Vehicle Suspension Control Using Recurrent Neurofuzzy Wavelet Network

www.seipub.org/ve Vehicle Engineering (VE), Volume 3, 2015 doi: 10.14355/ve.2015.03.002

Vehicle Suspension Control Using Recurrent Neurofuzzy Wavelet Network Shahid Qamar*1, Usman Khalid2, M. Bilal Qureshi3 Electronic Engineering Department, International Islamic University, Islamabad, Pakistan

1

Electrical Engineering Department, COMSATS Institute of Information Technology, Abbottabad, Pakistan

2

Electrical and Computer Engineering Department, North Dakota State Univrsity, Fargo, ND, USA

3

*1

shahidqamar@ciit.net.pk; 2usmankhalid@ciit.net.pk; 3Muhammad.qureshi@ndsu.edu

Abstract The main aim of this paper is to design the controller for a vehicle suspension system to reduce the uneasiness felt by passengers which arises from road disturbances and to increase the road holding related with the movements of pitch and roll of the vehicle. This demands an accurate and quick adaptive controller to obtain such control objectives, because, the passive suspension system and semi‐active suspension cannot perform better. Therefore, an adaptive Recurrent Fuzzy Wavelet Neural Network (RFWNN) based active suspension systems are designed to give better ride comfort and vehicle stability. The proposed adaptive RFWNN model combines the traditional TSK fuzzy model and the wavelet neural networks. The RFWNN controller is highly nonlinear and robust to meet the control objectives and can handle the nonlinearities faster than other conventional controllers. An online learning algorithm, which consists of parameter learning, is also presented. The learning parameters are based on the steepest‐descent method, to train the proposed RFWNN. The proposed approach is used to minimize the vibrations of seat, heave pitch and roll of the vehicle when traveling on rough road. The performance of the proposed RFWNN control strategy is being assessed by comparing with passive and semi‐active suspension systems.

Keywords Fuzzy Logic; Neural Network; Wavelet; Full Car; Suspension System

Introduction For many years vehicle dynamics engineers have struggled to achieve a compromise between vehicle handling, ride comfort and stability. The results of this are clear in the vehicles we see today. In general, at one extreme are large sedan and luxury cars with excellent ride qualities but only adequate handling behavior.

Passive suspension system is capable to a mass energy through the spring and dissipate it through damper.

Parameters of passive suspension system are usually fixed and are chosen to attain the compromise between vehicle control and the comfort of passenger. In case of passive suspension, only damper and spring are used. So, the only choice is to design an active controller to deal with stiffness and damping rate. Feature of the passive suspension is its simplicity and cost. In semi‐active suspension, damper having variable damping constant is used.

Though, having largetime constant its damping can be varied, i.e., can be of several distinct or continues values.

Furthermore, energy is dissipated only. The feature is that energy demand is small. An active suspension system is capable to store, dissipate and introduce energy into the system. Its parameters are usually variable and depend upon the operating conditions. Whereas, in an active suspension system the energy source is added hence passengerʹs comfort and vehicle handling can be improved. As a consequence, complexity in design, larger cost and particularly big amount of energy demand. As vehicle suspension system is very important as far as vehicleʹs stability and ride comfort is concerned. So, many researchers worked on the control of suspension system of car to give better ride comfort and vehicleʹs stability. (S.I.Frank. et al. 2000) presented an active suspension control where an ʺinput decoupling transformationʺ and altered feedback control scheme was combined. In order to minimize roll, pitch and heave motions and to perk up the passengerʹs ride comfort, both inner and outer control loops were used. (D.Hana 2010) designed a semi‐active suspension system by mounting a variable shock absorber in parallel with that of passive suspension system. Intelligent system identication is used to capture the dynamics of car. The effect shows that semi‐active suspension system tracked the input signal well. This indicates that PID controller has

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controlled the variable shock absorber and has removed the effect of road disturbances. The study in (C.Supavut. and H.Peng. 2004) depicted that using the proposed PI sliding mode control had confirmed to be very successful to control vibrations of the vehicle and had attained better performance as compared to passive suspension system.

