Research Article Modelling and Experimental Study on ...downloads.hindawi.com/journals/sv/2016/6170275.pdf · Energy-Regenerative Suspension Structure with Variable Universe Fuzzy

Research ArticleModelling and Experimental Study on ActiveEnergy-Regenerative Suspension Structure withVariable Universe Fuzzy PD Control

Jiang Liu Xiaowei Li Zhenghao Wang and Ye Zhang

School of Automobile and Traffic Qingdao University of Technology Qingdao 266520 China

Correspondence should be addressed to Jiang Liu zeh163com

Received 20 June 2016 Revised 29 August 2016 Accepted 4 October 2016

Academic Editor Vadim V Silberschmidt

Copyright copy 2016 Jiang Liu et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A novel electromagnetic active suspension with an energy-regenerative structure is proposed to solve the suspensionrsquos controlconsumption problem For this new system a 2-DOF quarter-car model is built and dynamics performances are studied using thevariable universe fuzzy theory and thePDcontrol approachA self-powered efficiency concept is defined to describe the regenerativestructurersquos contribution to the whole control consumption and its influent factors are also discussed Simulations are carried outusing software MatlabSimulink and experiments are conducted on the B-class road The results demonstrate that the variableuniverse fuzzy control can recycle more than 18 percent vibration energy and provide over 11 percent power for the control demandFurthermore the new suspension system offers a smaller body acceleration and decreases dynamic tire deflection compared to thepassive ones so as to improve both the ride comfort and the safety

1 Introduction

It has been proved by many scholarsrsquo studies that theactive vehicle suspension technology can improve the vehicledynamic performance [1ndash3] but it is still not widely appliedin practice owing to its high cost on the energy consumptionMeanwhile the suspension vibration excited by the unevenroad surfaces is usually wasted as thermal energy by theshock absorber If the consumption energy could be reusedproperly the suspension vibration is also a kind of resourceTherefore many researches on these potential benefits havebeen carried out theoretically and experimentally [4ndash6]

Suda and Shiiba firstly noticed the regenerative solutionfor the suspension control [7] Then the energy feedbacktechniques both the new structures design and the advancedcontrol algorithm have been well studied Nakano et alproposed a method based on a single electric actuator toanalyze the balance between consumed and regenerativeenergy [8] Nakano et al developed an active suspensionwith the self-powered via linear DC motors which can beused as an energy-regenerative damper through the actu-ator [9] Kawamoto et al proposed an electromechanical

suspension (EMS) system which consists of a ball screwmechanism via the DC motors [10] Also they discussedthe nexus of the contour maps for the energy consumptionand vibration isolation For instance Zhang et al designedthe active suspension and energy-regenerative controllersrespectively based on the 119867infin control which are the sameas the electromechanical suspension (EMS) system [11] TheEMS system indicated that the energy regeneration with arestriction strategy can be realized Chen et al proposedthe electromagnetic damper which can absorb the vibrationenergy to improve the suspension dynamic performance [12]Guo et al proposed a hydraulic electromagnetic energy-regenerative shock absorber (HESA) which can absorbthe vibration energy harvest and improve the vehicle ridecomfort and handling [13 14] Although the above studiesindicate that the energy-regenerative systems can obtain theelectric energy via the considerable complex structures theexisting energy-regenerative suspension (ESS) systems haveto increase the unsprung mass and change the original sus-pensions structure Saito et al converted the vibration energyto electric energy with an electrical suspension system whichcan offer quicker responses and higher operating accuracy

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 6170275 11 pageshttpdxdoiorg10115520166170275

2 Shock and Vibration

than the hydraulic system [15] Subsequently some electro-magnetic actuators (EA) have received attention for their easyenergy regeneration higher efficiency quick response andgood controllability [16ndash19]

In last decades many researchers applied some linearand nonlinear control methods to quarter-car models whichwere simple and preferred In most cases the energy-regeneration efficiency is closely related to the control algo-rithm The question is how to compromise the disunitybetween the accuracy and the efficiency such as119867infin and PIDPan et al used a composite 119867infin adaptive fuzzy controller(CHAFC) on an uncertain nonlinear system to solve thefuzzy approximation problem [20 21] The variable universefuzzy (VUF) controller is regarded as a promising algorithmowing to its outstanding accusation-efficiency balance Shanet al developed an analog circuit of a VUF controller [22]Wang et al applied the VUF control to the hydropneumaticsuspension andmagnetic-rheology absorber (MRA) [23 24]Li et al succeeded via the VUF controller based on consciousknowledge to simulate the model of the quadruple invertedpendulum [25] It is noteworthy that Pan et al proposedthe novel VUF controllers with an adaptive control strategythrough the Lyapunov synthesis [26 27] For instance Liuet al proposed a method of the VUF based on the two stagecontrol rules and introduced it to the semiactive suspension(SAE) of the magneto rheological (MR) armored vehicle[28] As a consequence the method also can get an idealperformance of the vehicles control and effectively improvethe vehicle ride comfort However the high performanceof the control algorithm mentioned above is still diffi-cult to solve the high energy consumption of the suspen-sion and limited its wide application especially in electricvehicles

In this paper a 2-DOF quarter-car model is built Basedon the dynamic model three algorithms such as the optimalcontrol algorithm fuzzy control algorithm and variable uni-verse fuzzy control algorithm are designedThe influences onthe control effects and the energy-regenerative effects choos-ing different road inputs and different control algorithmsare analyzed respectively The simulation results show thatdifferent road inputs have similar control effects for LQGcontrollerThe experiment results show that the performanceof active energy-regeneration suspension system is highlydependent on the choice of algorithmemployed and theVUFcontrol strategy exhibits an excellent integrated performanceBut for the fuzzy controller and variable universe fuzzycontroller the worse the road condition is the better thecontrol effect of the body acceleration and dynamic tiredeflection is The energy-regenerative efficiency did not varyfrom road inputs in three controllers The main studyingcontributions are (1) to propose a novel active energy-regeneration suspension (AERS) systemwhich can transformthe electrical power efficiently (2) to utilize VUF and PDtheories for the AERS control (3) to define a self-poweredefficiency concept in order to describe the regenerativestructuresrsquo contribution to the control consumption (4) to dosimulations and experiments so as to demonstrate the energy-regenerative and the suspension control performances

Random roadinputs Desired force

Actuator force

2-DOF quarter-car model

e(SWS)

ecVUF

controller

PDcontroller Desired current

Controlcircuitmodel

1

120593

Figure 1 The VUF control schematic of the AERS

F

f

xb

mb

xw

xg

mw

Kt

Ks

Cs

Figure 2 2 DOF of the quarter-car model

2 A Novel Model of the AERS System

21 Principle of Suspension Control To propose a new controlmodel for the active electromagnetic energy-regenerativesuspension (AEERS) we firstly add a VUF controller anda simple PD controller to the traditional 2-DOF car modelThe principle of the control theory is shown in Figure 1 Oneof the 2-DOF car modelrsquos output parameters namely thesuspension working space (SWS) is taken as the inputs forVUF controller That is to say the parameters e and ec arerespectively the deviation and its rate of the SWS Then theVUF controller could offer a desired force or current for thePD controller and through the circuitmodel themotorrsquos forcewould be fed back to the car model 120593 is the constant of thescrewmotorTherefore this control algorithm can ensure theconsistency of the two forces that is the actual control forceon the car model and the ideal control force from the VUF

