Intelligent Semi-Active Vibration Control Suspension System
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Transcript of Intelligent Semi-Active Vibration Control Suspension System
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Journal of Mechanical Science and Technology 26 (2) (2012) 323~334
www.springerlink.com/content/1738-494xDOI 10.1007/s12206-011-1007-6
12
Intelligent semi-active vibration control of eleven degrees of freedom suspensionsystem using magnetorheological dampers
Seiyed Hamid Zareh*, Atabak Sarrafan, Amir Ali Akbar Khayyat and Abolghassem Zabihollah
School of Science and Engineering, Sharif University of Technology, Iran
(Manuscript Received February 1, 2011; Revised August 8, 2011; Accepted September 13, 2011)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Abstract
A novel intelligent semi-active control system for an eleven degrees of freedom passenger cars suspension system using magnetor-
heological (MR) damper with neuro-fuzzy (NF) control strategy to enhance desired suspension performance is proposed. In comparison
with earlier studies, an improvement in problem modeling is made. The proposed method consists of two parts: a fuzzy control strategyto establish an efficient controller to improve ride comfort and road handling (RCH) and an inverse mapping model to estimate the force
needed for a semi-active damper. The fuzzy logic rules are extracted based on Sugeno inference engine. The inverse mapping model is
based on an artificial neural network and incorporated into the fuzzy controller to enhance RCH. To verify the performance of the NF
controller (NFC), comparisons with existing semi-active techniques are made. The typical control strategy are linear quadratic regulator
(LQR) and linear quadratic Gaussian (LQG) controllers with clipped optimal control algorithm, while inherent time-delay and non-linear
properties of MR damper lie in these strategies. Simulation results demonstrated that the NFC has better control performance and less
control effort than the optimal in improving the service life of the suspension system and the ride comfort of a car.
Keywords: Clipped optimal control algorithm; Full car model; Linear quadraticGaussian; MR damper; Neuro-fuzzy strategy; Suspension system
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1. Introduction
Suspension systems have long been of great concern for car
industries. It performs multiple tasks such as maintaining con-
tact between vehicle tires and the road, addressing the stability
of the vehicle, and isolating the frame of the vehicle from
road-induced vibration and shocks. In general, ride comfort,
road handling, and stability are the most important factors in
evaluating suspension performance.
In present work, passenger car suspension system is modi-
fied to reduce the amplitude of the car vibration caused by
applied road profile. In the passive suspension system, the
stiffness and damping parameters are fixed and effective over
a certain range of frequencies.
To overcome this problem, the use of semi-active suspen-sion systems which have the capability of adapting to chang-
ing road conditions by the use of an actuator has been consid-
ered; therefore an MR damper is added to the usual suspen-
sion systems while the other parts of suspension system are
intact. The significance of MR damper is that its viscosity
changes as the magnetic field is changed. A schematic model
of MR damper is shown in Fig. 1.
Considered suspension model is controlled by applied Lin-
ear quadratic regulator (LQR) and linear quadratic Gaussian(LQG). By using employed controller results, the amount of
viscosity of MR damper can be calculated incorporated with
clipped optimal strategy. Unfortunately, due to the inherent
nonlinear nature of the MR damper to generate a force, a
model like that for its inverse dynamics is difficult to obtain
mathematically. Because of this reason, a neural network with
fuzzy logic controller is constructed to copy the inverse dy-
namics of the MR damper.
Neuro-fuzzy controller is an artificial neural network, which
is used to aggregate rules and provides control result for the
This paper was recommended for publication in revised form by Associate Editor
Hyoun Jin Kim*Corresponding author. Tel.: +989378550656, Fax.: +987224223895
E-mail address: [email protected]
KSME & Springer 2012
Fig. 1. A schematic model of MR damper.
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324 S. H. Zareh et al. / Journal of Mechanical Science and Technology 26 (2) (2012) 323~334
designed fuzzy logic controller. Application of fuzzy inference
systems as a fuzzy logic controller (FLC) has gradually been
recognized as the most significant and fruitful application for
fuzzy logic and fuzzy set theory.
Finally, the results of applied control strategies are com-
pared. There are three models for modeling passenger cars
suspension systems: quarter-car, half-car and full-car model.In quarter-car model, it is assumed that each of four-wheel has
independent suspension to simulate the actions of an active
vehicle suspension system, and therefore, quarter-car models
are using for many simulations of suspension system. The
model of quarter-car for vehicle suspension system has been
used by Wang et al. [1]. Narayanan et al. [2] applied half-car
model for simulating semi-active suspension system. They
modeled MR damper parameters by the modified BoucWen
model and determined them to fit the hysteretic behavior.
Vibration control of passenger car utilizing half-car was dis-
cussed by Yahaya et al. [3]. To improve the accuracy of car
model Zabihollah et al. [4] modeled the vehicle suspension
system by a full car model; in which the accuracy of model
improved compared to quarter-car and half-car models.
Semi-active and active control methods have been devel-
oped using different actuators such as electrorhrological (ER)
and MR dampers. Salem et al. [5] controlled an active quarter-
car suspension system by fuzzy logic controller. Hyun et al.
[6] utilized an adaptive LQG control for semi-active suspen-
sion system for quarter-car model. Semi-active control is used
by Chen et al. [7] where the MR damper utilized as actuator of
suspension system.
Jialin et al. [8] presented and designed a full-state LQR con-
troller for a half-car suspension system composed of actuators
in parallel with conventional spring-damper passive suspen-sion. Yang et al. [9] modeled and controlled an intelligent
active suspension system using fuzzy controller by adaptive
filter method. Zhou and Sun [10] have done a semi-active
vibration control on five degrees of freedom suspension sys-
tem using adaptive fuzzy PID control. They combined the
advantages of PID and fuzzy controllers and applied them to
the vibration control of engineering vehicle. The parameters of
PID tuned on line by fuzzy controller.
