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Middle-East Journal of Scientific Research 16 (10): 1348-1360, 2013

ISSN 1990-9233

IDOSI Publications, 2013

DOI: 10.5829/idosi.mejsr.2013.16.10.11842

Corresponding Author: Shahid Qamar, Department of Electrical Engineering,

COMSATS Institute of Information Technology, Abbottabad, Pakistan.1348

Adaptive B-Spline Based Neuro-Fuzzy Control for Full

Car Active Suspension System

Shahid Qamar, Laiq Khan and Saima Ali

Department of Electrical Engineering,

COMSATS Institute of Information Technology, Abbottabad, Pakistan

Abstract: The main role of a car suspension system is to improve the ride comfort and road holding. The

traditional spring-damper suspension is currently being replaced by either a semi-active or active suspension

system, because, passive suspension system cannot give better ride comfort and handling property. In order

to improve the capability of active suspension systems, a robust Adaptive B-spline Neuro-fuzzy (ABNF) based

control strategies are used to give better road handling and passenger comfort. In this paper, different ordersof B-spline membership functions are used in the proposed ABNFs control strategies. The shape of B-spline

membership functions can be adjusted self-adaptively by changing control points during learning process.

The order of the B-spline membership functions gives a structure for choosing the shape of the fuzzy sets.

The update parameters of ABNFs are trained by gradient descent based technique during the learning process.

The ABNFs control techniques are successfully applied to full car suspension model which reduces the seat

heave pitch and roll displacement, suspension travel and wheel displacement of the vehicle. The performance

index of the proposed techniques is taken on the basis of seat, heave, pitch and roll of the vehicle. Simulation

is based on the full car mathematical model by using MATLAB/SIMULINK. The simulation results show that

the ABNFs control techniques give better results than passive and semi-active suspension systems.

Key words: B-spline Fuzzy logic Neural network Full car Suspension system

INTRODUCTION The main objective of an active suspension is to

In vehicle's suspension systems, the suspension road disturbances, to improve the vehicle stability and the

system plays a very important role for the vehicles passenger comfort. The primary requirements of a good

stability or road handling and ride comfort against the vehicle suspension design are possession of good ride

road disturbances. So, the passive system cannot give comfort, road handling and road holding characteristics

better road handling and passengers comfort. The within an acceptable suspension travel range [1-4].

conventional passive suspension system comprises of The conflicting nature of these design objectives makes

combination of springs and dampers. Unlike conventional a necessary trade-off between them.

passive and semi-active suspension systems, an active In the last few years, many researchers applied

vehicle suspension systems external excitation is different linear and nonlinear control methods to thecounteracted with the generation of a control force vehicle suspension models. The linear suspension control

depending on the vehicle response through an actuator strategies range from PID to robust multivariable

driven by an external energy source. Therefore, the use controllers. It is supposed that the systems states reveal

active vibration control mechanism for design of only small oscillations about a stability point so that a

advanced suspension system has attracted considerable linear estimated model can be used. PID and direct

attention in the recent years. adaptive neural control of a nonlinear half car active

reduce the vibrations of the vehicle body induced by the

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Middle-East J. Sci. Res., 16 (10): 1348-1360, 2013

1349

suspension system is established in [5-9]. To examine the functions at any arbitrary precision as long as the network

robustness of quarter car suspension system based on is large enough [28]. B-spline neural network is illustrated

stochastic stability robustness presented by [10], but this by a local weight updating scheme with the advantages of

technique needs large feedback gains and an appropriate low computation complexity and fast convergence speed.

phase must be chosen. Adaptive control involves the The B-spline has been identified as very smoothest curveadjustment of feedback gains according to changes in the in the engineering applications. This is, because of the

system parameters and road conditions. In [11] they divergence-moderate property of the B-spline wave.

combined the benefits of adaptive and robust control in These characteristics make it more appropriate for the on-

the design of adaptive vehicle suspension system line adaptive situations. The plus point of the B-spline

controller and focused on the actuator force control. The functions over other radial functions are the local controls

adaptive robust controller for the quarter car active of the curve shape, since the curve changes in the

suspension is designed [12]. In [13], they designed the locality of a few control points that have been changed

feedback linearization control for full car suspension. A [29]. B-spline neural network comprises of the piecewise

variety of simulations showed that the fuzzy logic control polynomials with a set of local basis functions to model

is proficient to give a better ride quality than the other an unknown function for which a finite set of input-output

common control approaches [14-16]. The genetic samples are available. In [30], the authors used B-spline

algorithm-based fuzzy PI and PD controller for the active neurofuzzy technique with different orders of B-splinesuspension system for a quarter car model is designed by functions.

