unsprungmass

119906The input of secondary pathmodel

(a) is active control force 119865119888which is achieved by FxLMS

controller The output of the secondary path model (a) is 1015840119906

which is compared with the output of primary path 119906to

get the control error Secondary path model (b) is used tocompensate for the negative effects of secondary path model(a) If there is no motor eccentricity at all SRM verticalforce becomes zero There are many researches on vehiclesuspension system which take no account of SRM verticalforce [46 47] so we will not repeat it here

5 Results and Discussion

Computer simulations are performed to verify the effective-ness of the FxLMS controller designed in this study withlevel B and level C road input The suspension performanceunder FxLMS control is analysed at vehicle velocities 2 kmh11 kmh and 60 kmh respectively The PSD of different


1

05

0

minus05

minus1

PassiveControl

103

100

10minus3

100

50

0

minus50

minus100

minus150

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)

Figure 13 Suspension performance under FxLMS control at velocity 2 kmh (a1) Time history of sprung mass acceleration (a2) PSD ofsprung mass acceleration (b1) Time history of tyre dynamic load (b2) PSD of tyre dynamic load (c1) Time history of suspension controlforce (c2) PSD of suspension control force

suspension performances for FxLMS controller is comparedwith the passive system in which the control force is zero119865119888= 0 Figures 13 14 and 15 illustrate vehicle suspension

performance under FxLMS controller at different velocitiesFrom Figure 13(a) it can be seen that under the sprung

mass resonance case better comfort can be achieved byFxLMS control in low frequencies (0ndash6Hz) compared withthe passive system Moreover the vibration of wheel undercontrol is decreased in the low frequencies as shown inFigure 13(b) The PSD of active suspension control force isalso presented in Figure 13(c)

From Figure 14(a) it can be seen that better comfort canbe achieved by FxLMS control in medium and high frequen-cies (6ndash8Hz and 8ndash50Hz) under the wheel resonance caseAnd the vibration peaks at SRM vertical force fundamentalfrequency and multiple frequency decreases dramaticallyBesides that the PSD of tyre dynamics is decreased obviouslyat the vibration peaks and the frequency below 1Hz whichmeans the vehicle road-holding ability is improved comparedto the passive system

Figure 15 shows the suspension performance underFxLMS control at velocity 60 kmh From Figure 15(a) it


4

2

0

minus2

PassiveControl

105

100

10minus5

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)


can be seen that there are different degree decrease at thevibration peaks A better road-holding ability can be achievedin the low frequencies below 1Hz

Table 2 summaries the root mean squared (RMS) valueof sprung mass under level B and level C road It can beseen that the vibration of sprungmass decreases dramaticallycompared with the passive system under two resonancecases And the acceleration of sprung mass under FxLMScontrol decreases to a certain degree at 60 kmh which isthe no-resonance case Compared with the resonance casesthe controller is not very powerful under the nonresonanceconditions It is because that SRM vertical force has a more

significant effect on the vibration of vehicle body and wheelunder the resonance cases Collectively we can say thesuspension performance is improved under FxLMS control

6 Conclusions

SRM are well suited for in-wheel motor due to their hightorque high efficiency and excellent power-speed charac-teristics However SRM used as in-wheel motor brings newproblems SRM vertical force excitation Like road excita-tion SRM vertical force excitation also has great effect onsuspension performance In this paper the characteristics of


2

3

1

0

minus2

minus1

PassiveControl

105

100

10minus5

600

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)

Figure 15 Suspension performance under LMS control at velocity 60 kmh (a1) Time history of sprungmass acceleration (a2) PSD of sprungmass acceleration (b1) Time history of tyre dynamic load (b2) PSD of tyre dynamic load (c1) Time history of suspension control force (c2)PSD of suspension control force

Table 2 Comparison of RMS values of sprung mass acceleration

Level B road Level C road2 kmh 11 kmh 60 kmh 2 kmh 11 kmh 60 kmh

Passive 041 133 075 045 142 146Control 009 031 066 018 062 131Relative change 7719 7659 1256 5840 5632 1027


Table 3 Parameters of IWM-EV active suspension

Definition Symbol Units ValueSprung mass 119898

119904kg 338

Unsprung mass 119898119906

kg 78Suspension stiffness 119896

119904Nm 22500

Tyre stiffness 119896119905

Nm 150000Suspension damping 119889

119901Nsdotsm 1695

Table 4 Out-rotor 64 SRM nomenclature and value

Definition ValueNumber of stator poles 6Number of rotor poles 4Stator pole arc angle 29 degreesRotor pole arc angle 30 degreesAir gap 025mmOuter diameter of rotor 312mmOuter diameter of stator 185mmLength of stack 63mmMinimum inductance 00019HMaximum inductance 00318HSaturated inductance 00013HMaximum flux linkage 09WbMotor rated voltage 240VMotor rated power 8 kWMotor rated speed 2000 rpm

SRM vertical force and the effect on IWM-EV suspensionperformance are discussed In order to suppress SRM verticalforce and improve suspension performance the FxLMScontroller is investigated in this paper And the importantfindings are as follows

(1) SRM vertical force is an important factor to sus-pension performance analysis It is very commondue to the manufacture tolerance and SRM workcondition And the frequency of SRM vertical forcecovers the natural frequency of passive suspensionsystem which will easily induce suspension reso-nance especially in vehicle start-up and low speedconditions So SRMvertical force cannot be neglectedin the analysis of suspension performance

(2) The effect of SRM vertical force on suspension perfor-mance is considerable Under sprung mass resonanceand wheel resonance severe cases the acceleration ofvehicle suspension increases dramatically The wheelvibration also increases greatly

(3) Aiming at the above-mentioned problems FxLMScontroller is proposed to improve suspension per-formance The FxLMS controller is based on activesuspensions which can generate the controllable forceto suppress SRMvertical force Under FxLMS controlthe sprung mass acceleration is reduced obviouslycompared with passive system The results show thatFxLMS control is effective And it is feasible to take

advantage of active suspensions to reduce the effectof SRM vertical force

This paper is focused on the analysis of SRM verticalforce proposition of SRM vertical force suppression methodto improve suspension performance However the effects ofvehicle acceleration or braking the yaw moment inducedby SRM vertical force and the mechanical connection partsbetween SRM and wheel are not considered since the actionmechanism of these factors is implicit and intricate Amore comprehensive research is needed to make a thoroughinvestigation on SRM vertical force SRM vertical forcesuppression methods for example semiactive suspensionsolution and experiments need to be further studied Thesefactors will be taken into account in the next work

