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Control of an Active Suspension Based on Fuzzy Logic

Yang-Hai Nan, Dong-Ji Xuan, Jin-Wan Kim, Qian Ning*and Young-Bae Kim

**

Department of Mechanical Engineering, Chonnam National University, Gwangju, Korea

E-mail:nyh0428@hotmail.com

*School of Electronics and Information Engineering, Sichuan University, Chengdu, China

** School of Mechanical Engineering, Chonnam National University, Gwangju, Korea

Abstract

In this paper, a control strategy of active suspension

based on the fuzzy logic control has been investigated.

Using incorporating feedback from force sensor at

front and rear active suspension system, the control

system shows the improvement of the dynamic

responses of the vehicle. A multi degree-of-freedom

nonlinear model is co-simulated by MATLAB/Simulink

and ADAMS/Car. The simulation results indicate that

the proposed active suspension is very effective in the

vibration isolation.

NOMENCLATURE

a Distance from CG to front axleb Distance from CG to rear axle

fc Damping coefficients of front sprung

rc Damping coefficients of rear sprung

1F

Front active force

2F Rear active forceJ Moment of inertia around Y-axis

fk Spring stiffness of front sprung

rk Spring stiffness of rear sprung

tfk Spring stiffness of front tires

trk Spring stiffness of rear tire

fm1 Front unsprung mass

rm1 Rear unsprung mass

2m Vehicle body mass

fq Road inputs to front tires

rq Road inputs to rear tires

fz1 Vertical displacements of the front tires

rz1 Vertical displacements of the rear tires

fz2 Vertical displacements of the front sprung

rz2 Vertical displacements of the rear sprung

cz Vehicle body bounces

I Pitch angle

1. Introduction

Suspension system is used to connect a vehicle and

its wheel, and then it contributes to the cars handling,

braking for good active safety and driving pleasure as

well as keeps vehicle occupants comfortable and

reasonably well isolates from road noise, bumps, and

vibrations. Therefore, simply the passive suspension is

widely used in the usual vehicle. However, it could not

satisfy the ride comfort and handing stability

simultaneously. As the recent trends of the vehicle

industry is to be luxurious and driver comfort is more

required, the electrical controlled suspension system is

now installed and widely utilized. [1~3] Especially, the

active suspension is widely adopted for the luxuriousvehicle because it can overcome the shortage of the

passive suspension by providing the ride comfort and

vehicle stability at the same time. However, a key task

for active suspension design is to determine a control

law, which is capable of giving good system

performance and better robustness. During the past two

decades, various approaches to derive the control

scheme have been proposed by many researchers. [4~5]

2008 International Conference on Computer and Electrical Engineering

978-0-7695-3504-3/08 $25.00 2008 IEEE

DOI 10.1109/ICCEE.2008.10

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The optimal control and robust control have been

introduced for active suspension application and some

good performances have been achieved on the

assumption of a linear vehicle model. In fact, vehicle is

a complicated, nonlinear system with uncertainties of

itself, and also operating condition is changeable. Thus,

the control approaches for active suspensions based on

the linear assumption of vehicle model havedifficulties in practical application for good

performance and robustness.

In this paper, the controller is designed by using

fuzzy logic control (FLC) as a type of intelligent

control method. The most important factor in FLC is to

prove to be one of the most efficient and systematic

approaches to deal with such kinds of problems in that

its control capability arises from emulating human

logic instead of accurate mathematical model. As a

new approach, nonlinear model is introduced by

ADAMS/Car, which is the worlds most widely used

mechanical system simulation software. [6]

By using the ADAMS nonlinear mathematic model

and the fuzzy logic control toolbox provided by theMATLAB/simulink software, the co-simulation of the

active suspension system with fuzzy controller under

the different input conditions are implemented. The

result shows that the active suspension system has

attractive benefit in regarding to the vehicle ride

comfort improvement.

The paper is organized as follows: section 2 presents

the vehicle model used for the active suspension

system control design. Section 3 represents the FLC

controller which is designed by integration of the

feedback signal. Section 4 represents the co-simulation

results by ADAMS/ Car and MATLAB. The

simulations are made to verify the proposed algorithm

under different road conditions: sine wave road surface

and white noise road surface.

2. Planar vehicle model

This chapter will describe the vehicle model used

for controller analysis. Fig.1 shows a half car model

consisting of sprung mass referring to the part of the

car that is supported on springs and unsprung mass

which refers to the mass of wheel assembly. Tire has

been replaced with its equivalent stiffness, and tire

damping is neglected. The suspension and tire are

modeled by linear springs in parallel with dampers.

