Modelling and Analysis of Automobile Vibration System ...
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Research Article Modelling and Analysis of Automobile Vibration System Based on Fuzzy Theory under Different Road Excitation Information Xue-wen Chen and Yue Zhou College of Automobile and Traffic Engineering, Liaoning University of Technology, Jinzhou 121001, China Correspondence should be addressed to Xue-wen Chen; [email protected] Received 16 May 2017; Revised 23 June 2017; Accepted 6 November 2017; Published 2 January 2018 Academic Editor: Sigurdur F. Hafstein Copyright © 2018 Xue-wen Chen and Yue Zhou. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A fuzzy increment controller is designed aimed at the vibration system of automobile active suspension with seven degrees of freedom (DOF). For decreasing vibration, an active control force is acquired by created Proportion-Integration-Differentiation (PID) controller. e controller’s parameters are adjusted by a fuzzy increment controller with self-modifying parameters functions, which adopts the deviation and its rate of change of the body’s vertical vibration velocity and the desired value in the position of the front and rear suspension as the input variables based on 49 fuzzy control rules. Adopting Simulink, the fuzzy increment controller is validated under different road excitation, such as the white noise input with four-wheel correlation in time-domain, the sinusoidal input, and the pulse input of C-grade road surface. e simulation results show that the proposed controller can reduce obviously the vehicle vibration compared to other independent control types in performance indexes, such as, the root mean square value of the body’s vertical vibration acceleration, pitching, and rolling angular acceleration. 1. Introduction It is generally known that automobile active suspension system can produce and adjust the active control force in time to restrain the vehicle body’s vibration for improving the ride comfort according to the road surface excitation. Recently, there have been large research achievements in the automobile suspension system, such as the optimiza- tion control theory, the PID theory, the theory of variable structure control, and the skyhook damping theory which have been applied generally to the vibration control system. Zhang et al. proposed a semiactive suspension controller with magnetorheological dampers to realize independent control based on modified skyhook damping scheme of quarter- vehicle subsuspension system in the full vehicle [1]. Ren et al. presented an adaptive hybrid control algorithm combined with the ground-hook and skyhook control strategies based on quarter car model of semiactive suspension and designed an unscented Kalman filter to estimate the suspension states [2]. Singh and Aggarwal designed a hybrid Fuzzy-PID con- troller to evaluate the passenger ride comfort based on a semiactive quarter car model having MR shock absorber [3]. Du et al. presented an approach in designing a robust controller for half-car model active suspensions considering changes in vehicle inertial properties, such as the suspension deflection limitation and the controller saturation problem [4]. Owing to the randomness of road surface roughness and the nonlinearity and uncertainty of vehicle system, the above- mentioned method has its disadvantages and adaptability [5–7]. It has been known that the intelligent control theory has the ability of logical reasoning and decision-making, and it is best suited to solve the complexity and uncertainty system [8–10]. erefore, a variety of intelligent control methods has been widely used like the fuzzy control, neural network, genetic algorithm, and so on [11–14]. Huang et al. designed a fuzzy controller for converting chaos into periodic motion of stable performance based on the neural- net tyre model [10]. Riaz et al. presented adaptive Neuro Fuzzy Takagi-Sugeno-Kang control strategies for the vehicle active suspension to improve the ride quality and vehicle stability [13]. Zirkohi and Lin proposed an interval type-2 fuzzy-neural network approach incorporating the Lyapunov design approach and SMC method to improve controller robustness [14]. Balamurugan et al. designed two controllers Hindawi Complexity Volume 2018, Article ID 2381568, 9 pages https://doi.org/10.1155/2018/2381568
Transcript of Modelling and Analysis of Automobile Vibration System ...
Research ArticleModelling and Analysis of Automobile Vibration System Basedon Fuzzy Theory under Different Road Excitation Information
Xue-wen Chen and Yue Zhou
College of Automobile and Traffic Engineering Liaoning University of Technology Jinzhou 121001 China
Correspondence should be addressed to Xue-wen Chen xuewenchen163com
Received 16 May 2017 Revised 23 June 2017 Accepted 6 November 2017 Published 2 January 2018
Academic Editor Sigurdur F Hafstein
Copyright copy 2018 Xue-wenChen andYue ZhouThis is an open access article distributed under the Creative CommonsAttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited
A fuzzy increment controller is designed aimed at the vibration system of automobile active suspension with seven degrees offreedom (DOF) For decreasing vibration an active control force is acquired by created Proportion-Integration-Differentiation(PID) controllerThe controllerrsquos parameters are adjusted by a fuzzy increment controller with self-modifying parameters functionswhich adopts the deviation and its rate of change of the bodyrsquos vertical vibration velocity and the desired value in the position of thefront and rear suspension as the input variables based on 49 fuzzy control rules Adopting Simulink the fuzzy increment controlleris validated under different road excitation such as thewhite noise input with four-wheel correlation in time-domain the sinusoidalinput and the pulse input of C-grade road surface The simulation results show that the proposed controller can reduce obviouslythe vehicle vibration compared to other independent control types in performance indexes such as the root mean square value ofthe bodyrsquos vertical vibration acceleration pitching and rolling angular acceleration
1 Introduction
It is generally known that automobile active suspensionsystem can produce and adjust the active control force intime to restrain the vehicle bodyrsquos vibration for improvingthe ride comfort according to the road surface excitationRecently there have been large research achievements inthe automobile suspension system such as the optimiza-tion control theory the PID theory the theory of variablestructure control and the skyhook damping theory whichhave been applied generally to the vibration control systemZhang et al proposed a semiactive suspension controller withmagnetorheological dampers to realize independent controlbased on modified skyhook damping scheme of quarter-vehicle subsuspension system in the full vehicle [1] Ren etal presented an adaptive hybrid control algorithm combinedwith the ground-hook and skyhook control strategies basedon quarter car model of semiactive suspension and designedan unscented Kalman filter to estimate the suspension states[2] Singh and Aggarwal designed a hybrid Fuzzy-PID con-troller to evaluate the passenger ride comfort based on asemiactive quarter car model having MR shock absorber [3]
Du et al presented an approach in designing a robustcontroller for half-car model active suspensions consideringchanges in vehicle inertial properties such as the suspensiondeflection limitation and the controller saturation problem[4] Owing to the randomness of road surface roughness andthe nonlinearity and uncertainty of vehicle system the above-mentioned method has its disadvantages and adaptability[5ndash7] It has been known that the intelligent control theoryhas the ability of logical reasoning and decision-makingand it is best suited to solve the complexity and uncertaintysystem [8ndash10] Therefore a variety of intelligent controlmethods has been widely used like the fuzzy control neuralnetwork genetic algorithm and so on [11ndash14] Huang etal designed a fuzzy controller for converting chaos intoperiodic motion of stable performance based on the neural-net tyre model [10] Riaz et al presented adaptive NeuroFuzzy Takagi-Sugeno-Kang control strategies for the vehicleactive suspension to improve the ride quality and vehiclestability [13] Zirkohi and Lin proposed an interval type-2fuzzy-neural network approach incorporating the Lyapunovdesign approach and SMC method to improve controllerrobustness [14] Balamurugan et al designed two controllers
HindawiComplexityVolume 2018 Article ID 2381568 9 pageshttpsdoiorg10115520182381568
2 Complexity
lr
M4M3
M2 M1
kt3
k3
k1
kt2 kt1
k2
k4
kt4
f1
f3
f2
f4c3
c1c2
c4
x
V
la
lf
y
z
lb
zq4zq3
z4z3
z1
zq1
zs
z2
zs2
zq2
zs1
Figure 1 Vehicle model of the active suspension with seven DOF
to generate the desired damping force and adjust the volt-age level to MR damper based on the quarter car vehiclemodel of semiactive suspension [15] Zhang et al designed asemiactive controller based on the inverse model and slidingmode control strategies for the quarter-vehicle suspensionwith the magnetorheological damper [16] Bououden et alinvestigated the problem of time-varying delays and inputconstraints for active suspension systems with a quarter-vehicle model based on the Lyapunov-Krasovskii method[17] From the analysis results on automobile active suspen-sion research we learned that much of the relevant literaturefocus on a quarter- or a half-car model that cannot fullyreflect or evaluate riding comfort of a whole vehicle [18ndash22]So it is our goal to research the time-domain response of theautomobile active suspension with seven DOF for decreasingthe body vibration considering the pitching and rollingmotion under the condition of the white noise input withfour wheels correlated effects and different road excitationAt last the submodule of fuzzy increment controller and therandom inputmodel have been given and the effectiveness ofproposed controller has been validated adopting Simulink
2 Vehicle Vibration Model of the ActiveSuspension with Seven DOF
21 DynamicModel of Active Suspension Figure 1 describes avehicle vibration model of the active suspension with sevenDOF including the bodyrsquos vertical motion pitching androlling motion and four vertical motions of the unsprungmass
In Figure 1 Ms represents the sprung mass M1 M2M4 and M3 represent the mass between the front andrear wheels on left and right sides respectively zs denotesthe vertical displacement of the body center of mass (7)120579 and 120593 denote the pitch and roll angle displacement zs1zs2 zs4 and zs3 represent the body vertical displacement inposition of the front and rear suspension on left and right
sides respectively z1 z2 z4 and z3 represent the verticaldisplacement in position of the front and rear wheel on leftand right sides respectively zq1 zq2 zq4 and zq3 representthe road irregularity excitation respectively k1 k2 k4 andk3 represent the elastic stiffness of the front and the rearsuspension kt1 kt2 kt4 and kt3 represent the elastic stiffnessof the front and rear wheel on left and right sides respectivelyc1 c2 c4 and c3 represent the damping of the front andrear suspension respectively f 1 f 2 f 4 and f 3 represent thecontrol force from the active controller in position of the frontand rear suspension on left and right sides respectively la andlb denote the distance of front and rear axle to the body centerof mass 119897119891 119897119903 denote the distance between the left and rightwheel V represents the vehiclersquos driving direction
22 Dynamic Differential Equation According to the vehiclevibration model of the active suspension the dynamic differ-ential equations with seven DOF are derived as follows
The dynamic differential equation of the bodyrsquos verticalmotion is listed as follows
119872119904119904 +4
sum119894=1
119865119894 = 0 (119894 = 1 4) (1)
The dynamic differential equation of the bodyrsquos pitchmotion is listed as follows
119868119910 minus (1198651 + 1198652) sdot 119897119886 + (1198653 + 1198654) sdot 119897119887 = 0 (2)
The dynamic differential equation of the bodyrsquos rollmotion is listed as follows
119868119909 + (1198652 minus 1198651) sdot 1198971198912 + (1198653 minus 1198654) sdot 119897119903
2 = 0 (3)
The dynamic differential equation of the vertical motionof four unsprung mass is listed as shown in equation (3)
119872119894119894 minus 119865119894 + 119896119905119894 (119911119894 minus 119911119902119894) = 0 (119894 = 1 4) (4)
where 119865119894 from (1) to (4) is expressed as
119865119894 = 119888119894 (119904119894 minus 119894) + 119896119894 (119911119904119894 minus 119911119894) minus 119891119894 (119894 = 1 4) (5)
Here 119904119894 is listed as follows
1199111199041 = 119911119904 minus 119897119886120579 minus 1205931198971198912
1199111199042 = 119911119904 minus 119897119886120579 + 1205931198971198912
1199111199043 = 119911119904 + 119897119887120579 + 1205931198971199032
1199111199044 = 119911119904 + 119897119887120579 minus 1205931198971199032
(6)
In the above expression 119904 and represent the verticalvibration and the pitch and roll angle acceleration of the bodycenter of mass respectively 1 2 4 and 3 represent the
Complexity 3
PID controller
Parameter self-adaptingfuzzy controller
Suspension system
ke
kec
minus
+
dudt
p i d
zsi
zs0
Figure 2 Principle diagram of the Fuzzy-PID controller
vertical vibration and the pitch and roll angle acceleration inposition of the front and rear wheel on left and right sidesrespectively 1 2 4 and 3 represent the vertical vibrationvelocity in position of the front and rear wheel on left andright sides respectively 1199041 1199042 1199044 and 1199043 represent thevertical vibration velocity in position of the front and rearsuspension on left and right sides respectively 119904 denotesthe vertical vibration velocity of the body center of mass Ixand Iy represent the rotary inertia about the 119909 and 119910 axisrespectively
3 Design of the Fuzzy Increment Controller ofAutomobile Active Suspension
31 Fuzzy Controller Design The fuzzy increment controllerincludes two parts the parameter self-adapting fuzzy con-troller and the PID controller where the fuzzy controlleradopts the deviation and its rate of change of the bodyvertical vibration velocity (119904119894) and the desired value (1199040)in the position of the front and rear suspension is the inputvariables the increments (ΔKp ΔKi and ΔKd) of the PIDcontroller parameters (Kp Ki and Kd) are derived accordingto a fuzzy control rule The working principle of fuzzyincrement controller is as shown in Figure 2
1198701015840119901 = 119870119901 + 120572119901 sdot Δ1198701199011198701015840119894 = 119870119894 + 120572119894 sdot Δ1198701198941198701015840119889 = 119870119889 + 120572119889 sdot Δ119870119889
(7)
where ke and kec represent the conversion factor from theexact value to the fuzzy variable 120572p 120572i and 120572d representthe modified coefficient of the increments value of the PIDcontroller parameters
311 Fuzzification of Input and Output Variable The inputvariable of the parameter self-adapting fuzzy controller (119904119894and 119904119894 (119894 = 1 4)) and the output variable of thecontroller (ΔKpΔKi andΔKd) are described by the followingseven fuzzy language variables such as NB (Negative Big)NM (Negative Middle) NS (Negative Small) ZO (Zero) PS(Positive Small) PM (PositiveMiddle) and PB (Positive Big)Here the domain ranges of the input variable (119904119894 and 119904119894)and the output variable (ΔKp ΔKi and ΔKd) are between minus3and 3 and between minus1 and 1 respectively The membership
NMNB ZO PM PB1
05
0Mem
bers
hip
degr
ee NS PS
minus2 2minus1minus3 0 31The domain range of input variable zsi (or zsi)
Figure 3 The membership functions of the input variable
functions of all the variables are similar and as shown inFigure 3
312 Construct Rule Base Table 1 describes the relationbetween the input and output variable where the fuzzy con-trol rules are characterized by If-Then statements involvingfuzzy linguistic variables For example the generic form ofthe fuzzy rules in the case of MIMO is as follows
If x is Ai and y is Bi Then z is Ci k is Di m is Ei119894 = 1 2 119899For Table 1 if the deviation of the body vertical vibration
velocity (119904119894) is NB and the change rate of the velocitydeviation (119904119894) is NB then the output variable ΔKp is PB ΔKiis NB and ΔKd is PS
313 Defuzzification The defuzzifier is utilized to yield anonfuzzy decision or control action from an inferred fuzzycontrol action by the fuzzy reasoner The method on thecenter of Gravity is used to calculate the defuzzified outputas follows 119880 = sum119873119894=1 120596119894119906119894sum119873119894=1 120596119894 where N is the number offuzzy rules ui is the output of fuzzy rule base and 119908119894 is theweight of ui
32 PIDController Design Adopting the deviation of verticalvibration velocity (119904119894) and its desired value (1199040) in theposition of the front and rear suspension as the input variablesof the PID controller in the Figure 2 an active control force(119891119894 (119894 = 1 4)) is obtained as shown in
119891 (119905) = 119870119901119890 (119905) + 119870119894 int119905
0119890 (119905) 119889119905 + 119870119889 119889119890 (119905)
119889119905 (8)
4 Complexity