In (S.Chantranuwathana. and H.Peng. 1999), controller had been designed for force control loop. When force sensor is eliminated from the system, a customized adaptive robust control technique has been proposed to keep the stability. It has been shown by the results that the proposed controllers work very efficiently when compared to PID controller, both having the same two‐loop approach. A single‐loop LQG controller is also used for comparison.

Adaptive control involves the adjustment of feedback gains according to changes in the system parameters and road conditions. (A.Hseyin. and S.Trkay. 2009) suggested the output feedback for the active suspension control.

H norm was used to evaluate the passengerʹs ride comfort. Results have shown that the proposed controller when applied on half car model with four degrees of freedom has increased the passengerʹs ride comfort to a great extent, also, control input and suspension stroke were in limits. The fuzzy active suspension control of the half car model was investigated in (W.Jen. et al. 2004), but did not consider the passenger’s comfort. The full car active suspension systems were designed by (A.Farazandeh. and R.Kazemi. 2006, P.E.Uys., P.Els., and M.Thoresson. 2007). But they only discussed the velocities of the heave pitch and roll. For a quarter car model, semi‐active suspension based on fuzzy logic controller was designed (W.Jen. et al. 2004). The main objective was to reduce the bodyʹs displacement and velocity. This controller performed very well as compared to a passive suspension system. One of the drawback of fuzzy systems is the requirement of large number of linguistic rules. It is not practically feasible to use so many rules. Also the parameters involved in suspension systems need to change with time. So, there must be a continuous learning mechanism so that they can adapt with different road profiles. Neural networks may be one good choice. Various methods for neural net‐work training had been described in (R.Hampo. and K.Marko. 1991), so that these neural networks can be best utilized for linear or nonlinear systems. These methods were compared with conventional controllers and were found reasonable in terms of performance. Neurofuzzy, the blend of fuzzy logic and neural networks, have shown considerable results in modeling of the nonlinear functions and can also process perception based information (fuzzy) as well as measurement based information. To improve ride comfort and damping the vibrations of semi‐active suspension, neurofuzzy controller was designed (S.Foda 2001).

The combination of a fuzzy wavelet neural inference system comprises the strength of the optimal dentition of the antecedent part and the consequent part of the fuzzy rules. A neuro‐fuzzy wavelet scheme combines wavelet theory with fuzzy logic and neural networks. Wavelet neural networks are based on wavelet transform which has the capability to examine non‐stationary signals to determine their local details (Hidaya 2008). In (C.Jiacong. and X.Lin. 2008) authors used a recurrent wavelet neural network (WNN) for irradiation forecast. However, a major drawback of the neurofuzzy system is that its application field is restricted to static problems due to its feedforward network composition. Processing sequential problems using the neurofuzzy system is inefficient. On the other hand, ARNF structure is based on supervised learning, which is a dynamic mapping network and is more appropriate for dealing with dynamic systems than the neurofuzzy system (C.Juang. and C.Hsieha. 2010, Y.Lin., J.Chang., and C.Lin. 2013).

In this study, adaptive recurrent fuzzy wavelet neural network (RFWNN) control is proposed for the active suspension system. The antecedent part of the network is made recurrent to improve the performance of the RFWNN technique. The adaptive RFWNN controller has the ability to handle the control problems and can give better ride comfort and vehicle stability. The suspension systems are very dynamic in nature while the neurofuzzy controller lacks the dynamic elements so, copying the previous states is not easy and practically feasible, because, it may require extra nodes and consequently, network convergence is slow. Another choice might be the use of recurrent fuzzy neural networks approach to better control of active suspension system.

In this study, an adaptive RFWNN strategy is successfully implemented on highly nonlinear, i.e., active full car suspension model to improve the ride comfort and road handling. In these techniques, five different RFWNNs controllers have been designed, i.e. four controllers for tyres and one for seat in order to minimize the displacements of heave, pitch, roll and seat. The paper is divided into five sections. Section II discusses the full

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vehicleʹs model. Section III, discusses the proposed RFWNN controltechnique for full car suspension control.