22 The 2-DOF Car Model A quarter-car model is estab-lished to evaluate the dynamic performance and energyregeneration of AERS system as shown in Figure 2 Itis assumed that each of the four wheels has independentsuspension to simulate the actions of an active vehicle suspen-sion system and therefore quarter-car models are used formany simulations of suspension system where 119898119887 and 119898119908respectively denoted the sprung mass (the vehicle body) andunsprung mass (the wheels) which are considered as rigidbody 119909119887 and 119909119908 respectively denoted the displacement ofthe sprung mass and unsprung mass namely the 2 degreesof freedom 119909119892 is the road displacement The tire is denotedby a linear spring 119870119904 and 119870119905 represent the suspensionand tire stiffness respectively Besides the actuator force f

Shock and Vibration 3

L

U

I

R

M

(a) Generator

M

I

R

U

L

(b) Motor

Figure 3 Schematics of the circuit model

the control force F from the generatormotor and the ballscrew assembly could also offer the suspension an adjustabledamping coefficient 119862119904 So there is 119865 = minus119862119904(119887 minus 119908) + 119891

From 2-DOF quarter-car model the dynamic equationscan be written as follows

119898119887119887 = minus119870119904 (119909119887 minus 119909119908) + 119865119898119908119908 = 119870119904 (119909119887 minus 119909119908) + 119870119905 (119909119892 minus 119909119908) minus 119865

(1)

23 Random Road Input The road profile input is a veryimportant factor for a pavement vehiclersquos dynamic responsesIt is usually regarded as a space-domain vibrationmotivationThe road roughness is assumed to be a Gaussian randomprocess via shaping filters [29] The road profile input forthe quarter-car model can be described by the equation asfollows

119892 (119905) = minus21205871198910119909119892 (119905) + 21205871198990radic1198660V0 sdot 120596 (119905) (2)

where 1198910 denotes the lower limiting frequency 1198990 is thereference spatial frequency and regarded as 01mminus1 1198660 is theuneven road coefficient V0 represents the vehiclersquos velocity120596(119905) is a zero-mean Gaussian white noise

24 Control Circuit Model The actuator consisted of a ballscrew for motion translation and a permanent magneticbrushless linear DC motor The motor not only is for theactive control but also functioned as an energy-regenerativegeneratorThe circuit schematics for the twoworking patternsare shown in Figures 3(a) and 3(b) and respectively repre-sented the circuit diagram as a generator or a motor U isthe supply voltage of power source R and L are the motorresistance and inductance respectively I is the armaturecurrent

The ideal actuator has the following characteristics

119864119872 = 120593 (3)

119865 = 120593119868 (4)

where 119864119872 is the electromotive force (EMF) of the motor is the axial velocity of the ball screw 120593 is the motor constantof the screw 120593 = 119896119897 119896 is the motor constant 119897 is the leadscrew

241 Circuit of the PD Control From Figure 3(b) the circuitequation is described as follows

119880 = 119871119889119868119889119905 + 119877119868 + 119864119872 (5)

From this equation we can know that the armature current 119868would change with the controller voltage 119880

By (4) when the geometric structure of themotor and theball screw is certain the active control force 119865 is a function ofthe armature current 119868

According to (4) we can obtain the desired ideal current1198680

1198680 = 1198650120593 (6)

The current deviation is obtained as follows

1198900 = 1198680 minus 119868 (7)

The PD control voltage is written as follows

119880 = 1198701198751198900 + 119870119889 1198891198900119889119905 (8)

where 1198680 is the ideal current of the armature 1198650 is the idealactive control force 1198900 is the error of armature current 119870119875is the proportion coefficient of the PD controller 119870119875 is thedifferential coefficient of the PD controller

Based on (3) (5) and (8) there is another equation asfollows

1198701198751198900 + 119870119889 1198891198900119889119905 minus 120593 = 119871119889119868119889119905 + 119877119868 (9)

Using (9) to Laplace transform obtains the following

119868 (119904) = [(119870119875 + 119870119889119904) 119890 (119904) minus 120593119911 (119904) 119904] sdot 1119871119904 + 119877 (10)

where 119904 is the Laplace operatorThen we can get the PD controller schematic shown in

Figure 4

242 Self-Powered Efficiency According to Figure 3(a) themotor on the generator pattern would have a voltages balancewritten as follows

119880119888119903 = 119864119872 minus 119880119877 (11)


F F01120593

120593

120593I0 e0

+ +minusminus

Kp + Kds1

Ls + R

I

U

z

EM

Figure 4 PD controller

where119880119888119903 is the power supply voltage for the generator119880119877 isthe internal resistance voltage

Substituting the above expression to (11) the powersupply voltage 119880119888119903 is obtained as follows

119880119888119903 = 120593 minus 119868119877 = 120593 minus 119865120593 sdot 119877 (12)

On the other hand the power supply voltage on themotorpattern 119880119888119886 as shown in Figure 3(b) is written as follows

119880119888119886 = 119864119872 + 119864119877 = 120601 + 119865120601 sdot 119877 (13)

In order to evaluate the energy recycling efficiency forthe suspension vibration we assume 119875119903 as the power for theAERS and 119875119886 as the consumed power for active suspensionTherefore we have

119875119903 = 119880119888119903 sdot 119868 = 119865 minus 1198652 sdot 1198771205932

119875119886 = 119880119888119886 sdot 119868 = 119865 + 1198652 sdot 1198771205932

(14)

From (14) an equivalent damping coefficient 119888119890119902 is pro-posed to describe the damping coefficient of themotor whichcan be defined as follows

119888119890119902 = 1205932119877 (15)

The definition indicates both the electric-magmatic prop-erties and mechanism properties illustrating the physicalfeatures of the AERS model So (14) should be simplified as a2-order function of the control force 119865 without the constantitem

119875119903 = 119865 minus 11198881198901199021198652

119875119886 = 119865 + 11198881198901199021198652

(16)

Then we can define the ratio between the above twopowers as the self-powered efficiency (SPE) symbolized as120578119904 The mathematics equation is as follows

120578119904 = 119875119903119875119886 =

0 119875119903 le 01 minus 2

1 + 119888119890119902119865 119875119903 gt 0 (17)

where 119865 and both are algebraic values

According to (15) and (17) 120578119904 is related to 119888119890119902Themore theequivalent damping coefficient is the better the self-poweredefficiency can be achieved Therefore it is better to choose alinear motor with a larger motor constant 119896 or select a lowerinternal resistant with a certain motor constant 119896 or select alower internal resistant with a certain motor constant valueConsequently it can increase the damping coefficient andimprove the ride performance

After the motor structure is already designed or selected119888119890119902 has a constant value So the SPE is only related to the 119865ratio It means that the SPE is determined by the suspensiondynamics

120578119904 = 1 minus 21 + 119888119890119902119865 = 1 minus 2

1 + 119864119872119880119877 (18)