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is supported by the National Natural ScienceFoundation of China (Grant nos 51275541 and 51005256)National Nature Science Foundation of Chongqing (Grantno cstc2013jjB0022) and Foundation of State Key Laboratoryof Mechanical Transmission (Grant no SKLMT-ZZKT-2012ZD 06)

References

[1] S Murata ldquoInnovation by in-wheel-motor drive unitrdquo VehicleSystem Dynamics vol 50 no 6 pp 807ndash830 2012

[2] E Katsuyama ldquoDecoupled 3D moment control using in-wheelmotorsrdquo Vehicle System Dynamics vol 51 no 1 pp 18ndash31 2013

[3] K Nam H Fujimoto and Y Hori ldquoLateral stability control ofin-wheel-motor-driven electric vehicles based on sideslip angleestimation using lateral tire force sensorsrdquo IEEE Transactions onVehicular Technology vol 61 no 5 pp 1972ndash1985 2012

[4] X D Xue KW E Cheng T W Ng and N C Cheung ldquoMulti-objective optimization design of in-wheel switched reluctancemotors in electric vehiclesrdquo IEEE Transactions on IndustrialElectronics vol 57 no 9 pp 2980ndash2987 2010

[5] J de Santiago H Bernhoff B Ekergard et al ldquoElectrical motordrivelines in commercial all-electric vehicles a reviewrdquo IEEETransactions onVehicular Technology vol 61 no 2 pp 475ndash4842012

[6] K Urase K Kiyota H Sugimoto and A Chiba ldquoDesignof a switched reluctance generator competitive with the IPMgenerator in hybrid electrical vehiclesrdquo in Proceedings of the 15thInternational Conference on Electrical Machines and Systems(ICEMS rsquo12) pp 1ndash6 Sapporo Japan October 2012

[7] KM Rahman B Fahimi G Suresh A V Rajarathnam andMEhsani ldquoAdvantages of switched reluctance motor applicationsto EV and HEV design and control issuesrdquo IEEE Transactionson Industry Applications vol 36 no 1 pp 111ndash121 2000

[8] Y Gao and M D McCulloch ldquoA review of high powerdensity switched reluctance machines suitable for automotiveapplicationsrdquo inProceedings of the 20th International Conference


on Electrical Machines (ICEM rsquo12) pp 2610ndash2614 September2012

[9] H Torkaman E Afjei and H Amiri ldquoDynamic eccentricityfault diagnosis in switched reluctance motorrdquo in Proceedingsof the International Symposium on Power Electronics ElectricalDrives Automation and Motion (SPEEDAM rsquo10) pp 519ndash522Taormina Italy June 2010

[10] F Marques dos Santos J Anthonis and F Naclerio ldquoMulti-physics NVH modeling simulation of a switched reluctancemotor drivetrain for an electric vehiclerdquo IEEE Transactions onIndustrial Electronics vol 61 no 1 pp 469ndash476

[11] M Divandari and A Dadpour ldquoRadial force and torqueripple optimization for acoustic noise reduction of SRM drivesvia fuzzy logic controlrdquo in Proceedings of the 9th IEEEIASInternational Conference on Industry Applications (INDUSCONrsquo10) pp 1ndash6 Sao Paulo Brazil November 2010

[12] E Afjei and H Torkaman ldquoAirgap eccentricity fault diagnosisin switched reluctance motorrdquo in Proceedings of the 1st PowerElectronics and Drives Systems and Technologies Conference(PEDSTC rsquo10) pp 290ndash294 Tehran Iran February 2010

[13] M N Anwar I Husain and A V Radun ldquoA comprehensivedesign methodology for switched reluctance machinesrdquo IEEETransactions on Industry Applications vol 37 no 6 pp 1684ndash1692 2001

[14] K Kiyota and A Chiba ldquoDesign of switched reluctance motorcompetitive to 60-kW IPMSM in third-generation hybridelectric vehiclerdquo IEEE Transactions on Industry Applicationsvol 48 no 6 pp 2303ndash2309 2012

[15] B Fahimi G Suresh and M Ehsani ldquoDesign considerationsof switched reluctance motors vibration and control issuesrdquo inProceedings of the 1999 IEEE Industry Applications Conferencepp 2259ndash2266 October 1999

[16] C Sikder I Husain and Y Sozer ldquoSwitched reluctance gen-erator controls for optimal power generation with currentregulationrdquo in Proceedings of the 4th Annual IEEE EnergyConversion Congress and Exposition (ECCE rsquo12) pp 4322ndash4329Raleigh NC USA September 2012

[17] H Inagaki H Kato and H Kuzuya ldquoDrive train vibration andacoustic noise reduction control of switched reluctance motorfor electric vehiclerdquo SAE Technical Papers 6183176 SAE

[18] F L M dos Santos J Anthonis and H van der AuweraerldquoMultiphysics thermal and NVH modeling integrated simula-tion of a switched reluctance motor drivetrain for an electricvehiclerdquo in Proceedings of the IEEE International Electric VehicleConference (IEVC rsquo12) pp 1ndash7 March 2012

[19] J Li and Y Cho ldquoDynamic reduction of unbalanced magneticforce and vibration in switched reluctance motor by the parallelpaths in windingsrdquoMathematics and Computers in Simulationvol 81 no 2 pp 407ndash419 2010

[20] B M Ebrahimi J Faiz andM J Roshtkhari ldquoStatic- dynamic- and mixed-eccentricity fault diagnoses in permanent-magnetsynchronous motorsrdquo IEEE Transactions on Industrial Electron-ics vol 56 no 11 pp 4727ndash4739 2009

[21] J Faiz and S Pakdelian ldquoFinite element analysis of switchedreluctance motor under dynamic eccentricity faultrdquo in Pro-ceedings of the 12th International Power Electronics and MotionControl Conference pp 1042ndash1046 September 2006

[22] N K Sheth and K R Rajagopal ldquoEffects of nonuniform airgapon the torque characteristics of a switched reluctance motorrdquoIEEE Transactions on Magnetics vol 40 no 4 pp 2032ndash20342004

[23] I Husain and A Radun ldquoUnbalanced force calculation inswitched-reluctance machinesrdquo IEEE Transactions on Magnet-ics vol 36 no 1 pp 330ndash338 2000

[24] N K Sheth and K R Rajagopal ldquoVariations in overalldeveloped torque of a switched reluctance motor with airgapnonuniformityrdquo IEEE Transactions on Magnetics vol 41 no 10pp 3973ndash3975 2005

[25] K R Rajagopal B Singh and B P Singh ldquoStatic torque profilesof a hybrid stepper motor having relative eccentricity betweenstator and rotor axesrdquo Journal of Applied Physics vol 93 no 10pp 8701ndash8703 2003

