Research Journal of Applied Sciences, Engineering and Technology 4(16): 2744-2747, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: March 26, 2012
Accepted: April 17, 2012
Published: August 15, 2012
The Application of Fuzzy Control Algorithm of Vehicle with Active Suspensions
1
1
Chuan-yin Tang, 1Guang-yao Zhao, 1Yi-min Zhang and 2Yan Ma
School of Mechanical Engineering and Automation, North Eastern University,
Shenyang, 110819, China
2
Shenyang Academy of Instrumentation Science, Shenyang, 110043, China
Abstract: In this study, a fuzzy logic control design is represented for the control of an active suspension
system. A seven degrees of freedom non linear full vehicle model is established, instead of two degrees of
freedom one quarter model and four degrees of freedom half body model and the road roughness intensity is
modeled as a white noise stochastic process. Then a fuzzy logic controller is designed for the control of the
seven degrees of freedom full vehicle model, the input variables are the suspension displacement and the output
variables are the control force. The time responses of the full vehicle model are obtained, not only the vertical
body acceleration, but also the roll angular acceleration and pitch angular acceleration. Finally, uncontrolled
and controlled cases are compared. With the aid of software Matlab/simulink, simulation process is done.
Simulation results indicate that the proposed active suspension system proves to be effective in the vibration
isolation of the suspension system both in ride comfort and in stability.
Keywords: Fuzzy logic algorithm, seven DOF full body model, simulation analysis, suspensions control
INTRODUCTION
The job of a car suspension is to minimize the friction
between the tires and the road surface, to provide steering
stability with good handling and to ensure the comfort of
the passengers. The vehicle designer can do little to
improve road surface roughness, so designing a good
suspension system with good vibration performance under
different road conditions becomes a prevailing philosophy
in the automobile industry. Due to the developments in
the control technology, electronically controlled
suspensions have gained more interests. These
suspensions have active components controlled by a
microprocessor. By using this arrangement, significant
achievements in vehicle response can be carried out.
Selection of the control method is also important during
the design process. In this study, fuzzy logic controller is
used. During the last decade, many researchers have
applied some control methods to vehicle models. Due to
simplicity, quarter car models were mostly preferred.
Researchers (Redfield and Karnopp, 1998) examined the
optimal performance comparisons of variable component
suspensions on a quarter car model. Yue et al. (1989) also
applied LQR and LQG controller to a quarter car model.
Hac (1992) applied optimal linear preview control on the
active suspensions of a quarter car model. But a full
vehicle body model can provide more details, although it
is more complicated (Crolla and Abdel Hady, 1991). The
study presented a seven degrees of freedom whole body
vehicle model, the dynamic equations of the whole body
vehicle model are constructed first, then the fuzzy logic
controller according to the seven degrees of freedom
model is gained and some simulation analysis is done,
finally some remarks are given.
METHODOLOGY
Full vehicle model: Schematic diagram of active
suspension control system is shown in Fig. 1, The full
body seven degrees of freedom suspension system is
represented (Guclua and Kayhan, 2008). The assumptions
during the process of modeling are considered as
followings:
C
C
C
C
C
The vehicle body, including the engine part is
considered as a rigid body, which means the effect of
engine is neglected
The roll and yaw movement of the vehicle is
considered
The vehicle consists of a single sprung mass
connected to four unsprung masses
The axle and the tires connected are regarded as the
unsprung mass, the contact manner of the center tire
line and the road is point to point method
The tires are modeled as simple linear springs
without damping
In the equations, ct1, ct2, ct3 and ct4 denote the
damping coefficients of the left front tire, the left rear tire,
the right rear tire and the right front tire, respectively. z1,
z2, z3 and z4 represent the vertical displacement of the
Corresponding Author: Chuan-yin TANG, School of Mechanical Engineering and Automation, North Eastern University,
Shenyang, 110819, China
2744
Res. J. Appl. Sci. Eng. Technol., 4(16): 2744-2747, 2012
Fig. 1: Model of full body seven degrees of freedom of suspension
left front wheel-axle, the left rear wheel-axle, the right
rear wheel-axle and the right front wheel-axle,
respectively. y1, y2, y3 and y4 denote the road
disturbance input for left front wheel, the left rear wheel,
the right rear wheel and the right front wheel,
respectively. Ft1, Ft2, Ft3 and Ft4 denote the left front
wheel force, the left rear wheel force, the right rear wheel
force and the right front wheel force, respectively.
After applying a force-balance analysis to the model
in Fig. 1 the dynamics equation is governed by:
m3 
z3  k t 3  y3  z3   k s3  z3'  z3   c3  z3'  z3   F3
m4 
z4  k t 4  y 4  z4   k s 4  z4'  z4   c4  z4'  z4   F4
and
 k s 4 ( z 4  z )  c1  z1  z   c2  z2  z
'
1
'
2
X = AX +BQ, Y = CX +DQ