When 119875119903 gt 0 (17) can be rewritten as (18) whichconcernsmore the generatormotor structureWedefined theratio between the motor electromotive force and the internalresistances voltage as the feedback energy coefficient (FEC)symbolized with119870

119870 = 119864119872119880119877 (19)

When119870 = 1 the motor feedback energy (MFE) is totallyconverted into a dissipating thermal energy by the internalresistance In this case we have the AERS power 119875119903 = 0 andthe SPE coefficient 120578119904 = 0

When 119870 = 0 (119880119877 = 0) the SPE coefficient 120578119904 rarr 1 theMFE is totally converted into the electrical energy and thedissipation energy is zero

3 Variable Universe Fuzzy Controller Design

31 Variables of Input and Output Fuzzification and Methodto Resolve The suspension working space (SWS) (119909119887 minus 119909119908)and the relative velocity (119887minus119908) between the unsprungmassand the sprung mass are regarded as the two input variablesTherefore there are 119890 = 119909119887minus119909119908 and 119890119888 = 119887minus119908The desiredforce F0 is used as the output variable of the controller

All of the fuzzy domains for 1198650 e and ec are set to be[minus1 1] The fuzzy language subset is donated as

119873119861119873119872119873119878 119885119874 119875119878 119875119872 119875119887 (20)

32 Fuzzy Control Rules The fuzzy control is used in anexternal-loop controller which does not depend on theaccurate controlled model It is decided on the basis of thecontrol knowledge and experience which can ensure thegood robustness [30]

As shown in Figure 1 it is vital to analyze the motionsof the quarter-car model Firstly we clarify the equilibriumposition as the origin of the coordinate system and thedirection position is specified according to the SAE standard

When 119909119887 minus 119909119908 gt 0 the suspension is in a stretchingcondition If 119887 minus 119908 gt 0 the tendency of the suspensionsamplitude is increasing so the output variable should bechosen at a larger negative value On the other hand if


NB NM NS ZO PS PM PB

minusE E0

x

1

120583

(a)

0

x

1

Con

trac

ting

univ

erse

Expa

ndin

gun

iver

se

120583

minus120572(x)E 120572(x)E

(b)

x

1

0

120583

minus120572(x998400)E minus120572(x998400)E

(c)

Figure 5 (a) The initial universe of its partition (b) and (c) contracting-expending universes

Table 1 Fuzzy control rules

1198650 ecNB NM NS ZO PS PM PB

e

NB PB PB PB NS NS NS NSNM PB PB PM NS NM NM NSNS PB PM PS NS NS NM NMZO PM PS ZO ZO NS NM NMPS PS PM PM PS NM NM NBPM PS PM PB PS NM NB NBPB PM PM PB PS NB NB NB

119887 minus 119908 lt 0 the trend of the suspensions amplitude is drop-ping Therefore it is better to select a lower positive controlvalue

When 119909119887 minus 119909119908 lt 0 the suspension is in compressioncondition If 119887 minus 119908 gt 0 the compression of the suspensionsamplitude is droppingTherefore it is better to select a smallernegative control value If 119887 minus 119908 lt 0 a larger number ofa positive control value should be chosen in terms of thesuspension amplitude compression increasing

According to the principle of the above we can build thefuzzy controller rules which are listed in Table 1

33 Extension Factor The VUF controller is an effectivenonlinear control method The basic structure of the VUFcontroller is briefly introduced in Section 33 In this paper weselect the variable universe fuzzy controller on AERS systemcontrol which is described as a double input and a singleoutput structure

The universes 119883119894 = [minus119864 119864] (119894 = 1 2) and 119884 = [minus119880119880]would automatically adjust with the changing of variables 119909119894and 119910 respectively which offers a certain adaptive featuresThe relationships between the two variables and the initialuniverses are shown in Figure 5 120583 is the membership

function of fuzzy sets 119884 They can also be described asfollows

119883119894 (119909119894) = [minus119886119894 (119909119894) 119864119894 119886119894 (119909119894) 119864119894]119884 (119910) = [minus120573 (119910)119880 120573 (119910)119880]

(21)

where120572119894(119909119894) (119894 = 1 2) and120573(119910) represent the universe factorsof the contraction-expansion The universes 119883119894 and 119884 wererelated to the initial universe

Generally there are 2 types extension factor for examplea proportional type and an exponential type The two practi-cal contraction-expansion factors are given as follows

119886 (119909) = ( |119909|119864 )120591

+ 120576 120591 gt 0

119886 (119909) = 1 minus 120582 exp (minus1198961199092) 120582 isin (0 1) 119896 gt 0(22)

where 120576 is a very small constantIt is clear that these contraction-expansion factors include

double inputs and single output with a similar form Con-sidering the relevance between the input variables and thepractical vehicle parameters we define them as follows

119886 (119890) = 1 minus 05 exp (minus031198902)119886 (119890119888) = 1 minus 05 exp (minus031198901198882)120573 (119865) = 1 minus 05 exp (minus031198652)

(23)

4 Simulations and Experiments

41 Simulation Results and Analysis In order to verify theeffect of the controller and the superiority of the AERSsystem three typical controller models are simulated inthis study In the process of the simulations the dynamicresponse and performance of three vehicles are compared


Table 2 Main parameters of the simulation

Parameterunit Value119898119887 (kg) 130119870119904 (Nm) 20000119862119904 (Nsdotsm) 1000V0 (kmh) 20119871 (H) 03120593 (NA) 90119898119908 (kg) 15119870119905 (Nm) 2000001198910 (Hz) 011198990 (mminus1) 01119877 (Ω) 10

0 2 4 6 8 10

0

50

100

Time (s)

Mag

nitu

de (N

)

Desired forceActual force

minus100

minus50

Figure 6 Control force

These three vehicles are respectively with the proposedcontrol algorithm with the fuzzy controller and withoutany controller The performances can be evaluated by thebody acceleration (BA) the suspensionworking space (SWS)and the dynamic tire deflection (DTD) All the simulationparameters for the VUF model are listed in Table 2

Set the PD controller ratio coefficient 119870119875 = 300 and thedifferential coefficient 119870119889 = 02 Figure 6 shows the actuatorforce which is compared with the desired force on the B-classroad

From Figure 6 we can know that the actuator force isalmost the same as the desired force The root mean square(RMS) values of the actuator and the desired force arerespectively 467N and 4658N and the difference is merely045 Obviously the results show that the actuator forcematches the desired force well

Figures 7ndash9 demonstrate the time domain and frequencydomain responses with the three typical suspension modelsnamely passive one with fuzzy controller and with NUFcontroller respectively The BA SWS and DTD are respec-tively selected to evaluate the ride comfort and the stabilityperformance

Besides the above simulations the RMS values forthe three typical systems are listed in Tables 3 and 4

