Applied Mechanics and Materials Vol. 192 (2012) pp 106-110
© (2012) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMM.192.106
Design of a New Suspension System Controlled by Fuzzy-PID with
Wheelbase Preview
Pak-kin Wong1,a, Shaojia Huang2,b,Tao Xu3,c, Hang Cheong Wong4,d,
Zhengchao Xie5,e
Department of Electromechanical Engineering, Faculty of Science and Technology
University of Macau
Macau, China
a
b
fstpkw@umac.mo, mb15480@umac.mo, cmb15482@umac.mo, dhcwong@umac.mo,
e
zxie@umac.mo
Keywords: Vehicle Suspension, Fuzzy-PID control, Wheelbase preview control, System
Simulation
Abstract. This paper studies a new active vehicle suspension controlled by Fuzzy-PID controller
with wheel base preview. By this new algorithm, the fuzzy controller controls the parameters of the
PID in time .Then the wheelbase preview is integrated to ensure the future road information is
combined with the current state of the vehicle effectively. A sensor is placed on the front suspension
collects and feeds forward the preview information as an input to the rear suspension system .
MATLAB simulations show that using such control strategy can obtain a low noise and better
robustness performance than the traditional PID control algorithm.
Introduction
Suspension systems support vehicle and provide a good ride quality [1]. Recently, active and
semi-active suspensions have been introduced to improve vehicle suspension systems, while the
active suspension has a better performance than the semi-active suspension since more power
consumed by the active suspension [2].
Vehicle model usually should be established first to be combined with control algorithm. Recently,
compared with the most commonly used quarter-car model, half-car suspension model have been
investigated [3].
PID controllers sometimes perform poorly in some complicated condition. Therefore，this
research studies the Fuzzy-PID controllers to overcome the limitation of PID. Such new control
strategy has self-tuning ability and on-line adaptation to nonlinear, time varying systems [4].
In Recent years, the preview control has been utilized frequently due to its effectiveness. In this
paper, wheelbase preview is proposed due to its simplicity.
Vehicle Dynamic Model and Control
In this section, a half car dynamics model will be established and then implemented by using
Simulink. Next, the control strategy of an active vehicle suspension will be illustrated through the
dynamic model. A half car model is shown in Figure 1, which was proposed in [2].
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Applied Mechanics and Materials Vol. 192
a
zf
z1
z01
b
zr
θ
K1
U f K2 C
r
Cf
107
M wf
Ur
z2
M wr
K tf
K tr
z02
Fig. 1 Structure of a half car model
Half-car Suspension Model. The half car model as show in Fig.1 [2], a and b are the longitudinal
distances of the front and rear wheel center to the body center of gravity respectively. The front and
rear wheel un-sprung masses are shown as
respectively of front and rear suspensions.
and
,
.
,
and
and
are the damping constants
are the stiffness of the front
wheel, rear wheel, front suspension and rear suspension respectively. The input of the road of front
and rear wheels are mentioned as
and
respectively. ,
, , and
are the vertical
displacements of the front vehicle body, the front wheel, the rear vehicle body, the rear wheel
measured with respect to the position of equilibrium and the pitch angle of the vehicle respectively.
Fuzzy-PID Controller. Fuzzy-PID means a control algorithm based on fuzzy logic control
algorithm combined with PID control algorithm. In this paper, the regular fuzzy control system is a
two-dimensions structure controller，and three PID parameters as its output [5]. Fuzzy controller
controls the parameters of the PID in time to satisfy the different requirement of the controller
parameters when the input is changing [6]. The active force of the suspension system is then
controlled by the PID controller. The design process of Fuzzy- PID controller is as follows:
Define the input and output design variables according to the system. In this paper we choose the
acceleration of rear wheel un-sprung mass
and its derivative z r as input variables and KP, KI, KD
as the fuzzy controller outputs. Then the active force Ur which produced by the actuator is controlled
by the PID as the output variables of whole controller. It can represent by:
(1)
Define the fuzzy universe of discourse of input and output variables and transformation factor. We
define the universe of
and
are {-6 6} and the universe of KP, KI, KD is {-6 6} [7] .
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Advanced Mechanical Engineering II
Establish fuzzy control law, this paper define the {NB, NM, NS, ZE, PS, PM, PB} as the linguistic
variables of E, EC and KP, KI, KD. Then define the trigonometric functions as the membership
function of the linguistic variables.
The formulation of fuzzy control rules with changes in the system from time to time in accordance
with the deviation e and the deviation rate of change ec. The control rules show in Table 1.