 c3  z3  z3'   c4  z4  z4'   F1  F2  F3  F4


j y   k s1  z1  z1'   c1  z1  z1'   k s 3  z3  z3'   c3  z3  z3'  a


 k s2  z2  z   c2  z2  z2'   k s4  z4  z4'   c4  z4  z4'  b
'
2
  F1  F3 a   F2  F4 b

X is defined as state variable, where Y is the output
vector, Q is the input vector, A is the state matrix, B is the
input matrix, C is the output matrix, D is the feed forward
matrix.
This results in the system state variables below:
 z1  z1'

X   y2  z2
 z3

j x   k s4  z4  z4'   c4  z4  z4'   k s 3  z3  z3' c3  z3  z3'  c


 k s 2  z2  z   c2  z2  z   k s1  z1  z c1  z1  z  d
'
2
'
2
'
1
'
1
  F4  F3 c   F2  F1 d
 
z
Y 
'
 z3  z 3
'
1
m2 
z2  kt 2  y2  z2   k s2  z2'  z2   c2  z2'  z2   F2
z2  z2'
y3  z3
z4
z2  z2'
y4  z4
z
z3  z 3'
z1

y1  z1

z2  
 
T
The output matrix is defined as:
m1
z1  k t 1  y1  z1   k s1  z  z1   c1  z  z1   F1
'
1
z3'  z  a  c z4'  z  b  c
The state space equations in matrix are given by:
mz  k s1 ( z1  z1' )  k s2 ( z 2  z2' )  k s3 ( z 3  z3' )
'
4
z1'  z  a  d z2'  z  b  d


z4  z 4'
y1  z1
z1  z1'
y 2  z2
with the disturbance input defined as:
2745
z2  z 2'
y3  z3
 