Table 3 Suspension performance of B-class random road

Performanceindex

RMS

Passivesuspension Fuzzy control

Variableuniverse

fuzzy controlBA(ms2) 051 046 042SWSmm 196 197 196DTDmm 038 037 036

Table 4 Suspension performance of C-class random road

Performanceindex

RMS


Variableuniverse


which are achieved on the B-class road and C-class roadrespectively

Through the comparisons among the simulation datafrom Tables 3 and 4 it is clear that the VUF controller has theminor values of BA and DTD which means the best comfortand safety That is to say the VUF controller is effective inguaranteeing the vehicle performances for the AERS systemIf the ride comfort is regarded as a control target the peakvalues of the BA and the DTD are reduced by 1765 and562 on the B-class road compared with the passive oneMeanwhile on the C-class road the peak values are reducedby 1959 and 933 Although the SWS value is a little morethan that of the passive suspension it is acceptable

According to (17) and (18) the SPE and the energy-regenerative efficiency (ERE) for the AERS system are calcu-lated and the results are listed in Table 5 The calculations arecarried out on different random roads B- C- and D-classroads

According to Table 5 all ERE values are more than18 percent It is very interesting that the rougher the roadinputs are the less the energy recycling ratio will get Themain reason would be due to the nonlinear factors andthe hysteresis phenomena inevitably existing in most of theAERS structures The AERS structure can also provide over11 percent power for the suspension control in most of theregular road conditions so the proposed system is also a goodsolution for the active control consumption

42 Road Test and Analysis Comparative tests between theactive energy-regenerative suspension (AERS) and a passivesuspension are carried outThe test car is a self-made electricvehicle and the test data acquisition systems are based ona NI test system as shown in Figure 10 Tire stiffness issimulated by the four dampers The acceleration and thedynamic deflection are obtained by using two accelerationsensors and displacement sensor from the sprung mass andunsprungmass respectivelyThe relative velocity between the


PassiveFuzzyVUF

0 2 4 6 8 10minus15

minus1

minus05

0

05

1

15

Time (s)

Mag

nitu

de (m

s2)

(a)

PassiveFuzzyVUF

0 5 10 15 2000

02

04

06

08

Frequency (Hz)

Mag

nitu

de (m

s2)

times103

(b)

Figure 7 Body acceleration (a) time domain and (b) frequency domain

0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)

Frequency (Hz)0 5 10 15 20

00

05

10

15

20

25

Mag

nitu

de (m

m)

PassiveFuzzyVUF

(b)

Figure 8 Suspension dynamic flexibility (a) time domain and (b) frequency domain

Table 5 Self-powered efficiency

Random road Pr(W) Pa(W) Pd(W) ERElowast SPEB-class 514 4580 2741 1875 1122C-class 7026 59629 37849 1856 1178D-class 29865 259531 162583 1837 1151lowastThe energy-regenerative efficiency is the ratio of the ERP to DDP

sprung mass and unsprung mass is calculated through thefurther differential processes

The B random road is selected as the test input excita-tions and the vehicle speed is 20 kmh Limited by the testconditions the test parameters are slightly different from the

simulation parameters which are listed in Table 2 but theirinfluences can be neglected for these performance analysesThe results of the road test are shown in Figures 11ndash13 andTable 6

According to the experimental curves shown in Figures11ndash13 and the RMS values in Table 6 the ride comfort isimproved when the frequency is lower than the unsprungmassrsquos resonance frequency Also the RMS value of thevertical body acceleration (BA) is reduced by 1632 andthe dynamic tire deflection (DTD) is reduced by 555 Theresults also show that the ride comfort for the active energy-regenerative suspension is improved

According to (16) and (17) the ERE and the SPE for theAERS system are calculated based on the experimental data


0 2 4 6 8 10minus1

minus05

0

05

1

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)

0 5 10 15 2000

02

04

06

08

10

12

Mag

nitu

de (m

m)

Frequency (Hz)

PassiveFuzzyVUF

(b)

Figure 9 Tire dynamic displacement (a) time domain and (b) frequency domain

Figure 10 Road test

0 2 4 6 8 10minus15

minus10

minus05

00

05

10

15

Time (s)

PassiveVUF

Mag

nitu

de (m

s2)

(a)

PassiveVUF

0 3 6 9 12 1500

04

08

12

16

20

Frequency (Hz)

Mag

nitu

de (m

s2)

(b)

Figure 11 Experimental results of the body acceleration (a) time domain and (b) frequency domain


0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

05

10

15

20

25

Mag

nitu

de (m

m)

Frequency (Hz)

(b)

Figure 12 Experimental results of the suspension working space (a) time domain and (b) frequency domain

0 2 4 6 8 10

minus10

minus05

00

05

10

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

03

06

09

12

15

Mag

nitu

de (m

m)

Frequency (Hz)

(b)

Figure 13 Experimental results of the tire dynamic displacement (a) time domain and (b) frequency domain


Performance index

RMS

Passivesuspension

Variableuniverse fuzzy

controlBA(ms2) 049 041SWSmm 194 194DTDmm 036 034

The two test values are respectively 1824 and 1105 a littleless (about 2) than the simulation values list in Table 5The test results also validated the feasibility of the energyregeneration and self-powered ability

5 Conclusions

In this paper a novel AERS is proposed by integratingthe adjustable shock absorber with a ball screw motor Thevariable universe fuzzy control theory is applied to the activeelectromagnetic AERS The RMS values of the vertical bodyacceleration and the dynamic tire deflection are significantlyreduced on different random road inputs With the energy-regenerative PD control to the generatormotor circuit theactuator force showed good consistency with the desiredforce

A concept of the self-powered efficiency is proposed inorder to evaluate the energy-regenerative structurersquos contri-bution to the suspension control The study also demon-strated that the external resistance 119877 and the motor constant119896 are the two key factors for the self-powered efficiency


The simulation results with B- C- and D-class roadinputs showed that the energy-regenerative efficiency is over18 percent and the self-power efficiency is over 11 for theARS system with the VUF controller

The experimental data on the B-class road is differedno more than 2 from the simulations Both the test andcalculating results indicated the feasibility of the energyregeneration aswell as improvements on the ride comfort anddriving safety

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grant no 51575288) The authors alsoexpress great gratitude for the help of the research team andthe editors

References

[1] K Nakano Y Suda M Yamaguchi and H Kohno ldquoApplicationof combined type self-powered active suspensions to rubber-tired vehiclesrdquo JSAE Annual Congress vol 6 pp 19ndash22 2003

[2] P Hsu ldquoPower recovery property of electrical active suspensionsystemsrdquo in Proceedings of the 31st IEEE Conference EnergyConversion Engineering vol 3 pp 1899ndash1904 1996

[3] L Zuo and P-S Zhang ldquoEnergy harvesting ride comfort androad handling of regenerative vehicle suspensionsrdquo Journal ofVibration amp Acoustics vol 135 no 1 Article ID 011002 pp 1ndash82013

[4] D Karnopp ldquoPower requirements for traversing uneven road-waysrdquo Vehicle System Dynamics vol 7 no 3 pp 135ndash152 1978

[5] S A Velinsky and R A White ldquoVehicle energy dissipation dueto road roughnessrdquo Vehicle System Dynamics vol 9 no 6 pp359ndash384 1980

[6] L Segel and X P Lu ldquoVehicular resistance to motion as influ-enced by road roughness and highway alignmentrdquo AustralianRoad Research vol 12 no 4 pp 211ndash222 1982

[7] Y Suda and T Shiiba ldquoA new hybrid suspension systemwith active control and energy regenerationrdquo Vehicle SystemDynamics vol 25 pp 641ndash654 1996