Golnaraghi et al. [11] controlled a semi-active quarter car
suspension system intelligently. They utilized an inverse map-
ping model to estimate the current based on an artificial Neu-
ral Network and incorporated into the fuzzy logic controller.
Sadati et al. [12] designed a neuro-fuzzy controller for a vehi-
cle suspension system. They controlled a half car model with
four degrees of freedom using feedback error learning.
The previous studies made full use of the advantages of the
neural-network and the fuzzy logic controller and solved the
different problems in suspension systems. Few researches
involved combination of the two techniques to solve the time-
delay and the inherent nonlinear nature of the MR dampers in
semi-active strategy for full car model with high degrees of
freedom. In this paper, four MR dampers are added in a sus-
pension system between body and wheels parallel with pas-
sive dampers. For the intelligent system, fuzzy controller
which inputs are relative velocities across MR dampers that
are excited by road profile for predicting the force of MRdamper to receive a desired passengers displacement and
velocity is applied. When predicting the displacement and
velocity of MR dampers, a four-layer feed forward neural
network, trained on-line under the LevenbergMarquardt
(LM) algorithm, is adopted. In order to verify the effective-
ness of the proposed neuro-fuzzy control strategy, the uncon-
trolled system and the clipped optimal controlled suspension
system are compared with the neuro-fuzzy controlled system.
Through a numerical example under actual road profile excita-
tion, it can be concluded that the control strategy is very im-
portant for semi-active control, the neuro-fuzzy control strat-
egy can determine currents of the MR damper quickly andaccurately, and the control effect of the neuro-fuzzy control
strategy is better than that of the other control strategy.
2. Full car model
In the full-car model, 11-DOFs are assumed; all wheels and
passengers are dependent on each other and on the cars body.
It is assumed that each wheel has an effect on the spring and
damper of other wheels, and two axes of vehicle are relevant.
MR actuator is utilized to damp the effect of road profile on
the passengers. Note that MR shock absorber is added to the
axel and car body. In a full-car model, the effect of body rota-
tions around roll and yaw axis is simulated. The suspension
system using a full-car model has 11-DOFs, four of them for
the four wheels, three for body displacement and its rotations
and the last four for passengers. A schematic of a full-car
model with 11-DOFs and addition MR damper is shown in
Fig. 2.
The dynamic equations of each DOF are given as in Eq. (1)-
(11). As a result, the state space form of the equation is shown
in Eq. (12). The state space form and the corresponding matri-
ces are observed in Eq. (13)-(19). E is a location matrix of
actuators. Matrices K, S and T are defined as stiffness, damp-
Fig. 2. A full-car model with 11-DOFs.
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S. H. Zareh et al. / Journal of Mechanical Science and Technology 26 (2) (2012) 323~334 325
ing coefficient and input matrix due to wheels stiffness, re-
spectively.
1 1 1 1 1 1 5 1 11 1 12
1 1 1 5 1 11 1 12 1 1
( )
0
t
t i
m x k k x k x k r k r
b x b x b r b r k x
+ +
+ =
&&
&&& &(1)
2 2 2 2 2 2 5 2 21 2 22
2 2 2 5 2 21 2 22 2 2
( )
0
t
t i
m x k k x k x k r k r
b x b x b r b r k x
+ + +
+ + =
&&
&&& &(2)
3 3 3 3 3 3 5 3 31 3 32
3 3 3 5 3 31 3 32 3 3
( )
0
t
t i
m x k k x k x k r k r
b x b x b r b r k x
+ + +
+ + =
&&
&&& &(3)
4 4 4 4 4 4 5 4 41 4 42
4 4 4 5 4 41 4 42 4 3
( )
0
t
t i
m x k k x k x k r k r
b x b x b r b r k x
+ + + +
+ + + =
&&
&&& &
(4)
5 1 1 2 2 3 3 4 4 1 2
3 4 5 6 7 8 5 5 6 6 7
7 8 8 9 1 11 2 21 3 31 4 41 5 51
6 61 7 71 8 81 1 12 2 22 3 32
4 42 5 52 6 62 7 72 8 82 1 1
2 2 3 3 4 4
(
)
(
) (
)
bM x k x k x k x k x k k
k k k k k k x k x k x
k x k x k r k r k r k r k r
k r k r k r k r k r k r
k r k r k r k r k r b x
b x b x b x
+ +
+ + + + + +
+ + +
+ + +
+ +
&&
&
& & & 1 2 3 4 5
6 7 8 5 5 6 6 7 7 8 8 9
1 11 2 21 3 31 4 41 5 51 6 61
7 71 8 81 1 12 2 22 3 32 4 42
5 52 6 62 8 82 8 82
(
)
(
) (
) 0
b b b b b
b b b x b x b x b x b x
b r b r b r b r b r b r
b r b r b r b r b r b r
b r b r b r b r
+ + + + +
+ + +
+ + + + +
+ +
+ =
& & & & &
&
&
(5)
1 1 11 1 2 21 2 3 31 3 4 41 4
1 11 2 21 3 31 4 41 5 51 6 61
7 71 8 81 5 5 51 6 6 61 7 7 71 8