Table 1 Fuzzy control rule of the PID increment parameters
ΔKpΔKiΔKd
119904119894NB NM NS ZE PS PM PB
119904119894NB
PB PB PM PM PS ZE ZENB NB NM NM NS ZE ZEPS NS NB NB NB NM PS
NMPB PB PM PS PS ZE NSNB NB NM NS NS ZE ZEPS NS NM NM NM NS ZE
NSPM PM PM PS ZE NS NSNB NM NS NS ZE PS PSZE NS NM NM NS NS ZE
ZEPM PM PS ZE NS NM NMNM NM NS ZE PS PM PMZE NS NS NS NS NS ZE
PSPS PS ZE NS NS NM NMNM NS ZE PS PS PM PMZE ZE ZE ZE ZE ZE ZE
PMPS ZE NS NM NM NM NBZE ZE PS PS PM PB PBPM NS PS PS PS PS PB
PBZE ZE NM NM NM NB NBZE ZE PS PM PM PB PBPB PM PM PM PS PS PB
where Kp Ki and Kd represent the gain coefficient of theproportion integral and differential The 119890(119905) denotes adeviation between the body vertical vibration velocity (119904119894)and its desired value (1199040 is set to zero) Here 119870119901 = 3000119870119894 = 20 and 119870119889 = 30
4 Simulation
41 Modelling Road Input Excitation with Four-Wheel Corre-lation in Time-Domain In order to validate the effectivenessof fuzzy increment controller the white noise random inputwith four wheels correlated in time-domain the sinusoidalinput and the pulse input of C-grade road surface areadopted respectively Here the white noise random input onthe left front wheel is shown as
1199021 (119905) = minus2120587V1198910119885119902 (119905) + 21205871198990radic119866119902 (1198990) V119908 (119905) (9)
where 1198990 denotes a referenced spatial frequency and the valueequals 01 (mminus1) 119866119902(1198990) equals 256 times 10minus6 (m2mminus1) and itdenotes a road roughness coefficient of C-grade road surface119908(119905) represents a white noise with mean zero V denotes thevehicle speed (V = 20 ms) and 1198910 equals 001
Considering the delay effect the random input on the leftrear wheel is denoted as 1199024(119905) = 1199021(119905 minus 120591) Here 120591 = 119871V
and L represents wheelbase So the random input on the leftrear wheel is expressed as
1199024 (119905) = minus1199021 (119905) + 2V1198851199021 (119905)119871 minus 2V1198851199024 (119905)
119871 (10)
According to the early literatures the random input onthe right front wheel is derived as
1199022 (119905) = 1199021 (119905) minus 12V1198851199021 (119905)119861 + 1199092 (11)
Also the random input on the right rear wheel is denotedas 1199023(119905) = 1199022(119905 minus 120591) Therefore the random input on theright rear wheel is calculated as
1199023 (119905) = minus1199022 (119905) + 2V1198851199022 (119905)119871 minus 2V1198851199023 (119905)
119871 (12)
where
1 = minus12V1198851199021 (119905)119861 + 1199092
2 =72V21198851199021 (119905)
1198612 minus 12V211990911198612 minus 6V1199092
119861 (13)
In formula (10) and formula (11) B denotes the lateraldistance between the left and right wheel 119871 represents thelongitudinal distance between the front and rear wheel (iethe wheelbase) and V is car speed at the moment
Complexity 5
q1 q2 q4
q3
Zq1 Zq2 Zq4
Zq3
-K- -K-
-K-
-K-
-K-
-K-
-K-
x1 x2
-K-
-K--K-
-K-
minus minus
minus
minus
minus
minus
minus
+
+
+
+
+
+
minus
minus
+
2 1 3
4
Add 3
Add 1Add 4
Add
Add 2
Integrator 4Integrator 1
Integrator Integrator 2Integrator 5
Integrator 3
2L
2L1
2L2
2L
Band-limitedwhite noise 1
12L
6B
2 lowast pi lowast n0
2 lowast pi lowast nc lowast
12 lowast B
72 lowast lowast (B lowast B)
12 lowast lowast (B lowast B)
1
s
1
s
1
s
1
s
1
s1
s
Figure 4 Random input model with four-wheel correlation in time-domain
Table 2 Suspension structure parameters of a test car
Variable Value Dimension119872119904 770 kg1198721 1198722 35 kg1198723 1198724 30 kg119868119910 830 kgsdotm2119868119909 235 kgsdotm21198701 1198702 206 KNsdotmminus11198703 1198704 152 KNsdotmminus11198621 1198622 1570 Nsdotssdotmminus11198623 1198624 1760 Nsdotssdotmminus11198701199051 1198701199052 138 KNsdotmminus11198701199053 1198701199054 138 KNsdotmminus1119897119891 119897119903 136 m119897119886 0958 m119897119887 1377 m
42 Simulation Module Design In order to validate thefeasibility of the fuzzy increment controller car suspensionparameters are as given in Table 2
Using MATLABSimulink the simulation modular ofactive suspension with seven DOF is designed Accordingto formula (9) to formula (12) a road excitation simulationmodule of white noise in time-domain is designed as shownin Figure 4 taking into account the delay and correlationcharacteristic between the wheels Here the submodule offuzzy increment controller in a wheel side is described asin Figure 5 The simulation submodule of the other threecontrollers is similar to Figure 5
43 Simulation Analysis Figures 6ndash8 show the accelerationrsquoscomparison results of the body vertical vibration pitchingand rolling motion under the condition of white noise roadsurface excitation adopting different control modes
As you can see from Figures 6ndash8 these indexes valueson the vertical vibration pitching and rolling angular accel-eration of the vehicle body have been improved adoptingthe Fuzzy-PID code compared to other modes under thecondition of white noise road surface excitation In otherwords the fuzzy increment controller can obviously reducethe bodyrsquos vibration because the acceleration peak amplitudeabove indexes is far less than other modes
Figures 9ndash11 show the accelerationrsquos comparison resultsof the body vertical vibration pitching and rolling motionunder the condition of pulse excitation adopting differentcontrol mode
FromFigures 9ndash11 we can see that the vibration amplitudeon vehicle bodyrsquos acceleration is also far less than othermodesadopting the Fuzzy-PID code under the condition of pulseexcitation
Figures 12ndash14 show the accelerationrsquos comparison resultsof the body vertical vibration pitching and rolling motionunder the condition of sinusoidal excitation adopting dif-ferent control mode As you can see from Figures 6ndash14 thefuzzy increment controller (ie the Fuzzy-PID code name)has good control effect in improving the body vertical vibra-tion acceleration pitching and rolling angular accelerationcomparingwith the independent types of controls such as thepassive suspension the PID control and the fuzzy control
In addition to comparison curves the root mean squarevalue of bodyrsquos acceleration is counted regarding four kinds of
6 Complexity
1Out 1
3000
kp
ap20
ki
ai
22
kec1
24
ke1
30
kd10ad
Zero-orderhold 3
Zero-orderhold 2
Scope
Saturation 3
Saturation 2
Product 2
Product 1
Product
MemoryFuzzy logiccontroller 1dudt
dudt
1In 2
-K-
-K-
+
+
+
+
+
+
+
+
+
1
s
times
times
times
Figure 5 The submodule of fuzzy increment controller
PassivePID
FuzzyFuzzy-PID
minus1
minus05
0
05
1
Body
acce
lera
tion
(ms
2)
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 6 Comparison result of the body vertical vibration acceler-ation
minus06
minus04
minus02
04
The p
itchi
ng an
gula
rac
cele
ratio
n(r
ads
2)
06
05 1 15 2 25 3 35 4 45 50Time (s)
PassivePID
FuzzyFuzzy-PID
02
0
Figure 7 Comparison result of the body pitching angular accelera-tion
minus15
minus1
minus05
0
05
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
1
15
05 1 15 2 25 3 35 4 45 50Time (s)
PassivePID
FuzzyFuzzy-PID
Figure 8 Comparison result of the body rolling angular accelera-tion
PassivePID
FuzzyFuzzy-PID
minus050
051
152
253
Body
acce
lera
tion
(ms
2)
1 2 3 4 50Time (s)
Figure 9 Comparison result of the body vertical vibration acceler-ation
Complexity 7Th
e pitc
hing
angu
lar
acce
lera
tion
(rad
s2)
minus1
0
1
2
3
4
1 2 3 4 50Time (s)
PassivePID
FuzzyFuzzy-PID
Figure 10 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus2
4
2
0
6
1 2 3 4 50Time (s)
Figure 11 Comparison result of the body rolling angular accelera-tion
PassivePID
FuzzyFuzzy-PID
minus15minus1
minus050
051
152
Body
acce
lera
tion
(ms
2)
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 12 Comparison result of the vertical vibration acceleration
controlmode under the condition of different speed as shownin Table 3
As seen from Table 3 the root mean square value ofthe bodyrsquos acceleration the pitching and rolling angularacceleration adopting the Fuzzy-PID mode reduces 375percent 289 percent and 262 percent compared with thepassivemode under the condition of white noise road surfaceexcitationThe rootmean square values of indexesmentioned
PassivePID
FuzzyFuzzy-PID
The p
itchi
ng an
gula
rac
cele
ratio
n(r
ads
2)
minus05
0
05
1
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 13 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus03
minus02
minus01
0
01
02
03
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 14 Comparison result of the rolling angular acceleration
above reduce 562 476 and 520 percent under the conditionof sinusoidal excitation respectively
You can also see that the root mean square values ofindexesmentioned above adopting the Fuzzy-PIDmode havebeen improved obviously compared to other modes at 30meters per second Through analysis we can see that thedesigned controller can reduce obviously the vehicle vibra-tion and has good control effect compared to the independentcontrol type
5 Conclusions
(1) The vibration model with seven degrees of freedomof automobile active suspension is derived and four fuzzyincrement controllers are designed based on 49 rules foradapting the different real-time road input information
(2) The white noise input model with four wheels cor-related in characteristics of time-domain is designed that iscloser to the actual road information input
(3) Using MATLABSimulink the simulation module ofactive suspension with seven DOF has been built and thefuzzy increment controller is validated taking the white noiseexcitation with four-wheel correlation in time-domain thesinusoidal excitation and the pulse excitation of C-graderoad surface as the road input The simulation results show
8 Complexity
Table 3 The root mean square value of acceleration
Input Speed Controlmode
Body verticalacceleration
Pitching angularacceleration
Rolling angularacceleration
White noiseexcitation
20ms
Passive 03800 02075 04937PID 02862 01720 04462Fuzzy 03031 01700 04237
Fuzzy-PID 02374 01475 03640
30ms
Passive 05383 02232 04247PID 04205 01936 03828Fuzzy 03987 01819 03217
Fuzzy-PID 03344 01673 02938
The sinusoidalexcitation
20ms
Passive 11386 05525 01858PID 07232 03722 00938Fuzzy 07950 03734 01159
Fuzzy-PID 04983 02891 00892
30ms
Passive 12356 02857 02111PID 07881 02055 01111Fuzzy 08587 02113 01225
Fuzzy-PID 06001 01653 01189
that designed fuzzy increment controller can reduce 375percent 289 percent and 262 percent in evaluation indexof the body vertical vibration acceleration pitching androlling acceleration compared with the passive mode underthe condition of white noise road surface excitation and canimprove 562 476 and 520 percent under the condition ofsinusoidal excitation respectively
In a word the designed fuzzy increment controller inthis paper is feasible to adapt to real-time change of roadsituations and can reduce obviously the vehicle vibrationand has a superior control effect compared to other controlmodesThe research achievements havemuch reference valuefor developing the product of suspension controller
As future work we intend to build the prototypes anddevelop products by single-chip technology
Conflicts of Interest
The authors declared no potential conflicts of interest withrespect to the research authorship andor publication of thisarticle
Acknowledgments
This work was supported in part by the Natural ScienceFoundation of China underGrant 61473139 and the joint fundof the Natural Science Foundation of Liaoning Province ofChina 201602368
References
[1] H Zhang E Wang F Min R Subash and C Su ldquoSkyhook-based semi-active control of full-vehicle suspension withmagneto-rheological dampersrdquo Chinese Journal of MechanicalEngineering vol 26 no 3 pp 498ndash505 2013
[2] H-B Ren S-Z Chen Y-Z Zhao G Liu and L YangldquoObserver-based hybrid control algorithm for semi-active sus-pension systemsrdquo Journal of Central South University vol 23no 9 pp 2268ndash2275 2016
[3] D Singh and M L Aggarwal ldquoPassenger seat vibration controlof a semi-active quarter car system with hybrid fuzzy-PIDapproachrdquo International Journal of Dynamics and Control vol5 no 2 pp 287ndash296 2017
[4] H-P Du and N Zhang ldquoRobust active suspension designsubject to vehicle inertial parameter variationsrdquo InternationalJournal of Automation and Computing vol 7 no 4 pp 419ndash4272010
[5] Y-J Liu and S Tong ldquoAdaptive fuzzy control for a classof unknown nonlinear dynamical systemsrdquo Fuzzy Sets andSystems vol 263 pp 49ndash70 2015
[6] Y-J Liu Y Gao S Tong andY Li ldquoFuzzy approximation-basedadaptive backstepping optimal control for a class of nonlineardiscrete-time systems with dead-zonerdquo IEEE Transactions onFuzzy Systems 1 page 2015
[7] Y Gao and Y-J Liu ldquoAdaptive fuzzy optimal control usingdirect heuristic dynamic programming for chaotic discrete-time systemrdquo Journal of Vibration and Control vol 22 no 2pp 595ndash603 2016
[8] H Li G Chen X Liao and T Huang ldquoLeader-followingconsensus of discrete-time multiagent systems with encoding-decodingrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 63 no 4 pp 401ndash405 2016
[9] H Li C Huang G Chen X Liao and T Huang ldquoDistributedConsensus Optimization in Multiagent Networks With Time-Varying Directed Topologies and Quantized CommunicationrdquoIEEE Transactions on Cybernetics 2017
[10] C Huang L Chen H Jiang C Yuan and T Xia ldquoFuzzy chaoscontrol for vehicle lateral dynamics based on active suspensionsystemrdquo Chinese Journal of Mechanical Engineering vol 27 no4 pp 793ndash801 2014
Complexity 9
[11] H Li S Liu Y C Soh and L Xie ldquoEvent-Triggered Communi-cation and Data Rate Constraint for Distributed OptimizationofMultiagent Systemsrdquo IEEETransactions on SystemsMan andCybernetics Systems pp 1ndash12
[12] H Li G Chen T Huang and Z Dong ldquoHigh-performanceconsensus control in networked systems with limited band-width communication and time-varying directed topologiesrdquoIEEE Transactions on Neural Networks and Learning Systemspp 1ndash12 2016
[13] S Riaz and L Khan ldquoNeuroFuzzy Adaptive Control for Full-Car Nonlinear Active Suspension withOnboard Antilock Brak-ing Systemrdquo Arabian Journal for Science and Engineering vol40 no 12 pp 3483ndash3505 2015
[14] M M Zirkohi and T-C Lin ldquoInterval type-2 fuzzy-neuralnetwork indirect adaptive sliding mode control for an activesuspension systemrdquo Nonlinear Dynamics vol 79 no 1 pp 513ndash526 2015
[15] L Balamurugan J Jancirani and M A Eltantawie ldquoGener-alized magnetorheological (MR) damper model and its appli-cation in semi-active control of vehicle suspension systemrdquoInternational Journal of Automotive Technology vol 15 no 3pp 419ndash427 2014
[16] H L Zhang E RWangN Zhang FMin R Subash andC SuldquoSemi-active sliding mode control of vehicle suspension withmagneto-rheological damperrdquo Chinese Journal of MechanicalEngineering vol 28 no 1 pp 63ndash75 2015
[17] S Bououden M Chadli L Zhang and T Yang ldquoConstrainedmodel predictive control for time-varying delay systems Appli-cation to an active car suspensionrdquo International Journal ofControl Automation and Systems vol 14 no 1 pp 51ndash58 2016
[18] L Wu and W-J Zhang ldquoHierarchical modeling of semi-activecontrol of a full motorcycle suspension with six degrees offreedomsrdquo International Journal of Automotive Technology vol11 no 1 pp 27ndash32 2010
[19] ZMao YWang B Jiang andG Tao ldquoFault diagnosis for a classof active suspension systems with dynamic actuatorsrsquo faultsrdquoInternational Journal of Control Automation and Systems vol14 no 5 pp 1160ndash1172 2016
[20] H Trabelsi P-A Yvars J Louati and M Haddar ldquoEvaluationof the effectiveness of the interval computation method tosimulate the dynamic behavior of subdefinite system applica-tion on an active suspension systemrdquo International Journal onInteractive Design and Manufacturing vol 9 no 2 pp 83ndash962015
[21] CWang K DengW Zhao G Zhou andX Li ldquoRobust controlfor active suspension system under steering conditionrdquo ScienceChina Technological Sciences vol 60 no 2 pp 199ndash208 2017
[22] X Dong D Zhao B Yang and C Han ldquoFractional-ordercontrol of active suspension actuator based on parallel adaptiveclonal selection algorithmrdquo Journal of Mechanical Science andTechnology vol 30 no 6 pp 2769ndash2781 2016
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2 Complexity
lr
M4M3
M2 M1
kt3
k3
k1
kt2 kt1
k2
k4
kt4
f1
f3
f2
f4c3
c1c2
c4
x
V
la
lf
y
z
lb
zq4zq3
z4z3
z1
zq1
zs
z2
zs2
zq2
zs1
Figure 1 Vehicle model of the active suspension with seven DOF
to generate the desired damping force and adjust the volt-age level to MR damper based on the quarter car vehiclemodel of semiactive suspension [15] Zhang et al designed asemiactive controller based on the inverse model and slidingmode control strategies for the quarter-vehicle suspensionwith the magnetorheological damper [16] Bououden et alinvestigated the problem of time-varying delays and inputconstraints for active suspension systems with a quarter-vehicle model based on the Lyapunov-Krasovskii method[17] From the analysis results on automobile active suspen-sion research we learned that much of the relevant literaturefocus on a quarter- or a half-car model that cannot fullyreflect or evaluate riding comfort of a whole vehicle [18ndash22]So it is our goal to research the time-domain response of theautomobile active suspension with seven DOF for decreasingthe body vibration considering the pitching and rollingmotion under the condition of the white noise input withfour wheels correlated effects and different road excitationAt last the submodule of fuzzy increment controller and therandom inputmodel have been given and the effectiveness ofproposed controller has been validated adopting Simulink