[8] K Nakano Y Suda and S Nakadai ldquoSelf-powered activevibration control using a single electric actuatorrdquo Journal ofSound and Vibration vol 260 no 2 pp 213ndash235 2003

[9] K Nakano Y Suda and S Nakadai ldquoSelf-powered active vibra-tion control using continuous control inputrdquo JSME Interna-tional Journal Series C Mechanical Systems Machine Elementsand Manufacturing vol 43 no 3 pp 726ndash731 2000

[10] Y Kawamoto Y Suda H Inoue and T Kondo ldquoModeling ofelectromagnetic damper for automobile suspensionrdquo Journal ofSystem Design and Dynamics vol 1 no 3 pp 524ndash535 2007

[11] G Zhang J Y Cao and F Yu ldquoDesign of active andenergy-regenerative controllers for DC-motor-based suspen-sionrdquoMechatronics vol 22 no 8 pp 1124ndash1134 2012

[12] L Chen D Shi R Wang and H Zhou ldquoEnergy conservationanalysis and control of hybrid active semiactive suspensionwith

three regulating damping levelsrdquo Shock and Vibration vol 2016Article ID 6196542 14 pages 2016

[13] Z Fang X Guo L Xu and H Zhang ldquoAn optimal algo-rithm for energy recovery of hydraulic electromagnetic energy-regenerative shock absorberrdquo Applied Mathematics amp Informa-tion Sciences vol 7 no 6 pp 2207ndash2214 2013

[14] R L Teixeira F P L Neto and J F Ribeiro ldquoModelling andexperimental investigation of an active damperrdquo Shock andVibration vol 13 no 4-5 pp 343ndash354 2006

[15] T Saito Y Sumino and S Kawano ldquoResearch on energyconversion of mechanical vibrationrdquo in Proceedings of theDynamics and Design Conference B vol 93 pp 105ndash108 1993

[16] Y Suda K Suematsu K Nakano and T Shiiba ldquoStudy on elec-tromagnetic suspension for automobilessimulation and experi-ments of performancerdquo in Proceedings of the 5th InternationalSymposium on Advanced Vehicle Control pp 699ndash704 AnnArbor Mich USA 2000

[17] K E Graves P G Iovenitti and D Toncich ldquoElectromagneticregenerative damping in vehicle suspension systemsrdquo Interna-tional Journal of Vehicle Design vol 24 no 2-3 pp 182ndash1972000

[18] R B Goldner P Zerigian and J R Hull ldquoA preliminary studyof energy recovery in vehicles by using regenerative magneticshock absorbersrdquo SAE Paper 2001-01-2071 2001

[19] Y Okada and H Harada ldquoRegenerative control of activevibration damper and suspension systemsrdquo in Proceedings of the35th IEEE Conference on Decision and Control vol 4 pp 4715ndash4720 1996

[20] Y P Pan Y Zhou T R Sun and M J Er ldquoCompositeadaptive fuzzy tracking control of uncertain nonlinear systemsrdquoNeurocomputing vol 99 no 10 pp 15ndash24 2013

[21] Y P Pan M J Er L Pan and H Y Yu ldquoComposite learningfrom model reference adaptive fuzzy controlrdquo in Proceedings ofthe International Conference on Fuzzy Theory and Its Applica-tions (iFUZZY rsquo15) pp 91ndash96 IEEE Yilan Taiwan November2015

[22] W Shan Y Ma R W Newcomb and D Jin ldquoAnalog circuitimplementation of a variable universe adaptive fuzzy logiccontrollerrdquo IEEETransactions onCircuits and Systems II ExpressBriefs vol 55 no 10 pp 976ndash980 2008

[23] D-L Wang L Gu and G-X Ma ldquoSimulation analysis andexperimental research on the variable universe fuzzy control ofhydro-pneumatic suspensionrdquoTransaction of Beijing Institute ofTechnology vol 29 no 4 pp 314ndash317 2009

[24] QDWangQWang andWWChen ldquoSimulation analysis andexperimental research on the variable universe fuzzy control ofhydro-pneumatic suspensionrdquo Journal of Vibration Engineeringvol 22 no 5 pp 512ndash518 2009

[25] H X Li Z H Miao and J Y Wang ldquoVariable universe stableadaptive fuzzy control of a nonlinear systemrdquo Computers andMathematics with Applications vol 44 no 5 pp 799ndash815 2002

[26] Y P Pan and M J Er ldquoEnhanced adaptive fuzzy control withoptimal approximation error convergencerdquo IEEE Transactionson Fuzzy Systems vol 21 no 6 pp 1123ndash1132 2013

[27] Y PanM J Er D Huang andQWang ldquoAdaptive fuzzy controlwith guaranteed convergence of optimal approximation errorrdquoIEEE Transactions on Fuzzy Systems vol 19 no 5 pp 807ndash8182011

[28] F Liu Y N Li and L Zheng ldquoVariable universe fuzzy controlfor themagneto-rheological semi-active suspension in armoredvehiclesrdquo Automotive Engineering vol 35 no 8 pp 735ndash7392013


[29] L Soria B Peeters and J Anthonis ldquoOperational modalanalysis and the performance assessment of vehicle suspensionsystemsrdquo Shock and Vibration vol 19 no 5 pp 1099ndash1113 2012

[30] D H Shi L Chen R CWang H Jiang and Y J Shen ldquoDesignand experiment study of a semi-active energy-regenerativesuspension systemrdquo Smart Materials and Structures vol 24 no1 Article ID 015001 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



than the hydraulic system [15] Subsequently some electro-magnetic actuators (EA) have received attention for their easyenergy regeneration higher efficiency quick response andgood controllability [16ndash19]

In last decades many researchers applied some linearand nonlinear control methods to quarter-car models whichwere simple and preferred In most cases the energy-regeneration efficiency is closely related to the control algo-rithm The question is how to compromise the disunitybetween the accuracy and the efficiency such as119867infin and PIDPan et al used a composite 119867infin adaptive fuzzy controller(CHAFC) on an uncertain nonlinear system to solve thefuzzy approximation problem [20 21] The variable universefuzzy (VUF) controller is regarded as a promising algorithmowing to its outstanding accusation-efficiency balance Shanet al developed an analog circuit of a VUF controller [22]Wang et al applied the VUF control to the hydropneumaticsuspension andmagnetic-rheology absorber (MRA) [23 24]Li et al succeeded via the VUF controller based on consciousknowledge to simulate the model of the quadruple invertedpendulum [25] It is noteworthy that Pan et al proposedthe novel VUF controllers with an adaptive control strategythrough the Lyapunov synthesis [26 27] For instance Liuet al proposed a method of the VUF based on the two stagecontrol rules and introduced it to the semiactive suspension(SAE) of the magneto rheological (MR) armored vehicle[28] As a consequence the method also can get an idealperformance of the vehicles control and effectively improvethe vehicle ride comfort However the high performanceof the control algorithm mentioned above is still diffi-cult to solve the high energy consumption of the suspen-sion and limited its wide application especially in electricvehicles