[17]. In [18], designed a hybrid neurofuzzy based sliding In [31], the authors proved that B-spline are

mode control to enhance the convenience of the equivalent to certain fuzzy systems. Therefore, the

passenger and stability of vehicle body. B-spline basis functions may be examined as fuzzy

Fuzzy logic has ability to decrease the complexity and membership functions and can be used to obtain fuzzy

to deal with vagueness and uncertainties of the data rules. B-splines basis functions are better to get the

[19, 20]. Their arrangement permits to build up a system desired properties like, local compact support, low

with fast learning abilities that can explain nonlinear computational and partition of unity. These techniques

structure that are described with uncertainties. Neural are non-adaptive, so can approximate the unknown

networks have self-learning qualities that raise the nonlinear dynamical systems. But the adaptive controllers

precision of the model. The combination of fuzzy logic have the ability to estimate the unknown nonlinear

and wavelets neural network provides the platform for dynamical system, because, the updated parameters hasresolving control problems and signal processing flexibility to update their values according to the system's

problems [21, 22]. There are several probable alternatives requirement. To estimate the nonlinearity of the unknown

for the basis functions to propose local activation system, the adaptive B-spline fuzzy neural network is

functions of neural networks, such as associated memory established. By using the online updating algorithm, both

networks, wavelets, radial basis function [23] and B-spline the B-spline membership functions of the fuzzy sets and

functions [24]. Unlike a global activation function which weighting parameters of the adaptive fuzzy neural

is non zero for all finite inputs, a local activation function network is updated. This online adaptation method will

is nonzero only in a local area of the input space. improves the robustness and the convergence of the

However, fuzzy neural networks with local activation system.

functions are more competent than the global activation In this study, adaptive B-spline Fuzzy Neural

functions in speed and memory, because, only nonzero Network strategies with different orders of B-spline

functions and the weights are calculated [25]. In case of membership function, i.e. B-spline of order 2 and B-spline

local activation functions, the estimators of nonlinear of order 3, are successfully implemented on nonlinear full

mapping can be expressed as a linear combination of basis car active suspension model to improve the ride comfort

functions. An appropriate choice of B-spline membership and road handling. The paper is divided into 6 sections.

and basis functions is the B-spline [26]. Section II describes the full car model. In Section III

The ability of neural networks to approximate various discusses the construction of proposed ABNFs

complex nonlinear functions relating input-output data techniques and section IV gives the online ABFNN

from a nonlinear system has attracted many researchers control algorithm. Finally, simulation results and

[27]. B-spline neural network can also estimate continuous conclusion are given in section V and VI respectively.

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M , M , M , Mf, r f, l r, r r, l

.. .

s s s s s s s s s sM Z +k (Z -Z-X -Y f)+c ( Z -Z-X -Y f)=0

.MZ+k (Z-a +Wf-Z )+c (Z-a +Wf-Z ))+k (Z+b +Wf-Z )+f1 f,l f1 f,l r1 r,l

. .c (Z+b +Wf-Z )+k (Z-a -Wf-Z )+c (Z-a -Wf-Z ) +r1 r,l f2 f,r f2 f,r

. .k (Z+b -Wf-Z )+c (Z+b -Wf-Z )-c (Z -Z-X -Y f)-f -f -f -f =0r2 r,r r2 r,r s s s s 1 2 3 4


1350

Table 1: Simulation variables for full car model

Variable Name Variable Value

Front Left Spring Constant ks1 15000 N/m

Front Right Spring Constant Ks2 15000 N/m

Rear Left Spring Constant ks3 17000 N/m

Rear Right Spring Constant ks4 17000 N/m

Seat Spring Constant ks5 15000 N/m

Front Left Damper Constant cs1 2500 N.s/m

Front Right Damper Constant cs2 2500 N.s/m

Front Left Damper Constant cs3 2500 N.s/m

Front Right Damper Constant cs4 2500 N.s/m

Seat Spring Constant cs5 150 N.s/m

Front Left Tire Suspension kt1 250000 N/m

Front Right Tire Suspension kt2 250000 N/m

Rear Left Tire Suspension kt3 250000 N/m

Rear Right Tire Suspension kt4 250000 N/m

Length of Axle Suspension from C.O.G a 1.2 mLength of Axle Suspension from C.O.G b 1.4 m