2 Vehicle Vibration Model of the ActiveSuspension with Seven DOF
21 DynamicModel of Active Suspension Figure 1 describes avehicle vibration model of the active suspension with sevenDOF including the bodyrsquos vertical motion pitching androlling motion and four vertical motions of the unsprungmass
In Figure 1 Ms represents the sprung mass M1 M2M4 and M3 represent the mass between the front andrear wheels on left and right sides respectively zs denotesthe vertical displacement of the body center of mass (7)120579 and 120593 denote the pitch and roll angle displacement zs1zs2 zs4 and zs3 represent the body vertical displacement inposition of the front and rear suspension on left and right
sides respectively z1 z2 z4 and z3 represent the verticaldisplacement in position of the front and rear wheel on leftand right sides respectively zq1 zq2 zq4 and zq3 representthe road irregularity excitation respectively k1 k2 k4 andk3 represent the elastic stiffness of the front and the rearsuspension kt1 kt2 kt4 and kt3 represent the elastic stiffnessof the front and rear wheel on left and right sides respectivelyc1 c2 c4 and c3 represent the damping of the front andrear suspension respectively f 1 f 2 f 4 and f 3 represent thecontrol force from the active controller in position of the frontand rear suspension on left and right sides respectively la andlb denote the distance of front and rear axle to the body centerof mass 119897119891 119897119903 denote the distance between the left and rightwheel V represents the vehiclersquos driving direction
22 Dynamic Differential Equation According to the vehiclevibration model of the active suspension the dynamic differ-ential equations with seven DOF are derived as follows
The dynamic differential equation of the bodyrsquos verticalmotion is listed as follows
119872119904119904 +4
sum119894=1
119865119894 = 0 (119894 = 1 4) (1)
The dynamic differential equation of the bodyrsquos pitchmotion is listed as follows
119868119910 minus (1198651 + 1198652) sdot 119897119886 + (1198653 + 1198654) sdot 119897119887 = 0 (2)
The dynamic differential equation of the bodyrsquos rollmotion is listed as follows
119868119909 + (1198652 minus 1198651) sdot 1198971198912 + (1198653 minus 1198654) sdot 119897119903
2 = 0 (3)
The dynamic differential equation of the vertical motionof four unsprung mass is listed as shown in equation (3)
119872119894119894 minus 119865119894 + 119896119905119894 (119911119894 minus 119911119902119894) = 0 (119894 = 1 4) (4)
where 119865119894 from (1) to (4) is expressed as
119865119894 = 119888119894 (119904119894 minus 119894) + 119896119894 (119911119904119894 minus 119911119894) minus 119891119894 (119894 = 1 4) (5)
Here 119904119894 is listed as follows
1199111199041 = 119911119904 minus 119897119886120579 minus 1205931198971198912
1199111199042 = 119911119904 minus 119897119886120579 + 1205931198971198912
1199111199043 = 119911119904 + 119897119887120579 + 1205931198971199032
1199111199044 = 119911119904 + 119897119887120579 minus 1205931198971199032
(6)
In the above expression 119904 and represent the verticalvibration and the pitch and roll angle acceleration of the bodycenter of mass respectively 1 2 4 and 3 represent the
Complexity 3
PID controller
Parameter self-adaptingfuzzy controller
Suspension system
ke
kec
minus
+
dudt
p i d
zsi
zs0
Figure 2 Principle diagram of the Fuzzy-PID controller
vertical vibration and the pitch and roll angle acceleration inposition of the front and rear wheel on left and right sidesrespectively 1 2 4 and 3 represent the vertical vibrationvelocity in position of the front and rear wheel on left andright sides respectively 1199041 1199042 1199044 and 1199043 represent thevertical vibration velocity in position of the front and rearsuspension on left and right sides respectively 119904 denotesthe vertical vibration velocity of the body center of mass Ixand Iy represent the rotary inertia about the 119909 and 119910 axisrespectively
3 Design of the Fuzzy Increment Controller ofAutomobile Active Suspension
31 Fuzzy Controller Design The fuzzy increment controllerincludes two parts the parameter self-adapting fuzzy con-troller and the PID controller where the fuzzy controlleradopts the deviation and its rate of change of the bodyvertical vibration velocity (119904119894) and the desired value (1199040)in the position of the front and rear suspension is the inputvariables the increments (ΔKp ΔKi and ΔKd) of the PIDcontroller parameters (Kp Ki and Kd) are derived accordingto a fuzzy control rule The working principle of fuzzyincrement controller is as shown in Figure 2
1198701015840119901 = 119870119901 + 120572119901 sdot Δ1198701199011198701015840119894 = 119870119894 + 120572119894 sdot Δ1198701198941198701015840119889 = 119870119889 + 120572119889 sdot Δ119870119889
(7)
where ke and kec represent the conversion factor from theexact value to the fuzzy variable 120572p 120572i and 120572d representthe modified coefficient of the increments value of the PIDcontroller parameters
311 Fuzzification of Input and Output Variable The inputvariable of the parameter self-adapting fuzzy controller (119904119894and 119904119894 (119894 = 1 4)) and the output variable of thecontroller (ΔKpΔKi andΔKd) are described by the followingseven fuzzy language variables such as NB (Negative Big)NM (Negative Middle) NS (Negative Small) ZO (Zero) PS(Positive Small) PM (PositiveMiddle) and PB (Positive Big)Here the domain ranges of the input variable (119904119894 and 119904119894)and the output variable (ΔKp ΔKi and ΔKd) are between minus3and 3 and between minus1 and 1 respectively The membership
NMNB ZO PM PB1
05
0Mem
bers
hip
degr
ee NS PS
minus2 2minus1minus3 0 31The domain range of input variable zsi (or zsi)
Figure 3 The membership functions of the input variable
functions of all the variables are similar and as shown inFigure 3
312 Construct Rule Base Table 1 describes the relationbetween the input and output variable where the fuzzy con-trol rules are characterized by If-Then statements involvingfuzzy linguistic variables For example the generic form ofthe fuzzy rules in the case of MIMO is as follows
If x is Ai and y is Bi Then z is Ci k is Di m is Ei119894 = 1 2 119899For Table 1 if the deviation of the body vertical vibration
velocity (119904119894) is NB and the change rate of the velocitydeviation (119904119894) is NB then the output variable ΔKp is PB ΔKiis NB and ΔKd is PS
313 Defuzzification The defuzzifier is utilized to yield anonfuzzy decision or control action from an inferred fuzzycontrol action by the fuzzy reasoner The method on thecenter of Gravity is used to calculate the defuzzified outputas follows 119880 = sum119873119894=1 120596119894119906119894sum119873119894=1 120596119894 where N is the number offuzzy rules ui is the output of fuzzy rule base and 119908119894 is theweight of ui
32 PIDController Design Adopting the deviation of verticalvibration velocity (119904119894) and its desired value (1199040) in theposition of the front and rear suspension as the input variablesof the PID controller in the Figure 2 an active control force(119891119894 (119894 = 1 4)) is obtained as shown in
119891 (119905) = 119870119901119890 (119905) + 119870119894 int119905
0119890 (119905) 119889119905 + 119870119889 119889119890 (119905)
119889119905 (8)
4 Complexity
Table 1 Fuzzy control rule of the PID increment parameters
ΔKpΔKiΔKd
119904119894NB NM NS ZE PS PM PB
119904119894NB
PB PB PM PM PS ZE ZENB NB NM NM NS ZE ZEPS NS NB NB NB NM PS
NMPB PB PM PS PS ZE NSNB NB NM NS NS ZE ZEPS NS NM NM NM NS ZE
NSPM PM PM PS ZE NS NSNB NM NS NS ZE PS PSZE NS NM NM NS NS ZE
ZEPM PM PS ZE NS NM NMNM NM NS ZE PS PM PMZE NS NS NS NS NS ZE
PSPS PS ZE NS NS NM NMNM NS ZE PS PS PM PMZE ZE ZE ZE ZE ZE ZE
PMPS ZE NS NM NM NM NBZE ZE PS PS PM PB PBPM NS PS PS PS PS PB
PBZE ZE NM NM NM NB NBZE ZE PS PM PM PB PBPB PM PM PM PS PS PB
where Kp Ki and Kd represent the gain coefficient of theproportion integral and differential The 119890(119905) denotes adeviation between the body vertical vibration velocity (119904119894)and its desired value (1199040 is set to zero) Here 119870119901 = 3000119870119894 = 20 and 119870119889 = 30
4 Simulation
41 Modelling Road Input Excitation with Four-Wheel Corre-lation in Time-Domain In order to validate the effectivenessof fuzzy increment controller the white noise random inputwith four wheels correlated in time-domain the sinusoidalinput and the pulse input of C-grade road surface areadopted respectively Here the white noise random input onthe left front wheel is shown as
1199021 (119905) = minus2120587V1198910119885119902 (119905) + 21205871198990radic119866119902 (1198990) V119908 (119905) (9)
where 1198990 denotes a referenced spatial frequency and the valueequals 01 (mminus1) 119866119902(1198990) equals 256 times 10minus6 (m2mminus1) and itdenotes a road roughness coefficient of C-grade road surface119908(119905) represents a white noise with mean zero V denotes thevehicle speed (V = 20 ms) and 1198910 equals 001
Considering the delay effect the random input on the leftrear wheel is denoted as 1199024(119905) = 1199021(119905 minus 120591) Here 120591 = 119871V
and L represents wheelbase So the random input on the leftrear wheel is expressed as
1199024 (119905) = minus1199021 (119905) + 2V1198851199021 (119905)119871 minus 2V1198851199024 (119905)
119871 (10)
According to the early literatures the random input onthe right front wheel is derived as
1199022 (119905) = 1199021 (119905) minus 12V1198851199021 (119905)119861 + 1199092 (11)
Also the random input on the right rear wheel is denotedas 1199023(119905) = 1199022(119905 minus 120591) Therefore the random input on theright rear wheel is calculated as
1199023 (119905) = minus1199022 (119905) + 2V1198851199022 (119905)119871 minus 2V1198851199023 (119905)
119871 (12)
where
1 = minus12V1198851199021 (119905)119861 + 1199092
2 =72V21198851199021 (119905)
1198612 minus 12V211990911198612 minus 6V1199092
119861 (13)
In formula (10) and formula (11) B denotes the lateraldistance between the left and right wheel 119871 represents thelongitudinal distance between the front and rear wheel (iethe wheelbase) and V is car speed at the moment
Complexity 5
q1 q2 q4
q3
Zq1 Zq2 Zq4
Zq3
-K- -K-
-K-
-K-
-K-
-K-
-K-
x1 x2
-K-
-K--K-
-K-
minus minus
minus
minus
minus
minus
minus
+
+
+
+
+
+
minus
minus
+
2 1 3
4
Add 3
Add 1Add 4
Add
Add 2
Integrator 4Integrator 1
Integrator Integrator 2Integrator 5
Integrator 3
2L
2L1
2L2
2L
Band-limitedwhite noise 1
12L
6B
2 lowast pi lowast n0
2 lowast pi lowast nc lowast
12 lowast B
72 lowast lowast (B lowast B)
12 lowast lowast (B lowast B)
1
s
1
s
1
s
1
s
1
s1
s
Figure 4 Random input model with four-wheel correlation in time-domain
Table 2 Suspension structure parameters of a test car
Variable Value Dimension119872119904 770 kg1198721 1198722 35 kg1198723 1198724 30 kg119868119910 830 kgsdotm2119868119909 235 kgsdotm21198701 1198702 206 KNsdotmminus11198703 1198704 152 KNsdotmminus11198621 1198622 1570 Nsdotssdotmminus11198623 1198624 1760 Nsdotssdotmminus11198701199051 1198701199052 138 KNsdotmminus11198701199053 1198701199054 138 KNsdotmminus1119897119891 119897119903 136 m119897119886 0958 m119897119887 1377 m
42 Simulation Module Design In order to validate thefeasibility of the fuzzy increment controller car suspensionparameters are as given in Table 2
Using MATLABSimulink the simulation modular ofactive suspension with seven DOF is designed Accordingto formula (9) to formula (12) a road excitation simulationmodule of white noise in time-domain is designed as shownin Figure 4 taking into account the delay and correlationcharacteristic between the wheels Here the submodule offuzzy increment controller in a wheel side is described asin Figure 5 The simulation submodule of the other threecontrollers is similar to Figure 5
43 Simulation Analysis Figures 6ndash8 show the accelerationrsquoscomparison results of the body vertical vibration pitchingand rolling motion under the condition of white noise roadsurface excitation adopting different control modes
As you can see from Figures 6ndash8 these indexes valueson the vertical vibration pitching and rolling angular accel-eration of the vehicle body have been improved adoptingthe Fuzzy-PID code compared to other modes under thecondition of white noise road surface excitation In otherwords the fuzzy increment controller can obviously reducethe bodyrsquos vibration because the acceleration peak amplitudeabove indexes is far less than other modes
Figures 9ndash11 show the accelerationrsquos comparison resultsof the body vertical vibration pitching and rolling motionunder the condition of pulse excitation adopting differentcontrol mode
FromFigures 9ndash11 we can see that the vibration amplitudeon vehicle bodyrsquos acceleration is also far less than othermodesadopting the Fuzzy-PID code under the condition of pulseexcitation
Figures 12ndash14 show the accelerationrsquos comparison resultsof the body vertical vibration pitching and rolling motionunder the condition of sinusoidal excitation adopting dif-ferent control mode As you can see from Figures 6ndash14 thefuzzy increment controller (ie the Fuzzy-PID code name)has good control effect in improving the body vertical vibra-tion acceleration pitching and rolling angular accelerationcomparingwith the independent types of controls such as thepassive suspension the PID control and the fuzzy control
In addition to comparison curves the root mean squarevalue of bodyrsquos acceleration is counted regarding four kinds of
6 Complexity
1Out 1
3000
kp
ap20
ki
ai
22
kec1
24
ke1
30
kd10ad
Zero-orderhold 3
Zero-orderhold 2
Scope
Saturation 3
Saturation 2
Product 2
Product 1
Product
MemoryFuzzy logiccontroller 1dudt
dudt
1In 2
-K-
-K-
+
+
+
+
+
+
+
+
+
1
s
times
times
times
Figure 5 The submodule of fuzzy increment controller
PassivePID
FuzzyFuzzy-PID
minus1
minus05
0
05
1
Body
acce
lera
tion
(ms
2)
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 6 Comparison result of the body vertical vibration acceler-ation
minus06
minus04
minus02
04
The p
itchi
ng an
gula
rac
cele
ratio
n(r
ads
2)
06
05 1 15 2 25 3 35 4 45 50Time (s)
PassivePID
FuzzyFuzzy-PID
02
0
Figure 7 Comparison result of the body pitching angular accelera-tion
minus15
minus1
minus05
0
05
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
1
15
05 1 15 2 25 3 35 4 45 50Time (s)
PassivePID
FuzzyFuzzy-PID
Figure 8 Comparison result of the body rolling angular accelera-tion
PassivePID
FuzzyFuzzy-PID
minus050
051
152
253
Body
acce
lera
tion
(ms
2)
1 2 3 4 50Time (s)
Figure 9 Comparison result of the body vertical vibration acceler-ation
Complexity 7Th
e pitc
hing
angu
lar
acce
lera
tion
(rad
s2)
minus1
0
1
2
3
4
1 2 3 4 50Time (s)
PassivePID
FuzzyFuzzy-PID
Figure 10 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus2
4
2
0
6
1 2 3 4 50Time (s)
Figure 11 Comparison result of the body rolling angular accelera-tion
PassivePID
FuzzyFuzzy-PID
minus15minus1
minus050
051
152
Body
acce
lera
tion
(ms
2)
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 12 Comparison result of the vertical vibration acceleration
controlmode under the condition of different speed as shownin Table 3
As seen from Table 3 the root mean square value ofthe bodyrsquos acceleration the pitching and rolling angularacceleration adopting the Fuzzy-PID mode reduces 375percent 289 percent and 262 percent compared with thepassivemode under the condition of white noise road surfaceexcitationThe rootmean square values of indexesmentioned
PassivePID
FuzzyFuzzy-PID
The p
itchi
ng an
gula
rac
cele
ratio
n(r
ads
2)
minus05
0
05
1
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 13 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus03
minus02
minus01
0
01
02
03
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 14 Comparison result of the rolling angular acceleration
above reduce 562 476 and 520 percent under the conditionof sinusoidal excitation respectively
You can also see that the root mean square values ofindexesmentioned above adopting the Fuzzy-PIDmode havebeen improved obviously compared to other modes at 30meters per second Through analysis we can see that thedesigned controller can reduce obviously the vehicle vibra-tion and has good control effect compared to the independentcontrol type
5 Conclusions
(1) The vibration model with seven degrees of freedomof automobile active suspension is derived and four fuzzyincrement controllers are designed based on 49 rules foradapting the different real-time road input information
(2) The white noise input model with four wheels cor-related in characteristics of time-domain is designed that iscloser to the actual road information input
(3) Using MATLABSimulink the simulation module ofactive suspension with seven DOF has been built and thefuzzy increment controller is validated taking the white noiseexcitation with four-wheel correlation in time-domain thesinusoidal excitation and the pulse excitation of C-graderoad surface as the road input The simulation results show
8 Complexity
Table 3 The root mean square value of acceleration