Table 1．Fuzzy rules
KP/KI/KD
NB
NM
NS
ZO
PS
PM
PB
NB
PB/NB/PS
PB/NB/NS
PM/NM/NB
M/NM/NB
PS/NS/NB
ZO/ZO/NM
ZO/ZO/PS
NM
PB/NB/PS
PB/NB/NS
PM/NM/NB
PS/NS/NM
PS/NS/NM
ZO/ZO/NS
NS/ZO/ZO
NS
M/NB/ZP
PM/NM/NS
PM/NS/MN
PS/NS/NM
ZO/ZO/NS
NS/PS/NS
NS/PS/ZP
ZO
PM/NB/ZP
PM/NM/NS
PS/NS/NS
ZO/ZO/ZO
NS/PS/NS
NM/PM/NS
NM/PM/ZO
PS
PS/NM/ZO
PS/NS/ZO
ZO/ZO/ZO
NS/PS/ZO
NS/PS/ZO
NM/PM/ZO
NM/PB/ZO
PM
PS/ZO/PB
ZO/ZO/NS
NS/PS/PS
NM/PS/PS
NM/PM/PS
NM/PB/PS
NB/PB/PB
PB
ZO/ZO/PB
ZO/ZO/PM
NM/PS/PM
NM/PM/PM
NM/PM/PS
NB/PB/PS
PB/PB/PB
De-fuzzy the output variables are finished the transfer from fuzzy variables to precise variables.
This paper uses Center of Area Method (COA) since it can get a better smooth curve. In the case of
discrete universe of discours.
Preview Control. The wheelbase preview is adopted in this work due. A disturbance observer [1]
is used for accomplishing this strategy in this paper.
Numerical Simulation
MATLAB simulations are showed in Fig. 2 , Fig. 3 in this part to show the advantages of proposed
control strategy. The parameters of suspension system are given in Table 2 [1]. All simulation tests
are done based on the following step input.
(2)
Fig. 2 Comparison of Fuzzy-PID and PID
Fig. 3 Comparison of Fuzzy-PID with preview
and without preview
Applied Mechanics and Materials Vol. 192
109
Table 2．Parameters of the simulated suspension system
Parameter
a
b
Cf
Cr
I
K1
K2
Ktf
Ktr
M
Mwf
Mwr
v
S
Unit
[mm]
[mm]
[N·s/m]
[N·s/m]
[Kg m]2
[kN/m]
[kN/m]
[kN/m]
[kN/m]
[Kg]
[Kg]
[Kg]
[m/s]
[N/v]
Value
1444
1305
3040
3040
3128.1
130
85
405
405
803.7
90
115
20
900
Fig. 2 compares the proposed Fuzzy-PID controller with preview information to conventional PID
controller under high sensor noise. Obviously, the Fuzzy-PID controller can effectively suppress the
influence of the sensor noise. Moreover, Fig.3 shows a Fuzzy -PID active vehicle suspension system
with preview information to another same vehicle suspension system without preview information. It
can be seen that the acceleration of the rear wheel sprung mass is reduced significantly after adding the
preview information.
Summary
The research has proposed a new active vehicle suspension system controlled by a Fuzzy-PID
controller with wheelbase preview by using a half-car model. From the above example, we can get the
result that the sensor noise can be reduced effectively and the controller gets a better adaptive ability
since by suing the Fuzzy-PID algorithm. Moreover, the wheelbase preview can greatly restrain the
acceleration of the rear wheel sprung mass.
References
[1] Pak-kin Wong, Zhengchao Xie, Hang-cheong Wong, Xinzheng Huang: Design of a Fuzzy
Preview Active Suspension System for Automobiles, Proceedings of 2011 International
Conference on System Science and Engineering (ICSSE 2011), pp. 525-529, Macau, June
2011.
[2] T. Yoshimura, A. Kume, M. Kurimoto and J. Hino: A study of random vibration
characteristics of the quarter-car model,Journal of Sound and Vibration, Vol. 239, Issue 2, pp.
187-199, 2001.
[3] Yoshimura, T, Kume, A., Kurimoto, M. and Hino, J: Construction of an active suspension
system of a quarter car model using the concept of sliding mode control. Journal of Sound and
Vibration, 2001, 239, 187-199.
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Advanced Mechanical Engineering II
[4] Han-Xiong Li, Lei Zhang, Kai-Yuan Cai, and Guanrong Chen:An Improved Robust
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