By neglecting the roll and yaw motion, the

vehicles dynamics in the Y, Z plane can be

represented by a single-track half car model. The

model is valid for the assumed suspension elements.

Fig.1 Single-track half car linear model

Derivation of the equations of the motion for the

single-track half car linear model will be obtained from

the force and moment balance. Using the Newtons

second law of motion and free-body diagram concept,

equations of motion for the car body are derived in

Eq.1.

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fftfffffffff qzkFzzczzkzm

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FzzczzkaFzzczzkbJ ffffffrrrrrrM

(1)

The relationships among vertical displacements of

the front sprung fz2 , rear sprung rz2 and vehicle body

bounce cz are shown in Eq.2

Matgzz cf 2

Mbtgzz cr 2 (2)Under the condition of small pitch angleI around

CG, the relationships among fz2 , rz2 and cz are

rewritten in Eq.3.xxx

Mazz cf2xxx

Mbzz cr2 (3)Substituting above variables into Eq. (1-3), the state

equation for the bicycle model can be written as:

LWBUAXX x

DUCXY (4)

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3. Controller design

3.1. Fuzzy Control Theory

Fuzzy control, developed by L. A. Zadeh (1965) [7],

is a practical alternative for a variety of challenging

control applications since it provides a convenient

method for constructing nonlinear controllers via the

use of heuristic information. Fuzzy logic has two

different meanings. In a narrow sense, fuzzy logic is a

logical system, which is an extension of multivalued

logic. But in a wider sense, which is in predominant

use today, fuzzy logic (FL) is almost synonymous with

the theory of fuzzy sets, a theory which relates to

classes of objects with unsharp boundaries in which

membership is a matter of degree. The synthesis of

FLC can be designed in accordance with following

steps. [8]

(1) A rule-base (a sent of If-Then rules), which

contains a fuzzy logic quantification of the expert's

linguistic description of how to achieve good control.

(2) An inference mechanism, which emulates the

expert's decision making in interpreting and applying

knowledge about how best to control the plant.

(3) A fuzzification interface, which converts controller

inputs into information that the inference mechanism

can easily use to active and apply rules.

(4) A defuzzification interface, which converts the

conclusions of the inference mechanism into actual

inputs for the process.

3.2. Controller Design

Fig.2 Block diagram of integrated control system

It is a well-known fact that the derivation of thecontrol needs the accurate vehicle dynamics, which is

expressed as a linear model, whereas the vehicle

dynamics generally includes nonlinearities and

uncertainties. Therefore, for the design of active

suspension systems, the use of fuzzy logic control has

been proposed.

Active suspension system method has been used to

improve the vehicle ride comfort and reduce pinch

movement. As shown in Fig.2, there are two inputs for

vertical motion and pitch movement, respectively: (1)

body velocity v and acceleration a (2) pitching anglevelocityZand accelerationH . Two output are desired

actuator force 1F, 2F . Additionally, Mandani method

for fuzzy inference engine and centre of gravitymethod for defuzzification action are selected. Fuzzy

controller needs to tune input and output scaling

factors carefully to achieve a good performance. The

membership functions for bounce and pitch controllers

are shown in Figures 3 and 4, and rule bases are

represented in Table 1 and 2.

Fig. 3 inputs of fuzzy controller ( HZ,,,av )

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Fig. 4 outputs of fuzzy controller

Table 1 Bounce Rule Bases

vaNL NS NULL PS PL

NL PL PL PL PM PS

NS PL PM PS PS PS

NULL PL PS NULL NS NL

PS NS NS NS NM NL

PL NS NM NL NL NL

Table 2 Pitch Rule Bases

Z

H NL NS NULL PS PLNL PL PL PL PS NULL

NS PL PM PS NULL NS

NULL PL PS NULL NS NL

PS PS NULL NS NM NL

PL NULL NS NL NL NL

4. Co-simulation

The vehicle model is built using ADAMS/Car as a

full vehicle assembly. The ADAMS/Car is highly

dependable software which simulates the real vehicle

before the proto-type car is built. [9] The proposed full

vehicle model has six subsystems: front suspension,rear suspension, steering, front tire, rear tire and engine.

The subsystems based on one or more ADAMS

templates are connected via communicators, which are

components for exchanging information between

subsystems.