Input Speed Controlmode
Body verticalacceleration
Pitching angularacceleration
Rolling angularacceleration
White noiseexcitation
20ms
Passive 03800 02075 04937PID 02862 01720 04462Fuzzy 03031 01700 04237
Fuzzy-PID 02374 01475 03640
30ms
Passive 05383 02232 04247PID 04205 01936 03828Fuzzy 03987 01819 03217
Fuzzy-PID 03344 01673 02938
The sinusoidalexcitation
20ms
Passive 11386 05525 01858PID 07232 03722 00938Fuzzy 07950 03734 01159
Fuzzy-PID 04983 02891 00892
30ms
Passive 12356 02857 02111PID 07881 02055 01111Fuzzy 08587 02113 01225
Fuzzy-PID 06001 01653 01189
that designed fuzzy increment controller can reduce 375percent 289 percent and 262 percent in evaluation indexof the body vertical vibration acceleration pitching androlling acceleration compared with the passive mode underthe condition of white noise road surface excitation and canimprove 562 476 and 520 percent under the condition ofsinusoidal excitation respectively
In a word the designed fuzzy increment controller inthis paper is feasible to adapt to real-time change of roadsituations and can reduce obviously the vehicle vibrationand has a superior control effect compared to other controlmodesThe research achievements havemuch reference valuefor developing the product of suspension controller
As future work we intend to build the prototypes anddevelop products by single-chip technology
Conflicts of Interest
The authors declared no potential conflicts of interest withrespect to the research authorship andor publication of thisarticle
Acknowledgments
This work was supported in part by the Natural ScienceFoundation of China underGrant 61473139 and the joint fundof the Natural Science Foundation of Liaoning Province ofChina 201602368
References
[1] H Zhang E Wang F Min R Subash and C Su ldquoSkyhook-based semi-active control of full-vehicle suspension withmagneto-rheological dampersrdquo Chinese Journal of MechanicalEngineering vol 26 no 3 pp 498ndash505 2013
[2] H-B Ren S-Z Chen Y-Z Zhao G Liu and L YangldquoObserver-based hybrid control algorithm for semi-active sus-pension systemsrdquo Journal of Central South University vol 23no 9 pp 2268ndash2275 2016
[3] D Singh and M L Aggarwal ldquoPassenger seat vibration controlof a semi-active quarter car system with hybrid fuzzy-PIDapproachrdquo International Journal of Dynamics and Control vol5 no 2 pp 287ndash296 2017
[4] H-P Du and N Zhang ldquoRobust active suspension designsubject to vehicle inertial parameter variationsrdquo InternationalJournal of Automation and Computing vol 7 no 4 pp 419ndash4272010
[5] Y-J Liu and S Tong ldquoAdaptive fuzzy control for a classof unknown nonlinear dynamical systemsrdquo Fuzzy Sets andSystems vol 263 pp 49ndash70 2015
[6] Y-J Liu Y Gao S Tong andY Li ldquoFuzzy approximation-basedadaptive backstepping optimal control for a class of nonlineardiscrete-time systems with dead-zonerdquo IEEE Transactions onFuzzy Systems 1 page 2015
[7] Y Gao and Y-J Liu ldquoAdaptive fuzzy optimal control usingdirect heuristic dynamic programming for chaotic discrete-time systemrdquo Journal of Vibration and Control vol 22 no 2pp 595ndash603 2016
[8] H Li G Chen X Liao and T Huang ldquoLeader-followingconsensus of discrete-time multiagent systems with encoding-decodingrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 63 no 4 pp 401ndash405 2016
[9] H Li C Huang G Chen X Liao and T Huang ldquoDistributedConsensus Optimization in Multiagent Networks With Time-Varying Directed Topologies and Quantized CommunicationrdquoIEEE Transactions on Cybernetics 2017
[10] C Huang L Chen H Jiang C Yuan and T Xia ldquoFuzzy chaoscontrol for vehicle lateral dynamics based on active suspensionsystemrdquo Chinese Journal of Mechanical Engineering vol 27 no4 pp 793ndash801 2014
Complexity 9
[11] H Li S Liu Y C Soh and L Xie ldquoEvent-Triggered Communi-cation and Data Rate Constraint for Distributed OptimizationofMultiagent Systemsrdquo IEEETransactions on SystemsMan andCybernetics Systems pp 1ndash12
[12] H Li G Chen T Huang and Z Dong ldquoHigh-performanceconsensus control in networked systems with limited band-width communication and time-varying directed topologiesrdquoIEEE Transactions on Neural Networks and Learning Systemspp 1ndash12 2016
[13] S Riaz and L Khan ldquoNeuroFuzzy Adaptive Control for Full-Car Nonlinear Active Suspension withOnboard Antilock Brak-ing Systemrdquo Arabian Journal for Science and Engineering vol40 no 12 pp 3483ndash3505 2015
[14] M M Zirkohi and T-C Lin ldquoInterval type-2 fuzzy-neuralnetwork indirect adaptive sliding mode control for an activesuspension systemrdquo Nonlinear Dynamics vol 79 no 1 pp 513ndash526 2015
[15] L Balamurugan J Jancirani and M A Eltantawie ldquoGener-alized magnetorheological (MR) damper model and its appli-cation in semi-active control of vehicle suspension systemrdquoInternational Journal of Automotive Technology vol 15 no 3pp 419ndash427 2014
[16] H L Zhang E RWangN Zhang FMin R Subash andC SuldquoSemi-active sliding mode control of vehicle suspension withmagneto-rheological damperrdquo Chinese Journal of MechanicalEngineering vol 28 no 1 pp 63ndash75 2015
[17] S Bououden M Chadli L Zhang and T Yang ldquoConstrainedmodel predictive control for time-varying delay systems Appli-cation to an active car suspensionrdquo International Journal ofControl Automation and Systems vol 14 no 1 pp 51ndash58 2016
[18] L Wu and W-J Zhang ldquoHierarchical modeling of semi-activecontrol of a full motorcycle suspension with six degrees offreedomsrdquo International Journal of Automotive Technology vol11 no 1 pp 27ndash32 2010
[19] ZMao YWang B Jiang andG Tao ldquoFault diagnosis for a classof active suspension systems with dynamic actuatorsrsquo faultsrdquoInternational Journal of Control Automation and Systems vol14 no 5 pp 1160ndash1172 2016
[20] H Trabelsi P-A Yvars J Louati and M Haddar ldquoEvaluationof the effectiveness of the interval computation method tosimulate the dynamic behavior of subdefinite system applica-tion on an active suspension systemrdquo International Journal onInteractive Design and Manufacturing vol 9 no 2 pp 83ndash962015
[21] CWang K DengW Zhao G Zhou andX Li ldquoRobust controlfor active suspension system under steering conditionrdquo ScienceChina Technological Sciences vol 60 no 2 pp 199ndash208 2017
[22] X Dong D Zhao B Yang and C Han ldquoFractional-ordercontrol of active suspension actuator based on parallel adaptiveclonal selection algorithmrdquo Journal of Mechanical Science andTechnology vol 30 no 6 pp 2769ndash2781 2016
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Hindawiwwwhindawicom Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Hindawiwwwhindawicom Volume 2018Volume 2018
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Complexity 3
PID controller
Parameter self-adaptingfuzzy controller
Suspension system
ke
kec
minus
+
dudt
p i d
zsi
zs0
Figure 2 Principle diagram of the Fuzzy-PID controller
vertical vibration and the pitch and roll angle acceleration inposition of the front and rear wheel on left and right sidesrespectively 1 2 4 and 3 represent the vertical vibrationvelocity in position of the front and rear wheel on left andright sides respectively 1199041 1199042 1199044 and 1199043 represent thevertical vibration velocity in position of the front and rearsuspension on left and right sides respectively 119904 denotesthe vertical vibration velocity of the body center of mass Ixand Iy represent the rotary inertia about the 119909 and 119910 axisrespectively
3 Design of the Fuzzy Increment Controller ofAutomobile Active Suspension
31 Fuzzy Controller Design The fuzzy increment controllerincludes two parts the parameter self-adapting fuzzy con-troller and the PID controller where the fuzzy controlleradopts the deviation and its rate of change of the bodyvertical vibration velocity (119904119894) and the desired value (1199040)in the position of the front and rear suspension is the inputvariables the increments (ΔKp ΔKi and ΔKd) of the PIDcontroller parameters (Kp Ki and Kd) are derived accordingto a fuzzy control rule The working principle of fuzzyincrement controller is as shown in Figure 2
1198701015840119901 = 119870119901 + 120572119901 sdot Δ1198701199011198701015840119894 = 119870119894 + 120572119894 sdot Δ1198701198941198701015840119889 = 119870119889 + 120572119889 sdot Δ119870119889
(7)
where ke and kec represent the conversion factor from theexact value to the fuzzy variable 120572p 120572i and 120572d representthe modified coefficient of the increments value of the PIDcontroller parameters
311 Fuzzification of Input and Output Variable The inputvariable of the parameter self-adapting fuzzy controller (119904119894and 119904119894 (119894 = 1 4)) and the output variable of thecontroller (ΔKpΔKi andΔKd) are described by the followingseven fuzzy language variables such as NB (Negative Big)NM (Negative Middle) NS (Negative Small) ZO (Zero) PS(Positive Small) PM (PositiveMiddle) and PB (Positive Big)Here the domain ranges of the input variable (119904119894 and 119904119894)and the output variable (ΔKp ΔKi and ΔKd) are between minus3and 3 and between minus1 and 1 respectively The membership
NMNB ZO PM PB1
05
0Mem
bers
hip
degr
ee NS PS
minus2 2minus1minus3 0 31The domain range of input variable zsi (or zsi)
Figure 3 The membership functions of the input variable
functions of all the variables are similar and as shown inFigure 3
312 Construct Rule Base Table 1 describes the relationbetween the input and output variable where the fuzzy con-trol rules are characterized by If-Then statements involvingfuzzy linguistic variables For example the generic form ofthe fuzzy rules in the case of MIMO is as follows
If x is Ai and y is Bi Then z is Ci k is Di m is Ei119894 = 1 2 119899For Table 1 if the deviation of the body vertical vibration
velocity (119904119894) is NB and the change rate of the velocitydeviation (119904119894) is NB then the output variable ΔKp is PB ΔKiis NB and ΔKd is PS
313 Defuzzification The defuzzifier is utilized to yield anonfuzzy decision or control action from an inferred fuzzycontrol action by the fuzzy reasoner The method on thecenter of Gravity is used to calculate the defuzzified outputas follows 119880 = sum119873119894=1 120596119894119906119894sum119873119894=1 120596119894 where N is the number offuzzy rules ui is the output of fuzzy rule base and 119908119894 is theweight of ui
32 PIDController Design Adopting the deviation of verticalvibration velocity (119904119894) and its desired value (1199040) in theposition of the front and rear suspension as the input variablesof the PID controller in the Figure 2 an active control force(119891119894 (119894 = 1 4)) is obtained as shown in
119891 (119905) = 119870119901119890 (119905) + 119870119894 int119905
0119890 (119905) 119889119905 + 119870119889 119889119890 (119905)
119889119905 (8)
4 Complexity
Table 1 Fuzzy control rule of the PID increment parameters
ΔKpΔKiΔKd
119904119894NB NM NS ZE PS PM PB
119904119894NB
PB PB PM PM PS ZE ZENB NB NM NM NS ZE ZEPS NS NB NB NB NM PS
NMPB PB PM PS PS ZE NSNB NB NM NS NS ZE ZEPS NS NM NM NM NS ZE
NSPM PM PM PS ZE NS NSNB NM NS NS ZE PS PSZE NS NM NM NS NS ZE
ZEPM PM PS ZE NS NM NMNM NM NS ZE PS PM PMZE NS NS NS NS NS ZE
PSPS PS ZE NS NS NM NMNM NS ZE PS PS PM PMZE ZE ZE ZE ZE ZE ZE
PMPS ZE NS NM NM NM NBZE ZE PS PS PM PB PBPM NS PS PS PS PS PB
PBZE ZE NM NM NM NB NBZE ZE PS PM PM PB PBPB PM PM PM PS PS PB
where Kp Ki and Kd represent the gain coefficient of theproportion integral and differential The 119890(119905) denotes adeviation between the body vertical vibration velocity (119904119894)and its desired value (1199040 is set to zero) Here 119870119901 = 3000119870119894 = 20 and 119870119889 = 30
4 Simulation
41 Modelling Road Input Excitation with Four-Wheel Corre-lation in Time-Domain In order to validate the effectivenessof fuzzy increment controller the white noise random inputwith four wheels correlated in time-domain the sinusoidalinput and the pulse input of C-grade road surface areadopted respectively Here the white noise random input onthe left front wheel is shown as
1199021 (119905) = minus2120587V1198910119885119902 (119905) + 21205871198990radic119866119902 (1198990) V119908 (119905) (9)
where 1198990 denotes a referenced spatial frequency and the valueequals 01 (mminus1) 119866119902(1198990) equals 256 times 10minus6 (m2mminus1) and itdenotes a road roughness coefficient of C-grade road surface119908(119905) represents a white noise with mean zero V denotes thevehicle speed (V = 20 ms) and 1198910 equals 001
Considering the delay effect the random input on the leftrear wheel is denoted as 1199024(119905) = 1199021(119905 minus 120591) Here 120591 = 119871V
and L represents wheelbase So the random input on the leftrear wheel is expressed as
1199024 (119905) = minus1199021 (119905) + 2V1198851199021 (119905)119871 minus 2V1198851199024 (119905)
119871 (10)
According to the early literatures the random input onthe right front wheel is derived as
1199022 (119905) = 1199021 (119905) minus 12V1198851199021 (119905)119861 + 1199092 (11)
Also the random input on the right rear wheel is denotedas 1199023(119905) = 1199022(119905 minus 120591) Therefore the random input on theright rear wheel is calculated as
1199023 (119905) = minus1199022 (119905) + 2V1198851199022 (119905)119871 minus 2V1198851199023 (119905)
119871 (12)
where
1 = minus12V1198851199021 (119905)119861 + 1199092
2 =72V21198851199021 (119905)
1198612 minus 12V211990911198612 minus 6V1199092
119861 (13)
In formula (10) and formula (11) B denotes the lateraldistance between the left and right wheel 119871 represents thelongitudinal distance between the front and rear wheel (iethe wheelbase) and V is car speed at the moment
Complexity 5
q1 q2 q4
q3
Zq1 Zq2 Zq4
Zq3
-K- -K-
-K-
-K-
-K-
-K-
-K-
x1 x2
-K-
-K--K-
-K-
minus minus
minus
minus
minus
minus
minus
+
+
+
+
+
+
minus
minus
+
2 1 3
4
Add 3
Add 1Add 4
Add
Add 2
Integrator 4Integrator 1
Integrator Integrator 2Integrator 5
Integrator 3
2L
2L1
2L2
2L
Band-limitedwhite noise 1
12L
6B
2 lowast pi lowast n0
2 lowast pi lowast nc lowast
12 lowast B
72 lowast lowast (B lowast B)
12 lowast lowast (B lowast B)
1
s
1
s
1
s
1
s
1
s1
s
Figure 4 Random input model with four-wheel correlation in time-domain
Table 2 Suspension structure parameters of a test car
Variable Value Dimension119872119904 770 kg1198721 1198722 35 kg1198723 1198724 30 kg119868119910 830 kgsdotm2119868119909 235 kgsdotm21198701 1198702 206 KNsdotmminus11198703 1198704 152 KNsdotmminus11198621 1198622 1570 Nsdotssdotmminus11198623 1198624 1760 Nsdotssdotmminus11198701199051 1198701199052 138 KNsdotmminus11198701199053 1198701199054 138 KNsdotmminus1119897119891 119897119903 136 m119897119886 0958 m119897119887 1377 m
42 Simulation Module Design In order to validate thefeasibility of the fuzzy increment controller car suspensionparameters are as given in Table 2
Using MATLABSimulink the simulation modular ofactive suspension with seven DOF is designed Accordingto formula (9) to formula (12) a road excitation simulationmodule of white noise in time-domain is designed as shownin Figure 4 taking into account the delay and correlationcharacteristic between the wheels Here the submodule offuzzy increment controller in a wheel side is described asin Figure 5 The simulation submodule of the other threecontrollers is similar to Figure 5
43 Simulation Analysis Figures 6ndash8 show the accelerationrsquoscomparison results of the body vertical vibration pitchingand rolling motion under the condition of white noise roadsurface excitation adopting different control modes
As you can see from Figures 6ndash8 these indexes valueson the vertical vibration pitching and rolling angular accel-eration of the vehicle body have been improved adoptingthe Fuzzy-PID code compared to other modes under thecondition of white noise road surface excitation In otherwords the fuzzy increment controller can obviously reducethe bodyrsquos vibration because the acceleration peak amplitudeabove indexes is far less than other modes
Figures 9ndash11 show the accelerationrsquos comparison resultsof the body vertical vibration pitching and rolling motionunder the condition of pulse excitation adopting differentcontrol mode
FromFigures 9ndash11 we can see that the vibration amplitudeon vehicle bodyrsquos acceleration is also far less than othermodesadopting the Fuzzy-PID code under the condition of pulseexcitation
Figures 12ndash14 show the accelerationrsquos comparison resultsof the body vertical vibration pitching and rolling motionunder the condition of sinusoidal excitation adopting dif-ferent control mode As you can see from Figures 6ndash14 thefuzzy increment controller (ie the Fuzzy-PID code name)has good control effect in improving the body vertical vibra-tion acceleration pitching and rolling angular accelerationcomparingwith the independent types of controls such as thepassive suspension the PID control and the fuzzy control
In addition to comparison curves the root mean squarevalue of bodyrsquos acceleration is counted regarding four kinds of
6 Complexity
1Out 1
3000
kp
ap20
ki
ai
22
kec1
24
ke1
30
kd10ad
Zero-orderhold 3
Zero-orderhold 2
Scope
Saturation 3
Saturation 2
Product 2
Product 1
Product
MemoryFuzzy logiccontroller 1dudt
dudt
1In 2
-K-
-K-
+
+
+
+
+
+
+
+
+
1
s
times
times
times
Figure 5 The submodule of fuzzy increment controller
PassivePID
FuzzyFuzzy-PID
minus1
minus05
0
05
1
Body
acce