2 2 2 2 28 81 9 1 11 2 21 3 31 4 41 5 51
2 2 26 61 7 71 8 81 1 11 12 2 21 22
(
)
(
) (
I k r x k r x k r x k r x
k r k r k r k r k r k r
k r k r x k r x k r x k r x
k r x k r k r k r k r k r
k r k r k r k r r k r r
+ +
+ + + +
+
+ + + + + +
+ + + +
&&
3 31 32 4 41 42 5 51 52 6 61 62 7 71 72
8 81 82 1 11 1 2 21 2 3 31 3 4 41 4
1 11 2 21 3 31 4 41 5 51 6 61 7 71
8 81 5 5 51 6 6 61 7 7 71 8 8 81 9
2 21 11 2 21 3 3
)
(
)
(
k r r k r r k r r k r r k r r
k r r b r x b r x b r x b r x
b r b r b r b r b r b r b r
b r x b r x b r x b r x b r x
b r b r b r
+ + +
+ + +
+ + + +
+ +
+ + +
& & & &
& & & & &
2 2 2 21 4 41 5 51 6 61
2 27 71 8 81 1 11 12 2 21 22 3 31 32
4 41 42 5 51 52 6 61 62 7 71 72 8 81 82
) (
) 0
b r b r b r
b r b r b r r b r r b r r
b r r b r r b r r b r r b r r
+ + +
+ + +
+ + + + =
&
&
(6)
2 1 12 1 2 22 2 3 32 3 4 42 4 1 12
2 22 3 32 4 42 5 52 6 62 7 72
8 82 5 5 52 6 6 62 7 7 72 8 8 82 9
1 12 11 2 22 21 3 32 31 4 42 41 5 52 51
6 62 61 7 72 71 8 82 81 1
(
)
(
) (
I k r x k r x k r x k r x k r
k r k r k r k r k r k r
k r x k r x k r x k r x k r x
k r r k r r k r r k r r k r r
k r r k r r k r r k
+ + +
+ + +
+ +
+ + +
+ +
&&
2 212 2 22
2 2 2 2 2 23 32 4 42 5 52 6 62 7 72 8 82
1 12 1 2 22 2 3 32 3 4 42 4 1 12
2 22 3 32 4 42 5 52 6 62 7 72
)
(
r k r
k r k r k r k r k r k r
b r x b r x b r x b r x b r
b r b r b r b r b r b r
+
+ + + + + +
+ + +
+ + +
& & & &
(7)
8 82 5 5 52 6 6 62 7 7 72 8 8 82 9
1 12 11 2 22 21 3 32 31 4 42 41 5 52 51
2 26 62 61 7 72 71 8 82 81 1 12 2 22
2 2 2 2 2 23 32 4 42 5 52 6 62 7 72 8 82
)
(
) (
) 0
b r x b r x b r x b r x b r x
b r r b r r b r r b r r b r r
b r r b r r b r r b r b r
b r b r b r b r b r b r
+ +
+ + +
+ + +
+ + + + + + =
& & & & &
&
&
5 6 5 5 5 6 5 51 5 52
5 5 5 6 5 51 5 52 0m x k x k x k r k r
b x b x b r b r
+
=
&&
&&& &(8)
6 7 6 5 6 7 6 61 6 62
6 5 6 7 6 61 6 62 0
m x k x k x k r k r
b x b x b r b r
+ +
+ + =
&&
&&& &(9)
7 8 7 5 7 8 7 71 7 72
7 5 7 8 7 71 7 72 0
m x k x k x k r k r
b x b x b r b r
+ +
+ + =
&&
&&& &(10)
8 9 8 5 8 9 8 81 8 82
8 5 8 9 8 81 8 82 0
m x k x k x k r k r
b x b x b r b r
+ + +
+ + + =
&&
&&& &
(11)
1 1 2 2 3 3 4 4 5 5
6 6 7 7 8 8 9 9 10
11 1 12 2 13 3 14 4 15
5 16 6 17 7 18 8 19 9 20
21 22
, , , , ,
, , , , ,
, , , ,
, , , , ,
,
x x x x x x x x x x
x x x x x x x x x
x x x x x x x x x
x x x x x x x x x x
x x
= = = = =
= = = = =
= = = = =
= = = = =
= =
& & & &
& & & & &
&&
(12)
x Ax Bu Gw
y Cx
= + +
=
&
(13)
1 1
0 I
A K M S
= (14)
1
0B
T
=
(15)
1
0G
E
=
(16)
1 2 3 4
5 6 7 8 1 2 11 11
bm m m m M M diag
m m m m I I
=
L(17)
1 23 4
[ , 0, 0,0; 0, , 0, 0;0, 0,
,0;0,0,0, ; (7,4)]t t
t t
T k k
k k zeros
=(18)
11 21 31 41 12 22 32 42
[ (4,4);1,1,1,1; (4,4);
, , , ; , , , ]
E eye zeros
r r r r r r r r
=
(19)
whereMb, m1, m2, m3, m4, m5, m6, m7and m8 stand for the mass
of the car body, masses of four wheels and mass of passengers,
respectively. I1 and I2 are the moments of inertia of the car
body around two axes, respectively. The terms k1, k2, k3, k4, k5,
k6, k7 and k8 are stiffnesses of the springs of the suspension
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326 S. H. Zareh et al. / Journal of Mechanical Science and Technology 26 (2) (2012) 323~334
system and stiffnesses of the springs of passengers seat, re-
spectively. The terms kt1, kt2, kt3 and kt4 are stiffnesses of the
tires. The terms b1, b2, b3, b4, b5, b6, b7 and b8 are coefficients
of car and passengers seat dampers, respectively. Then, br1, br2,
br3 and br4 are coefficients of the MR dampers, respectively.x1,
x2, x3, x4, x5, x6, x7, x8, x9, and indicate the DOFs of the
suspension system model, respectively. The terms xi1, xi2, xi3
andxi4 indicate load profile disturbance, respectively.
The numerical values of models dimensions for obtaining
the responses are shown in Table 1 [4].
3. LQR controller strategy
LQR controller responds to changes in the location of the
poles of the system to the optimal place. Time response, over-
shoot and steady state errors depend on the location of the
systems poles. LQR controller controls the system by a ma-
trix gain Eq. (20). This gain is achieved from Eq. (21). To
solve this energy equation of the system, Riccati equation isused, and this relation is given in Eq. (22), in which Q is a
symmetric positive semi-definite matrix and Ris a symmetric
positive definite matrix. The result of solving Riccati equation
is matrix S. Gain of pole placement is achieved from Eq. (23)
by using S matrix.