Length of Unsprung mass from C.O.G c 0.5 m

Length of Unsprung mass from C.O.G d 1 m

Length of Seat from C.O.G e 0.3 m

Length of Sear from C.O.G f 0.25 m

Front Left Unsprung mass m1 25 kg

Front Right Unsprung mass m2 25 kg

Rear Left Unsprung mass m3 45 kg

Rear Right Unsprung mass m4 45 kg

Seat Mass m5 90 kg

Vehicle Body Mass M 1100 kg

Moment of Inertia for Pitch Ix7 1848 kg.m

2

Moment of Inertia for Roll Ix8 550 kg.m2

Shyhook Damper Constant Csky1 -2500 N.s/m

Full Car Model: There are eight degrees of freedom for a

full car, i.e. Roll, Pitch, Z Heave, Z front left

tyre, Z front right tire, Z rear left tyre, Z rearf,1 f,r r,r right tyre. It comprises only a sprung mass attached to

the four unsprung masses

(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 masses are

allowed only to have heave. For simplicity all other

motions are ignored for 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

professionally ensures passenger safety and ride comfort.

This model considers only one seat and this is very

important to take into consideration other fixed with

chassis [32].

Fig 1: Full car model

The eight degrees of freedom consists of (x , x , x , x ,1 2 3 4x , x , x = , x = four wheels displacement, seat5 6 7 8displacement, heave displacement, pitch displacement and

roll displacement. The model of a full-car suspension

system is shown in Fig. 1. The suspensions between thesprung mass and unsprung masses are modeled 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 [33].The full car model

will be used as a good approximation of the whole car.

MATERIALS AND METHODS

As full-car model has eight-degrees of freedom, then

equations of motion for this model are explained by the

Newton's 2nd law of motion as:

For the Passenger Seat:

(1)

For the Vehicle's heave motion of the body:

(2)

For the Vehicle's Roll motion of the body:

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.I f+Wk (Z-a +Wf-Z )-Wc (Z-a +Wf- Z )+Wk (Z+b +Wf-Z )+x f1 f,l f1 f,l r1 r,l

. .Wc (Z+b +Wf- Z )-Wk (Z-a -Wf-Z )-Wc (Z-a -Wf- Z )-r1 r,l f2 f,r f2 f,r

.Wk (Z+b -Wf-Z )-Wc (Z+b -Wf- Z )+Y k (Z -Z-X -Y f)+r2 r,r r2 r,r s s s s s

.Y c (Z -Zs s s

- X -Y f)-Wf -Wf +Wf +Wf =0s s 1 2 3 4

.I -ak (Z-a +Wf-Z )+ac (Z-a +Wf-Z )+bk (Z+b +Wf-Z )y f1 f,l f1 f,l r1 r,l

.+bc (Z+b +Wf-Z )-r1 r,l

.ak (Z-a -Wf-Z )-ac (Z-a -Wf- Z )+bk (Z+b -Wf-Z )f2 f,r f2 f,r r2 r,r

.+bc (Z+b -Wf- Z ) +r2 r,r

.X k (Z -Z-X -Y f)+X c (Z -Zs s s s s s s s

-X -Y f)+af -bf +af -bf =0s s 1 2 3 4

..

f,l f,l f1 f,l f1

.

f,l t f,l g1 1

M Z -k (Z-a +W -Z )-c

(Z-a +W -Z )+k (Z -z )+f =0

..

r,l r,l r1 r,l r1

.

r,l t r,l g3 2

M Z -k (Z+b +W -Z )-c

(Z+b +W -Z )+k (Z -z )+f =0

..

f,r f,r f2 f,r f2

.f,r t f,r g2 3

M Z -k (Z-a -W -Z )-c

(Z-a ?+ W -Z )+k (Z -z )+f =0

..

r,r r,r r2 r,r r2

.