lera
tion
(ms
2)
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 6 Comparison result of the body vertical vibration acceler-ation
minus06
minus04
minus02
04
The p
itchi
ng an
gula
rac
cele
ratio
n(r
ads
2)
06
05 1 15 2 25 3 35 4 45 50Time (s)
PassivePID
FuzzyFuzzy-PID
02
0
Figure 7 Comparison result of the body pitching angular accelera-tion
minus15
minus1
minus05
0
05
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
1
15
05 1 15 2 25 3 35 4 45 50Time (s)
PassivePID
FuzzyFuzzy-PID
Figure 8 Comparison result of the body rolling angular accelera-tion
PassivePID
FuzzyFuzzy-PID
minus050
051
152
253
Body
acce
lera
tion
(ms
2)
1 2 3 4 50Time (s)
Figure 9 Comparison result of the body vertical vibration acceler-ation
Complexity 7Th
e pitc
hing
angu
lar
acce
lera
tion
(rad
s2)
minus1
0
1
2
3
4
1 2 3 4 50Time (s)
PassivePID
FuzzyFuzzy-PID
Figure 10 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus2
4
2
0
6
1 2 3 4 50Time (s)
Figure 11 Comparison result of the body rolling angular accelera-tion
PassivePID
FuzzyFuzzy-PID
minus15minus1
minus050
051
152
Body
acce
lera
tion
(ms
2)
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 12 Comparison result of the vertical vibration acceleration
controlmode under the condition of different speed as shownin Table 3
As seen from Table 3 the root mean square value ofthe bodyrsquos acceleration the pitching and rolling angularacceleration adopting the Fuzzy-PID mode reduces 375percent 289 percent and 262 percent compared with thepassivemode under the condition of white noise road surfaceexcitationThe rootmean square values of indexesmentioned
PassivePID
FuzzyFuzzy-PID
The p
itchi
ng an
gula
rac
cele
ratio
n(r
ads
2)
minus05
0
05
1
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 13 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus03
minus02
minus01
0
01
02
03
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 14 Comparison result of the rolling angular acceleration
above reduce 562 476 and 520 percent under the conditionof sinusoidal excitation respectively
You can also see that the root mean square values ofindexesmentioned above adopting the Fuzzy-PIDmode havebeen improved obviously compared to other modes at 30meters per second Through analysis we can see that thedesigned controller can reduce obviously the vehicle vibra-tion and has good control effect compared to the independentcontrol type
5 Conclusions
(1) The vibration model with seven degrees of freedomof automobile active suspension is derived and four fuzzyincrement controllers are designed based on 49 rules foradapting the different real-time road input information
(2) The white noise input model with four wheels cor-related in characteristics of time-domain is designed that iscloser to the actual road information input
(3) Using MATLABSimulink the simulation module ofactive suspension with seven DOF has been built and thefuzzy increment controller is validated taking the white noiseexcitation with four-wheel correlation in time-domain thesinusoidal excitation and the pulse excitation of C-graderoad surface as the road input The simulation results show
8 Complexity
Table 3 The root mean square value of acceleration
Input Speed Controlmode
Body verticalacceleration
Pitching angularacceleration
Rolling angularacceleration
White noiseexcitation
20ms
Passive 03800 02075 04937PID 02862 01720 04462Fuzzy 03031 01700 04237
Fuzzy-PID 02374 01475 03640
30ms
Passive 05383 02232 04247PID 04205 01936 03828Fuzzy 03987 01819 03217
Fuzzy-PID 03344 01673 02938
The sinusoidalexcitation
20ms
Passive 11386 05525 01858PID 07232 03722 00938Fuzzy 07950 03734 01159
Fuzzy-PID 04983 02891 00892
30ms
Passive 12356 02857 02111PID 07881 02055 01111Fuzzy 08587 02113 01225
Fuzzy-PID 06001 01653 01189
that designed fuzzy increment controller can reduce 375percent 289 percent and 262 percent in evaluation indexof the body vertical vibration acceleration pitching androlling acceleration compared with the passive mode underthe condition of white noise road surface excitation and canimprove 562 476 and 520 percent under the condition ofsinusoidal excitation respectively
In a word the designed fuzzy increment controller inthis paper is feasible to adapt to real-time change of roadsituations and can reduce obviously the vehicle vibrationand has a superior control effect compared to other controlmodesThe research achievements havemuch reference valuefor developing the product of suspension controller
As future work we intend to build the prototypes anddevelop products by single-chip technology
Conflicts of Interest
The authors declared no potential conflicts of interest withrespect to the research authorship andor publication of thisarticle
Acknowledgments
This work was supported in part by the Natural ScienceFoundation of China underGrant 61473139 and the joint fundof the Natural Science Foundation of Liaoning Province ofChina 201602368
References
[1] H Zhang E Wang F Min R Subash and C Su ldquoSkyhook-based semi-active control of full-vehicle suspension withmagneto-rheological dampersrdquo Chinese Journal of MechanicalEngineering vol 26 no 3 pp 498ndash505 2013
[2] H-B Ren S-Z Chen Y-Z Zhao G Liu and L YangldquoObserver-based hybrid control algorithm for semi-active sus-pension systemsrdquo Journal of Central South University vol 23no 9 pp 2268ndash2275 2016
[3] D Singh and M L Aggarwal ldquoPassenger seat vibration controlof a semi-active quarter car system with hybrid fuzzy-PIDapproachrdquo International Journal of Dynamics and Control vol5 no 2 pp 287ndash296 2017
[4] H-P Du and N Zhang ldquoRobust active suspension designsubject to vehicle inertial parameter variationsrdquo InternationalJournal of Automation and Computing vol 7 no 4 pp 419ndash4272010
[5] Y-J Liu and S Tong ldquoAdaptive fuzzy control for a classof unknown nonlinear dynamical systemsrdquo Fuzzy Sets andSystems vol 263 pp 49ndash70 2015
[6] Y-J Liu Y Gao S Tong andY Li ldquoFuzzy approximation-basedadaptive backstepping optimal control for a class of nonlineardiscrete-time systems with dead-zonerdquo IEEE Transactions onFuzzy Systems 1 page 2015
[7] Y Gao and Y-J Liu ldquoAdaptive fuzzy optimal control usingdirect heuristic dynamic programming for chaotic discrete-time systemrdquo Journal of Vibration and Control vol 22 no 2pp 595ndash603 2016
[8] H Li G Chen X Liao and T Huang ldquoLeader-followingconsensus of discrete-time multiagent systems with encoding-decodingrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 63 no 4 pp 401ndash405 2016
[9] H Li C Huang G Chen X Liao and T Huang ldquoDistributedConsensus Optimization in Multiagent Networks With Time-Varying Directed Topologies and Quantized CommunicationrdquoIEEE Transactions on Cybernetics 2017
[10] C Huang L Chen H Jiang C Yuan and T Xia ldquoFuzzy chaoscontrol for vehicle lateral dynamics based on active suspensionsystemrdquo Chinese Journal of Mechanical Engineering vol 27 no4 pp 793ndash801 2014
Complexity 9
[11] H Li S Liu Y C Soh and L Xie ldquoEvent-Triggered Communi-cation and Data Rate Constraint for Distributed OptimizationofMultiagent Systemsrdquo IEEETransactions on SystemsMan andCybernetics Systems pp 1ndash12
[12] H Li G Chen T Huang and Z Dong ldquoHigh-performanceconsensus control in networked systems with limited band-width communication and time-varying directed topologiesrdquoIEEE Transactions on Neural Networks and Learning Systemspp 1ndash12 2016
[13] S Riaz and L Khan ldquoNeuroFuzzy Adaptive Control for Full-Car Nonlinear Active Suspension withOnboard Antilock Brak-ing Systemrdquo Arabian Journal for Science and Engineering vol40 no 12 pp 3483ndash3505 2015
[14] M M Zirkohi and T-C Lin ldquoInterval type-2 fuzzy-neuralnetwork indirect adaptive sliding mode control for an activesuspension systemrdquo Nonlinear Dynamics vol 79 no 1 pp 513ndash526 2015
[15] L Balamurugan J Jancirani and M A Eltantawie ldquoGener-alized magnetorheological (MR) damper model and its appli-cation in semi-active control of vehicle suspension systemrdquoInternational Journal of Automotive Technology vol 15 no 3pp 419ndash427 2014
[16] H L Zhang E RWangN Zhang FMin R Subash andC SuldquoSemi-active sliding mode control of vehicle suspension withmagneto-rheological damperrdquo Chinese Journal of MechanicalEngineering vol 28 no 1 pp 63ndash75 2015
[17] S Bououden M Chadli L Zhang and T Yang ldquoConstrainedmodel predictive control for time-varying delay systems Appli-cation to an active car suspensionrdquo International Journal ofControl Automation and Systems vol 14 no 1 pp 51ndash58 2016
[18] L Wu and W-J Zhang ldquoHierarchical modeling of semi-activecontrol of a full motorcycle suspension with six degrees offreedomsrdquo International Journal of Automotive Technology vol11 no 1 pp 27ndash32 2010
[19] ZMao YWang B Jiang andG Tao ldquoFault diagnosis for a classof active suspension systems with dynamic actuatorsrsquo faultsrdquoInternational Journal of Control Automation and Systems vol14 no 5 pp 1160ndash1172 2016
[20] H Trabelsi P-A Yvars J Louati and M Haddar ldquoEvaluationof the effectiveness of the interval computation method tosimulate the dynamic behavior of subdefinite system applica-tion on an active suspension systemrdquo International Journal onInteractive Design and Manufacturing vol 9 no 2 pp 83ndash962015
[21] CWang K DengW Zhao G Zhou andX Li ldquoRobust controlfor active suspension system under steering conditionrdquo ScienceChina Technological Sciences vol 60 no 2 pp 199ndash208 2017
[22] X Dong D Zhao B Yang and C Han ldquoFractional-ordercontrol of active suspension actuator based on parallel adaptiveclonal selection algorithmrdquo Journal of Mechanical Science andTechnology vol 30 no 6 pp 2769ndash2781 2016
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Hindawiwwwhindawicom Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Hindawiwwwhindawicom Volume 2018Volume 2018
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
4 Complexity
Table 1 Fuzzy control rule of the PID increment parameters
ΔKpΔKiΔKd
119904119894NB NM NS ZE PS PM PB
119904119894NB
PB PB PM PM PS ZE ZENB NB NM NM NS ZE ZEPS NS NB NB NB NM PS
NMPB PB PM PS PS ZE NSNB NB NM NS NS ZE ZEPS NS NM NM NM NS ZE
NSPM PM PM PS ZE NS NSNB NM NS NS ZE PS PSZE NS NM NM NS NS ZE
ZEPM PM PS ZE NS NM NMNM NM NS ZE PS PM PMZE NS NS NS NS NS ZE
PSPS PS ZE NS NS NM NMNM NS ZE PS PS PM PMZE ZE ZE ZE ZE ZE ZE
PMPS ZE NS NM NM NM NBZE ZE PS PS PM PB PBPM NS PS PS PS PS PB
PBZE ZE NM NM NM NB NBZE ZE PS PM PM PB PBPB PM PM PM PS PS PB
where Kp Ki and Kd represent the gain coefficient of theproportion integral and differential The 119890(119905) denotes adeviation between the body vertical vibration velocity (119904119894)and its desired value (1199040 is set to zero) Here 119870119901 = 3000119870119894 = 20 and 119870119889 = 30
4 Simulation
41 Modelling Road Input Excitation with Four-Wheel Corre-lation in Time-Domain In order to validate the effectivenessof fuzzy increment controller the white noise random inputwith four wheels correlated in time-domain the sinusoidalinput and the pulse input of C-grade road surface areadopted respectively Here the white noise random input onthe left front wheel is shown as
1199021 (119905) = minus2120587V1198910119885119902 (119905) + 21205871198990radic119866119902 (1198990) V119908 (119905) (9)
where 1198990 denotes a referenced spatial frequency and the valueequals 01 (mminus1) 119866119902(1198990) equals 256 times 10minus6 (m2mminus1) and itdenotes a road roughness coefficient of C-grade road surface119908(119905) represents a white noise with mean zero V denotes thevehicle speed (V = 20 ms) and 1198910 equals 001
Considering the delay effect the random input on the leftrear wheel is denoted as 1199024(119905) = 1199021(119905 minus 120591) Here 120591 = 119871V
and L represents wheelbase So the random input on the leftrear wheel is expressed as
1199024 (119905) = minus1199021 (119905) + 2V1198851199021 (119905)119871 minus 2V1198851199024 (119905)
119871 (10)
According to the early literatures the random input onthe right front wheel is derived as
1199022 (119905) = 1199021 (119905) minus 12V1198851199021 (119905)119861 + 1199092 (11)
Also the random input on the right rear wheel is denotedas 1199023(119905) = 1199022(119905 minus 120591) Therefore the random input on theright rear wheel is calculated as
1199023 (119905) = minus1199022 (119905) + 2V1198851199022 (119905)119871 minus 2V1198851199023 (119905)
119871 (12)
where
1 = minus12V1198851199021 (119905)119861 + 1199092
2 =72V21198851199021 (119905)
1198612 minus 12V211990911198612 minus 6V1199092
119861 (13)
In formula (10) and formula (11) B denotes the lateraldistance between the left and right wheel 119871 represents thelongitudinal distance between the front and rear wheel (iethe wheelbase) and V is car speed at the moment
Complexity 5
q1 q2 q4
q3
Zq1 Zq2 Zq4
Zq3
-K- -K-
-K-
-K-
-K-
-K-
-K-
x1 x2
-K-
-K--K-
-K-
minus minus
minus
minus
minus
minus
minus
+
+
+
+
+
+
minus
minus
+
2 1 3
4
Add 3
Add 1Add 4
Add
Add 2
Integrator 4Integrator 1
Integrator Integrator 2Integrator 5
Integrator 3
2L
2L1
2L2
2L
Band-limitedwhite noise 1
12L
6B
2 lowast pi lowast n0
2 lowast pi lowast nc lowast
12 lowast B
72 lowast lowast (B lowast B)
12 lowast lowast (B lowast B)
1
s
1
s
1
s
1
s
1
s1
s
Figure 4 Random input model with four-wheel correlation in time-domain
Table 2 Suspension structure parameters of a test car
Variable Value Dimension119872119904 770 kg1198721 1198722 35 kg1198723 1198724 30 kg119868119910 830 kgsdotm2119868119909 235 kgsdotm21198701 1198702 206 KNsdotmminus11198703 1198704 152 KNsdotmminus11198621 1198622 1570 Nsdotssdotmminus11198623 1198624 1760 Nsdotssdotmminus11198701199051 1198701199052 138 KNsdotmminus11198701199053 1198701199054 138 KNsdotmminus1119897119891 119897119903 136 m119897119886 0958 m119897119887 1377 m
42 Simulation Module Design In order to validate thefeasibility of the fuzzy increment controller car suspensionparameters are as given in Table 2
Using MATLABSimulink the simulation modular ofactive suspension with seven DOF is designed Accordingto formula (9) to formula (12) a road excitation simulationmodule of white noise in time-domain is designed as shownin Figure 4 taking into account the delay and correlationcharacteristic between the wheels Here the submodule offuzzy increment controller in a wheel side is described asin Figure 5 The simulation submodule of the other threecontrollers is similar to Figure 5
43 Simulation Analysis Figures 6ndash8 show the accelerationrsquoscomparison results of the body vertical vibration pitchingand rolling motion under the condition of white noise roadsurface excitation adopting different control modes
As you can see from Figures 6ndash8 these indexes valueson the vertical vibration pitching and rolling angular accel-eration of the vehicle body have been improved adoptingthe Fuzzy-PID code compared to other modes under thecondition of white noise road surface excitation In otherwords the fuzzy increment controller can obviously reducethe bodyrsquos vibration because the acceleration peak amplitudeabove indexes is far less than other modes
Figures 9ndash11 show the accelerationrsquos comparison resultsof the body vertical vibration pitching and rolling motionunder the condition of pulse excitation adopting differentcontrol mode
FromFigures 9ndash11 we can see that the vibration amplitudeon vehicle bodyrsquos acceleration is also far less than othermodesadopting the Fuzzy-PID code under the condition of pulseexcitation
Figures 12ndash14 show the accelerationrsquos comparison resultsof the body vertical vibration pitching and rolling motionunder the condition of sinusoidal excitation adopting dif-ferent control mode As you can see from Figures 6ndash14 thefuzzy increment controller (ie the Fuzzy-PID code name)has good control effect in improving the body vertical vibra-tion acceleration pitching and rolling angular accelerationcomparingwith the independent types of controls such as thepassive suspension the PID control and the fuzzy control
In addition to comparison curves the root mean squarevalue of bodyrsquos acceleration is counted regarding four kinds of
6 Complexity
1Out 1
3000
kp
ap20
ki
ai
22
kec1
24
ke1
30
kd10ad
Zero-orderhold 3
Zero-orderhold 2
Scope
Saturation 3
Saturation 2
Product 2
Product 1
Product
MemoryFuzzy logiccontroller 1dudt
dudt
1In 2
-K-
-K-
+
+
+
+
+
+
+
+
+
1
s
times
times
times
Figure 5 The submodule of fuzzy increment controller
PassivePID
FuzzyFuzzy-PID
minus1
minus05
0
05
1
Body
acce
lera
tion
(ms
2)
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 6 Comparison result of the body vertical vibration acceler-ation
minus06
minus04
minus02
04
The p
itchi
ng an
gula
rac
cele
ratio
n(r
ads
2)
06
05 1 15 2 25 3 35 4 45 50Time (s)
PassivePID
FuzzyFuzzy-PID
02
0
Figure 7 Comparison result of the body pitching angular accelera-tion
minus15
minus1
minus05
0
05
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
1
15
05 1 15 2 25 3 35 4 45 50Time (s)
PassivePID
FuzzyFuzzy-PID
Figure 8 Comparison result of the body rolling angular accelera-tion
PassivePID
FuzzyFuzzy-PID
minus050
051
152
253
Body
acce
lera
tion
(ms
2)
1 2 3 4 50Time (s)
Figure 9 Comparison result of the body vertical vibration acceler-ation
Complexity 7Th
e pitc
hing
angu
lar
acce
lera
tion
(rad
s2)
minus1
0
1
2
3
4
1 2 3 4 50Time (s)
PassivePID
FuzzyFuzzy-PID
Figure 10 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus2
4