[26] S B A Kashem M Ektesabi and R Nagarajah ldquoComparisonbetween different sets of suspension parameters and introduc-tion of new modified skyhook control strategy incorporatingvarying road conditionrdquo Vehicle System Dynamics vol 50 no7 pp 1173ndash1190 2012

[27] R D Naik and P M Singru ldquoResonance stability and chaoticvibration of a quarter-car vehicle model with time-delay feed-backrdquo Communications in Nonlinear Science and NumericalSimulation vol 16 no 8 pp 3397ndash3410 2011

[28] B L J Gysen J J H Paulides J L G Janssen and EA Lomonova ldquoActive electromagnetic suspension system forimproved vehicle dynamicsrdquo IEEE Transactions on VehicularTechnology vol 59 no 3 pp 1156ndash1163 2010

[29] N H Amer R Ramli H M Isa W N L Mahadi and MA Z Abidin ldquoA review of energy regeneration capabilities incontrollable suspension for passengerscarrdquo Energy EducationScience and Technology A Energy Science and Research vol 30no 1 pp 143ndash158 2012

[30] D A Torrey X-M Niu and E J Unkauf ldquoAnalytical modellingof variable-reluctance machine magnetisation characteristicsrdquoIEE Proceedings Electric Power Applications vol 142 no 1 pp14ndash22 1995

[31] H Le-Huy and P Brunelle ldquoA versatile nonlinear switchedreluctance motor model in simulink using realistic and ana-lytical magnetization characteristicsrdquo in Proceedings of the 31stAnnual Conference of IEEE Industrial Electronics Society pp1556ndash1561 Raleigh NC USA November 2005

[32] D Cajander and H Le-Huy ldquoDesign and optimization of atorque controller for a switched reluctance motor drive forelectric vehicles by simulationrdquoMathematics and Computers inSimulation vol 71 no 4ndash6 pp 333ndash344 2006

[33] R Krishnan Switched Reluctance Motor Drives-Modeling Sim-ulation Analysis Design and Applications CRC press BocaRaton Fla USA 2001

[34] J Liang D-H Lee and J-W Ahn ldquoDirect instantaneoustorque control of switched reluctance machines using 4-levelconvertersrdquo IET Electric Power Applications vol 3 no 4 pp313ndash323 2009

[35] N R Garrigan W L Soong and C M Stephens ldquoRadial forcecharacteristics of a switched reluctancemachinerdquo inProceedingsof the 1999 IEEE Industry Applications Conference pp 2250ndash2258 Phoenix Ariz USA October 1999

[36] K T Chau D Zhang J Z Jiang C Liu and Y Zhang ldquoDesignof a magnetic-geared outer-rotor permanent-magnet brushlessmotor for electric vehiclesrdquo IEEETransactions onMagnetics vol43 no 6 pp 2504ndash2506 2007

[37] L Jiongkang K W E Cheng and Z Zhu ldquoExperimentalinvestigation of in-wheel switched reluctance motor drivingsystem for future electric vehiclesrdquo in Proceedings of the 3rdInternational Conference on Power Electronics Systems andApplications (PESA rsquo09) pp 1ndash6 Hong Kong May 2009


[38] A Labak and N C Kar ldquoOuter rotor switched reluctancemotor design for in-wheel drive of electric bus applicationsrdquoin Proceedings of the 20th International Conference on ElectricalMachines (ICEM rsquo12) pp 418ndash423Marseille France September2012

[39] S Ayari M Besbes M Lecrivain and M Gabsi ldquoEffects of theairgap eccentricity on the SRM vibrationsrdquo in Proceedings of theInternational Conference Electric Machines and Drives pp 138ndash140 1999

[40] H Torkaman and E Afjei ldquoMagnetostatic field analysis regard-ing the effects of dynamic eccentricity in switched reluctancemotorrdquo Progress in Electromagnetics Research vol 8 pp 163ndash180 2009

[41] I Husain ldquoMinimization of torque ripple in SRM drivesrdquo IEEETransactions on Industrial Electronics vol 49 no 1 pp 28ndash392002

[42] Y A Beromi Z Moravej and S Darabi ldquoTorque ripplereduction of switched reluctance motor using PID fuzzy logiccontrollerrdquo in Proceedings of the 7th International Conferenceand Exposition on Electrical and Power Engineering (EPE rsquo12)pp 456ndash459 Iasi Romania October 2012

[43] S M Kuo and D R Morgan Active Noise Control SystemsWiley New York NY USA 1996

[44] L Vicente and E Masgrau ldquoNovel FxLMS convergence condi-tion with deterministic referencerdquo IEEE Transactions on SignalProcessing vol 54 no 10 pp 3768ndash3774 2006

[45] D Zhou and V DeBrunner ldquoEfficient adaptive nonlinearfilters for nonlinear active noise controlrdquo IEEE Transactions onCircuits and Systems I Regular Papers vol 54 no 3 pp 669ndash681 2007

[46] D Karnopp ldquoActive damping in road vehicle suspension sys-temsrdquo Vehicle System Dynamics vol 12 no 6 pp 291ndash316 1983

[47] C Ting T S Li and F Kung ldquoDesign of fuzzy controller foractive suspension systemrdquo Mechatronics vol 5 no 4 pp 365ndash383 1995

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



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Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



paths and unbalanced radial force could be reduced Theseexisting researches contribute to suppress SRM vibrationhowever the SRM vibration effect on vehicle stability andcomfort is seldom considered The role and effect of IWM-EV suspension performance need to be considered further

Unbalanced radial force caused by rotor eccentricity maydegrade the performance of SRM increasing vibration andacoustic noise [12 19ndash23] In practice some degree of rotoreccentricity is always present due to the tolerances introducedduring the manufacturing process wear of bearings andstatic friction especially when the rotor is sitting idle as wellas other reasons [9 12 24]The air gap of the SRM is generallybetween 02 and 1mm which is much smaller than any othertype of motor and is more sensitive to rotor eccentricity Arelative eccentricity between the stator and rotor of 10 iscommon [24 25] On the other hand SRMunbalanced radialforce will be magnified by the vehicle continuously idlingroad excitation and unbalanced load This phenomenon isparticularly serious to IWM-EV because the vertical compo-nent of SRM unbalanced radial force namely SRM verticalforce applies directly on vehicle wheels and will change thetyre load Although SRMunbalanced radial force is inevitableand serious the contributions of SRM unbalanced radialforce to IWM-EV stability and comfort have not been studiedthoroughly yet