r,r t r,r g4 4

M Z -k (Z+b +W -Z )-c

(Z+b +W -Z )+k (Z -z )+f =0

p ps s(r)

ij j ij j

i=1 i=1 i=1 i=1

y =A(x)+ B (x)u + G (x)z

p1r -1r -1 T rx=[y ,y ,...,y ,...,y ,y ,...,y ] R 1 1 p p p1

T sr +r +...+r =r, u=[u ,u ,...,u ] R 1 2 p 21 s

T py=[y ,y ,...,y ] R 1 2 p

T sz=[z ,z ,...,z ] R 1 2 s

T1 2 pA=[A (x) A (x) . ..A (x)]

11 1s

p1 ps ps

b (x) b (x)

B(x)= M M

b (x) b (x)

p1 2

11 1s

p1 ps ps

(r )(r ) (r )(r) Tp1 2

g (x) g (x)

G(x)= M M

g (x) g (x)

y =[y ,y , ..., y ]

y=f(x)+B(x).u+G(x).z

(161) (164) (164)f(x) R , B(x) R , G(x) R

x R(161), u R(41) and z R(41)

T1 2

1 2 3

3

6

16

1f(x) = [A (x) A (x) A (x) .

x=[x x x ...

.. A (x)

x ]

]

T

1 2 z 4z=[z z x z ]


1351

(3)

For the Vehicle's Pitch motion of the body:

(4)

For the Vehicle's Wheels motion:

(5)

(6)

(7)

(8)

The simulation parameters for full car model are

shown in Table 1.

The general class of nonlinear MIMO system is

described by [3,21]:

(9)

Where is the overall

state vector, which is assumed available and

is the control input vector,

is the output vector and

is the disturbance vector. A (x), i =i

1,...,p are continuous nonlinear functions, B (x), i = 1,...,p,ij

j = 1, ...,s are continuous nonlinear control functions and

G (x), i = 1,...,p, j = 1,..., s are continuous nonlinearijdisturbance functions.

Let

(10)

The control matrix is:

(11)

The disturbance matrix is:

(12)

Also, the generic nonlinear car model is,

(13)

, state vector

. The above matrices can be

shown in state-space form, with state vector x that is also

represented in row matrix form.

A (x) to A (x) are velocity states and A (x) to A (x) are1 8 9 16acceleration states of four tires, seat, heave, pitch and roll

[16]. The disturbance inputs for each tire individually are

represented in the form of z matrix.

z are n disturbances applied to full car model. u are nn ncontrollers output to full car model, to regulate the car

model disturbances. y are n states of car. r are nn ndesired outputs of the controller.

Abfnn for Full Car Suspension Control: In this section,

the structure of the fuzzy B-spline neural network is

described. Firstly, the fuzzy B-spline membership function

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k-1

ij i q q,2 i

q=0

(x )= c N (x )

i q q+k iq,k i q,k-1 i q+1,k-1 i

q+k-1 q q+k q+1

x -t t -xN (x )= N (x )+ N (x )

t -t t -t

i q q+2 iq,2 i q,1 i q+1,1 i

q+1 q q+2 q+1

x -t t -xN (x )= N (x )+ N (x )

t -t t -t

q q+1q,1 i

1 ; x [t ,t )N (x )=

0 ; otherwise

q+1 q+2q+1,1 i

1 ; x [t ,t )N (x )=

0 ; otherwise

i 00 i 0 1

1 0

2 i i 10 1 i 1 2

2 1 2 1

q+2 i i q+1q q+1 i q+1 q+2ij i

q+2 q+2 q+2 q+1

i q-1k ik-2 z-1 i k-1 k

k k-1 k k-1

k+1 ik-1 i k k+1

k+1 k

x -tc x [t ,t ]

t -t

t -x x -tc +c x [t ,t )

t -t t -t

t -x x -tc +c x [t ,t )t (x )=

t -t t -t

x -tt -xc +c x [t ,t )

t -t t -t

t -xc x [t ,t )

t -t

i ix X q,2 ia=1/sup N (x )

q,2 i q,2 iaN (x )=A (x )

ik ik (x , s(x ))

ikq,2 i

1 ; if round(x )=qA (x )=

0 ; otherwise

m ij ik ik c =t (x )=s(x )


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and B-spline basis function is explained. Secondly, B-

spline fuzzy neural network is described and finally the

update parameters of the B-spline fuzzy neural network

are given.