2
0
6
1 2 3 4 50Time (s)
Figure 11 Comparison result of the body rolling angular accelera-tion
PassivePID
FuzzyFuzzy-PID
minus15minus1
minus050
051
152
Body
acce
lera
tion
(ms
2)
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 12 Comparison result of the vertical vibration acceleration
controlmode under the condition of different speed as shownin Table 3
As seen from Table 3 the root mean square value ofthe bodyrsquos acceleration the pitching and rolling angularacceleration adopting the Fuzzy-PID mode reduces 375percent 289 percent and 262 percent compared with thepassivemode under the condition of white noise road surfaceexcitationThe rootmean square values of indexesmentioned
PassivePID
FuzzyFuzzy-PID
The p
itchi
ng an
gula
rac
cele
ratio
n(r
ads
2)
minus05
0
05
1
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 13 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus03
minus02
minus01
0
01
02
03
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 14 Comparison result of the rolling angular acceleration
above reduce 562 476 and 520 percent under the conditionof sinusoidal excitation respectively
You can also see that the root mean square values ofindexesmentioned above adopting the Fuzzy-PIDmode havebeen improved obviously compared to other modes at 30meters per second Through analysis we can see that thedesigned controller can reduce obviously the vehicle vibra-tion and has good control effect compared to the independentcontrol type
5 Conclusions
(1) The vibration model with seven degrees of freedomof automobile active suspension is derived and four fuzzyincrement controllers are designed based on 49 rules foradapting the different real-time road input information
(2) The white noise input model with four wheels cor-related in characteristics of time-domain is designed that iscloser to the actual road information input
(3) Using MATLABSimulink the simulation module ofactive suspension with seven DOF has been built and thefuzzy increment controller is validated taking the white noiseexcitation with four-wheel correlation in time-domain thesinusoidal excitation and the pulse excitation of C-graderoad surface as the road input The simulation results show
8 Complexity
Table 3 The root mean square value of acceleration
Input Speed Controlmode
Body verticalacceleration
Pitching angularacceleration
Rolling angularacceleration
White noiseexcitation
20ms
Passive 03800 02075 04937PID 02862 01720 04462Fuzzy 03031 01700 04237
Fuzzy-PID 02374 01475 03640
30ms
Passive 05383 02232 04247PID 04205 01936 03828Fuzzy 03987 01819 03217
Fuzzy-PID 03344 01673 02938
The sinusoidalexcitation
20ms
Passive 11386 05525 01858PID 07232 03722 00938Fuzzy 07950 03734 01159
Fuzzy-PID 04983 02891 00892
30ms
Passive 12356 02857 02111PID 07881 02055 01111Fuzzy 08587 02113 01225
Fuzzy-PID 06001 01653 01189
that designed fuzzy increment controller can reduce 375percent 289 percent and 262 percent in evaluation indexof the body vertical vibration acceleration pitching androlling acceleration compared with the passive mode underthe condition of white noise road surface excitation and canimprove 562 476 and 520 percent under the condition ofsinusoidal excitation respectively
In a word the designed fuzzy increment controller inthis paper is feasible to adapt to real-time change of roadsituations and can reduce obviously the vehicle vibrationand has a superior control effect compared to other controlmodesThe research achievements havemuch reference valuefor developing the product of suspension controller
As future work we intend to build the prototypes anddevelop products by single-chip technology
Conflicts of Interest
The authors declared no potential conflicts of interest withrespect to the research authorship andor publication of thisarticle
Acknowledgments
This work was supported in part by the Natural ScienceFoundation of China underGrant 61473139 and the joint fundof the Natural Science Foundation of Liaoning Province ofChina 201602368
References
[1] H Zhang E Wang F Min R Subash and C Su ldquoSkyhook-based semi-active control of full-vehicle suspension withmagneto-rheological dampersrdquo Chinese Journal of MechanicalEngineering vol 26 no 3 pp 498ndash505 2013
[2] H-B Ren S-Z Chen Y-Z Zhao G Liu and L YangldquoObserver-based hybrid control algorithm for semi-active sus-pension systemsrdquo Journal of Central South University vol 23no 9 pp 2268ndash2275 2016
[3] D Singh and M L Aggarwal ldquoPassenger seat vibration controlof a semi-active quarter car system with hybrid fuzzy-PIDapproachrdquo International Journal of Dynamics and Control vol5 no 2 pp 287ndash296 2017
[4] H-P Du and N Zhang ldquoRobust active suspension designsubject to vehicle inertial parameter variationsrdquo InternationalJournal of Automation and Computing vol 7 no 4 pp 419ndash4272010
[5] Y-J Liu and S Tong ldquoAdaptive fuzzy control for a classof unknown nonlinear dynamical systemsrdquo Fuzzy Sets andSystems vol 263 pp 49ndash70 2015
[6] Y-J Liu Y Gao S Tong andY Li ldquoFuzzy approximation-basedadaptive backstepping optimal control for a class of nonlineardiscrete-time systems with dead-zonerdquo IEEE Transactions onFuzzy Systems 1 page 2015
[7] Y Gao and Y-J Liu ldquoAdaptive fuzzy optimal control usingdirect heuristic dynamic programming for chaotic discrete-time systemrdquo Journal of Vibration and Control vol 22 no 2pp 595ndash603 2016
[8] H Li G Chen X Liao and T Huang ldquoLeader-followingconsensus of discrete-time multiagent systems with encoding-decodingrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 63 no 4 pp 401ndash405 2016
[9] H Li C Huang G Chen X Liao and T Huang ldquoDistributedConsensus Optimization in Multiagent Networks With Time-Varying Directed Topologies and Quantized CommunicationrdquoIEEE Transactions on Cybernetics 2017
[10] C Huang L Chen H Jiang C Yuan and T Xia ldquoFuzzy chaoscontrol for vehicle lateral dynamics based on active suspensionsystemrdquo Chinese Journal of Mechanical Engineering vol 27 no4 pp 793ndash801 2014
Complexity 9
[11] H Li S Liu Y C Soh and L Xie ldquoEvent-Triggered Communi-cation and Data Rate Constraint for Distributed OptimizationofMultiagent Systemsrdquo IEEETransactions on SystemsMan andCybernetics Systems pp 1ndash12
[12] H Li G Chen T Huang and Z Dong ldquoHigh-performanceconsensus control in networked systems with limited band-width communication and time-varying directed topologiesrdquoIEEE Transactions on Neural Networks and Learning Systemspp 1ndash12 2016
[13] S Riaz and L Khan ldquoNeuroFuzzy Adaptive Control for Full-Car Nonlinear Active Suspension withOnboard Antilock Brak-ing Systemrdquo Arabian Journal for Science and Engineering vol40 no 12 pp 3483ndash3505 2015
[14] M M Zirkohi and T-C Lin ldquoInterval type-2 fuzzy-neuralnetwork indirect adaptive sliding mode control for an activesuspension systemrdquo Nonlinear Dynamics vol 79 no 1 pp 513ndash526 2015
[15] L Balamurugan J Jancirani and M A Eltantawie ldquoGener-alized magnetorheological (MR) damper model and its appli-cation in semi-active control of vehicle suspension systemrdquoInternational Journal of Automotive Technology vol 15 no 3pp 419ndash427 2014
[16] H L Zhang E RWangN Zhang FMin R Subash andC SuldquoSemi-active sliding mode control of vehicle suspension withmagneto-rheological damperrdquo Chinese Journal of MechanicalEngineering vol 28 no 1 pp 63ndash75 2015
[17] S Bououden M Chadli L Zhang and T Yang ldquoConstrainedmodel predictive control for time-varying delay systems Appli-cation to an active car suspensionrdquo International Journal ofControl Automation and Systems vol 14 no 1 pp 51ndash58 2016
[18] L Wu and W-J Zhang ldquoHierarchical modeling of semi-activecontrol of a full motorcycle suspension with six degrees offreedomsrdquo International Journal of Automotive Technology vol11 no 1 pp 27ndash32 2010
[19] ZMao YWang B Jiang andG Tao ldquoFault diagnosis for a classof active suspension systems with dynamic actuatorsrsquo faultsrdquoInternational Journal of Control Automation and Systems vol14 no 5 pp 1160ndash1172 2016
[20] H Trabelsi P-A Yvars J Louati and M Haddar ldquoEvaluationof the effectiveness of the interval computation method tosimulate the dynamic behavior of subdefinite system applica-tion on an active suspension systemrdquo International Journal onInteractive Design and Manufacturing vol 9 no 2 pp 83ndash962015
[21] CWang K DengW Zhao G Zhou andX Li ldquoRobust controlfor active suspension system under steering conditionrdquo ScienceChina Technological Sciences vol 60 no 2 pp 199ndash208 2017
[22] X Dong D Zhao B Yang and C Han ldquoFractional-ordercontrol of active suspension actuator based on parallel adaptiveclonal selection algorithmrdquo Journal of Mechanical Science andTechnology vol 30 no 6 pp 2769ndash2781 2016
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Submit your manuscripts atwwwhindawicom
Complexity 5
q1 q2 q4
q3
Zq1 Zq2 Zq4
Zq3
-K- -K-
-K-
-K-
-K-
-K-
-K-
x1 x2
-K-
-K--K-
-K-
minus minus
minus
minus
minus
minus
minus
+
+
+
+
+
+
minus
minus
+
2 1 3
4
Add 3
Add 1Add 4
Add
Add 2
Integrator 4Integrator 1
Integrator Integrator 2Integrator 5
Integrator 3
2L
2L1
2L2
2L
Band-limitedwhite noise 1
12L
6B
2 lowast pi lowast n0
2 lowast pi lowast nc lowast
12 lowast B
72 lowast lowast (B lowast B)
12 lowast lowast (B lowast B)
1
s
1
s
1
s
1
s
1
s1
s
Figure 4 Random input model with four-wheel correlation in time-domain
Table 2 Suspension structure parameters of a test car
Variable Value Dimension119872119904 770 kg1198721 1198722 35 kg1198723 1198724 30 kg119868119910 830 kgsdotm2119868119909 235 kgsdotm21198701 1198702 206 KNsdotmminus11198703 1198704 152 KNsdotmminus11198621 1198622 1570 Nsdotssdotmminus11198623 1198624 1760 Nsdotssdotmminus11198701199051 1198701199052 138 KNsdotmminus11198701199053 1198701199054 138 KNsdotmminus1119897119891 119897119903 136 m119897119886 0958 m119897119887 1377 m
42 Simulation Module Design In order to validate thefeasibility of the fuzzy increment controller car suspensionparameters are as given in Table 2
Using MATLABSimulink the simulation modular ofactive suspension with seven DOF is designed Accordingto formula (9) to formula (12) a road excitation simulationmodule of white noise in time-domain is designed as shownin Figure 4 taking into account the delay and correlationcharacteristic between the wheels Here the submodule offuzzy increment controller in a wheel side is described asin Figure 5 The simulation submodule of the other threecontrollers is similar to Figure 5
43 Simulation Analysis Figures 6ndash8 show the accelerationrsquoscomparison results of the body vertical vibration pitchingand rolling motion under the condition of white noise roadsurface excitation adopting different control modes
As you can see from Figures 6ndash8 these indexes valueson the vertical vibration pitching and rolling angular accel-eration of the vehicle body have been improved adoptingthe Fuzzy-PID code compared to other modes under thecondition of white noise road surface excitation In otherwords the fuzzy increment controller can obviously reducethe bodyrsquos vibration because the acceleration peak amplitudeabove indexes is far less than other modes
Figures 9ndash11 show the accelerationrsquos comparison resultsof the body vertical vibration pitching and rolling motionunder the condition of pulse excitation adopting differentcontrol mode
FromFigures 9ndash11 we can see that the vibration amplitudeon vehicle bodyrsquos acceleration is also far less than othermodesadopting the Fuzzy-PID code under the condition of pulseexcitation
Figures 12ndash14 show the accelerationrsquos comparison resultsof the body vertical vibration pitching and rolling motionunder the condition of sinusoidal excitation adopting dif-ferent control mode As you can see from Figures 6ndash14 thefuzzy increment controller (ie the Fuzzy-PID code name)has good control effect in improving the body vertical vibra-tion acceleration pitching and rolling angular accelerationcomparingwith the independent types of controls such as thepassive suspension the PID control and the fuzzy control
In addition to comparison curves the root mean squarevalue of bodyrsquos acceleration is counted regarding four kinds of
6 Complexity
1Out 1
3000
kp
ap20
ki
ai
22
kec1
24
ke1
30
kd10ad
Zero-orderhold 3
Zero-orderhold 2
Scope
Saturation 3
Saturation 2
Product 2
Product 1
Product
MemoryFuzzy logiccontroller 1dudt
dudt
1In 2
-K-
-K-
+
+
+
+
+
+
+
+
+
1
s
times
times
times
Figure 5 The submodule of fuzzy increment controller
PassivePID
FuzzyFuzzy-PID
minus1
minus05
0
05
1
Body
acce
lera
tion
(ms
2)
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 6 Comparison result of the body vertical vibration acceler-ation
minus06
minus04
minus02
04
The p
itchi
ng an
gula
rac
cele
ratio
n(r
ads
2)
06
05 1 15 2 25 3 35 4 45 50Time (s)
PassivePID
FuzzyFuzzy-PID
02
0
Figure 7 Comparison result of the body pitching angular accelera-tion
minus15
minus1
minus05
0
05
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
1
15
05 1 15 2 25 3 35 4 45 50Time (s)
PassivePID
FuzzyFuzzy-PID
Figure 8 Comparison result of the body rolling angular accelera-tion
PassivePID
FuzzyFuzzy-PID
minus050
051
152
253
Body
acce
lera
tion
(ms
2)
1 2 3 4 50Time (s)
Figure 9 Comparison result of the body vertical vibration acceler-ation
Complexity 7Th
e pitc
hing
angu
lar
acce
lera
tion
(rad
s2)
minus1
0
1
2
3
4
1 2 3 4 50Time (s)
PassivePID
FuzzyFuzzy-PID
Figure 10 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus2
4
2
0
6
1 2 3 4 50Time (s)
Figure 11 Comparison result of the body rolling angular accelera-tion
PassivePID
FuzzyFuzzy-PID
minus15minus1
minus050
051
152
Body
acce
lera
tion
(ms
2)
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 12 Comparison result of the vertical vibration acceleration
controlmode under the condition of different speed as shownin Table 3
As seen from Table 3 the root mean square value ofthe bodyrsquos acceleration the pitching and rolling angularacceleration adopting the Fuzzy-PID mode reduces 375percent 289 percent and 262 percent compared with thepassivemode under the condition of white noise road surfaceexcitationThe rootmean square values of indexesmentioned
PassivePID
FuzzyFuzzy-PID
The p
itchi
ng an
gula
rac
cele
ratio
n(r
ads
2)
minus05
0
05
1
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 13 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus03
minus02
minus01
0
01
02
03
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 14 Comparison result of the rolling angular acceleration
above reduce 562 476 and 520 percent under the conditionof sinusoidal excitation respectively
You can also see that the root mean square values ofindexesmentioned above adopting the Fuzzy-PIDmode havebeen improved obviously compared to other modes at 30meters per second Through analysis we can see that thedesigned controller can reduce obviously the vehicle vibra-tion and has good control effect compared to the independentcontrol type
5 Conclusions
(1) The vibration model with seven degrees of freedomof automobile active suspension is derived and four fuzzyincrement controllers are designed based on 49 rules foradapting the different real-time road input information
(2) The white noise input model with four wheels cor-related in characteristics of time-domain is designed that iscloser to the actual road information input
(3) Using MATLABSimulink the simulation module ofactive suspension with seven DOF has been built and thefuzzy increment controller is validated taking the white noiseexcitation with four-wheel correlation in time-domain thesinusoidal excitation and the pulse excitation of C-graderoad surface as the road input The simulation results show
8 Complexity
Table 3 The root mean square value of acceleration
Input Speed Controlmode
Body verticalacceleration
Pitching angularacceleration
Rolling angularacceleration
White noiseexcitation
20ms
Passive 03800 02075 04937PID 02862 01720 04462Fuzzy 03031 01700 04237
Fuzzy-PID 02374 01475 03640
30ms
Passive 05383 02232 04247PID 04205 01936 03828Fuzzy 03987 01819 03217
Fuzzy-PID 03344 01673 02938
The sinusoidalexcitation
20ms
Passive 11386 05525 01858PID 07232 03722 00938Fuzzy 07950 03734 01159
Fuzzy-PID 04983 02891 00892
30ms
Passive 12356 02857 02111PID 07881 02055 01111Fuzzy 08587 02113 01225
Fuzzy-PID 06001 01653 01189
that designed fuzzy increment controller can reduce 375percent 289 percent and 262 percent in evaluation indexof the body vertical vibration acceleration pitching androlling acceleration compared with the passive mode underthe condition of white noise road surface excitation and canimprove 562 476 and 520 percent under the condition ofsinusoidal excitation respectively
In a word the designed fuzzy increment controller inthis paper is feasible to adapt to real-time change of roadsituations and can reduce obviously the vehicle vibrationand has a superior control effect compared to other controlmodesThe research achievements havemuch reference valuefor developing the product of suspension controller
As future work we intend to build the prototypes anddevelop products by single-chip technology
Conflicts of Interest
The authors declared no potential conflicts of interest withrespect to the research authorship andor publication of thisarticle
Acknowledgments
This work was supported in part by the Natural ScienceFoundation of China underGrant 61473139 and the joint fundof the Natural Science Foundation of Liaoning Province ofChina 201602368