To investigate the effectiveness of the integrated

control system using fuzzy control, a simulation mode

with multi-body dynamics and active suspension is

constructed based on the co-simulation which

simulates the real vehicle before the proto-type vehicle

model is built. By combining ADAMS/Car and

MATLAB/Simulink, it is possible to add the control

algorithms to a model from ADAMS/Car. The vehicle

mass, cornering stiffness, distance from center ofgravity to the front and rear axles are defined, whilst

the vehicle velocity and the road surface are set.

Fig.5 Adams/Car Model

The full process using ADAMS/Car and MATLAB

was applied as a control simulation environment. The

parameters used in the paper are summarized in Table

3, and these values are obtained from the full car

ADAMS vehicle model as shown in Fig.5.

Table 3 Parameters used in vehicle mode

fm1 53 )(kg rm1 117 )(kg

2

m 663 )(kg J 1067 )( 2

mkg

fk 58636 )/( mN rk 58636 )/( mN

tfk 310000 )/( mN trk 310000 )/( mN

fc 4165 )/( msN rc 4165 )/( msN

a 1.233 )(m b 1.327 )(m

4.1. Sinusoid Road Surface

Fig.6 sine-wave hole test

In the co-simulation, one input condition, sinusoid

input is used to excite the fuzzy control suspension

system.

Under sinusoid input in Fig.6, the responses of body

acceleration and pitching angle acceleration are shown

in Fig.7~8, respectively.

0 1 2 3 4 5 6 7-3

-2

-1

0

1

2

3

time [s]

verticalacceleration[m/s*2]

passive

fuzzy

Fig.7 Time response of the body acceleration

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0 1 2 3 4 5 6 7-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

time [s]

pitchingangleacceleration[deg/s*2]

passive

fuzzy

Fig.8 Time response of the pitching angle acceleration

4.2. White noise road surface

Fig.9 white-noise road test

Fig.9~10 shows the co-simulation results of white

noise road conditions in Fig.9. The vehicle responsesof body acceleration and pitching angle acceleration

are compared.

0 1 2 3 4 5 6 7-4

-3

-2

-1

0

1

2

3

4

time [sec]

verticalacceleration[m/s*2]

passive

fuzzy

Fig. 10 Time response of the body acceleration

0 1 2 3 4 5 6 7-3

-2

-1

0

1

2

3

time [sec]

pitchingangleacceleration[deg/s*2]

passive

active

Fig.11Time response of the pitching angle acceleration

From these figures, it is manifest that FLC has a

superior benefit in isolating road vibration in compared

with passive suspension, while the vehicle runs at the

sine-wave road and white noise one.

5. Conclusions

In this paper, the active suspension control system is

proposed to attain ride comfort. It has been shown that

the performance of fuzzy logic control is better thanthat of the passive suspension under irregular road

condition. Co-simulation results with MATLAB and

ADAMS/Car clarifies the vehicle ride comfort could

be much improved via the proposed control scheme.

6. References

[1] Wikipedia suspension (vehicle) internet 17 April 2008.

[2] Celnikeer G W, Gedrick J K. Rail Vehicle Active

Suspensions for Lateral Ride and Stability

Improvement ASME J. of Dynamic Systems

Measurement and Control, 1982, 104, pp.101-106.

[3] Alleyne A, Hedrick J K. Nonlinear Adaptive Control ofActive Suspension IEEE Transactions on control

systems Technology, 1995, 3(1), pp.94-101.

[4] Abdelhaleem, A.M. and Crolla, D.A. (2000). Analysis

and Design of Limited Bandwidth Active

Hydropneumatic Vehicle Suspension Systems. SAE

Paper No.2000-01-1631

[5] Yoshimura, T., Nakaminami, K., Kurimoto, M. and Hino,

J (1999). Active suspension of passenger cars using

linear and fuzzy logic controls. Control Engineering

practice 7, 1, pp.41-47.

[6] Uys, P.E., P. S. and Thoresson, M. (2007) suspension

settings for optimal ride comfort of off-road vehicles

traveling on roads with different roughness and speeds,

Journal of Terramechanics, Vol.44, No.2, pp.163-175.

[7] Zadeh, L.A., Fuzzy sets information and control, Vol.8,

1965, pp.338-353.

[8] Kevin M. Passino, Stephen Yurkovich, Fuzzy Control

Addison-Wesley, 1998.

[9] Westbom D. and Frejinger P (2006) Yaw control using

rear wheel steering, Masters thesis, Linkoping

University, Sweden.

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