Abnfs for Full Car Suspension Control: In this section,

the structure of the fuzzy B-spline neural network is

described. As B-spline has localibility properties, fast

convergence and low complexity calculation, so, it can

approximate the nonlinear functions of the dynamical

system. Firstly, the fuzzy B-spline membership function

and B-spline basis function of order 2 and order 3 are

explained. Secondly, B-spline fuzzy Neural Network is

described and finally the update parameters of the

B-spline fuzzy neural networks are given. (19)

Fuzzy B-spline Membership Function of Order 2: Generally, the B-spline basis functions with higherB-spline are the parametric surfaces that give flexibility for order, i.e. more than 1 are not a normal fuzzy set, because,

the visualization and modeling of the numerous types of the maximum value of these basis function does not reach

data [34]. All the B-spline fuzzy membership functions of at 1. This can be resolved by multiplying a positive

fuzzy logic rules are defined here as of order 2 and number with B-spline basis function, so that maximum

calculated by the algorithm explained below. The fuzzy value of basis function reaches at 1. i.e.

B-spline membership function is given by

(14)

Where (x ) is the membership function of the fuzzyij i

variable x to the c fuzzy set, q = 0,1,2,..,k-1, are controli qpoints, is the number of control points. The general form

of the B-spline membership function is ca be expressed as:

(15)

The B-spline basis function for order order (k=2), i.e.

N is cab be written as:q,2

(16)

(17)

(18)

Where t ,t and t are the nodes defined in the intervalq q+1 q+2of x . On substituting (16), (17) and (18) into (14), iti

becomes

Or,

(20)

Fig. 2 shows the shapes of B-spline membershipfunction.

The modeling potentials of the network is depends

on the distribution of the control points, shape and size of

the B-spline membership function. Where the knots and

the order determine the shape and the smoothness of the

B- spline membership function. The fuzzy B-spline

membership function shape can be regulated by changing

the value of the control points c . All the controls pointsqare equally allocated over the fuzzy set and is

the kth targeted value. Thus the values of control points

c can be adjusted asq

(21)

Where round(x ) is the new value $m$ of the closestikcontrol point c from the targeted value s(x ). Now fromm ik(16) and (19), it gives

(22)

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s-1

ij i q q,3 i

q=0

t (x )= c N (x )

t (x )ij i

i q q+3 iq,3 i q,2 i q+1,2 i

q+2 q q+3 q+1

x -t t -xN (x )= N (x )+ N (x )

t -t t -t

q q+2q,2 i

1 ; x [t ,t )N (x )=0 ;o therwise

q+1 q+3q+1,2 i

1 ; x [t , t )N (x )=

0 ;o therwise

1 1i 2 2i

m mi i

If x is A and x is A and

... x is A Then u is y


1353

Fig. 2: (a) B-spline membership (order=2) and (b) Fig. 3: (a) B-spline membership (order=3) and (b)

Adjusted B-spline membership function (order=2) Adjusted B-spline membership function.

The output of the network depends on the B-spline basis

function, because, the B-spline basis function uses the (25)product operator and their smoothness is affected by the

output of the network. For example, the Fig. 2 depicted (26)

that the control points of fuzzy set and the kth target

datum change the shape of the B-spline membership

function. Where t ,t ,t and t , t ,t ,t and t are the nodes

Fuzzy B-Spline Membership Function of Order 3: The The normalized third order basis function can be

fuzzy B-spline membership function of order 3 is given by obtained by the (20). The control points for order 3 are

(23) membership function. Fig. 3 shows the shape of B-spline

Where is the membership function of the fuzzy Fuzzy B-Spline Neural Network Algorithm: A fuzzy

variable x to the jth fuzzy set, c are control points, q=0, 1,i q2,... s-1, s is the number of control points and N is theq,3B-spline basis function of order 3. The B-spline basis

function N is expressed as:q,3

(24)

q q+1 q+2 q+3 q q+1 q+2 q+3

defined in the interval of x .i

changing same as explained in order 2 B-spline

membership function of order 3.

logic system normally accumulates its data in the shape

of a fuzzy algorithm [35], which consists of a fuzzy

linguistic rules relating to the input and output of the

network. Then the ith rule has the form:

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m

i i

i=1m

i

i=1

w

u=

z-1

ij q q,2

q=0

(x)= c N (x)

ij i i ij i (x )=? ? (x )

m

i pi

i=1m

ii=1

w

u=

21J= e2

2d i

1J= (y -y )

2

pi pipi

Jw (t+1)=w (t)-

w

ij ijij

J(t+1)= (t)-

?