( )x A BK x Gw
y Cx
= +
=
&
(20)
0
1( ( ) ( ) ( ) ( ))
2
T Tx t Qx t u t Ru t dt
= + (21)
1 0T TA S SA SBR B S Q+ + = (22)1 TK R B S= (23)
Gain Kby B matrix made a square matrix, subtracted from
A matrix, and changes dynamic properties and the pole of the
control system. The A matrix presents the dynamic properties
of the system. New A matrix shows the system with new posi-
tion pole. Therefore by finding optimal gain, pole of the sys-
tem is shifted to the optimal position. Here, Q22*22 is an iden-
tity matrix (I22*22) because all states are important and the best
responses are obtained by this value. R4*4 is 45*I4*4, which is
obtained by trial and error to receive the desired response.
4. LQG controller strategy
In order to control a system with disturbance and noise by
modern control method a controller with noise filter must be
used. Optimal control, linear quadratic Gaussian, is the most
appropriate to control the full car model. The LQG controller
is simply the combination of a Kalman filter (i.e., a linear-
quadratic-estimator (LQE) with a linear-quadratic-regulator).
To eliminate the effect of disturbance on the suspension
system, the LQE part of the LQG controller is utilized. Per-
haps, the main step to design the LQE is to identify the ampli-
tude and position of disturbance. As a result, disturbance vec-tor and position of disturbance entrance should be identified.
The disturbance of the system is entered to the system as the
input part. In the present work, it is assumed that some states
of the system can be detected by sensors attached to the parts
of the suspension system (seven states of twenty two states
that are denoted as Clqg). Consequently, the controller of the
suspension system is not a full state control. The state space of
the suspension system is controllable and observable.
To design the LQG controller, first, the disturbance vector
needs to be identified. Then, the matrices W and V are pro-
duced; the process noise (disturbance) is simulated by road
Table 1. Numerical values of model.
Symbol Quantity Value
Mb Mass of car body (kg) 670
I1 Inertia around yaw (kg/m^2) 800
I2 Inertia around roll (kg/m^2) 1100
m1-4 Masses of Wheels (kg) 30
m5-8 Masses of passengers (kg) 120
k1-4 Stiffnesses of car springs (N/m) 17500
k5-8 Stiffnesses of seats (N/m) 1750
b1-4 Viscosity of car dampers (Ns/m) 1460
b5-8 Viscosity of seats damper (Ns/m) 700
kt1-4 Stiffnesses of wheels (N/m) 175500
r11Length distance between the front left
wheel and center of mass (m)1.9975
r12Width distance between the front left
wheel and center of mass (m)0.8025
r21Length distance between the front right
wheel and center of mass (m) 1.9975
r22Width distance between the front right
wheel and center of mass (m)0.8025
r31Length distance between the back right
wheel and center of mass (m)1.9975
r32Width distance between the back right
wheel and center of mass (m)0.8025
r41Length distance between the back left
wheel and center of mass (m)1.9975
r42Width distance between the back left
wheel and center of mass (m)0.8025
r51Length distance between the driver seat
and center of mass (m)1.9975
r52 Width distance between the driver seatand center of mass (m)
0.8025
r61Length distance between the front right
seat and center of mass (m)1.9975
r62Width distance between the front right
seat and center of mass (m)0.8025
r71Length distance between the back left
seat and center of mass (m)1.9975
r72Width distance between the back left
seat and center of mass (m)0.8025
r81Length distance between the back right
seat and center of mass (m)1.9975
r82Width distance between the back right
seat and center of mass (m)0.8025
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S. H. Zareh et al. / Journal of Mechanical Science and Technology 26 (2) (2012) 323~334 327
profile that is explained in next subsection; the measurement
noise is simulated by fraction of road profile. Kalman filter is
a state estimator given a state-space model of the plant and the
process and measurement noise covariance data. The Kalman
estimator provides the optimal solution to the following con-
tinuous or discrete estimation problems.
x Ax Bu Gw= + +& (24)
lqgy C x v= + (25)
The observer structure with known inputs u, white process
noise w, and white measurement noise v, is in the form of:
( )lqgx Ax Bu L y C x= + + & (26)
where x is an LQG optimal estimate ofx.
In the next step, the energy equation of the LQE must be
solved, as expressed in Eq. (27). In order to solve the energy
equation, Riccati equation is produced. Riccati equation isgiven in Eq. (28). Solving Riccati equation, the P matrix will
be achieved. The P matrix is utilized to find the observer gain,
L, in Eq. (29).
0
[ ]T TJ x Vx u Wu dt
= + (27)
1 0T Tlqg lqg AP PA PC V C P W+ + = (28)
1TlqgL PC V
= (29)
where [ ]TW E ww= , [ ]TV E vv= are the plant disturbance
and measurement noise covariances. The input u itself is gen-erated by a state feedback law as:
.u Kx= (30)
Finally, using LQG controller in close-loop system, it leads
the original system convert to following equations:
0
0
lqg lqg
x A BK x
LC A BK LC xx
G w
L v
=
+
&
&
(31)
11
(11 11) (11 11)
(11 11)lqg
zeros zerosC
zeros C
=
(32)
11
(5 5) (5 4) (5 2)
(4 5) (4 4) (4 2) .
(2 5) (2 4) (2 2)
I zeros zeros
C zeros zeros zeros
zeros zeros I
=
(33)
Here,Iis a identity matrix. The optimal force vectorfc regulated
only by the state vectorx that is calculated by Eq. (34) [13].
c LQRf K x= (34)
5. Clipped optimal algorithm
The clipped optimal control strategy for an MR damper
usually involves two steps. The first step is to assume an ideal
activelycontrolled device and construct an optimal controller
for this active device. In the second step, a secondary control-
ler finally determines the input voltage of the MR damper.That is, the secondary controller clips the optimal force in a
manner consistent with the dissipative nature of the device.
The block diagram of clipped optimal algorithm is shown in
Fig. 3.