Finally, simulation results and conclusionare given in section IV and V respectively.

Full Car Model The full car suspension model is known to be a nonlinear system, which has eight degrees of freedom. It comprises only a sprung mass attached to the four unsprung masses M fr , M fl , M rr , M rl (front‐right, front‐left, rear‐right and rear‐left wheels) at each corner. The sprung mass is allowed to have pitch, heave and roll and where the unsprung mass is allowed only to have heave. For simplicity all other motions are ignored in this model. This model has eight degrees of freedom and allocates the body acceleration and upright body displacement, pitch and roll motion of the vehicle body. Full car is professionally ensuring passenger safety and ride comfort (S.Qamar., L.Khan., and S.Ali. 2013). This model is considering only one seat and this is very important to take into consideration other fixed with chassis. The eight degrees of freedom consists of

 x1 , x2 , x3 , x4 , x5 , x6 , x7   , x8    four wheels displacement, seat displacement, heave displacement, pitch

displacement and roll displacement. The model of a full car suspension system is shown in Fig. 1. The suspensions between the sprung mass and unsprung mass are modelled as nonlinear viscous dampers and spring components and the tyres are modeled as simple nonlinear springs without damping elements. The actuator gives forces that determine the displacement of the actuator between the sprung mass and the wheels. The dampers between the wheels and car body signify sources of conventional damping like friction among the mechanical components. The inputs of full car model are four disturbances coming through the tyres, and the four outputs are the heave, pitch, seat, and roll displacement (L.Khan., S.Qamar., and M.U.Khan. 2014, D.Rosheila 2008). The full car model will be used as a good approximation of the whole car.

FIG. 1 FULL CAR MODEL

Mathematical Modeling As full‐car model has eight‐degrees of freedom, then equations of motion for this model are explained by the Newtonʹs 2nd law of motion as: For the Passenger Seat: ..

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M s Z s  ks ( Zs ‐ Z ‐ X s ‐ Ys f )  cs (Zs ‐ Z‐ Xs  ‐ Ys f )  0 (1)

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For the vehicle heave motion of the body: ..

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M Z  k f 1 ( Z  a  W   Z f ,l )  c f 1 ( Z s  a  W   Z f ,l ))  k r 1 ( Z  b  W   Z f ,l )  cr1 ( Z  b   W   Z r , l )  .

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k f 2 ( Z  a  W   Z f , r )  c f 2 ( Z  a   W   Z .

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f ,r ) 

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k r 2 ( Z  b  W   Z r , r )  cr 2 ( Z  b   W   Z r , r ) 

(2)

.

c s ( Z s  Z  X s   Ys  )  f 1  f 2  f 3  f 4  0

For the vehicle Roll motion of the body: ..

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I x   Wk f 1 ( Z  a  W   Z f ,l )  Wc f 1 ( Z  a   W   Z f ,l )  Wkr 1 ( Z  b  W   Zr ,l )  Wcr 1 ( Z  b   W   Z r ,l )  .

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Wk f 2 ( Z  a  W   Z f ,r )  Wc f 2 ( Z  a   W   Z f ,r )  Wkr 2 ( Z  b  W   Zr ,r )  Wcr 2 ( Z  b  W   Z r ,r )  .

.

.

(3)

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Ys k s ( Zs  Z  X s  Ys )  Ys c s ( Z s  Z  X s   Ys  )  Wf1  Wf 2  Wf 3  Wf 4  0

For the vehicle Pitch motion of the body: ..

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I y   ak f 1 ( Z  a  W   Z f ,l )  ac f 1 ( Z  a   W   Z f ,l )  bk r1 ( Z  b  W   Z r ,l )  bcr1 ( Z  b   W   Z r ,l )  .

.

.

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ak f 2 ( Z  a  W   Z f , r )  ac f 2 ( Z  a   W   Z f , r )  bk r 2 ( Z  b  W   Z r , r )  bcr 2 ( Z  b  W   Z r , r )  .

(4)

.