After a review of the past studies on in-wheel motorand SRM it is found that one key problem needs to beconsidered for example the effect of SRM vertical force onvehicle suspension performance needs to be discovered areasonable method to solve this new problem needs to bedeveloped and such work is consequently investigated in thisresearch

This paper is organized as follows first of all the quarter-car suspension model of a IWM-EV is given followed bythe development of SRM model and vertical force modelThen the effect of SRM vertical force on suspension perfor-mance is investigated under wheel resonance in Section 3To reduce the effect of SRM vertical force and improvesuspension performance the FxLMS (filtered-X least meansquare) controller is developed based on active suspensionin Section 4 Computer simulations and discussions of theresults are provided in Section 5 And finally the conclusionsdrawn from this research are presented

2 Vehicle Modeling

The vehicle model consists of three submodels the suspen-sion model that emphasizes the effect of SRM vertical forcewhich is a new vertical excitement of vehicle suspension theSRMmodel that provides the desired torque for vehicle SRMvertical force model which works out the vertical force thatSRM exerts on wheel

21 Suspension Model A two-degree-of-freedom (2DOF)vehicle suspension system is used as shown in Figure 1 Thissuspension model is widely used to study the conflictingdynamic performances of a vehicle suspension such as ridequality and road holding [26ndash29] The vehicle suspension

ms

mu

q

dp Fc

F

Car

Suspension

Wheel

Tyre

zs

zu

ks

Figure 1 Quarter-car suspension

system mainly includes three components sprung masssuspension actuator and unsprung mass which is shownin Figure 1 of the paper The sprung mass represents thevehicle body of which the vibration will reduce vehiclecomfort performance The unsprung mass represents thewheel and tyre The vibration of unsprung mass is related tovehicle stability Due to the road and external excitation beingtime-varying the desired force which is used to suppressvehicle vibration is expected to be adjustable So the activesuspension actuator is used to suppress the vibration whichcan generate the controllable force SRM is a new type ofin-wheel motor which is mounted in wheel as a part ofvehicle unsprung mass SRM vertical force is directly exertedon the wheel What is important in this study is that SRMvertical force is brought into the in-wheel motored vehiclesuspensionThe governing equations of suspension dynamicscan be described as

119898119904119904= minus 119889

119901(119904minus 119906) minus 119896119904(119911119904minus 119911119906) minus 119865119888

119898119906119906= 119889119901(119904minus 119906) + 119896119904(119911119904minus 119911119906) minus 119896119905(119911119906minus 119902) + 119865

119888+ 119865V

(1)

where 119898119904is the sprung mass which represents the vehicle

body 119898119906is the unsprung mass which represents the wheel

assembly 119911119904and 119911

119906are the displacement of sprung and

unsprung mass respectively and 119896119905serves to model the

compressibility of the pneumatic tyre 119902 is the road displace-ment input 119865V is the vertical force generated by SRM 119865

119888

means the controllable force of active suspension 119889119901and 119896

119904

are damping and stiffness of the passive suspension systemrespectively Note that if the controllable force 119865

119888= 0

and without considering SRM vertical force then the activesuspension system becomes a passive suspension systemAnd the parameters of the suspension of IWM-EV are listedin Table 3

The tyre dynamic load is

119878119911= 119896119905(119911119906minus 119902) (2)


Tref Torquedirect

controllerCurrent


section

120579 120579120579120579

ΨΨ(t)

i

i

T

T

SpeedTorquePosition

ix iy Vx Vyi(Ψ 120579) T(i 120579)


1

4

3

2

5

6

y

x120579998400

Fr F

Fto


1

4

y

x

F

3

2

5

6

o




1205961=

1

2120587radic119896119904

119898119904

1205962=

1

2120587radic119896119905+ 119896119904

119898119906

(3)



119909 119894119910is determined





120595 (119905) = int

119905

0

(119881 minus 119877119894) 119889119905 (4)



119871 (119894 120579) = 119871119902+ [119871119889sat +

119860 (1 minus 119890minus119861119894

)

119894minus 119871119902]119891 (120579)

120595 (119894 120579) = 119871 (119894 120579) 119894

(5)

where 119860 = Ψ119898minus 119871 sat119868119898 119861 = (119871

119889minus 119871119889sat)119860 119891(120579) = (2 lowast

1198733

1199031205873

)1205793


1199031205872

)1205792


119889





003

002

001

0

100

50

00

50

100

Indu

ctan

ce (H

)



0

100

50

00

50

100


1

05

Flux

(Wb)


100

50

00

50

100


100

0

minus100

Torq

ue (N

m)



626

624

622

62

618

6160 1 2 3 4 5

DesiredActual

Roto

r spe

ed (r

ads

)

Time (s)

(a) Speed of SRM

0 1 2 3 4 5

DesiredActual

Time (s)

60

40

20

0

Torq

ue (N

m)

(b) Torque of SRM





119879 (119894 120579) = minus1198942

2

120597119871

120597120579 (6)


3000

2000

1000

0

Vert

ical

forc

e (N

)

0 1 2 3 4 5

Time (s)

4 42 44 46 48 5

Time (s)

3000

2000

1000

0

Vert

ical

forc

e (N

)

4000

3000

2000

1000

0

45 46 47 48 49 5

Time (s)

Vert

ical

forc

e (N

)105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

(a1) (a2)

(b1) (b2)

(c1) (c2)




119879 = 119869119889Ω

119889119905+ 119861Ω + 119879

119871 (7)







7000

4000

100080

40

0 5

10

15

Vert

ical

forc

e (N

)





1198651= minus

119903 sin (120579119900)

119892119898minus Δ119892

119865119905

1198652= minus

119903 sin (120579119900)

119892119898+ Δ119892

119865119905

(8)


119865119903= 1198651minus 1198652 (9)


119865V = 119865119903 sin (1205791015840

) (10)








120576 =119909

119892100 (11)








15

1

05

0

minus05

minus1

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)







20 1321 2666 404340 1523 3070 457260 1800 3573 542880 2168 4410 6636




4

2

0

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)




119866119908(119891) = 4120587

2

119866 (1198990) 1198992

0V (12)


0is reference


0= 01 For level B











3

2

1

0

minus1

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)



minusPrimary path

y(k)W(z) S(z)

yf(k)

Secondly pathS(z)

x(k) FxLMSalgorithm

P(z)







119908 (119896 + 1) = 119908 (119896) + 120583119909 (119896) 119890 (119896) (13)




119890 (119896) = 119889 (119896) + 119908119879

(119896) 119909 (119896) (14)


Primary path


[Road]

[Road]

[Road]

0

00

[F]

[F]