The clipped optimal control approach is to append a force
feedback loop to induce the MR damper to produce approxi-
mately a desired control forcefc. The linear quadratic regulator
algorithm has been employed both for active control and for
semi-active control. Using this algorithm, the optimal control
forcefc for f, which is force generated by a MR damper, may
be obtained by minimizing the following scalar performance
index
0
( ) .
ft
T T
t
x Qx F RF dt= + (35)
Q and R are weighting matrices and their values are se-
lected depending on the relative importance given to different
terms in their contributions to the performance index J.
Solving the optimal control problem with J defined by Eq.
(35), results in a optimal force vectorfc regulated only by the
state vectorx, such that
1( )Tcf R B P x Gx= = (36)
where matrix G represents the gain matrix; and the matrix P is
the solution of the classical Riccati equation given by Eq. (37)
1 0 .T TPA A P PBR B P Q+ + = (37)
The force generated by the MR damper cannot be com-
manded. When the MR damper is providing the desired opti-
mal force (i.e., f = fc ), the voltage applied to the damper
Fig. 3. Clipped optimal algorithm block diagram.
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328 S. H. Zareh et al. / Journal of Mechanical Science and Technology 26 (2) (2012) 323~334
should remain at the present level. If the magnitude of the
force produced by the damper is smaller than the magnitude of
the desired optimal force and the two forces have the same
sign, the voltage applied to the current driver [14] varies con-
tinuously in the range of [0-Vmax]. The secondary controller for
continuously varying the command voltage can be stated as
{ }( )i ci ci i iv V H f f f = (38)
max
max max
,
,
i ci cici
ci
f for f fV
V for f f
=
>(39)
where Vmax is 12v and fmax is maximum force produced by
the damper (=3,000 N); is coefficient relating the voltage to
the force (= Vmax/fmax);H (.) is the heaviside step function ex-
pressed as 0 or 1 [14]; fi is the force produced by ith
MR
dampers which is applied to the structure.
In this paper, a simple mechanical model consisting of a
Bouc-Wen element in parallel with a viscous damper is used,
as shown in Fig. 4. This model has been verified to accuratelypredict the behavior of a prototype shear-mode MR damper
over a wide range of inputs in a set of experiments, and is also
expected to be appropriate for modeling a full-scale MR
damper.
The equations governing the force fi exerted by this model
are as follows:
0if c x z= +& (40)
1n nmz x z z x z A x
= +& & && & (41)
wherex is the displacement of the device andzis the evolu-
tionary variable that accounts for the history dependence of
the response. The parameters , , n andAm adjusted to deter-
mine the linearity in the unloading and the smoothness of the
transition from the pre-yield region to the post-yield region.
Device model parameters and c0 are determined by the de-
pendency on the control voltage u, as follows:
( ) a bu u = = + (42)
0 0 0 0( ) .a bc c u c c u= = + (43)
Moreover, to account for a time-lag in the response of the
device to the changes in the command input, the first-order
filter dynamics are introduced to the system as follows:
( )u u = & (44)
where v is a command voltage applied to the control circuitand is the time constant of the first-order filter.
The numerical values of parameters are shown in Tables 2
and 3 [23].
The hysteretic behavior of the MR damper model according
to the input voltage is shown in Fig. 5.
6. Road profile simulation
The random road excitation is generated using white noise
as a road irregularity as a disturbance. The power spectral
density (PSD) function of road irregularity is assumed to be in
the form of Eq. (45).
2
2 2( ( ) )
rh
r
VS
V
=
+(45)
where 2
is the variance of the road profile, is the excitation
frequency of the road input Vis the vehicle forward constant
velocity and r is a coefficient depending on the type of road
surface. The typical properties of unpaved road profile are
shown in Table 4 [2].
The PSD of the road surface is obtained by using MATLAB.
Table 2. Numerical values of MR damper model.
a (N cm-1) b (N cm
-1 V-1) (cm-2) (cm-2)
140 695 363 363
Table 3. Numerical values of MR damper model.
c0a (Nscm-1) c0b (Nscm
-1 V-1) n (s-1) Am
21 3.5 1 190 301
Fig. 5. Hysteretic behavior of an MR damper.
Fig. 4. Mechanical model of a shear mode type MR damper.
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7. Neuro fuzzy strategy
Unfortunately, due to the inherent nonlinear nature of the
MR damper to generate a force, a model like that for its in-
verse dynamics is difficult to obtain mathematically. Because
of this reason, a neural network with fuzzy logic controller is
constructed to copy the inverse dynamics of the MR damper.
Unlike conventional controllers, such controllers do not re-
quire mathematical model and they can easily deal with the
nonlinearities and uncertainties of the controlled systems. Also,
a Levenberg-Marquardt neural controller has been designed
for variable geometry suspension systems with MR actuators.
In the present research, an optimal controller (LQR) is de-
signed for the control of a semi-active suspension system for a
full-model vehicle, using a neuro-fuzzy along with Leven-
berg-Marquardt learning. The purpose in a vehicle suspension
system is reduction of transmittance of vibrational effects
from the road to the vehicles passengers, hence providing ride
comfort. To accomplish this, one can first design a LQR con-
troller for the suspension system, using an optimal control
method and use it to train a neuro-fuzzy controller. This con-
troller can be trained using the LQR controller output error on
an online manner.
Once trained, the LQR controller is automatically removed
from the control loop and the neuro-fuzzy controller takes on.
In case of a change in the parameters of the system under con-
trol, the LQR controller enters the control loop again and theneural network gets trained again for the new condition [14].
An important characteristic of the proposed controller is that
no mathematical model is needed for the system components,
such as the non-linear actuator, spring, or shock absorbers.
The basic idea of the proposed neuro-fuzzy control strategy
is that the force of the MR dampers is determined by a fuzzy
controller, whose inputs are the measured displacement and
velocity response provided by a neural network. The architec-
ture of this strategy is shown in Fig. 6, which consists of four
parts to perform different tasks. The first part is the neural
network to be trained on-line. The numbers of the sample data
pairs are 3500, the training data pairs increase step by stepduring the entrance disturbance from road profile, predicted
voltage by clipped method.