In this paper a 2-DOF quarter-car model is built Basedon the dynamic model three algorithms such as the optimalcontrol algorithm fuzzy control algorithm and variable uni-verse fuzzy control algorithm are designedThe influences onthe control effects and the energy-regenerative effects choos-ing different road inputs and different control algorithmsare analyzed respectively The simulation results show thatdifferent road inputs have similar control effects for LQGcontrollerThe experiment results show that the performanceof active energy-regeneration suspension system is highlydependent on the choice of algorithmemployed and theVUFcontrol strategy exhibits an excellent integrated performanceBut for the fuzzy controller and variable universe fuzzycontroller the worse the road condition is the better thecontrol effect of the body acceleration and dynamic tiredeflection is The energy-regenerative efficiency did not varyfrom road inputs in three controllers The main studyingcontributions are (1) to propose a novel active energy-regeneration suspension (AERS) systemwhich can transformthe electrical power efficiently (2) to utilize VUF and PDtheories for the AERS control (3) to define a self-poweredefficiency concept in order to describe the regenerativestructuresrsquo contribution to the control consumption (4) to dosimulations and experiments so as to demonstrate the energy-regenerative and the suspension control performances

Random roadinputs Desired force

Actuator force

2-DOF quarter-car model

e(SWS)

ecVUF

controller

PDcontroller Desired current

Controlcircuitmodel

1

120593

Figure 1 The VUF control schematic of the AERS

F

f

xb

mb

xw

xg

mw

Kt

Ks

Cs

Figure 2 2 DOF of the quarter-car model

2 A Novel Model of the AERS System

21 Principle of Suspension Control To propose a new controlmodel for the active electromagnetic energy-regenerativesuspension (AEERS) we firstly add a VUF controller anda simple PD controller to the traditional 2-DOF car modelThe principle of the control theory is shown in Figure 1 Oneof the 2-DOF car modelrsquos output parameters namely thesuspension working space (SWS) is taken as the inputs forVUF controller That is to say the parameters e and ec arerespectively the deviation and its rate of the SWS Then theVUF controller could offer a desired force or current for thePD controller and through the circuitmodel themotorrsquos forcewould be fed back to the car model 120593 is the constant of thescrewmotorTherefore this control algorithm can ensure theconsistency of the two forces that is the actual control forceon the car model and the ideal control force from the VUF

22 The 2-DOF Car Model A quarter-car model is estab-lished to evaluate the dynamic performance and energyregeneration of AERS system as shown in Figure 2 Itis assumed that each of the four wheels has independentsuspension to simulate the actions of an active vehicle suspen-sion system and therefore quarter-car models are used formany simulations of suspension system where 119898119887 and 119898119908respectively denoted the sprung mass (the vehicle body) andunsprung mass (the wheels) which are considered as rigidbody 119909119887 and 119909119908 respectively denoted the displacement ofthe sprung mass and unsprung mass namely the 2 degreesof freedom 119909119892 is the road displacement The tire is denotedby a linear spring 119870119904 and 119870119905 represent the suspensionand tire stiffness respectively Besides the actuator force f


L

U

I

R

M

(a) Generator

M

I

R

U

L

(b) Motor





(1)






119864119872 = 120593 (3)

119865 = 120593119868 (4)



119880 = 119871119889119868119889119905 + 119877119868 + 119864119872 (5)




1198680 = 1198650120593 (6)


1198900 = 1198680 minus 119868 (7)


119880 = 1198701198751198900 + 119870119889 1198891198900119889119905 (8)



1198701198751198900 + 119870119889 1198891198900119889119905 minus 120593 = 119871119889119868119889119905 + 119877119868 (9)


119868 (119904) = [(119870119875 + 119870119889119904) 119890 (119904) minus 120593119911 (119904) 119904] sdot 1119871119904 + 119877 (10)


Figure 4


119880119888119903 = 119864119872 minus 119880119877 (11)


F F01120593

120593

120593I0 e0

+ +minusminus

Kp + Kds1

Ls + R

I

U

z

EM




119880119888119903 = 120593 minus 119868119877 = 120593 minus 119865120593 sdot 119877 (12)


119880119888119886 = 119864119872 + 119864119877 = 120601 + 119865120601 sdot 119877 (13)


119875119903 = 119880119888119903 sdot 119868 = 119865 minus 1198652 sdot 1198771205932

119875119886 = 119880119888119886 sdot 119868 = 119865 + 1198652 sdot 1198771205932

(14)


119888119890119902 = 1205932119877 (15)


119875119903 = 119865 minus 11198881198901199021198652

119875119886 = 119865 + 11198881198901199021198652

(16)


120578119904 = 119875119903119875119886 =

0 119875119903 le 01 minus 2

1 + 119888119890119902119865 119875119903 gt 0 (17)




120578119904 = 1 minus 21 + 119888119890119902119865 = 1 minus 2

1 + 119864119872119880119877 (18)


119870 = 119864119872119880119877 (19)






119873119861119873119872119873119878 119885119874 119875119878 119875119872 119875119887 (20)






minusE E0

x

1

120583

(a)

0

x

1

Con

trac

ting

univ

erse

Expa

ndin

gun

iver

se

120583

minus120572(x)E 120572(x)E

(b)

x

1

0

120583

minus120572(x998400)E minus120572(x998400)E

(c)




e








119883119894 (119909119894) = [minus119886119894 (119909119894) 119864119894 119886119894 (119909119894) 119864119894]119884 (119910) = [minus120573 (119910)119880 120573 (119910)119880]

(21)



119886 (119909) = ( |119909|119864 )120591

+ 120576 120591 gt 0





(23)






0 2 4 6 8 10

0

50

100

Time (s)

Mag

nitu

de (N

)


minus100

minus50








Performanceindex

RMS


Variableuniverse



Performanceindex

RMS


Variableuniverse








PassiveFuzzyVUF

0 2 4 6 8 10minus15

minus1

minus05

0

05

1

15

Time (s)

Mag

nitu

de (m

s2)

(a)

PassiveFuzzyVUF

0 5 10 15 2000

02

04

06

08

Frequency (Hz)

Mag

nitu

de (m

s2)

times103

(b)


0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)


00

05

10

15

20

25

Mag

nitu

de (m

m)

PassiveFuzzyVUF

(b)










0 2 4 6 8 10minus1

minus05

0

05

1

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)

0 5 10 15 2000

02

04

06

08

10

12

Mag

nitu

de (m

m)

Frequency (Hz)

PassiveFuzzyVUF

(b)


Figure 10 Road test

0 2 4 6 8 10minus15

minus10

minus05

00

05

10

15

Time (s)

PassiveVUF

Mag

nitu

de (m

s2)

(a)

PassiveVUF

0 3 6 9 12 1500

04

08

12

16

20

Frequency (Hz)

Mag

nitu

de (m

s2)

(b)



0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

05

10

15

20

25

Mag

nitu

de (m

m)

Frequency (Hz)

(b)


0 2 4 6 8 10

minus10

minus05

00

05

10

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

03

06

09

12

15

Mag

nitu

de (m

m)

Frequency (Hz)

(b)



Performance index

RMS

Passivesuspension




5 Conclusions






Competing Interests


Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










L

U

I

R

M

(a) Generator

M

I

R

U

L

(b) Motor





(1)