1354

Fig. 4: Structure of the ABNF

The output of the system can be expressed as:

(27)

The structure for the fuzzy B-spline neural

network is depicted in Fig. 4. It comprises of four

layers:

Layer I:This layer is the input layer, i.e. introduces the

inputs (x , x ,...x ). This layer accepts the input values and1 2 mtransmits it to the next layer.

Layer II: In this layer the fuzzification process is

performed and neurons represent fuzzy sets used in the

antecedents part of the linguistic fuzzy rules. The

outputs of this layer are the values of the membership

functions, i.e. . The membership of ith input variable toijjth fuzzy set is defined by B-spline function as

(28)

Where shows the membership function of the ithijinput to the jth fuzzy set. Where i=1,2,...m and j=1,2.

Layer III:This layer is the fuzzy inference layer. In this

layer each node represents a fuzzy rule. In order to

compute the firing strength of each rule and $min$

operation is used to estimate the output value of the layer.

i.e.

(29)

where is the meet operation, (x ) are the degrees of thei ij imembership function of the layer II and (x) are the inputij i

values for the next layer.

Layer IV: This layer is the output layer. In this layer, the

defuzzification process is made to calculate the output of

the entire network, i.e. It computes the overall output of

system. Therefore, the output for the fuzzy B-spline neural

network can be expressed as:

(30)

Where u is the output for the entire network. The

training of the network starts after estimating the output

value of the fuzzy B-spline neural network and w are thepiweights between the neurons of III and IV layers and p=1,

2,... n, n is the number of classes.

Parameters Update Rules: The fuzzy B-spline neural

network learning is to minimize a given function or input

and output values by adjusting network parameters. The

gradient descent method is used to adjust the values ofweights w and the control points c of B-spline function.ip qijTo minimize the error between the actual output value of

the system and the desired value. For this purpose,

gradient descent method is can be expressed as:

Then

(31)

Where y is the desired output of fuzzy neural network, yd iis the actual output of system. The updated amount for

the w and can be obtained as:pi ij

(32)

(33)

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J

wpi

J

?ij

i

pi i pi

J J y J= . .

w y u w

ji

ij i ij ij

J J y u= . . .

? y u ?

m

i i

i=1

d i mpi 2i

i=1

J

=-(y -y )w

( )

( )

ip

d i jij j

j

w -uJ= -(y -y )

(x)

y

u

m

i i

i=1pi pi d i m

2i

i=1

w (t+1)=w (t)+ (y -y )

( )

( )

ip

ij i d i jj

j

w -u(t+1)= j(t)+ (y -y )

(x)

p

N

i i i

i=1

-15 1 t 2, 3 4

15 7 t 8, 9 10

a (1-cos8pt) 13 t 14,15 16z(t)=

A sin(O s-? ) 19 t 22,23 26

0 otherwise

N

A sin(O s-i i

=1

)i

i

( ; i=(1)Ni


1355

Where is the learning rate.

By using chain rule the values of and can

be expressed as:

(34)

(35)

By taking the derivative of the above equations, it gives

(36)

(37)

Where the quantity is approximated by a constant

by Frechet derivative (Lin et al. 2000) or and (Khaldi et

al. 1993).

Therefore, updated values of w and can bepi ijobtained by substituting (36) and (37) in (32) and (33) as:

(38)

(39)

Where, = . Therefore, (38) and (39) gives the requiredupdated values for the parameters w , respectively.piFig. 5 depicts the closed loop diagram of the feedback

system.

Online Abnf Adaption Algorithm: Fig.5 shows the closed

loop control structure for the proposed ABNFs control.

This structure is employed to converge and update the

parameters of the ABNFs control. The calculations at any

instant of time can be described in the following steps.

Fig. 5: Control loop structure of ABNF

Step 1:Set the input-output, y and y of the system.d

Step 2: Update the parameters of the proposed ABNFs

scheme, i.e. and w by using (32) and (33) equations.ij pi

Step 3:Calculate the output of proposed ABNFs control

strategies.