+

+

+

dudt

dudt

dudt

FxLMS

Weight

Errorminus

Fck lowast u


x998400 = Ax + Buy = Cx + Du

x998400 = Ax + Buy = Cx + Du



119910 (119896) = 119908119879

(119896) 119909 (119896) (15)



= 119860119883 + 119861119880

119884 = 119862119883 + 119863119880

(16)




119860 =

[[[[[[[

[

0 1 0 0

minus119896119904

119898119904

minus119888119904

119898119904

119896119904

119898119904

119888119904

119898119904

0 0 0 1

119896119904

119898119906

119888119904

119898119906

minus119896119904+ 119896119905

119898119906

minus119888119904

119898119906

]]]]]]]

]

119861 =

[[[[[[[

[

0 0 0

minus1

119898119904

0 0

0 0 0

1

119898119906

119896119905

119898119906

minus1

119898119906

]]]]]]]

]

(17)



119906(119896) The primary


119908 (119896 + 1) = 119908 (119896) + 120583 [119865V (119896) + 119902 (119896)] 119890 (119896)

119890 (119896) = 119906(119896) + 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

119865119888(119896) = 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

(18)










1

05

0

minus05

minus1

PassiveControl

103

100

10minus3

100

50

0

minus50

minus100

minus150

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








4

2

0

minus2

PassiveControl

105

100

10minus5

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)





6 Conclusions



2

3

1

0

minus2

minus1

PassiveControl

105

100

10minus5

600

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








119904kg 338



119904Nm 22500



119901Nsdotsm 1695











Acknowledgments


References





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Tref Torquedirect

controllerCurrent


section

120579 120579120579120579

ΨΨ(t)

i

i

T

T

SpeedTorquePosition

ix iy Vx Vyi(Ψ 120579) T(i 120579)


1

4

3

2

5

6

y

x120579998400

Fr F

Fto


1

4

y

x

F

3

2

5

6

o




1205961=

1

2120587radic119896119904

119898119904

1205962=

1

2120587radic119896119905+ 119896119904

119898119906

(3)



119909 119894119910is determined





120595 (119905) = int

119905

0

(119881 minus 119877119894) 119889119905 (4)



119871 (119894 120579) = 119871119902+ [119871119889sat +

119860 (1 minus 119890minus119861119894

)

119894minus 119871119902]119891 (120579)

120595 (119894 120579) = 119871 (119894 120579) 119894

(5)

where 119860 = Ψ119898minus 119871 sat119868119898 119861 = (119871

119889minus 119871119889sat)119860 119891(120579) = (2 lowast

1198733

1199031205873

)1205793


1199031205872

)1205792


119889





003

002

001

0

100

50

00

50

100

Indu

ctan

ce (H

)



0

100

50

00

50

100


1

05

Flux

(Wb)


100

50

00

50

100


100

0

minus100

Torq

ue (N

m)



626

624

622

62

618

6160 1 2 3 4 5

DesiredActual

Roto

r spe

ed (r

ads

)

Time (s)

(a) Speed of SRM

0 1 2 3 4 5

DesiredActual

Time (s)

60

40

20

0

Torq

ue (N

m)

(b) Torque of SRM





119879 (119894 120579) = minus1198942

2

120597119871

120597120579 (6)


3000

2000

1000

0

Vert

ical

forc

e (N

)

0 1 2 3 4 5

Time (s)

4 42 44 46 48 5

Time (s)

3000

2000

1000

0

Vert

ical

forc

e (N

)

4000

3000

2000

1000

0

45 46 47 48 49 5

Time (s)

Vert

ical

forc

e (N

)105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

(a1) (a2)

(b1) (b2)

(c1) (c2)




119879 = 119869119889Ω

119889119905+ 119861Ω + 119879

119871 (7)







7000

4000

100080

40

0 5

10

15

Vert

ical

forc

e (N

)





1198651= minus

119903 sin (120579119900)

119892119898minus Δ119892

119865119905

1198652= minus

119903 sin (120579119900)

119892119898+ Δ119892

119865119905

(8)


119865119903= 1198651minus 1198652 (9)


119865V = 119865119903 sin (1205791015840

) (10)








120576 =119909

119892100 (11)








15

1

05

0

minus05

minus1

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)







20 1321 2666 404340 1523 3070 457260 1800 3573 542880 2168 4410 6636




4

2

0

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)




119866119908(119891) = 4120587

2

119866 (1198990) 1198992

0V (12)


0is reference


0= 01 For level B











3

2

1

0

minus1

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)



minusPrimary path

y(k)W(z) S(z)

yf(k)

Secondly pathS(z)

x(k) FxLMSalgorithm

P(z)







119908 (119896 + 1) = 119908 (119896) + 120583119909 (119896) 119890 (119896) (13)




119890 (119896) = 119889 (119896) + 119908119879

(119896) 119909 (119896) (14)


Primary path


[Road]

[Road]

[Road]

0

00

[F]

[F]

+

+

+

dudt

dudt

dudt

FxLMS

Weight

Errorminus

Fck lowast u


x998400 = Ax + Buy = Cx + Du

x998400 = Ax + Buy = Cx + Du



119910 (119896) = 119908119879

(119896) 119909 (119896) (15)



= 119860119883 + 119861119880

119884 = 119862119883 + 119863119880

(16)




119860 =

[[[[[[[

[

0 1 0 0

minus119896119904

119898119904

minus119888119904

119898119904

119896119904

119898119904

119888119904

119898119904

0 0 0 1

119896119904

119898119906

119888119904

119898119906

minus119896119904+ 119896119905

119898119906

minus119888119904

119898119906

]]]]]]]

]

119861 =

[[[[[[[

[

0 0 0

minus1

119898119904

0 0

0 0 0

1

119898119906

119896119905

119898119906

minus1

119898119906

]]]]]]]

]

(17)



119906(119896) The primary


119908 (119896 + 1) = 119908 (119896) + 120583 [119865V (119896) + 119902 (119896)] 119890 (119896)

119890 (119896) = 119906(119896) + 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

119865119888(119896) = 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

(18)










1

05

0

minus05

minus1

PassiveControl

103

100

10minus3

100

50

0

minus50

minus100

minus150

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








4

2

0

minus2

PassiveControl

105

100

10minus5

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)





6 Conclusions



2

3

1

0

minus2

minus1

PassiveControl

105

100

10minus5

600

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








119904kg 338



119904Nm 22500



119901Nsdotsm 1695











Acknowledgments


References





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










003

002

001

0

100

50

00

50

100

Indu

ctan

ce (H

)



0

100

50

00

50

100


1

05

Flux

(Wb)