The neural network is trained to generate the one step ahead
prediction of the displacement xk+1 and the velocity xk+1. In-
puts to this network are the delayed outputs (xk+3,xk+2,xk+1,xk,
xk+3, xk+2, xk+1, xk), the delayed force which is predicted by
fuzzy controller (fk+1), and the disturbance input (dk). At the
initial time, the inputs of the network will be taken to have the
value of zero in accordance with the actual initial circum-
stance. Before online training, the network trained off-line to
achieve update weights near to desired.
The second part is the fuzzy controller, whose inputs are the
measured displacement and velocity across MR dampers. The
disturbance can be calculated by road profile model. The out-
put of the fuzzy controller is control force of the MR dampers.
The main aim of this part is to determine control force of the
MR dampers quickly in accordance with the input excitation.
How to design the fuzzy controller will be explained in the
following section. In order to reach this aim, it is required to
predict the responses of passengers in accordance with the
optimal responses. At the same time, the actual responses will
feed back to the neural network and the weights and bias will
be revised real time. In this research work, the calculated re-
sults by optimal control history analysis method are used to
simulate the actual measured responses. The errors between
the predicted responses and the actual responses are used to
update the weights of the neural network on-line.
7.1 The neural network based on Levenberg-Marquardt
(LM) algorithm
The MR damper model discussed earlier in this research es-timates damper forces based on the inputs of the reactive ve-
locity. In such case, it is essential to develop an inverse dy-
namic model that predicts the corresponding control force to
be sent from dampers so that an appropriate damper force can
be generated [16].
Neural network is a simplified model of the biological
structure found in human brains. This model consists of ele-
mentary processing units (also called neurons). It is the large
amount of interconnections between these neurons and their
capabilities to learn from data to enable neural network as a
strong predicting and classification tool. In this study, Three-
layer feed forward neural network, which consists of an inputlayer, one hidden layer, and an output layer is selected to pre-
dict the responses with MR dampers. The net input value netk
of the neuron kin some layer and the output value Ok of the
same neuron can be calculated by the following Eqs. (46) and
(47):
k jk jnet w O= (46)( )k k kO f net = + (47)
where wjk is the weight between thejth
neuron in the previous
Fig. 6. Architecture of the Neuro-Fuzzy control strategy.
Table 4. Typical properties of unpaved road profile.
2 (m2 ) (rad/s ) V (m/s) r(rad/m)
3e-4 200 16.66 0.45
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330 S. H. Zareh et al. / Journal of Mechanical Science and Technology 26 (2) (2012) 323~334
layer and the kth
neuron in the current layer, Ojis the output of
thejth
neuron in the previous layer,f(.) is the neurons activa-
tion function which can be a linear function, a radial basis
function, and a sigmoid function, and yk is the bias of the kth
neuron. Feed forward neural network often has one or more
hidden layers of sigmoid neurons followed by an output layer
of linear neurons. Multiple layers of neurons with nonlineartransfer functions allow the network to learn nonlinear and
linear relationships between input and output vectors. In the
neural network architecture as shown in Fig. 6, the logarithmic
sigmoid transfer function is chosen as the activation function
of the hidden layer, Eq. (48):
( )
1( ) .
1 k kk k k net
O f net e
+= + =
+(48)
The linear transfer function is chosen as the activation func-
tion of the output layer, Eq. (49):
( ) .k k k k k O f net net = + = + (49)
We note that neural network needs to be trained before pre-
dicting responses. As the inputs are applied to the neural net-
work, the network outputs (.) are compared with the targets
(.). The difference or error between both is processed back
through the network to update the weights and biases of the
neural network so that the network outputs match closer with
the targets. The input and output data are usually represented
by vectors called training pairs. The process as mentioned
above is repeated for all the training pairs in the data set, until
the network error converged to a threshold minimum defined
by a corresponding performance function. In this research, themean square error (MSE) function is adopted (desired MSE is
1e-5).
LM algorithm is adapted to train the neural network, which
can be written as Eq. (50):
2
12
1i i
ii
E Ew w I
ww
+
= +
(50)
where i is the iteration index, / iE w is the gradient descent of
the performance functionEwith respect to the parameter ma-
trix
i
w , 0 is the learning factor, andIis the unity matrix.During the vibration process, the neural network updates
the weights and bias of neurons real time in accordance with
sampling pairs till the objective error is satisfied, i.e. the prop-
erty of the system is acquired. As we know, the main aim of
the neural network is to predict the dynamic responses of the
system and to provide inputs of fuzzy controller and data of
calculating control force of MR dampers. Thus outputs of the
neural network are predicted values of displacement xk+1 and
velocityxk+1. In order to predict the dynamic responses of the
system accurately, the most direct and important factors which
affect the predicted dynamic responses are considered, i.e. the
delayed outputs (xk+3,xk+2,xk+1,xk ,xk+3,xk+2,xk+1, xk), the pre-
dicted force (fk+1), and the disturbance input (dk). LM algo-
rithm is encoded in neural networks toolbox in MATLAB
software.
7.2 Design of fuzzy controller
The first step in designing a fuzzy controller is to determinethe basic domains of inputs and outputs. The desired dis-
placement and velocity responses are chosen as inputs of the
fuzzy controller. The output of fuzzy controller is the control
force of the MR damper, which basic domain is -700N
300N same as the working force of the MR damper calculated
using LQR.
The membership functions are usually chosen in accordance
with the characteristics of the membership functions and de-
signing experience. For simplifying the calculation, triangle or
trapezoid form functions are usually adopted as the member-
ship functions. The triangle membership function is more
Fig. 7. Membership function of front-left damper velocity (m/s).
Fig. 8. Membership function of front-right damper velocity (m/s).
Fig. 9. Membership function of back-left damper velocity (m/s).