References
[1] H Zhang E Wang F Min R Subash and C Su ldquoSkyhook-based semi-active control of full-vehicle suspension withmagneto-rheological dampersrdquo Chinese Journal of MechanicalEngineering vol 26 no 3 pp 498ndash505 2013
[2] H-B Ren S-Z Chen Y-Z Zhao G Liu and L YangldquoObserver-based hybrid control algorithm for semi-active sus-pension systemsrdquo Journal of Central South University vol 23no 9 pp 2268ndash2275 2016
[3] D Singh and M L Aggarwal ldquoPassenger seat vibration controlof a semi-active quarter car system with hybrid fuzzy-PIDapproachrdquo International Journal of Dynamics and Control vol5 no 2 pp 287ndash296 2017
[4] H-P Du and N Zhang ldquoRobust active suspension designsubject to vehicle inertial parameter variationsrdquo InternationalJournal of Automation and Computing vol 7 no 4 pp 419ndash4272010
[5] Y-J Liu and S Tong ldquoAdaptive fuzzy control for a classof unknown nonlinear dynamical systemsrdquo Fuzzy Sets andSystems vol 263 pp 49ndash70 2015
[6] Y-J Liu Y Gao S Tong andY Li ldquoFuzzy approximation-basedadaptive backstepping optimal control for a class of nonlineardiscrete-time systems with dead-zonerdquo IEEE Transactions onFuzzy Systems 1 page 2015
[7] Y Gao and Y-J Liu ldquoAdaptive fuzzy optimal control usingdirect heuristic dynamic programming for chaotic discrete-time systemrdquo Journal of Vibration and Control vol 22 no 2pp 595ndash603 2016
[8] H Li G Chen X Liao and T Huang ldquoLeader-followingconsensus of discrete-time multiagent systems with encoding-decodingrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 63 no 4 pp 401ndash405 2016
[9] H Li C Huang G Chen X Liao and T Huang ldquoDistributedConsensus Optimization in Multiagent Networks With Time-Varying Directed Topologies and Quantized CommunicationrdquoIEEE Transactions on Cybernetics 2017
[10] C Huang L Chen H Jiang C Yuan and T Xia ldquoFuzzy chaoscontrol for vehicle lateral dynamics based on active suspensionsystemrdquo Chinese Journal of Mechanical Engineering vol 27 no4 pp 793ndash801 2014
Complexity 9
[11] H Li S Liu Y C Soh and L Xie ldquoEvent-Triggered Communi-cation and Data Rate Constraint for Distributed OptimizationofMultiagent Systemsrdquo IEEETransactions on SystemsMan andCybernetics Systems pp 1ndash12
[12] H Li G Chen T Huang and Z Dong ldquoHigh-performanceconsensus control in networked systems with limited band-width communication and time-varying directed topologiesrdquoIEEE Transactions on Neural Networks and Learning Systemspp 1ndash12 2016
[13] S Riaz and L Khan ldquoNeuroFuzzy Adaptive Control for Full-Car Nonlinear Active Suspension withOnboard Antilock Brak-ing Systemrdquo Arabian Journal for Science and Engineering vol40 no 12 pp 3483ndash3505 2015
[14] M M Zirkohi and T-C Lin ldquoInterval type-2 fuzzy-neuralnetwork indirect adaptive sliding mode control for an activesuspension systemrdquo Nonlinear Dynamics vol 79 no 1 pp 513ndash526 2015
[15] L Balamurugan J Jancirani and M A Eltantawie ldquoGener-alized magnetorheological (MR) damper model and its appli-cation in semi-active control of vehicle suspension systemrdquoInternational Journal of Automotive Technology vol 15 no 3pp 419ndash427 2014
[16] H L Zhang E RWangN Zhang FMin R Subash andC SuldquoSemi-active sliding mode control of vehicle suspension withmagneto-rheological damperrdquo Chinese Journal of MechanicalEngineering vol 28 no 1 pp 63ndash75 2015
[17] S Bououden M Chadli L Zhang and T Yang ldquoConstrainedmodel predictive control for time-varying delay systems Appli-cation to an active car suspensionrdquo International Journal ofControl Automation and Systems vol 14 no 1 pp 51ndash58 2016
[18] L Wu and W-J Zhang ldquoHierarchical modeling of semi-activecontrol of a full motorcycle suspension with six degrees offreedomsrdquo International Journal of Automotive Technology vol11 no 1 pp 27ndash32 2010
[19] ZMao YWang B Jiang andG Tao ldquoFault diagnosis for a classof active suspension systems with dynamic actuatorsrsquo faultsrdquoInternational Journal of Control Automation and Systems vol14 no 5 pp 1160ndash1172 2016
[20] H Trabelsi P-A Yvars J Louati and M Haddar ldquoEvaluationof the effectiveness of the interval computation method tosimulate the dynamic behavior of subdefinite system applica-tion on an active suspension systemrdquo International Journal onInteractive Design and Manufacturing vol 9 no 2 pp 83ndash962015
[21] CWang K DengW Zhao G Zhou andX Li ldquoRobust controlfor active suspension system under steering conditionrdquo ScienceChina Technological Sciences vol 60 no 2 pp 199ndash208 2017
[22] X Dong D Zhao B Yang and C Han ldquoFractional-ordercontrol of active suspension actuator based on parallel adaptiveclonal selection algorithmrdquo Journal of Mechanical Science andTechnology vol 30 no 6 pp 2769ndash2781 2016
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Hindawiwwwhindawicom Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Hindawiwwwhindawicom Volume 2018Volume 2018
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
6 Complexity
1Out 1
3000
kp
ap20
ki
ai
22
kec1
24
ke1
30
kd10ad
Zero-orderhold 3
Zero-orderhold 2
Scope
Saturation 3
Saturation 2
Product 2
Product 1
Product
MemoryFuzzy logiccontroller 1dudt
dudt
1In 2
-K-
-K-
+
+
+
+
+
+
+
+
+
1
s
times
times
times
Figure 5 The submodule of fuzzy increment controller
PassivePID
FuzzyFuzzy-PID
minus1
minus05
0
05
1
Body
acce
lera
tion
(ms
2)
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 6 Comparison result of the body vertical vibration acceler-ation
minus06
minus04
minus02
04
The p
itchi
ng an
gula
rac
cele
ratio
n(r
ads
2)
06
05 1 15 2 25 3 35 4 45 50Time (s)
PassivePID
FuzzyFuzzy-PID
02
0
Figure 7 Comparison result of the body pitching angular accelera-tion
minus15
minus1
minus05
0
05
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
1
15
05 1 15 2 25 3 35 4 45 50Time (s)
PassivePID
FuzzyFuzzy-PID
Figure 8 Comparison result of the body rolling angular accelera-tion
PassivePID
FuzzyFuzzy-PID
minus050
051
152
253
Body
acce
lera
tion
(ms
2)
1 2 3 4 50Time (s)
Figure 9 Comparison result of the body vertical vibration acceler-ation
Complexity 7Th
e pitc
hing
angu
lar
acce
lera
tion
(rad
s2)
minus1
0
1
2
3
4
1 2 3 4 50Time (s)
PassivePID
FuzzyFuzzy-PID
Figure 10 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus2
4
2
0
6
1 2 3 4 50Time (s)
Figure 11 Comparison result of the body rolling angular accelera-tion
PassivePID
FuzzyFuzzy-PID
minus15minus1
minus050
051
152
Body
acce
lera
tion
(ms
2)
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 12 Comparison result of the vertical vibration acceleration
controlmode under the condition of different speed as shownin Table 3
As seen from Table 3 the root mean square value ofthe bodyrsquos acceleration the pitching and rolling angularacceleration adopting the Fuzzy-PID mode reduces 375percent 289 percent and 262 percent compared with thepassivemode under the condition of white noise road surfaceexcitationThe rootmean square values of indexesmentioned
PassivePID
FuzzyFuzzy-PID
The p
itchi
ng an
gula
rac
cele
ratio
n(r
ads
2)
minus05
0
05
1
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 13 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus03
minus02
minus01
0
01
02
03
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 14 Comparison result of the rolling angular acceleration
above reduce 562 476 and 520 percent under the conditionof sinusoidal excitation respectively
You can also see that the root mean square values ofindexesmentioned above adopting the Fuzzy-PIDmode havebeen improved obviously compared to other modes at 30meters per second Through analysis we can see that thedesigned controller can reduce obviously the vehicle vibra-tion and has good control effect compared to the independentcontrol type
5 Conclusions
(1) The vibration model with seven degrees of freedomof automobile active suspension is derived and four fuzzyincrement controllers are designed based on 49 rules foradapting the different real-time road input information
(2) The white noise input model with four wheels cor-related in characteristics of time-domain is designed that iscloser to the actual road information input
(3) Using MATLABSimulink the simulation module ofactive suspension with seven DOF has been built and thefuzzy increment controller is validated taking the white noiseexcitation with four-wheel correlation in time-domain thesinusoidal excitation and the pulse excitation of C-graderoad surface as the road input The simulation results show
8 Complexity
Table 3 The root mean square value of acceleration
Input Speed Controlmode
Body verticalacceleration
Pitching angularacceleration
Rolling angularacceleration
White noiseexcitation
20ms
Passive 03800 02075 04937PID 02862 01720 04462Fuzzy 03031 01700 04237
Fuzzy-PID 02374 01475 03640
30ms
Passive 05383 02232 04247PID 04205 01936 03828Fuzzy 03987 01819 03217
Fuzzy-PID 03344 01673 02938
The sinusoidalexcitation
20ms
Passive 11386 05525 01858PID 07232 03722 00938Fuzzy 07950 03734 01159
Fuzzy-PID 04983 02891 00892
30ms
Passive 12356 02857 02111PID 07881 02055 01111Fuzzy 08587 02113 01225
Fuzzy-PID 06001 01653 01189
that designed fuzzy increment controller can reduce 375percent 289 percent and 262 percent in evaluation indexof the body vertical vibration acceleration pitching androlling acceleration compared with the passive mode underthe condition of white noise road surface excitation and canimprove 562 476 and 520 percent under the condition ofsinusoidal excitation respectively
In a word the designed fuzzy increment controller inthis paper is feasible to adapt to real-time change of roadsituations and can reduce obviously the vehicle vibrationand has a superior control effect compared to other controlmodesThe research achievements havemuch reference valuefor developing the product of suspension controller
As future work we intend to build the prototypes anddevelop products by single-chip technology
Conflicts of Interest
The authors declared no potential conflicts of interest withrespect to the research authorship andor publication of thisarticle
Acknowledgments
This work was supported in part by the Natural ScienceFoundation of China underGrant 61473139 and the joint fundof the Natural Science Foundation of Liaoning Province ofChina 201602368
References
[1] H Zhang E Wang F Min R Subash and C Su ldquoSkyhook-based semi-active control of full-vehicle suspension withmagneto-rheological dampersrdquo Chinese Journal of MechanicalEngineering vol 26 no 3 pp 498ndash505 2013
[2] H-B Ren S-Z Chen Y-Z Zhao G Liu and L YangldquoObserver-based hybrid control algorithm for semi-active sus-pension systemsrdquo Journal of Central South University vol 23no 9 pp 2268ndash2275 2016
[3] D Singh and M L Aggarwal ldquoPassenger seat vibration controlof a semi-active quarter car system with hybrid fuzzy-PIDapproachrdquo International Journal of Dynamics and Control vol5 no 2 pp 287ndash296 2017
[4] H-P Du and N Zhang ldquoRobust active suspension designsubject to vehicle inertial parameter variationsrdquo InternationalJournal of Automation and Computing vol 7 no 4 pp 419ndash4272010
[5] Y-J Liu and S Tong ldquoAdaptive fuzzy control for a classof unknown nonlinear dynamical systemsrdquo Fuzzy Sets andSystems vol 263 pp 49ndash70 2015
[6] Y-J Liu Y Gao S Tong andY Li ldquoFuzzy approximation-basedadaptive backstepping optimal control for a class of nonlineardiscrete-time systems with dead-zonerdquo IEEE Transactions onFuzzy Systems 1 page 2015
[7] Y Gao and Y-J Liu ldquoAdaptive fuzzy optimal control usingdirect heuristic dynamic programming for chaotic discrete-time systemrdquo Journal of Vibration and Control vol 22 no 2pp 595ndash603 2016
[8] H Li G Chen X Liao and T Huang ldquoLeader-followingconsensus of discrete-time multiagent systems with encoding-decodingrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 63 no 4 pp 401ndash405 2016
[9] H Li C Huang G Chen X Liao and T Huang ldquoDistributedConsensus Optimization in Multiagent Networks With Time-Varying Directed Topologies and Quantized CommunicationrdquoIEEE Transactions on Cybernetics 2017
[10] C Huang L Chen H Jiang C Yuan and T Xia ldquoFuzzy chaoscontrol for vehicle lateral dynamics based on active suspensionsystemrdquo Chinese Journal of Mechanical Engineering vol 27 no4 pp 793ndash801 2014
Complexity 9
[11] H Li S Liu Y C Soh and L Xie ldquoEvent-Triggered Communi-cation and Data Rate Constraint for Distributed OptimizationofMultiagent Systemsrdquo IEEETransactions on SystemsMan andCybernetics Systems pp 1ndash12
[12] H Li G Chen T Huang and Z Dong ldquoHigh-performanceconsensus control in networked systems with limited band-width communication and time-varying directed topologiesrdquoIEEE Transactions on Neural Networks and Learning Systemspp 1ndash12 2016
[13] S Riaz and L Khan ldquoNeuroFuzzy Adaptive Control for Full-Car Nonlinear Active Suspension withOnboard Antilock Brak-ing Systemrdquo Arabian Journal for Science and Engineering vol40 no 12 pp 3483ndash3505 2015
[14] M M Zirkohi and T-C Lin ldquoInterval type-2 fuzzy-neuralnetwork indirect adaptive sliding mode control for an activesuspension systemrdquo Nonlinear Dynamics vol 79 no 1 pp 513ndash526 2015
[15] L Balamurugan J Jancirani and M A Eltantawie ldquoGener-alized magnetorheological (MR) damper model and its appli-cation in semi-active control of vehicle suspension systemrdquoInternational Journal of Automotive Technology vol 15 no 3pp 419ndash427 2014
[16] H L Zhang E RWangN Zhang FMin R Subash andC SuldquoSemi-active sliding mode control of vehicle suspension withmagneto-rheological damperrdquo Chinese Journal of MechanicalEngineering vol 28 no 1 pp 63ndash75 2015
[17] S Bououden M Chadli L Zhang and T Yang ldquoConstrainedmodel predictive control for time-varying delay systems Appli-cation to an active car suspensionrdquo International Journal ofControl Automation and Systems vol 14 no 1 pp 51ndash58 2016
[18] L Wu and W-J Zhang ldquoHierarchical modeling of semi-activecontrol of a full motorcycle suspension with six degrees offreedomsrdquo International Journal of Automotive Technology vol11 no 1 pp 27ndash32 2010
[19] ZMao YWang B Jiang andG Tao ldquoFault diagnosis for a classof active suspension systems with dynamic actuatorsrsquo faultsrdquoInternational Journal of Control Automation and Systems vol14 no 5 pp 1160ndash1172 2016
[20] H Trabelsi P-A Yvars J Louati and M Haddar ldquoEvaluationof the effectiveness of the interval computation method tosimulate the dynamic behavior of subdefinite system applica-tion on an active suspension systemrdquo International Journal onInteractive Design and Manufacturing vol 9 no 2 pp 83ndash962015
[21] CWang K DengW Zhao G Zhou andX Li ldquoRobust controlfor active suspension system under steering conditionrdquo ScienceChina Technological Sciences vol 60 no 2 pp 199ndash208 2017
[22] X Dong D Zhao B Yang and C Han ldquoFractional-ordercontrol of active suspension actuator based on parallel adaptiveclonal selection algorithmrdquo Journal of Mechanical Science andTechnology vol 30 no 6 pp 2769ndash2781 2016
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Hindawiwwwhindawicom Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Hindawiwwwhindawicom Volume 2018Volume 2018
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Complexity 7Th
e pitc
hing
angu
lar
acce
lera
tion
(rad
s2)
minus1
0
1
2
3
4
1 2 3 4 50Time (s)
PassivePID
FuzzyFuzzy-PID
Figure 10 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus2
4
2
0
6
1 2 3 4 50Time (s)
Figure 11 Comparison result of the body rolling angular accelera-tion
PassivePID
FuzzyFuzzy-PID
minus15minus1
minus050
051
152
Body
acce
lera
tion
(ms
2)
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 12 Comparison result of the vertical vibration acceleration
controlmode under the condition of different speed as shownin Table 3
As seen from Table 3 the root mean square value ofthe bodyrsquos acceleration the pitching and rolling angularacceleration adopting the Fuzzy-PID mode reduces 375percent 289 percent and 262 percent compared with thepassivemode under the condition of white noise road surfaceexcitationThe rootmean square values of indexesmentioned
PassivePID
FuzzyFuzzy-PID
The p
itchi
ng an
gula
rac
cele
ratio
n(r
ads
2)
minus05
0
05
1
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 13 Comparison result of the pitching angular acceleration
PassivePID
FuzzyFuzzy-PID
The r
ollin
g an
gula
rac
cele
ratio
n(r
ads
2)
minus03
minus02
minus01
0
01
02
03
05 1 15 2 25 3 35 4 45 50Time (s)
Figure 14 Comparison result of the rolling angular acceleration
above reduce 562 476 and 520 percent under the conditionof sinusoidal excitation respectively
You can also see that the root mean square values ofindexesmentioned above adopting the Fuzzy-PIDmode havebeen improved obviously compared to other modes at 30meters per second Through analysis we can see that thedesigned controller can reduce obviously the vehicle vibra-tion and has good control effect compared to the independentcontrol type
5 Conclusions
(1) The vibration model with seven degrees of freedomof automobile active suspension is derived and four fuzzyincrement controllers are designed based on 49 rules foradapting the different real-time road input information
(2) The white noise input model with four wheels cor-related in characteristics of time-domain is designed that iscloser to the actual road information input