X s cs ( Z s  Z  X s  Ys )  X s cs ( Z s  Z  X s   Ys  )  af1  bf 2  af3  bf 4  0

For the Vehicle’s Wheels motion: ..

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.

.

.

(5)

.

(6)

M f ,l Z f ,l  k f 1 (Z  a  W  Z f ,l )  c f 1 (Z  a   W   Z f ,l )  kt (Z f ,l  zg1 )  f1  0 ..

.

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M f ,l Z r ,l  k r1 ( Z  b  W   Z r ,l )  cr1 ( Z  b   W   Z r ,l )  kt ( Z r ,l  z g 3 )  f 2  0

M f ,r Z.. f , r  k f 2 ( Z  a  W   Z f , r )  c f 2 ( Z.  a .  W .  Z. f ,r )  kt ( Z f , r  z g 2 ) 

f 3  0 (7)

M r , r Z r ,r  k r 2 ( Z  b  W   Z r , r )  cr 2 ( Z  b   W   Z r ,r )  kt ( Z r , r  z g 4 )  f 4  0 (8) ..

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Here: M s is passenger seat Mass. (kg) M is Body Mass. (kg) M f ,l , M f , r , M r ,l , M r ,r are front left side, front right side, rear left side,and rear right side unsprung mass

respectively. (kg) cs , k s are the damping and spring coefficient of seat.  N m  ,  N s m 

c f 1 , k f 1 are the damping nd springcoefficient of front left side respectively.  N m  ,  N s m  c f 2 , k f 2 are the damping and spring coefficient of front right side respectively.  N m  ,  N s m 

cr1 , kr1 are the damping and spring coefficient of rear left side respectively.  N m  ,  N s m 

cr 2 , kr 2 are the damping and spring coefficient of rear right side respectively.  N m  ,  N s m 

a and b are the distance of axle from center of gravity. (m)





I x , I y are the moment of inertia of ass body. kg .m 2 X s , Ys are the seat distance from center of gravity. (m)

kt is tire stiffness.  N m 

f1 , f 2 , f3 , f 4 , f5 are actuator force for front left, front right, rear left andrear right tire respectively. z g1 , z g 2 , z g 3 , z g 4 are road disturbances to front left, front right, rear leftand rear right tire respectively.

Recurrent Fuzzy Wavelet Neural Network In this section, the proposed TSK based recurrent fuzzy wavelet neural network is presented to show that the RFWNN is a simplified from the fuzzy neural network. The key features of the RFWNN‐dynamic mapping ability, chronological information storage, universal estimation, and the fuzzy inference system are discussed here. The

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RFWNN will be shown to possess the same advantages over recurrent neural network (L.Cheng‐Jian. and C.Chin.

2004) RFWNN Structure As depicted in Fig. 2 that structure of the suggested RFWNN has seven layers. First three layers are the antecedent layers and rests are the consequent layers. In the first layer, number of nodes is equivalent to number of input signals and is used for input distribution.

Each node in the second (membership) layer depicts one linguistic term. Here, membership degree for each input signal, which enters into the system and also for the fuzzy set it belongs to, is computed. Gaussian membership function is being used to illustrate the linguistic terms.

The third layer is the rule layer where number of nodes depicts the number of rules i.e. R1 , R2 ,..., Rn and each node signifies one fuzzy rule. AND (Min) operation ineach rule is used to compute the output signalʹs value. Each G j (k ) computed is the input for the next (consequent ) layer.

FIG. 2 RFWNN STRUCTURE

The fourth layer comprises of ' n ' number of Wavelet Functions (WFs), i.e, Maxixan Hat. Where the lth waveletʹs I t  output is calculated by: zil  i il where dil and til are the WF’s parameters between the ith input  i  1,..., n  dil

and lth output  l  1,..., n  . Also weight  is multiplied to each WF calculated in the fourth layer, WFs are multiplied by the third layerʹs output signals.

The defuzzification is done in the fifth and sixth layer and output of the network is calculated in the seventh layer.

Hence there is an involvement of every wavelet in the output of the controller.