y4  z4 
T
Res. J. Appl. Sci. Eng. Technol., 4(16): 2744-2747, 2012

Q  y 1
y 2
y 3
y 4
0 F1
F2
F3
F4

T
NB
1.0
Denoting the irregular road excitation as band limited
white noise, which is determined by different road surface
condition and velocity, the equations of font and rear road
are expressed as followings:
NM
ZE
NS
PS
PM
PB
0.5
y   2f 0 y  2 G0 vw t 
0
where, f0 is the lowest frequency, irregular road
coefficients Gq(n0) = 256×10 !6 m2/m and velocity is
20 m/s.
-3
VNB
VNM
VZE
VNS
VPS
VPM
VPB
1.0
0.5
0
-3
Fuzzification: The first step in making a fuzzy logic
controller is to take the inputs and determine the degree to
which the inputs belong to each of the appropriate fuzzy
sets via fuzzy membership function. The input is always
a numerical value and must be fuzzified. The fuzzification
of the input becomes a membership function to be
evaluated. The fuzzy membership function can be
described as follows:
-2
-1
0
1
2
Input variable “dynamic suspension travel”
3
(b)
F1NB
F1NM
F1ZE
F1NS
F1PS
F1PM F1PB
1.0
0.5
 x, u  x x  K , u  x  0,1
k
3
(a)
Control system design: The fuzzy logic control is one of
the most attractive parts where fuzzy theory can be
effectively applied. The fuzzy logic translates the
mathematical control strategy into the linguistic control
strategy. The fuzzy logic controller is usually based on the
operator’s knowledge, fuzzy modeling of the operator’s
control actions and fuzzy modeling of the process.
The fuzzy logic controller consists of three steps. The
first step is the fuzzification, the second step is the
reasoning using the fuzzy rule base, the last step is the
defuzzification.
K
-2
-1
0
1
2
Input variable “dynamic suspension travel”
k
0
where, is the membership function specifying the grade of
degree for any element uk (x) in K which belongs to the
fuzzy set K. The lager values of uk (x) indicate the higher
degrees of membership. The trimf membership is
selected. It has seven grades; Negative Big (NB),
Negative Medium (NM), Negative Small (NS), Zero (ZE),
Positive Small (PS), Positive Medium (PM) and Positive
Big (PB).
Fuzzy rule base: The Mamdani fuzzy logic type is used.
In the study, the fuzzy controller controls the multi-inputsingle-output system and the fuzzy rule is described as
follows:
-1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Output variable “F”
(c)
Fig. 2: The fuzzy input and output membership functions
Negative Small (NS), Zero (ZE), Positive Small (PS),
Positive Medium (PM) and Positive Big (PB).
Deuzzification: In this study, the defuzzification using
the centre of area method is used and the defuzzification
outputs are the controlled force. This method yields:
  z
n
Z* 
Ri : IF x is Ai … and y is Bi … THEN z
= Ci, Di, Ei, Fi
j 1
A total of seven grades are used for the control force
in the study: Negative Big (NB), Negative Medium (NM),
1.0
c
 z   z 
n
j
j
j 1
c
j
where, n is the number of quantization levels of the
output, zj is the amount of control output at the
quantization level
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Res. J. Appl. Sci. Eng. Technol., 4(16): 2744-2747, 2012
j, :c(zj) represents its membership value in the fuzzy
output set. The membership function of dynamic travel of
suspension, the derivation of dynamic travel of
suspension and the control force are showed in Fig. 2.
SIMULATION AND DISCUSSION
The input of the fuzzy controller is composed of four
input variables and four output variables. The left front,
left rear, right front and right rear suspension
displacement are defined as the input variables and the
output variables are the four control force. Based on the
simulation software “Matlab/Simulink”. The performance
of the active control scheme is illustrated through a series
of simulations.
Pitch acceleration(rad/s 2 )
1.5
Figure 3 indicates the controlled body acceleration
response and the passive system body acceleration
response. For compare, they are shown in one figure. The
dash line represents the system before control and the
solid line indicates the system after control. And Fig. 4
shows the controlled roll angular acceleration response
and the passive system roll angular acceleration response.
Then Fig. 5 shows the controlled pitch angular
acceleration response and the passive system pitch
angular acceleration response.
The body acceleration and the roll angular
acceleration and pitch angular acceleration are decreased,
which indicate the fuzzy logic controller is effective in
ameliorating comprehensive performance.
Before control
After control
1.0
CONCLUSION
0.5
0
-0.5
-1.0
-1.5
0
1
2
4
3
6
5
Time (s)
8
7
9
10
In this study, Approaches are presented for
suspension design which uses fuzzy logic algorithm. It is
obvious from the response plots that vehicle body vertical
acceleration, roll angular acceleration response and pitch
angular acceleration response decreased compared with
the passive suspension system, which indicates that the
proposed controller proves to be effective in the comfort
and stability improvement of the suspension system.
ACKNOWLEDGMENT
Fig. 3: Vehicle body acceleration response
Pitch acceleration(rad/s 2)
25
Before control
After control
20
We thank school of mechanical engineering and
automation, Northeastern university for providing us with
the resources. And thanks for the funds supported by
National university basic scientific research fund
(N100403009) and Shenyang Science and Technology
Program (F10-205-1-75).
15
10
5
0
-5
REFERENCES
-10
-15
0
1
2
3
4
6
5
Time (s)
8
7
9
10
Fig. 4: Vehicle body roll angular acceleration response
Pitch acceleration(rad/s 2)
1.5
Before control
After control
1.0
0.5
0
-0.5
-1.0
-1.5
0
1
2
3
4
6
5
Time (s)
7
8
9
10
Fig. 5: Vehicle body pitch angular acceleration response
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suspension control: Performance comparisons using
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Dyn., 20: 107-120.
Guclua, R. and G. Kayhan, 2008. Neural network control
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1356-1371.
Hac, A., 1992. Optimal linear preview control of active
vehicle suspension. Vehicle Syst. Dyn., 21: 167-195.
Redfield, R.C. and D.C. Karnopp, 1998. Optimal
performance of variable component suspensions.
Vehicle Syst. Dyn., 17: 231-253.
Yue, C., T. Butsuen and J.K. Hedrick, 1989. Alternative
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