Fig. 10. Membership function of back-right damper velocity (m/s).
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sensitive to inputs than the trapezoid form function, in expec-
tation that the control forces of the MR dampers are sensitive
to excitations and responses [13], but in this case are used
Gaussian and triangle form because considered form had bet-
ter response by trial and error. In this research, Gaussian and
triangle functions are adopted as the membership functions of
velocity. The membership function curves of velocity are
shown in Figs. 7-10.
8. Results
The full-car model with MR damper and disturbance is
modeled by the dynamic equations and state space matrices.
One of the desired points of this study is to decrease the am-
plitude of passengers displacements, when the suspension
system excited from the road profile. Therefore the effect of
LQR and LQG controllers and neuro-fuzzy strategy are simu-
lated for road excitation with calculated their amplitude, and
then compared with each other. The random road surface are
generated compatible with the power spectral density given in
Eq. (45) using a sum of bumper with 7 cm height and 4 cm
width. The displacement and acceleration trajectories for
front-left passengers seat that is excited by bumper with 7 cm
height and 4 cm width with 60 and 30 km/h constant velocity
in unpaved road under front left wheel are shown in Figs. 11-
14, respectively. Notice that, in all graphs, time duration is
selected for the best resolution and critical responses are hap-
pened when car strikes with bumper.
The graphs which are presented show that LQR controller
designed cannot eliminate the effect of the distributed road,
but the LQG controller can eliminate the effect of the distrib-
uted road. However, this modeling and controller which have
been theoretically designed may be experimental model can-
not work such as the theoretical model. Also, the trajectories
of neuro-fuzzy strategy show that this strategy reduces the
amplitude of vibration lower than the passive system and also
to some extent as well as optimal controllers; because dis-
placements and acceleration are predicted by feed forward
neural networks. The primary oscillations are due to the less
number of network input to train, on the other hand, there are
not strong history in transient, therefore the transient part of
response not as well as steady state part. To investigate, are
there any primary unwanted oscillations due to use of neuro-
fuzzy strategy at the other bumpiness after the first one, is
Fig. 11. Displacement of front-left seat from front left wheel excited
with 60 km/h.
Fig. 12. Acceleration of front-left seat from front left wheel excited
with 60 km/h.
Fig. 13. Displacement of front-left seat from front left wheel excited
with 30 km/h.
Fig. 14. Acceleration of front-left seat from front left wheel excited
with 30 km/h.
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332 S. H. Zareh et al. / Journal of Mechanical Science and Technology 26 (2) (2012) 323~334
added another after five seconds. The displacement of front-
left seat due to two bumpers is shown in Fig. 15.
The graph which is presented is shown that the unwanted
oscillations due to use of neuro-fuzzy strategy at the beginning
of first excitation to some extent removed at the beginning of
second bumper. The road holding for front-left damper that is
excited by bumper with 7 cm height and 4 cm width with 60
km/h and 30 km/h constant velocity under front left wheel are
shown in Figs. 16 and17, respectively.
The stability of automobile due to use of neuro-fuzzy strat-
egy is better than other two strategies, because the oscillation
of front left wheel due to road excitation in neuro-fuzzy algo-rithm is less than other strategies. The trajectories of require-
ment forces to obtain the desire displacements and accelera-
tion is shown in Fig. 18.
The force is calculated by use of optimal controllers to some
extent have the same trend. But the forces of neuro-fuzzy can-
not follow them; because, optimal forces depend on twenty
two state variables and the forces obtained by the fuzzy part of
neuro-fuzzy strategy depend on one state variable (relative
velocity across MR damper). One of the main advantages of
using neuro-fuzzy, the control effort of dampers is less than
LQR and LQG responses. The clipped optimal method re-
sponses to generate a requirement voltage for two different
velocities are shown in Figs. 19 and 20, respectively. These
are obtained by another neuro-fuzzy strategy (the output of
fuzzy part is voltage).
The voltages are calculated by use of optimal controllers to
some extent have the same trend. The voltages are calculated
using neuro-fuzzy with less oscillations, therefore saving en-
ergy and cost.
9. Conclusions
Usual suspension systems are utilized in the vehicle, and
damped the vibration from road profile. However, passive
suspension systems have long settling time. When cars are
moved along bumpy road, the passive suspension system
driver cannot react in effective time. As a result, the usual
suspension system cannot damp the excitation with small time
interval. In order to remove this problem the properties of the
suspension system should be variable. This task is done by
adding MR dampers as an actuator to the suspension system.
In order to send commands to the actuator, LQR controller
is utilized. It can decrease the amplitude of the vibration of
passenger seats, but it cannot eliminate the effect of bumpy
roads as a disturbance. Therefore, LQG controller was de-
signed. This controller by LQE estimator can estimate the
Fig. 15. Displacement of front-left seat from front left wheel excited
with 60km/h due to two bumpers.
Fig. 16. Road holding for front-left damper excited with 60 km/h.
Fig. 17. Road holding for front-left damper excited with 30 km/h.
Fig. 18. Generated force by front-left MR damper from front left wheel
excited with 60 km/h.
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state of the system without disturbance effect. Then the esti-
mated system is controlled by LQR part of LQG controller.
Consequently, the disturbance effect is eliminated, and the
response of this controller in the theoretical model is much
performed. It is seen that the control forces with LQG algo-
rithm and LQR algorithm completely suitable for road excita-
tion, meaning that the Kalman filter gives accurate estimations
of structural states. As can be seen, LQG can eliminate the
effect of disturbances better than LQR.
Unfortunately, due to the inherent nonlinear nature of the
MR damper to generate force, a model like that for its inverse
dynamics is difficult to obtain mathematically. Because of this
reason, a neural network with fuzzy logic controller is con-
structed to copy the inverse dynamics of the MR damper.
According to the graphs that show above, the trajectories of
neuro-fuzzy strategy can reduce the amplitude of vibration to
some extent as well as optimal controllers with less control
effort and oscillation.