100

50

00

50

100


100

0

minus100

Torq

ue (N

m)



626

624

622

62

618

6160 1 2 3 4 5

DesiredActual

Roto

r spe

ed (r

ads

)

Time (s)

(a) Speed of SRM

0 1 2 3 4 5

DesiredActual

Time (s)

60

40

20

0

Torq

ue (N

m)

(b) Torque of SRM





119879 (119894 120579) = minus1198942

2

120597119871

120597120579 (6)


3000

2000

1000

0

Vert

ical

forc

e (N

)

0 1 2 3 4 5

Time (s)

4 42 44 46 48 5

Time (s)

3000

2000

1000

0

Vert

ical

forc

e (N

)

4000

3000

2000

1000

0

45 46 47 48 49 5

Time (s)

Vert

ical

forc

e (N

)105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

(a1) (a2)

(b1) (b2)

(c1) (c2)




119879 = 119869119889Ω

119889119905+ 119861Ω + 119879

119871 (7)







7000

4000

100080

40

0 5

10

15

Vert

ical

forc

e (N

)





1198651= minus

119903 sin (120579119900)

119892119898minus Δ119892

119865119905

1198652= minus

119903 sin (120579119900)

119892119898+ Δ119892

119865119905

(8)


119865119903= 1198651minus 1198652 (9)


119865V = 119865119903 sin (1205791015840

) (10)








120576 =119909

119892100 (11)








15

1

05

0

minus05

minus1

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)







20 1321 2666 404340 1523 3070 457260 1800 3573 542880 2168 4410 6636




4

2

0

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)




119866119908(119891) = 4120587

2

119866 (1198990) 1198992

0V (12)


0is reference


0= 01 For level B











3

2

1

0

minus1

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)



minusPrimary path

y(k)W(z) S(z)

yf(k)

Secondly pathS(z)

x(k) FxLMSalgorithm

P(z)







119908 (119896 + 1) = 119908 (119896) + 120583119909 (119896) 119890 (119896) (13)




119890 (119896) = 119889 (119896) + 119908119879

(119896) 119909 (119896) (14)


Primary path


[Road]

[Road]

[Road]

0

00

[F]

[F]

+

+

+

dudt

dudt

dudt

FxLMS

Weight

Errorminus

Fck lowast u


x998400 = Ax + Buy = Cx + Du

x998400 = Ax + Buy = Cx + Du



119910 (119896) = 119908119879

(119896) 119909 (119896) (15)



= 119860119883 + 119861119880

119884 = 119862119883 + 119863119880

(16)




119860 =

[[[[[[[

[

0 1 0 0

minus119896119904

119898119904

minus119888119904

119898119904

119896119904

119898119904

119888119904

119898119904

0 0 0 1

119896119904

119898119906

119888119904

119898119906

minus119896119904+ 119896119905

119898119906

minus119888119904

119898119906

]]]]]]]

]

119861 =

[[[[[[[

[

0 0 0

minus1

119898119904

0 0

0 0 0

1

119898119906

119896119905

119898119906

minus1

119898119906

]]]]]]]

]

(17)



119906(119896) The primary


119908 (119896 + 1) = 119908 (119896) + 120583 [119865V (119896) + 119902 (119896)] 119890 (119896)

119890 (119896) = 119906(119896) + 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

119865119888(119896) = 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

(18)










1

05

0

minus05

minus1

PassiveControl

103

100

10minus3

100

50

0

minus50

minus100

minus150

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








4

2

0

minus2

PassiveControl

105

100

10minus5

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)





6 Conclusions



2

3

1

0

minus2

minus1

PassiveControl

105

100

10minus5

600

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








119904kg 338



119904Nm 22500



119901Nsdotsm 1695











Acknowledgments


References





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










3000

2000

1000

0

Vert

ical

forc

e (N

)

0 1 2 3 4 5

Time (s)

4 42 44 46 48 5

Time (s)

3000

2000

1000

0

Vert

ical

forc

e (N

)

4000

3000

2000

1000

0

45 46 47 48 49 5

Time (s)

Vert

ical

forc

e (N

)105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

(a1) (a2)

(b1) (b2)

(c1) (c2)




119879 = 119869119889Ω

119889119905+ 119861Ω + 119879

119871 (7)







7000

4000

100080

40

0 5

10

15

Vert

ical

forc

e (N

)





1198651= minus

119903 sin (120579119900)

119892119898minus Δ119892

119865119905

1198652= minus

119903 sin (120579119900)

119892119898+ Δ119892

119865119905

(8)


119865119903= 1198651minus 1198652 (9)


119865V = 119865119903 sin (1205791015840

) (10)








120576 =119909

119892100 (11)








15

1

05

0

minus05

minus1

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)







20 1321 2666 404340 1523 3070 457260 1800 3573 542880 2168 4410 6636




4

2

0

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)




119866119908(119891) = 4120587

2

119866 (1198990) 1198992

0V (12)


0is reference


0= 01 For level B











3

2

1

0

minus1

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)



minusPrimary path

y(k)W(z) S(z)

yf(k)

Secondly pathS(z)

x(k) FxLMSalgorithm

P(z)







119908 (119896 + 1) = 119908 (119896) + 120583119909 (119896) 119890 (119896) (13)




119890 (119896) = 119889 (119896) + 119908119879

(119896) 119909 (119896) (14)


Primary path


[Road]

[Road]

[Road]

0

00

[F]

[F]

+

+

+

dudt

dudt

dudt

FxLMS

Weight

Errorminus

Fck lowast u


x998400 = Ax + Buy = Cx + Du

x998400 = Ax + Buy = Cx + Du



119910 (119896) = 119908119879

(119896) 119909 (119896) (15)



= 119860119883 + 119861119880

119884 = 119862119883 + 119863119880

(16)




119860 =

[[[[[[[

[

0 1 0 0

minus119896119904

119898119904

minus119888119904

119898119904

119896119904

119898119904

119888119904

119898119904

0 0 0 1

119896119904

119898119906

119888119904

119898119906

minus119896119904+ 119896119905

119898119906

minus119888119904

119898119906

]]]]]]]

]

119861 =

[[[[[[[

[

0 0 0

minus1

119898119904

0 0

0 0 0

1

119898119906

119896119905

119898119906

minus1

119898119906

]]]]]]]

]

(17)



119906(119896) The primary


119908 (119896 + 1) = 119908 (119896) + 120583 [119865V (119896) + 119902 (119896)] 119890 (119896)

119890 (119896) = 119906(119896) + 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

119865119888(119896) = 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

(18)