Update Parameters Learning To minimize the error a commonly used steepest‐descent method is expressed as; E

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1 ( y  yd ) 2 (9) 2

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where y and yd are the actual and desired value of the system. Gaussian membership function is given by; 

( I i ( k )  mij )2

 ij2

G j (k )  e

I i (k )  O1 (k )  O 2 (k )

(10)

k  1, 2,..., n

Where O 2 is given by

O 2 ( k )  G j ( k  1).ij Where mij is the mean,  ij is the standard deviation O1 ( k ) is the input (the first layer), G j ( k  1) is the past value of membership function while  ij is feedback parameter. It is clear that the input of this layer contains the memory terms, which store the previous information of the network. This is the clear difference between the neurofuzzy and recurrent neurofuzzy system.

Maxican hat wavelet is showns as

 j (I )  dj



1 2

1  1 tj  2  d j

   

(11)

Where t j and d j are the translation and dilation parameters of the wavelet, respectively. The update equations for the l (weight), dil (dilation), til (translation), mij (mean),  ij (Standard Deviation) and  ij (Feedback weight) can be expressed as;

l (t  1)  l (t )  

E l

dil (t  1)  dil (t )  

E

dil

til (t  1)  til (t )  

(13)

(14)

E

mij

(15)

E

 ij

E

 ij

E

til

mij (t  1)  mij (t )  

 ij (t  1)   ij (t )    ij (t  1)   ij (t )  

(12)

(16)

(17)

Where  is learning rate, m is the input signals (input neurons), n is the numberof rules (hidden neurons), i  1,..., m , j  1,..., n , l  1,..., n .

Where with the help of chain rule the values of

E E E E E E , , , , and are equivalent to;  ij l dil til mij  ij

E E O 7 Ol4  . . l O 7 Ol4 l

(18)

E E O7 Ol4  l Zil  . .

(19) dil O 7 Ol4  l Zil dil

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E E O7 Ol4  l Zi  . .

(20) til O 7 Ol4  l Zl tl

E E O7 O3  . .

(21) mij O7 O3 mij

E E O7 O3  . .

(22)  ij O7 O3  ij

E E O 7 O3  . .

(23)  ij O 7 O3  ij

The update equations (12‐17) will be equal to;

E E O7 O3 . .

(24)  ij O 7 O3 ij

  E 0.5   Zil2   l   3.5Zil  Zil3  e Zil  dil  

2

dil

 1 2

Zil    dil

   (25)  

2 E   l (3Zil  Zil3 )e  Zil /2 ( dil3 ) (26) tij

E O O .e  2e.  ij O 3 4

7



(O1 ( k ) G j ( k 1).ij  mij )2

 ij2

(27)

O ( k ) G j ( k 1).ij  mij 1

E 2 O4  O7  3 e. .e  ij  ij O 3



 ij2

1

E O 4  O7  2e.G j ( k  1). .e  ij O 3

where l  e l  I  .  Zl 

(28)



O

( k ) G j ( k 1).ij  mij2  ij2

(29)

n

   I  . These equations give the required update equations l

l 1

for RFWNN system. Substituting the values from equations (24 ‐ 29) in equation (12‐17), it gives;





n

l (t  1)  l (t )   O7 (t )  r (t )  ( I ). (Zl )  l ( I )

l 1

  0.5   Zil2 /2 dil (t  1)  dij (t )   l   3.5Zil  Zil3  e Zil   

dil

 1/2 

Zil    dil

(30)

   (31)  

til (t  1)  tit (t )   l (3Zil  Zil3 )e Zil /2 / ( dil3 ) (32)

2

mij (t  1)  mij (t )    2e.

O 4  O7

O

3



(O1 ( k ) G j ( k 1). ij  mij )

 2ij

.e

(33)

O ( k ) G j ( k 1).ij  mij 1

 ij (t  1)   ij (t )  

12

2

 ij

3

e.

O 4  O7

O

3



.e

 2ij

(34)

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 ij (t  1)   ij (t )  

2

 ij

3

e.