119864119872 = 120593 (3)

119865 = 120593119868 (4)



119880 = 119871119889119868119889119905 + 119877119868 + 119864119872 (5)




1198680 = 1198650120593 (6)


1198900 = 1198680 minus 119868 (7)


119880 = 1198701198751198900 + 119870119889 1198891198900119889119905 (8)



1198701198751198900 + 119870119889 1198891198900119889119905 minus 120593 = 119871119889119868119889119905 + 119877119868 (9)


119868 (119904) = [(119870119875 + 119870119889119904) 119890 (119904) minus 120593119911 (119904) 119904] sdot 1119871119904 + 119877 (10)


Figure 4


119880119888119903 = 119864119872 minus 119880119877 (11)


F F01120593

120593

120593I0 e0

+ +minusminus

Kp + Kds1

Ls + R

I

U

z

EM




119880119888119903 = 120593 minus 119868119877 = 120593 minus 119865120593 sdot 119877 (12)


119880119888119886 = 119864119872 + 119864119877 = 120601 + 119865120601 sdot 119877 (13)


119875119903 = 119880119888119903 sdot 119868 = 119865 minus 1198652 sdot 1198771205932

119875119886 = 119880119888119886 sdot 119868 = 119865 + 1198652 sdot 1198771205932

(14)


119888119890119902 = 1205932119877 (15)


119875119903 = 119865 minus 11198881198901199021198652

119875119886 = 119865 + 11198881198901199021198652

(16)


120578119904 = 119875119903119875119886 =

0 119875119903 le 01 minus 2

1 + 119888119890119902119865 119875119903 gt 0 (17)




120578119904 = 1 minus 21 + 119888119890119902119865 = 1 minus 2

1 + 119864119872119880119877 (18)


119870 = 119864119872119880119877 (19)






119873119861119873119872119873119878 119885119874 119875119878 119875119872 119875119887 (20)






minusE E0

x

1

120583

(a)

0

x

1

Con

trac

ting

univ

erse

Expa

ndin

gun

iver

se

120583

minus120572(x)E 120572(x)E

(b)

x

1

0

120583

minus120572(x998400)E minus120572(x998400)E

(c)




e








119883119894 (119909119894) = [minus119886119894 (119909119894) 119864119894 119886119894 (119909119894) 119864119894]119884 (119910) = [minus120573 (119910)119880 120573 (119910)119880]

(21)



119886 (119909) = ( |119909|119864 )120591

+ 120576 120591 gt 0





(23)






0 2 4 6 8 10

0

50

100

Time (s)

Mag

nitu

de (N

)


minus100

minus50








Performanceindex

RMS


Variableuniverse



Performanceindex

RMS


Variableuniverse








PassiveFuzzyVUF

0 2 4 6 8 10minus15

minus1

minus05

0

05

1

15

Time (s)

Mag

nitu

de (m

s2)

(a)

PassiveFuzzyVUF

0 5 10 15 2000

02

04

06

08

Frequency (Hz)

Mag

nitu

de (m

s2)

times103

(b)


0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)


00

05

10

15

20

25

Mag

nitu

de (m

m)

PassiveFuzzyVUF

(b)










0 2 4 6 8 10minus1

minus05

0

05

1

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)

0 5 10 15 2000

02

04

06

08

10

12

Mag

nitu

de (m

m)

Frequency (Hz)

PassiveFuzzyVUF

(b)


Figure 10 Road test

0 2 4 6 8 10minus15

minus10

minus05

00

05

10

15

Time (s)

PassiveVUF

Mag

nitu

de (m

s2)

(a)

PassiveVUF

0 3 6 9 12 1500

04

08

12

16

20

Frequency (Hz)

Mag

nitu

de (m

s2)

(b)



0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

05

10

15

20

25

Mag

nitu

de (m

m)

Frequency (Hz)

(b)


0 2 4 6 8 10

minus10

minus05

00

05

10

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

03

06

09

12

15

Mag

nitu

de (m

m)

Frequency (Hz)

(b)



Performance index

RMS

Passivesuspension




5 Conclusions






Competing Interests


Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










F F01120593

120593

120593I0 e0

+ +minusminus

Kp + Kds1

Ls + R

I

U

z

EM




119880119888119903 = 120593 minus 119868119877 = 120593 minus 119865120593 sdot 119877 (12)


119880119888119886 = 119864119872 + 119864119877 = 120601 + 119865120601 sdot 119877 (13)


119875119903 = 119880119888119903 sdot 119868 = 119865 minus 1198652 sdot 1198771205932

119875119886 = 119880119888119886 sdot 119868 = 119865 + 1198652 sdot 1198771205932

(14)


119888119890119902 = 1205932119877 (15)


119875119903 = 119865 minus 11198881198901199021198652

119875119886 = 119865 + 11198881198901199021198652

(16)


120578119904 = 119875119903119875119886 =

0 119875119903 le 01 minus 2

1 + 119888119890119902119865 119875119903 gt 0 (17)




120578119904 = 1 minus 21 + 119888119890119902119865 = 1 minus 2

1 + 119864119872119880119877 (18)


119870 = 119864119872119880119877 (19)






119873119861119873119872119873119878 119885119874 119875119878 119875119872 119875119887 (20)






minusE E0

x

1

120583

(a)

0

x

1

Con

trac

ting

univ

erse

Expa

ndin

gun

iver

se

120583

minus120572(x)E 120572(x)E

(b)

x

1

0

120583

minus120572(x998400)E minus120572(x998400)E

(c)




e








119883119894 (119909119894) = [minus119886119894 (119909119894) 119864119894 119886119894 (119909119894) 119864119894]119884 (119910) = [minus120573 (119910)119880 120573 (119910)119880]

(21)



119886 (119909) = ( |119909|119864 )120591

+ 120576 120591 gt 0





(23)






0 2 4 6 8 10

0

50

100

Time (s)

Mag

nitu

de (N

)


minus100

minus50








Performanceindex

RMS


Variableuniverse



Performanceindex

RMS


Variableuniverse








PassiveFuzzyVUF

0 2 4 6 8 10minus15

minus1

minus05

0

05

1

15

Time (s)

Mag

nitu

de (m

s2)

(a)

PassiveFuzzyVUF

0 5 10 15 2000

02

04

06

08

Frequency (Hz)

Mag

nitu

de (m

s2)

times103

(b)


0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)


00

05

10

15

20

25

Mag

nitu

de (m

m)

PassiveFuzzyVUF

(b)










0 2 4 6 8 10minus1

minus05

0

05

1

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)

0 5 10 15 2000

02

04

06

08

10

12

Mag

nitu

de (m

m)

Frequency (Hz)

PassiveFuzzyVUF

(b)


Figure 10 Road test

0 2 4 6 8 10minus15

minus10

minus05

00

05

10

15

Time (s)

PassiveVUF

Mag

nitu

de (m

s2)

(a)

PassiveVUF

0 3 6 9 12 1500

04

08

12

16

20

Frequency (Hz)

Mag

nitu

de (m

s2)

(b)



0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

05

10

15

20

25

Mag

nitu

de (m

m)

Frequency (Hz)

(b)