Step 4: Finally, output of the proposed controller added

with disturbances is given to the system.

Step 5:Repeat steps (2-4) until solution converges.

Simulation Result: In this study, it is assumed that the

vehicle is moving with uniform velocity unless the road

disturbances create the undesired oscillations in the

vehicle body. To check the performance of the proposed

ABNFs control strategies, a road profile containingbumps, pothole and white noise has the form, i.e.

(40)

Where -0.15 m is the pothole and 0.15 m is the bump.This type of road profile shows the low frequency high

amplitude response. The term a(1-cos8 t) shows the

bell shaped bumps and a =15 m, is the amplitude of thep

bumps on the road. Now the term shows

the road profile like white noise. Where value of A is theiamplitude of the road, is the number of waves and isi ithe phase angle ranging from 0 to 2 .

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v|=|v|

6 [1,2,3,4]v=x - x

v

v| |v, t 0 |


1356

(42)

Fig. 6: Road profile are compared with passive suspension and semi-active

Fig. 7: Seat displacement without controller 1 and ABNF-2 control, the maximum value for seat

Fig. 8: Seat displacement with controller state response is improved as compared to passive and

This road profile is very helpful for observing the heave, increased the passenger comfortability by 10% and 8% as

pitch and roll of the vehicle. This road profile is shown compared to the seat without controllers. The ABNF-1

in Fig. 6. ameliorates the ride comfort than ABNF-2 controlIn order to fulfill the aim of the active suspension strategy.

system, the proposed strategy ABNFs is successfully Fig. 9 to Fig. 11 shows that the response of heave,

implemented on full car suspension system to improve the pitch and roll is improved as compared to passive

vehicles stability and passengers comfort. The comfort suspension and semi-active suspension system. In

is examined by the vertical displacement and acceleration passive suspension and semi-active suspension, the

felt by the passenger. The controller goal is to minimize maximum value of displacement for heave are 0.105 m and

the vertical displacement of the vehicle body with 0.072 m while, for the ABFN-1 and ABFN-2 controls, the

reference to the open-loop, so, as to avoid the suspension maximum value of displacement for heave is 0.022 m and

travel hitting the rattle space limits. The lifetime of 0.025 m, respectively. Here, the ABFN-1 and ABFN-2

elements of the vehicle is conserved by keeping away increase the passenger comfort by 80% and 77% as

from hitting the rattle space limits i.e. to stay away from compared to passive suspension system and 70% and

which is the allowable peak to peak displacement of 67% as compared to semi-active suspension system. Inthe system. passive suspension and semi-active suspension, the

maximum value of displacement for pitch is 0.075 m and

Where 0.053 m while for the ABFN-1 and ABFN-2 controls, the

(41) 0.020 m, respectively. Here, the ABFN-1 and ABFN-2

increase the passenger comfort by 78% and 74% as

and is the maximum limit for bumps amplitudes. The compared to passive suspension system and 68% and

suspension travel can physically be expressed as 64% as compared to semi-active suspension system.

The controller performance is good when it reduces

the vehicle vibrations under road disturbances. In this

section, the simulation results of displacement of theheave, pitch, roll and seat (with and without controller) for

the above mentioned road profile is given. These results

suspension systems. The simulation time of this proposed

work is up to 30 seconds.

Fig. 7 and Fig. 8 show that the response of seat is

improved as compared to passive suspension and semi-

active suspension system. In passive suspension and

semi-active suspension, the maximum value for seat

displacement is 0.1796 m and 0.088 m while, for the ABNF-

displacements are 0.028 m and 0.031 m respectively. Here,

the ABFN-1 and ABFN-2 increase the passenger comfort

by 85% and 82% as compared to passive suspension

system and 69% and 65% as compared to semi-active

suspension system. The response of seat with controller

(wc) is better than seat without controller (woc). Also, the

settling time of ABNFs controllers is reduced and steady

semi-active suspension systems. The seat with controller

maximum value of displacement for pitch are 0.017 m and

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TTP P

0

1PI= (Z QZ )dt

2


1357

Fig. 9: Heave displacement Fig. 12: Suspension travel for front tyre

Fig. 10: Pitch displacement Fig .13: Suspension travel for rear tyre

Fig. 11: Roll displacement Fig. 14: Front tyres displacement

In passive suspension and semi-active suspension, the

maximum value of displacement for roll is 0.029 m and

0.017 m while, for the ABFN-1 and ABFN-2 controls, the

maximum value of displacement for roll are 0.009 m and

0.01 m, respectively. Here, the ABFN-1 and ABFN-2increase the passenger comfort by 69% and 66% as

compared to passive suspension system and 48% and Fig. 15: Rear tyres displacement