O 4  O7

O

3



O1 ( k ) G j ( k 1).ij  mij

.e

 2ij

(35)

Equation (30‐35) are the required update equations. The closed loop control structure for the RFWNN is depicted in Fig. 3.

Simulations Results The aim of this control strategy is to improve the ride comfort and vehicle stability against the road disturbances.

The comfort is examined by the vertical displacement felt by the passenger. The controller goal is to minimize the displacement of the vehicle body with reference to the openloop, to avoid the suspension travel should not hit the rattle space limits. So, the controller performance is good when it reduces the vehicle vibrations under road disturbances. In this study, a road profile containing pothole and bump has the form, i.e., 15  z(t )  15 0 

1  t  2, 4  5 9  t  10,12  13

(36)

otherwise

Here ‐0.15 m is the pothole and 0.15 m is the bump on the road. This road profile is helpful to calculate heave, pitch and roll of the vehicle. This type of road profile shows the low frequency high amplitude response.

Acceleration for Heave, Pitch, Roll and Seat Here, in this section simulation results of heave, pitch and roll accelerations are given in Fig. 4 to Fig. 6. Result of seat displacement with/without controller is also given in Fig. 7 and Fig. 8. All the results are compared with passive and semi‐active controller.

FIG. 4 HEAVE ACCELERATION

FIG. 5 PITCH ACCELERATION

FIG. 6 ROLL ACCELERATION

FIG. 7 SEAT ACCELERATION WITHOUT CONTROLLER

FIG. 8 SEAT ACCELERATION WITH CONTROLLER

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The maximum value for semi‐active controller acceleration are 24.252m / s2 , 18.193m / s2 and 10.5m / s2 , for heave, pitch and roll, while the maximum valuefor passive controller accelerations are 36.17m / s2 , 22.1m / s2 and 7.4m / s2 for heave, pitch and roll. For RFWNN controller the maximum value for heave, pitch, roll accelerations are 0.005m / s2 , 27.64m / s2 and 6.8m / s2 respectively. Results show that the response of the heave, pitch and roll acceleration for RFWNN based active suspension system. Also the transient response is reduced and the steady state response has increased.

Displacement for Heave, Pitch, Roll and Seat Here, in this section simulation results of heave, pitch and roll displacements are given in Fig. 9 to Fig. 11. Result of seat displacement with/without controller is also given in Fig. 12 and Fig. 13. All the results are compared with passive and semi active controller.

FIG. 9 HEAVE DISPLACEMENT

FIG. 10 PITCH DISPLACEMENT

FIG. 11 ROLL DISPLACEMENT

FIG. 12 SEAT DISPLACEMENT WITHOUT CONTROLLER

FIG. 13 SEAT DISPLACEMENT WITH CONTROLLER

The maximum value for semi‐active controller displacements are 0.035m , 0.088m and 0.061m for heave, pitch and roll respectively, while the maximum value for passive controller displacements are 0.181m , 0.106m and 0.075m for heave, pitch and roll respectively. For RFWNN controller the maximum value for heave, pitch, roll displacements are 0.105m , 0.036m and 0.035m respectively. Results show that the response of the heave, pitch and roll displacements have increased by 41.98% , 66.03% and 55.33% respectively. Also the transient response is reduced and the steady state response has increased. Fig. 14 shows the control efforts of RFWNN controller of front left tyre, front right tyre, rear left tyre, rear right tyre and seat controller. From the above results it is observed that the rear left tyre controller applied more force than other controllers.

In this paper, an adaptive RFWNN control strategy with wavelet function, i.e., Mexican hat wavelet is successfully implemented to the full car active suspension. The objective was to improve the passenger comfort and the road handling of the vehicle against the road disturbances. The proposed RFWNN active suspension system has the ability to achieve low steady‐state error and fast error convergence than the passive and semi‐active suspension

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systems. Therefore, RFWNN based active suspension system shows that it improves the vehicle stability and passenger comfort. The simulation results depict that heave, pitch, roll, seat displacement are improved for the active suspension systems as compared to passive and semi‐active suspension system.