Acknowledgment
The authors wish to express their gratitude to the Interna-
tional campus of Sharif University of Technology for the sup-
port provided for this research.
References
[1] Y. P. Wang, Y. Shio, J. Guo, M. H. Chiang and Y. K. Din,Semi-active control of vehicle suspension system using elec-trorheological dampers, 3rd Institution of Engineering and
Technology Conference (2007).
[2] R. S. Prabakar, C. Sujatha and S. Narayanan, Optimal semi-active preview control response of a half car vehicle model
with magnetorheological damper, Journal of sound and vi-
bration, 326 (2009) 400-420.
[3] Y. Md. Sam and J. H. S. B. Osman, Modeling and control ofthe active suspension system using proportional integral slid-
ing mode approach, Asian Journal of Control, 7 (2) (2005)
91-98.
[4] A. F. Jahromi, A. Zabihollah and Linear Quadratic Regulatorand fuzzy controller application in full-car model of suspen-
sion system with magnetorheological shock absorber,
IEEE/ASME International Conference on Mechanical and
Embedded Systems and Applications (2010) 522-528.
[5] M. M. M. Salem and Ayman A. Aly, Fuzzy control of aquarter-car suspension system, World Academy of Science
Engineering and Technology, 53 (2009) 258-263.
[6] H. C. Sohn and K. T. Hong, An adaptive LQG control forsemi-active suspension systems,International Journal Vehi-
cle Design, 34 (4) (2004) 309-326.
[7] Y. Chen, Tan, L. A. Bergman and T. C. Tsao, Smart suspen-sion systems for bridge-friendly vehicles, Annual Interna-
tional Symposium on Smart Structures and Materials (2002).
[8] S. Jialin, A. Ordys and K. Panahi, LQR-based linear control-ler of active suspension on a half-body model for improvedride comfort, 3rd IAR Workshop on Advanced Control and
Diagnosis (2008).
[9] J. Sun and Q. Yang, Modeling and intelligent control ofvehicle active suspension system, IEEE International con-
ference on RAM(2008) 239-242.
[10] J. Sun, Q. Zhou, Vibration control of vehicle suspensionwith five degrees of freedom, Proc. 9th IEEE International
conference on cognitive informatics (2010) 824-828.
[11] M. Biglarbegian, W. Melek and F. Golnaraghi, Intelligentcontrol of vehicle semi-active suspension system for im-
proved ride comfort and road handling,IEEE International
conference (2006) 19-24.
[12] S. H. Sadati, M. A. Shooredeli and A. D. Panah, Designinga neuro-fuzzy controller for a vehicle suspension system us-
ing feedback error learning,Journal of mechanics and aero-
space, 4 (3) (2008) 45-57.
[13] Zh. D. Xu, Y. Q. Guo and Neuro-Fuzzy control strategy forearthquake-excited nonlinear magnetorheological structures,
Soil Dynamics and Earthquake Engineering, 28 (2008) 717-
727.
[14] O. Yoshida and S. J. Dyke, Seismic control of a nonlinearbenchmark building using smart dampers,Journal of engi-
Fig. 19. Requirement voltage to front-left MR damper from front left
wheel excited with 60 km/h.
Fig. 20. Requirement voltage to front-left MR damper from front left
wheel excited with 30 km/h.
-
7/28/2019 Intelligent Semi-Active Vibration Control Suspension System
12/12
334 S. H. Zareh et al. / Journal of Mechanical Science and Technology 26 (2) (2012) 323~334
neering mechanics, 130 (2004) 386-392.
[15] A. Khajekaramodin, H. Hajikazemi, A. Rowhanimaneshand M. R. Akbarzade, Semi-active control of structures us-
ing neuro-inverse model of MR dampers, 1st Joint congress
on fuzzy and intelligent systems, Iran (2007).
[16] S. Yildirim and I. Eski, Vibration analysis of an experimen-tal suspension system using artificial neural networks, Jour-nal of Scientific & Industrial Research, 68 (2009) 522-529.
[17] S. Y. Ok, D. S. Kim, K. S. Park and H. M. Koh, Semi-active fuzzy control of cable-stayed bridges using magneto-
rheological dampers, Engineering Structures, 29 (2007) 776-
788.
[18] V. S. Atray and P. N. Roschke, Neuro-fuzzy control ofrailcar vibrations using semi active dampers, Computer-
Aided Civil and Infrastructure Engineering, 19 (2004) 81-92.
[19] S. G. Foda, Neuro-fuzzy control of a semi-active car sus-pension system,IEEE conference (2001) 686-689.
[20] S. Yildirim and I. Eski, Vibration analysis of an experimen-tal suspension system using artificial neural networks, Jour-
nal of Scientific & Industrial Research, 68 (2009) 522-529.
[21] M. Askari and A. H. Davaie-Markazi, Multi-objective op-timal fuzzy logic controller for nonlinear building-MR
damper system, 5th IEEE International Conference on Sig-
nals and Devices (2008) 3-8.
[22] M. Ahmadian and C. A. Pare, A quarter car experimentalanalysis of alternative semi-active control methods, Journal
of Intelligent Material Systems and Structures 11 (8) (2000)
604-612.
[23]
Y. Kim, R. Langari and S. Hurlebaus, Semi-active nonlin-ear control of a building with a magnetorhelogical damper
system, Mechanical Systems and Signal Processing, 23
(2009) 300-315.
[24] R. Stanway, J. L. Sproston and N. G. Stevens, Non-linearmodelling of an electrorheological vibration damper, Jour-
nal of Electrostatics, 20 (2) (1987) 167-184.
Seiyed Hamid Zareh is a MSc. Student
in Mechatronics at Sharif University of
Technology, School of Science and
Engineering, Iran. He was born in 1983
and also graduated in mechanical engi-neering in 2004 at Imam Hossein Uni-
versity of Tehran, Iran.