1

05

0

minus05

minus1

PassiveControl

103

100

10minus3

100

50

0

minus50

minus100

minus150

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








4

2

0

minus2

PassiveControl

105

100

10minus5

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)





6 Conclusions



2

3

1

0

minus2

minus1

PassiveControl

105

100

10minus5

600

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








119904kg 338



119904Nm 22500



119901Nsdotsm 1695











Acknowledgments


References





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










7000

4000

100080

40

0 5

10

15

Vert

ical

forc

e (N

)





1198651= minus

119903 sin (120579119900)

119892119898minus Δ119892

119865119905

1198652= minus

119903 sin (120579119900)

119892119898+ Δ119892

119865119905

(8)


119865119903= 1198651minus 1198652 (9)


119865V = 119865119903 sin (1205791015840

) (10)








120576 =119909

119892100 (11)








15

1

05

0

minus05

minus1

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)







20 1321 2666 404340 1523 3070 457260 1800 3573 542880 2168 4410 6636




4

2

0

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)




119866119908(119891) = 4120587

2

119866 (1198990) 1198992

0V (12)


0is reference


0= 01 For level B











3

2

1

0

minus1

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)



minusPrimary path

y(k)W(z) S(z)

yf(k)

Secondly pathS(z)

x(k) FxLMSalgorithm

P(z)







119908 (119896 + 1) = 119908 (119896) + 120583119909 (119896) 119890 (119896) (13)




119890 (119896) = 119889 (119896) + 119908119879

(119896) 119909 (119896) (14)


Primary path


[Road]

[Road]

[Road]

0

00

[F]

[F]

+

+

+

dudt

dudt

dudt

FxLMS

Weight

Errorminus

Fck lowast u


x998400 = Ax + Buy = Cx + Du

x998400 = Ax + Buy = Cx + Du



119910 (119896) = 119908119879

(119896) 119909 (119896) (15)



= 119860119883 + 119861119880

119884 = 119862119883 + 119863119880

(16)




119860 =

[[[[[[[

[

0 1 0 0

minus119896119904

119898119904

minus119888119904

119898119904

119896119904

119898119904

119888119904

119898119904

0 0 0 1

119896119904

119898119906

119888119904

119898119906

minus119896119904+ 119896119905

119898119906

minus119888119904

119898119906

]]]]]]]

]

119861 =

[[[[[[[

[

0 0 0

minus1

119898119904

0 0

0 0 0

1

119898119906

119896119905

119898119906

minus1

119898119906

]]]]]]]

]

(17)



119906(119896) The primary


119908 (119896 + 1) = 119908 (119896) + 120583 [119865V (119896) + 119902 (119896)] 119890 (119896)

119890 (119896) = 119906(119896) + 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

119865119888(119896) = 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

(18)










1

05

0

minus05

minus1

PassiveControl

103

100

10minus3

100

50

0

minus50

minus100

minus150

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








4

2

0

minus2

PassiveControl

105

100

10minus5

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)





6 Conclusions



2

3

1

0

minus2

minus1

PassiveControl

105

100

10minus5

600

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








119904kg 338



119904Nm 22500



119901Nsdotsm 1695











Acknowledgments


References





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










15

1

05

0

minus05

minus1

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)







20 1321 2666 404340 1523 3070 457260 1800 3573 542880 2168 4410 6636




4

2

0

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)




119866119908(119891) = 4120587

2

119866 (1198990) 1198992

0V (12)


0is reference


0= 01 For level B











3

2

1

0

minus1

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)



minusPrimary path

y(k)W(z) S(z)

yf(k)

Secondly pathS(z)

x(k) FxLMSalgorithm

P(z)







119908 (119896 + 1) = 119908 (119896) + 120583119909 (119896) 119890 (119896) (13)




119890 (119896) = 119889 (119896) + 119908119879

(119896) 119909 (119896) (14)


Primary path


[Road]

[Road]

[Road]

0

00

[F]

[F]

+

+

+

dudt

dudt

dudt

FxLMS

Weight

Errorminus

Fck lowast u


x998400 = Ax + Buy = Cx + Du

x998400 = Ax + Buy = Cx + Du



119910 (119896) = 119908119879

(119896) 119909 (119896) (15)



= 119860119883 + 119861119880

119884 = 119862119883 + 119863119880

(16)




119860 =

[[[[[[[

[

0 1 0 0

minus119896119904

119898119904

minus119888119904

119898119904

119896119904

119898119904

119888119904

119898119904

0 0 0 1

119896119904

119898119906

119888119904

119898119906

minus119896119904+ 119896119905

119898119906

minus119888119904

119898119906

]]]]]]]

]

119861 =

[[[[[[[

[

0 0 0

minus1

119898119904

0 0

0 0 0

1

119898119906

119896119905

119898119906

minus1

119898119906

]]]]]]]

]

(17)



119906(119896) The primary


119908 (119896 + 1) = 119908 (119896) + 120583 [119865V (119896) + 119902 (119896)] 119890 (119896)

119890 (119896) = 119906(119896) + 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

119865119888(119896) = 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

(18)










1

05

0

minus05

minus1

PassiveControl

103

100

10minus3

100

50

0

minus50

minus100

minus150

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








4

2

0

minus2

PassiveControl

105

100

10minus5

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)





6 Conclusions



2

3

1

0

minus2

minus1

PassiveControl

105

100

10minus5

600

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








119904kg 338



119904Nm 22500



119901Nsdotsm 1695











Acknowledgments


References





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










4

2

0

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)




119866119908(119891) = 4120587

2

119866 (1198990) 1198992

0V (12)


0is reference


0= 01 For level B











3

2

1

0

minus1

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)



minusPrimary path

y(k)W(z) S(z)

yf(k)

Secondly pathS(z)

x(k) FxLMSalgorithm

P(z)







119908 (119896 + 1) = 119908 (119896) + 120583119909 (119896) 119890 (119896) (13)




119890 (119896) = 119889 (119896) + 119908119879

(119896) 119909 (119896) (14)


Primary path


[Road]

[Road]

[Road]

0

00

[F]

[F]

+

+

+

dudt

dudt

dudt

FxLMS

Weight

Errorminus

Fck lowast u


x998400 = Ax + Buy = Cx + Du

x998400 = Ax + Buy = Cx + Du



119910 (119896) = 119908119879

(119896) 119909 (119896) (15)



= 119860119883 + 119861119880

119884 = 119862119883 + 119863119880

(16)




119860 =

[[[[[[[

[

0 1 0 0

minus119896119904

119898119904

minus119888119904

119898119904

119896119904

119898119904

119888119904

119898119904

0 0 0 1

119896119904

119898119906

119888119904

119898119906

minus119896119904+ 119896119905

119898119906

minus119888119904

119898119906

]]]]]]]