ACKNOWLEDGMENT

The authors would like to thank International Islamic University, Islamabad and COMSATS Institute of Information Technology, Abbottabad, Pakistan, for facilitating us to complete this research work.

REFERENCES

[1]

A.Farazandeh., and R.Kazemi. 2006. ʺFuzzy control for active suspension in adams/car full vehicle.ʺ Chinese Control Conference.

[2]

A.Hseyin., and S.Trkay. 2009. ʺInfluence of tire damping on mixed H2/H8 synthesis of half‐car active suspensions.ʺ Sound and Vibration 322 (1):15‐28.

[3]

C.Jiacong., and X.Lin. 2008. ʺStudy of hourly and daily solar irradiation forecast using diagonal recurrent wavelet neural networks.ʺ Energy Conversion and Management 49 (6):1396‐1406.

[4]

C.Juang., and C.Hsieha. 2010. ʺLocally recurrent fuzzy neural network with support vector regression for dynamic‐system modeling.ʺ IEEE Transactions On Fuzzy Systems 18 (2):261‐273.

[5]

C.Supavut., and H.Peng. 2004. ʺAdaptive robust force control for vehicle active suspensions.ʺ International Journal of Adaptive Control and Signal Processing 18 (2):83‐102.

[6]

D.Hana. 2010. ʺPID controller design for semi‐active car suspension based on model from intelligent system identication.ʺ Computer Engineering and Applications.

[7]

D.Rosheila. 2008. ʺModeling and control of active suspension for a full car Model.ʺ Master, Faculty of Electrical Engineering, Universiti Teknologi Malaysia.

[8]

Hidaya, A. Rahib. 2008. ʺFuzzy wavelet neural networks for identification and control of dynamic plants a novel structure and a comparative study.ʺ IEEE Transactions on Industrial Electronics 55 (8):3133‐3140.

[9]

L.Cheng‐Jian., and C.Chin. 2004. ʺPrediction and identification using wavelet‐based recurrent fuzzy neural networks.ʺ IEEE Transactions on Systems, Man, and Cybernetics 34 (5):2144‐2154.

[10] L.Khan., S.Qamar., and M.U.Khan. 2014. ʺComparative analysis of adaptive neuroFuzzy control techniques for full car active suspension system.ʺ Arabian Journal of Science and Engineering 39 (3):2045‐2069.

[11] P.E.Uys., P.Els., and M.Thoresson. 2007. ʺSuspension settings for optimal ride comfort of off‐road vehicles travelling on roads with different roughness and speeds.ʺ Journal of Terramechanics 44 (2):163‐175.

[12] R.Hampo., and K.Marko. 1991. ʺNeural Nntwork architectures for active suspension control.ʺ Seattle International Joint Conference on Neural Networks.

[13] S.Chantranuwathana., and H.Peng. 1999. ʺAdaptive robust control for active suspensions.ʺ American Control Conference.

[14] S.Foda. 2001. ʺNeuro‐Fuzzy Control of A Semi‐Active Car Suspension System.ʺ IEEE Conference on Communications, Computers and Signal Processing.

[15] S.I.Frank., F.L.Lewis., J.Campos., and L.Davis. 2000. ʺActive suspension control of ground vehicle based on a full‐vehicle model.ʺ American Control Conference.

[16] S.Qamar., L.Khan., and S.Ali. 2013. ʺAdaptive B‐spline based neuro‐fuzzy control for full car active suspension system.ʺ Middle‐East Journal of Scientific Research 16 (10):1348‐1360.

[17] W.Jen., H.Chiang., J.Chen., and T.Lee. 2004. ʺOptimal fuzzy control design for half‐car active suspension systems.ʺ IEEE International Conference on Networking, Sensing and Control.

[18] Y.Lin., J.Chang., and C.Lin. 2013. ʺIdentification and prediction of dynamic systems using an interactively recurrent self‐ evolving fuzzy neural network.ʺ IEEE Transactions on Neural Networks and Learning Systems 24 (2):310‐321.

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