44% as compared to semi-active suspension system. This

increased the vehicle stability, ride comfort and passenger Fig. 14 and Fig. 15 show the wheel displacement for

comfortability. Also, the settling time of ABFNN front and rear tyres. It is observed that the ABFN-1 and

controller is reduced and steady state response is ABFN-2 based active suspension system minimizes the

improved as compared to passive suspension. The wheel displacement by 60% and 56% as compared to

proposed active suspension shows better performance passive suspension and 49% and 45% than semi-active

and robustness. [33-35]From the above discussion it is suspension systems. This shows that the ABFN-1 based

observed that the ABFN-1 enhance the vehicle stability active suspension system improves the road handling of

and passenger comfortability than ABFN-2 control the vehicle, robustness and enhances the passenger

strategy. convenience than ABFN-2 control strategy.Fig. 12 and Fig. 13 show the suspension travel for The performance index used for evaluation of the

each front and rear tyres. The results show that the active control is given by,

ABFN-1 and ABFN-2 minimize the suspension travels by

68% and 64% than passive suspension system and 47% (43)

and 44% than semi-active suspension system. It is

observed that the ABFN-1 based active suspension

system provides better road handling and passenger where, Zp is the vector for displacement or

comfort than ABFN-2 control strategy. acceleration, Q i s the identity m atrix. T he R oot

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rmszdisp.

mszacc.

[ ]T

2rmsdisp. 6

0

1Z = x (t)

T

[ ]T

2rmsacc. 6

0

1Z = x (t)

T


1358

Table 2: Performance comparison

DOFs Control Algorithm PI

Seat (woc) Passive 0.0497 4.4034 9.6962

Semi-active 0.0395 3.3742 5.6933

ABNF-1 0.01296 0.8269 0.3419

ABNF-2 0.0110 0.6748 0.2277

Seat (wc) Passive 0.03606 3.211 4.5635

Semi-active 0.03092 2.813 3.9569

ABNF-1 0.01026 0.7045 0.2482

ABNF-2 0.0103 0.5169 0.1336

Heave Passive 0.03606 3.211 4.5635

Semi-active 0.03092 2.813 3.9569

ABNF-1 0.01775 0.1980 0.0197

ABNF-2 0.01382 0.1631 0.0133

Pitch Passive 0.0277 2.4623 3.0318

Semi-active 0.0227 1.9324 1.8673

ABNF-1 0.0072 0.5374 0.1444

ABNF-2 0.0056 0.4831 0.1167

Roll Passive 0.0084 1.5943 1.2709

Semi-active 0.0080 1.2065 0.7278

ABNF-1 0.0029 0.4105 0.00842

ABNF-2 0.0024 0.3619 0.0654

Mean Square (RMS) value for displacement and

acceleration of heave, pitch, roll and seat has been

calculated by,

(44)

(45)

Table 2 shows the performance index of ABNF-1 and

ABNF-2 control strategies as compared to passive and

semi-active suspension systems. The performance of

ABNF-1 and ABNF-2 based active suspension is checked

with the said road profile.

CONCLUSION

In the paper, an ABNF control strategies with

different orders of B-spline membership functions, i.e.

order 2 (ABNF-1) and order 3 (ABNF-2) are 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 ABNFs active suspension

system has ability to achieve low steady-state error and

fast error convergence than passive and semi-active

suspension systems. Therefore, ABNF-1 and ABNF-2

based active suspension system show that it improves

the vehicle stability and passenger comfort. The

simulations results depict that heave, pitch, roll, seat

displacement and suspension travel are reduced and road

handling is improved for the active suspension systemsas compared to passive and semi-active suspension

systems. Also, the experimental results show that the

ABNF-1 based active suspension a system performs

better than the ABNF-2 based active suspension system.

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