]

119861 =

[[[[[[[

[

0 0 0

minus1

119898119904

0 0

0 0 0

1

119898119906

119896119905

119898119906

minus1

119898119906

]]]]]]]

]

(17)



119906(119896) The primary


119908 (119896 + 1) = 119908 (119896) + 120583 [119865V (119896) + 119902 (119896)] 119890 (119896)

119890 (119896) = 119906(119896) + 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

119865119888(119896) = 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

(18)










1

05

0

minus05

minus1

PassiveControl

103

100

10minus3

100

50

0

minus50

minus100

minus150

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








4

2

0

minus2

PassiveControl

105

100

10minus5

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)





6 Conclusions



2

3

1

0

minus2

minus1

PassiveControl

105

100

10minus5

600

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








119904kg 338



119904Nm 22500



119901Nsdotsm 1695











Acknowledgments


References





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










3

2

1

0

minus1

minus2

Without FWith F

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

Without FWith F

1000

2000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

Without FWith F

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Without FWith F

(a1) (a2)

(b1) (b2)

Mag

nitu

de ((

ms

2)2H

z)



minusPrimary path

y(k)W(z) S(z)

yf(k)

Secondly pathS(z)

x(k) FxLMSalgorithm

P(z)







119908 (119896 + 1) = 119908 (119896) + 120583119909 (119896) 119890 (119896) (13)




119890 (119896) = 119889 (119896) + 119908119879

(119896) 119909 (119896) (14)


Primary path


[Road]

[Road]

[Road]

0

00

[F]

[F]

+

+

+

dudt

dudt

dudt

FxLMS

Weight

Errorminus

Fck lowast u


x998400 = Ax + Buy = Cx + Du

x998400 = Ax + Buy = Cx + Du



119910 (119896) = 119908119879

(119896) 119909 (119896) (15)



= 119860119883 + 119861119880

119884 = 119862119883 + 119863119880

(16)




119860 =

[[[[[[[

[

0 1 0 0

minus119896119904

119898119904

minus119888119904

119898119904

119896119904

119898119904

119888119904

119898119904

0 0 0 1

119896119904

119898119906

119888119904

119898119906

minus119896119904+ 119896119905

119898119906

minus119888119904

119898119906

]]]]]]]

]

119861 =

[[[[[[[

[

0 0 0

minus1

119898119904

0 0

0 0 0

1

119898119906

119896119905

119898119906

minus1

119898119906

]]]]]]]

]

(17)



119906(119896) The primary


119908 (119896 + 1) = 119908 (119896) + 120583 [119865V (119896) + 119902 (119896)] 119890 (119896)

119890 (119896) = 119906(119896) + 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

119865119888(119896) = 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

(18)










1

05

0

minus05

minus1

PassiveControl

103

100

10minus3

100

50

0

minus50

minus100

minus150

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








4

2

0

minus2

PassiveControl

105

100

10minus5

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)





6 Conclusions



2

3

1

0

minus2

minus1

PassiveControl

105

100

10minus5

600

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








119904kg 338



119904Nm 22500



119901Nsdotsm 1695











Acknowledgments


References





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Primary path


[Road]

[Road]

[Road]

0

00

[F]

[F]

+

+

+

dudt

dudt

dudt

FxLMS

Weight

Errorminus

Fck lowast u


x998400 = Ax + Buy = Cx + Du

x998400 = Ax + Buy = Cx + Du



119910 (119896) = 119908119879

(119896) 119909 (119896) (15)



= 119860119883 + 119861119880

119884 = 119862119883 + 119863119880

(16)




119860 =

[[[[[[[

[

0 1 0 0

minus119896119904

119898119904

minus119888119904

119898119904

119896119904

119898119904

119888119904

119898119904

0 0 0 1

119896119904

119898119906

119888119904

119898119906

minus119896119904+ 119896119905

119898119906

minus119888119904

119898119906

]]]]]]]

]

119861 =

[[[[[[[

[

0 0 0

minus1

119898119904

0 0

0 0 0

1

119898119906

119896119905

119898119906

minus1

119898119906

]]]]]]]

]

(17)



119906(119896) The primary


119908 (119896 + 1) = 119908 (119896) + 120583 [119865V (119896) + 119902 (119896)] 119890 (119896)

119890 (119896) = 119906(119896) + 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

119865119888(119896) = 119908

119879

(119896) [119865V (119896) + 119902 (119896)]

(18)










1

05

0

minus05

minus1

PassiveControl

103

100

10minus3

100

50

0

minus50

minus100

minus150

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








4

2

0

minus2

PassiveControl

105

100

10minus5

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)





6 Conclusions



2

3

1

0

minus2

minus1

PassiveControl

105

100

10minus5

600

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








119904kg 338



119904Nm 22500



119901Nsdotsm 1695











Acknowledgments


References





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1

05

0

minus05

minus1

PassiveControl

103

100

10minus3

100

50

0

minus50

minus100

minus150

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2) 100

10minus5

10minus10

0 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

1000

0

minus1000

minus2000Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








4

2

0

minus2

PassiveControl

105

100

10minus5

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)





6 Conclusions



2

3

1

0

minus2

minus1

PassiveControl

105

100

10minus5

600

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








119904kg 338



119904Nm 22500



119901Nsdotsm 1695











Acknowledgments


References





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










4

2

0

minus2

PassiveControl

105

100

10minus5

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)





6 Conclusions



2

3

1

0

minus2

minus1

PassiveControl

105

100

10minus5

600

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








119904kg 338



119904Nm 22500



119901Nsdotsm 1695











Acknowledgments


References





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2

3

1

0

minus2

minus1

PassiveControl

105

100

10minus5

600

400

200

0

minus200

minus400

PassiveControl

PassiveControl

PassiveControl

ACC

of sp

rung

mas

s (m

s2)

100

10minus5

10minus100 1 2 3 4 5

Time (s)100 101 102

Frequency (Hz)

2000

1000

0

minus1000

minus2000

Tyre

dyn

amic

load

(N)

0 1 2 3 4 5

Time (s)

105

100

100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

0 1 2 3 4 5

Time (s)100 101 102

Mag

nitu

de (N

2H

z)

Frequency (Hz)

Con

trol f

orce

(N)

(a1) (a2)

(b1) (b2)

(c1) (c2)

Mag

nitu

de ((

ms

2)2H

z)








119904kg 338



119904Nm 22500



119901Nsdotsm 1695











Acknowledgments


References





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119904kg 338



119904Nm 22500



119901Nsdotsm 1695











Acknowledgments


References





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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