(3) Using MATLABSimulink the simulation module ofactive suspension with seven DOF has been built and thefuzzy increment controller is validated taking the white noiseexcitation with four-wheel correlation in time-domain thesinusoidal excitation and the pulse excitation of C-graderoad surface as the road input The simulation results show
8 Complexity
Table 3 The root mean square value of acceleration
Input Speed Controlmode
Body verticalacceleration
Pitching angularacceleration
Rolling angularacceleration
White noiseexcitation
20ms
Passive 03800 02075 04937PID 02862 01720 04462Fuzzy 03031 01700 04237
Fuzzy-PID 02374 01475 03640
30ms
Passive 05383 02232 04247PID 04205 01936 03828Fuzzy 03987 01819 03217
Fuzzy-PID 03344 01673 02938
The sinusoidalexcitation
20ms
Passive 11386 05525 01858PID 07232 03722 00938Fuzzy 07950 03734 01159
Fuzzy-PID 04983 02891 00892
30ms
Passive 12356 02857 02111PID 07881 02055 01111Fuzzy 08587 02113 01225
Fuzzy-PID 06001 01653 01189
that designed fuzzy increment controller can reduce 375percent 289 percent and 262 percent in evaluation indexof the body vertical vibration acceleration pitching androlling acceleration compared with the passive mode underthe condition of white noise road surface excitation and canimprove 562 476 and 520 percent under the condition ofsinusoidal excitation respectively
In a word the designed fuzzy increment controller inthis paper is feasible to adapt to real-time change of roadsituations and can reduce obviously the vehicle vibrationand has a superior control effect compared to other controlmodesThe research achievements havemuch reference valuefor developing the product of suspension controller
As future work we intend to build the prototypes anddevelop products by single-chip technology
Conflicts of Interest
The authors declared no potential conflicts of interest withrespect to the research authorship andor publication of thisarticle
Acknowledgments
This work was supported in part by the Natural ScienceFoundation of China underGrant 61473139 and the joint fundof the Natural Science Foundation of Liaoning Province ofChina 201602368
References
[1] H Zhang E Wang F Min R Subash and C Su ldquoSkyhook-based semi-active control of full-vehicle suspension withmagneto-rheological dampersrdquo Chinese Journal of MechanicalEngineering vol 26 no 3 pp 498ndash505 2013
[2] H-B Ren S-Z Chen Y-Z Zhao G Liu and L YangldquoObserver-based hybrid control algorithm for semi-active sus-pension systemsrdquo Journal of Central South University vol 23no 9 pp 2268ndash2275 2016
[3] D Singh and M L Aggarwal ldquoPassenger seat vibration controlof a semi-active quarter car system with hybrid fuzzy-PIDapproachrdquo International Journal of Dynamics and Control vol5 no 2 pp 287ndash296 2017
[4] H-P Du and N Zhang ldquoRobust active suspension designsubject to vehicle inertial parameter variationsrdquo InternationalJournal of Automation and Computing vol 7 no 4 pp 419ndash4272010
[5] Y-J Liu and S Tong ldquoAdaptive fuzzy control for a classof unknown nonlinear dynamical systemsrdquo Fuzzy Sets andSystems vol 263 pp 49ndash70 2015
[6] Y-J Liu Y Gao S Tong andY Li ldquoFuzzy approximation-basedadaptive backstepping optimal control for a class of nonlineardiscrete-time systems with dead-zonerdquo IEEE Transactions onFuzzy Systems 1 page 2015
[7] Y Gao and Y-J Liu ldquoAdaptive fuzzy optimal control usingdirect heuristic dynamic programming for chaotic discrete-time systemrdquo Journal of Vibration and Control vol 22 no 2pp 595ndash603 2016
[8] H Li G Chen X Liao and T Huang ldquoLeader-followingconsensus of discrete-time multiagent systems with encoding-decodingrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 63 no 4 pp 401ndash405 2016
[9] H Li C Huang G Chen X Liao and T Huang ldquoDistributedConsensus Optimization in Multiagent Networks With Time-Varying Directed Topologies and Quantized CommunicationrdquoIEEE Transactions on Cybernetics 2017
[10] C Huang L Chen H Jiang C Yuan and T Xia ldquoFuzzy chaoscontrol for vehicle lateral dynamics based on active suspensionsystemrdquo Chinese Journal of Mechanical Engineering vol 27 no4 pp 793ndash801 2014
Complexity 9
[11] H Li S Liu Y C Soh and L Xie ldquoEvent-Triggered Communi-cation and Data Rate Constraint for Distributed OptimizationofMultiagent Systemsrdquo IEEETransactions on SystemsMan andCybernetics Systems pp 1ndash12
[12] H Li G Chen T Huang and Z Dong ldquoHigh-performanceconsensus control in networked systems with limited band-width communication and time-varying directed topologiesrdquoIEEE Transactions on Neural Networks and Learning Systemspp 1ndash12 2016
[13] S Riaz and L Khan ldquoNeuroFuzzy Adaptive Control for Full-Car Nonlinear Active Suspension withOnboard Antilock Brak-ing Systemrdquo Arabian Journal for Science and Engineering vol40 no 12 pp 3483ndash3505 2015
[14] M M Zirkohi and T-C Lin ldquoInterval type-2 fuzzy-neuralnetwork indirect adaptive sliding mode control for an activesuspension systemrdquo Nonlinear Dynamics vol 79 no 1 pp 513ndash526 2015
[15] L Balamurugan J Jancirani and M A Eltantawie ldquoGener-alized magnetorheological (MR) damper model and its appli-cation in semi-active control of vehicle suspension systemrdquoInternational Journal of Automotive Technology vol 15 no 3pp 419ndash427 2014
[16] H L Zhang E RWangN Zhang FMin R Subash andC SuldquoSemi-active sliding mode control of vehicle suspension withmagneto-rheological damperrdquo Chinese Journal of MechanicalEngineering vol 28 no 1 pp 63ndash75 2015
[17] S Bououden M Chadli L Zhang and T Yang ldquoConstrainedmodel predictive control for time-varying delay systems Appli-cation to an active car suspensionrdquo International Journal ofControl Automation and Systems vol 14 no 1 pp 51ndash58 2016
[18] L Wu and W-J Zhang ldquoHierarchical modeling of semi-activecontrol of a full motorcycle suspension with six degrees offreedomsrdquo International Journal of Automotive Technology vol11 no 1 pp 27ndash32 2010
[19] ZMao YWang B Jiang andG Tao ldquoFault diagnosis for a classof active suspension systems with dynamic actuatorsrsquo faultsrdquoInternational Journal of Control Automation and Systems vol14 no 5 pp 1160ndash1172 2016
[20] H Trabelsi P-A Yvars J Louati and M Haddar ldquoEvaluationof the effectiveness of the interval computation method tosimulate the dynamic behavior of subdefinite system applica-tion on an active suspension systemrdquo International Journal onInteractive Design and Manufacturing vol 9 no 2 pp 83ndash962015
[21] CWang K DengW Zhao G Zhou andX Li ldquoRobust controlfor active suspension system under steering conditionrdquo ScienceChina Technological Sciences vol 60 no 2 pp 199ndash208 2017
[22] X Dong D Zhao B Yang and C Han ldquoFractional-ordercontrol of active suspension actuator based on parallel adaptiveclonal selection algorithmrdquo Journal of Mechanical Science andTechnology vol 30 no 6 pp 2769ndash2781 2016
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Hindawiwwwhindawicom Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Hindawiwwwhindawicom Volume 2018Volume 2018
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
8 Complexity
Table 3 The root mean square value of acceleration
Input Speed Controlmode
Body verticalacceleration
Pitching angularacceleration
Rolling angularacceleration
White noiseexcitation
20ms
Passive 03800 02075 04937PID 02862 01720 04462Fuzzy 03031 01700 04237
Fuzzy-PID 02374 01475 03640
30ms
Passive 05383 02232 04247PID 04205 01936 03828Fuzzy 03987 01819 03217
Fuzzy-PID 03344 01673 02938
The sinusoidalexcitation
20ms
Passive 11386 05525 01858PID 07232 03722 00938Fuzzy 07950 03734 01159
Fuzzy-PID 04983 02891 00892
30ms
Passive 12356 02857 02111PID 07881 02055 01111Fuzzy 08587 02113 01225
Fuzzy-PID 06001 01653 01189
that designed fuzzy increment controller can reduce 375percent 289 percent and 262 percent in evaluation indexof the body vertical vibration acceleration pitching androlling acceleration compared with the passive mode underthe condition of white noise road surface excitation and canimprove 562 476 and 520 percent under the condition ofsinusoidal excitation respectively
In a word the designed fuzzy increment controller inthis paper is feasible to adapt to real-time change of roadsituations and can reduce obviously the vehicle vibrationand has a superior control effect compared to other controlmodesThe research achievements havemuch reference valuefor developing the product of suspension controller
As future work we intend to build the prototypes anddevelop products by single-chip technology
Conflicts of Interest
The authors declared no potential conflicts of interest withrespect to the research authorship andor publication of thisarticle
Acknowledgments
This work was supported in part by the Natural ScienceFoundation of China underGrant 61473139 and the joint fundof the Natural Science Foundation of Liaoning Province ofChina 201602368
References
[1] H Zhang E Wang F Min R Subash and C Su ldquoSkyhook-based semi-active control of full-vehicle suspension withmagneto-rheological dampersrdquo Chinese Journal of MechanicalEngineering vol 26 no 3 pp 498ndash505 2013
[2] H-B Ren S-Z Chen Y-Z Zhao G Liu and L YangldquoObserver-based hybrid control algorithm for semi-active sus-pension systemsrdquo Journal of Central South University vol 23no 9 pp 2268ndash2275 2016
[3] D Singh and M L Aggarwal ldquoPassenger seat vibration controlof a semi-active quarter car system with hybrid fuzzy-PIDapproachrdquo International Journal of Dynamics and Control vol5 no 2 pp 287ndash296 2017
[4] H-P Du and N Zhang ldquoRobust active suspension designsubject to vehicle inertial parameter variationsrdquo InternationalJournal of Automation and Computing vol 7 no 4 pp 419ndash4272010
[5] Y-J Liu and S Tong ldquoAdaptive fuzzy control for a classof unknown nonlinear dynamical systemsrdquo Fuzzy Sets andSystems vol 263 pp 49ndash70 2015
[6] Y-J Liu Y Gao S Tong andY Li ldquoFuzzy approximation-basedadaptive backstepping optimal control for a class of nonlineardiscrete-time systems with dead-zonerdquo IEEE Transactions onFuzzy Systems 1 page 2015
[7] Y Gao and Y-J Liu ldquoAdaptive fuzzy optimal control usingdirect heuristic dynamic programming for chaotic discrete-time systemrdquo Journal of Vibration and Control vol 22 no 2pp 595ndash603 2016
[8] H Li G Chen X Liao and T Huang ldquoLeader-followingconsensus of discrete-time multiagent systems with encoding-decodingrdquo IEEE Transactions on Circuits and Systems II ExpressBriefs vol 63 no 4 pp 401ndash405 2016
[9] H Li C Huang G Chen X Liao and T Huang ldquoDistributedConsensus Optimization in Multiagent Networks With Time-Varying Directed Topologies and Quantized CommunicationrdquoIEEE Transactions on Cybernetics 2017
[10] C Huang L Chen H Jiang C Yuan and T Xia ldquoFuzzy chaoscontrol for vehicle lateral dynamics based on active suspensionsystemrdquo Chinese Journal of Mechanical Engineering vol 27 no4 pp 793ndash801 2014
Complexity 9
[11] H Li S Liu Y C Soh and L Xie ldquoEvent-Triggered Communi-cation and Data Rate Constraint for Distributed OptimizationofMultiagent Systemsrdquo IEEETransactions on SystemsMan andCybernetics Systems pp 1ndash12
[12] H Li G Chen T Huang and Z Dong ldquoHigh-performanceconsensus control in networked systems with limited band-width communication and time-varying directed topologiesrdquoIEEE Transactions on Neural Networks and Learning Systemspp 1ndash12 2016
[13] S Riaz and L Khan ldquoNeuroFuzzy Adaptive Control for Full-Car Nonlinear Active Suspension withOnboard Antilock Brak-ing Systemrdquo Arabian Journal for Science and Engineering vol40 no 12 pp 3483ndash3505 2015
[14] M M Zirkohi and T-C Lin ldquoInterval type-2 fuzzy-neuralnetwork indirect adaptive sliding mode control for an activesuspension systemrdquo Nonlinear Dynamics vol 79 no 1 pp 513ndash526 2015
[15] L Balamurugan J Jancirani and M A Eltantawie ldquoGener-alized magnetorheological (MR) damper model and its appli-cation in semi-active control of vehicle suspension systemrdquoInternational Journal of Automotive Technology vol 15 no 3pp 419ndash427 2014
[16] H L Zhang E RWangN Zhang FMin R Subash andC SuldquoSemi-active sliding mode control of vehicle suspension withmagneto-rheological damperrdquo Chinese Journal of MechanicalEngineering vol 28 no 1 pp 63ndash75 2015
[17] S Bououden M Chadli L Zhang and T Yang ldquoConstrainedmodel predictive control for time-varying delay systems Appli-cation to an active car suspensionrdquo International Journal ofControl Automation and Systems vol 14 no 1 pp 51ndash58 2016
[18] L Wu and W-J Zhang ldquoHierarchical modeling of semi-activecontrol of a full motorcycle suspension with six degrees offreedomsrdquo International Journal of Automotive Technology vol11 no 1 pp 27ndash32 2010
[19] ZMao YWang B Jiang andG Tao ldquoFault diagnosis for a classof active suspension systems with dynamic actuatorsrsquo faultsrdquoInternational Journal of Control Automation and Systems vol14 no 5 pp 1160ndash1172 2016
[20] H Trabelsi P-A Yvars J Louati and M Haddar ldquoEvaluationof the effectiveness of the interval computation method tosimulate the dynamic behavior of subdefinite system applica-tion on an active suspension systemrdquo International Journal onInteractive Design and Manufacturing vol 9 no 2 pp 83ndash962015
[21] CWang K DengW Zhao G Zhou andX Li ldquoRobust controlfor active suspension system under steering conditionrdquo ScienceChina Technological Sciences vol 60 no 2 pp 199ndash208 2017
[22] X Dong D Zhao B Yang and C Han ldquoFractional-ordercontrol of active suspension actuator based on parallel adaptiveclonal selection algorithmrdquo Journal of Mechanical Science andTechnology vol 30 no 6 pp 2769ndash2781 2016
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Hindawiwwwhindawicom Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Hindawiwwwhindawicom Volume 2018Volume 2018
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Complexity 9
[11] H Li S Liu Y C Soh and L Xie ldquoEvent-Triggered Communi-cation and Data Rate Constraint for Distributed OptimizationofMultiagent Systemsrdquo IEEETransactions on SystemsMan andCybernetics Systems pp 1ndash12
[12] H Li G Chen T Huang and Z Dong ldquoHigh-performanceconsensus control in networked systems with limited band-width communication and time-varying directed topologiesrdquoIEEE Transactions on Neural Networks and Learning Systemspp 1ndash12 2016
[13] S Riaz and L Khan ldquoNeuroFuzzy Adaptive Control for Full-Car Nonlinear Active Suspension withOnboard Antilock Brak-ing Systemrdquo Arabian Journal for Science and Engineering vol40 no 12 pp 3483ndash3505 2015
[14] M M Zirkohi and T-C Lin ldquoInterval type-2 fuzzy-neuralnetwork indirect adaptive sliding mode control for an activesuspension systemrdquo Nonlinear Dynamics vol 79 no 1 pp 513ndash526 2015
[15] L Balamurugan J Jancirani and M A Eltantawie ldquoGener-alized magnetorheological (MR) damper model and its appli-cation in semi-active control of vehicle suspension systemrdquoInternational Journal of Automotive Technology vol 15 no 3pp 419ndash427 2014
[16] H L Zhang E RWangN Zhang FMin R Subash andC SuldquoSemi-active sliding mode control of vehicle suspension withmagneto-rheological damperrdquo Chinese Journal of MechanicalEngineering vol 28 no 1 pp 63ndash75 2015
[17] S Bououden M Chadli L Zhang and T Yang ldquoConstrainedmodel predictive control for time-varying delay systems Appli-cation to an active car suspensionrdquo International Journal ofControl Automation and Systems vol 14 no 1 pp 51ndash58 2016
[18] L Wu and W-J Zhang ldquoHierarchical modeling of semi-activecontrol of a full motorcycle suspension with six degrees offreedomsrdquo International Journal of Automotive Technology vol11 no 1 pp 27ndash32 2010
[19] ZMao YWang B Jiang andG Tao ldquoFault diagnosis for a classof active suspension systems with dynamic actuatorsrsquo faultsrdquoInternational Journal of Control Automation and Systems vol14 no 5 pp 1160ndash1172 2016
[20] H Trabelsi P-A Yvars J Louati and M Haddar ldquoEvaluationof the effectiveness of the interval computation method tosimulate the dynamic behavior of subdefinite system applica-tion on an active suspension systemrdquo International Journal onInteractive Design and Manufacturing vol 9 no 2 pp 83ndash962015
[21] CWang K DengW Zhao G Zhou andX Li ldquoRobust controlfor active suspension system under steering conditionrdquo ScienceChina Technological Sciences vol 60 no 2 pp 199ndash208 2017
[22] X Dong D Zhao B Yang and C Han ldquoFractional-ordercontrol of active suspension actuator based on parallel adaptiveclonal selection algorithmrdquo Journal of Mechanical Science andTechnology vol 30 no 6 pp 2769ndash2781 2016
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Hindawiwwwhindawicom Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Hindawiwwwhindawicom Volume 2018Volume 2018
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Hindawiwwwhindawicom Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Hindawiwwwhindawicom Volume 2018Volume 2018
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
![Technology & training86].pdfThe tests related to automobile sound and vibration include: NVH, automobile multimedia test, etc. Megasig product line provide sensors, acquisition device](https://static.fdocuments.in/doc/165x107/5f7c28fa5f89ef36f3329655/technology-86pdf-the-tests-related-to-automobile-sound-and-vibration-include.jpg)