0 2 4 6 8 10

minus10

minus05

00

05

10

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

03

06

09

12

15

Mag

nitu

de (m

m)

Frequency (Hz)

(b)



Performance index

RMS

Passivesuspension




5 Conclusions






Competing Interests


Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











minusE E0

x

1

120583

(a)

0

x

1

Con

trac

ting

univ

erse

Expa

ndin

gun

iver

se

120583

minus120572(x)E 120572(x)E

(b)

x

1

0

120583

minus120572(x998400)E minus120572(x998400)E

(c)




e








119883119894 (119909119894) = [minus119886119894 (119909119894) 119864119894 119886119894 (119909119894) 119864119894]119884 (119910) = [minus120573 (119910)119880 120573 (119910)119880]

(21)



119886 (119909) = ( |119909|119864 )120591

+ 120576 120591 gt 0





(23)






0 2 4 6 8 10

0

50

100

Time (s)

Mag

nitu

de (N

)


minus100

minus50








Performanceindex

RMS


Variableuniverse



Performanceindex

RMS


Variableuniverse








PassiveFuzzyVUF

0 2 4 6 8 10minus15

minus1

minus05

0

05

1

15

Time (s)

Mag

nitu

de (m

s2)

(a)

PassiveFuzzyVUF

0 5 10 15 2000

02

04

06

08

Frequency (Hz)

Mag

nitu

de (m

s2)

times103

(b)


0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)


00

05

10

15

20

25

Mag

nitu

de (m

m)

PassiveFuzzyVUF

(b)










0 2 4 6 8 10minus1

minus05

0

05

1

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)

0 5 10 15 2000

02

04

06

08

10

12

Mag

nitu

de (m

m)

Frequency (Hz)

PassiveFuzzyVUF

(b)


Figure 10 Road test

0 2 4 6 8 10minus15

minus10

minus05

00

05

10

15

Time (s)

PassiveVUF

Mag

nitu

de (m

s2)

(a)

PassiveVUF

0 3 6 9 12 1500

04

08

12

16

20

Frequency (Hz)

Mag

nitu

de (m

s2)

(b)



0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

05

10

15

20

25

Mag

nitu

de (m

m)

Frequency (Hz)

(b)


0 2 4 6 8 10

minus10

minus05

00

05

10

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

03

06

09

12

15

Mag

nitu

de (m

m)

Frequency (Hz)

(b)



Performance index

RMS

Passivesuspension




5 Conclusions






Competing Interests


Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












0 2 4 6 8 10

0

50

100

Time (s)

Mag

nitu

de (N

)


minus100

minus50








Performanceindex

RMS


Variableuniverse



Performanceindex

RMS


Variableuniverse








PassiveFuzzyVUF

0 2 4 6 8 10minus15

minus1

minus05

0

05

1

15

Time (s)

Mag

nitu

de (m

s2)

(a)

PassiveFuzzyVUF

0 5 10 15 2000

02

04

06

08

Frequency (Hz)

Mag

nitu

de (m

s2)

times103

(b)


0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)


00

05

10

15

20

25

Mag

nitu

de (m

m)

PassiveFuzzyVUF

(b)










0 2 4 6 8 10minus1

minus05

0

05

1

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)

0 5 10 15 2000

02

04

06

08

10

12

Mag

nitu

de (m

m)

Frequency (Hz)

PassiveFuzzyVUF

(b)


Figure 10 Road test

0 2 4 6 8 10minus15

minus10

minus05

00

05

10

15

Time (s)

PassiveVUF

Mag

nitu

de (m

s2)

(a)

PassiveVUF

0 3 6 9 12 1500

04

08

12

16

20

Frequency (Hz)

Mag

nitu

de (m

s2)

(b)



0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

05

10

15

20

25

Mag

nitu

de (m

m)

Frequency (Hz)

(b)


0 2 4 6 8 10

minus10

minus05

00

05

10

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

03

06

09

12

15

Mag

nitu

de (m

m)

Frequency (Hz)

(b)



Performance index

RMS

Passivesuspension




5 Conclusions






Competing Interests


Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










PassiveFuzzyVUF

0 2 4 6 8 10minus15

minus1

minus05

0

05

1

15

Time (s)

Mag

nitu

de (m

s2)

(a)

PassiveFuzzyVUF

0 5 10 15 2000

02

04

06

08

Frequency (Hz)

Mag

nitu

de (m

s2)

times103

(b)


0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)


00

05

10

15

20

25

Mag

nitu

de (m

m)

PassiveFuzzyVUF

(b)










0 2 4 6 8 10minus1

minus05

0

05

1

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)

0 5 10 15 2000

02

04

06

08

10

12

Mag

nitu

de (m

m)

Frequency (Hz)

PassiveFuzzyVUF

(b)


Figure 10 Road test

0 2 4 6 8 10minus15

minus10

minus05

00

05

10

15

Time (s)

PassiveVUF

Mag

nitu

de (m

s2)

(a)

PassiveVUF

0 3 6 9 12 1500

04

08

12

16

20

Frequency (Hz)

Mag

nitu

de (m

s2)

(b)



0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

05

10

15

20

25

Mag

nitu

de (m

m)

Frequency (Hz)

(b)


0 2 4 6 8 10

minus10

minus05

00

05

10

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

03

06

09

12

15

Mag

nitu

de (m

m)

Frequency (Hz)

(b)



Performance index

RMS

Passivesuspension




5 Conclusions






Competing Interests


Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 10minus1

minus05

0

05

1

Time (s)

Mag

nitu

de (m

)

PassiveFuzzyVUF

times10minus3

(a)

0 5 10 15 2000

02

04

06

08

10

12

Mag

nitu

de (m

m)

Frequency (Hz)

PassiveFuzzyVUF

(b)


Figure 10 Road test

0 2 4 6 8 10minus15

minus10

minus05

00

05

10

15

Time (s)

PassiveVUF

Mag

nitu

de (m

s2)

(a)

PassiveVUF

0 3 6 9 12 1500

04

08

12

16

20

Frequency (Hz)

Mag

nitu

de (m

s2)

(b)



0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

05

10

15

20

25

Mag

nitu

de (m

m)

Frequency (Hz)

(b)


0 2 4 6 8 10

minus10

minus05

00

05

10

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

03

06

09

12

15

Mag

nitu

de (m

m)

Frequency (Hz)

(b)



Performance index

RMS

Passivesuspension




5 Conclusions






Competing Interests


Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 10minus6

minus4

minus2

0

2

4

6

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

05

10

15

20

25

Mag

nitu

de (m

m)

Frequency (Hz)

(b)


0 2 4 6 8 10

minus10

minus05

00

05

10

Mag

nitu

de (m

)

Time (s)

PassiveVUF

times10minus3

(a)

PassiveVUF

0 3 6 9 12 1500

03

06

09

12

15

Mag

nitu

de (m

m)

Frequency (Hz)

(b)



Performance index

RMS

Passivesuspension




5 Conclusions






Competing Interests


Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Competing Interests


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











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Modelling and Experimental Study on ...downloads.hindawi.com/journals/sv/2016/6170275.pdf · Energy-Regenerative Suspension Structure with Variable Universe Fuzzy