Vibration Control of Active Vehicle Suspension System Using Fuzzy Logic Controller

Abstract

Fuzzy logic control (FLC) algorithm grants a means of converting a linguistic control technique and it is widely used in vehicle applications. This paper demonstrates the application of fuzzy logic technique to design a controller for the active vehicle suspension system to improve the suspension system performance by altering the number and arrangement of the rules set and the universe of discourses. A mathematical model and equations of motion of quarter vehicle active suspension is derived and solved using MATLAB/Simulink software. The proposed fuzzy controllers using 9, 25 and 49 rules set with two different types of membership functions, trapezoidal and triangle, are implemented in a closed loop control system to demonstrate the influence of the numbers of rule set and the type of membership function on the performance of suspension system. Suspension performance criteria were assessed in both time and frequency domains. Performance comparisons between the passive suspension, as a reference, and the proposed controllers of the active suspension were achieved. The simulation results indicate that the proposed active fuzzy controllers can dissipate the energy due to road excitation effectively and improves suspension performance. Among the investigated systems, the 25 rules set with a trapezoidal membership function for the fuzzy controller gives the best performance.

Full text

Vibration Control of Active Vehicle
Suspension System Using Fuzzy Logic
Controller
A. Shehata, H. Metered and Walid A.H. Oraby
Abstract Fuzzy logic control (FLC) algorithm grants a means of converting a
linguistic control technique and it is widely used in vehicle applications. This paper
demonstrates the application of fuzzy logic technique to design a controller for the
active vehicle suspension system to improve the suspension system performance by
altering the number and arrangement of the rules set and the universe of discourses.
A mathematical model and equations of motion of quarter vehicle active suspension
is derived and solved using MATLAB/Simulink software. The proposed fuzzy
controllers using 9, 25 and 49 rules set with two different types of membership
functions, trapezoidal and triangle, are implemented in a closed loop control system
to demonstrate the influence of the numbers of rule set and the type of membership
function on the performance of suspension system. Suspension performance criteria
were assessed in both time and frequency domains. Performance comparisons
between the passive suspension, as a reference, and the proposed controllers of the
active suspension were achieved. The simulation results indicate that the proposed
active fuzzy controllers can dissipate the energy due to road excitation effectively
and improves suspension performance. Among the investigated systems, the 25
rules set with a trapezoidal membership function for the fuzzy controller gives the
best performance.
Keywords Active suspension system Fuzzy logic control Ride comfort 
Vehicle stability Vehicle suspension control
A. Shehata (&)H. Metered W.A.H. Oraby
Helwan University, Cairo, Egypt
e-mail: ahmedshehatagad@yahoo.com
H. Metered
e-mail: hassan.metered@yahoo.com
W.A.H. Oraby
e-mail: waho911@hotmail.com
©Springer International Publishing Switzerland 2015
J.K. Sinha (ed.), Vibration Engineering and Technology of Machinery,
Mechanisms and Machine Science 23, DOI 10.1007/978-3-319-09918-7_35
389

1 Introduction
Through the design of a suspension system, a number of conflicting requirements
has to be solved. The suspension system has to provide a comfortable ride and
vertical vehicle stability at the same time. Also, enough contact between tires and
road surface is needed in various driving conditions in order to maximize vehicle
stability. Instead of a passive suspension, an active suspension can be applied in
order to provide better resolve the trade-off between these conflicting requirements.
Designing a good suspension system with optimum vibration performance under
different road conditions is a significant undertaking.
Fuzzy logic is used to hold the active suspension and the membership functions
are optimized by using genetic algorithm operations [1]. A fuzzy controller is
designed with Interval type-2 FLC to improve the disturbance rejection of the
suspension system which can be sourced by road shocks [2]. The vehicle vibration
and disturbance are reduced considerably with a fuzzy logic controller, to improve
comfort in riding faced with uncertain road terrains [3]. The ride comfort is
improved by means of the diminution of the body acceleration when road distur-
bances from smooth road and real road roughness [4]. Fuzzy logic is used to control
active suspension of a half-car model [5]. The fuzzy logic controller is based on two
inputs, namely, suspension velocity and body velocity. The output of the fuzzy
controller is the damping coefficient of the variable damper [6]. Fuzzy logic is used
to tune each parameter of PID Controller and input membership function of fuzzy
controller optimized by Discrete Action Reinforcement Learning Automata
(DARLA) technique [7].
Active suspension system of a quarter car model using adaptive fuzzy logic and
active force control strategies [8]. A fuzzy logic controller is designed for the
control of the seven degrees of freedom full vehicle model [9]. An active control
based on fuzzy logic is constructed such as a result as of the vehicle body accel-
eration, suspension working space and dynamic tire load. The amplitude of vertical
vehicle both, from the view of ride comfort of passengers, is minimized under the
restraint of the suspension travel, relative velocity, body velocity, wheel speed and
tire deflection. The development of a better-quality suspension system remains an
important increase objective for the automotive industry. A vehicle suspension
system should have the qualifications to reduce the displacement and acceleration
of the vehicle body, to achieve its advantages not only in the ride comfort aspect,
but also minimizes the dynamic binding of the tire to maintain better tire–terrain
contact. In this article, six fuzzy controllers are proposed for active suspension
system. Intervals of fuzzy rules are designed in order to improve system robustness
to noise measurement and external disturbances araised from road irregularities to
the systems studied (passive and active) suspension systems. The remainder of this
article is organized as follows; a quarter vehicle model is presented in Sect. 2.
Section 3introduces a brief description of the Fuzzy logic controller approach.
Finally, the results are discussed in Sect. 4and the extracted concliosions are in
Sect. 5.
390 A. Shehata et al.

2 Quarter Vehicle Model
Figure 1shows the two-degree-of-freedom system that represents the quarter
vehicle model. It consists of an upper or body mass, mb, as well as a lower or wheel
mass, mw.
By applying the Newton’s second law, the body and wheel accelerations can be
written as follows:
€
Zb¼fdksZbZw
ðÞcsð_
Zb_
ZwÞ
Mb
ð1Þ
€
Zw¼fdþksZbZw
ðÞþcs_
Zb_
Zw

ktðZwZrÞ
Mw ð2Þ
x¼x1;x2;x3;x4
½¼zb;zw;_
Zb;_
Zw
 ð3Þ
where
Z
b
Car body displacement
_
ZbCar body velocity
Z
w
Car wheel displacement
_
ZwCar wheel velocity
f
d
Actuator force
Z
r
Excitation due to road disturbance
As a result, in the state space equation, the state variables are described in the A,
B, C and D matrices as represented in the Eqs. (4) and (5)
_
xtðÞ¼Ax tðÞþBfdtðÞþDZrtðÞ ð4Þ
_
x1
_
x2
_
x3
_
x4
2
6
6
4
3
7
7
5
¼
00 10
00 01
ks
mb
ks
mb cs
mb
cs
mb
ks
mw ks þkt
mw
cs
mw cs
mw
2
6
6
4
3
7
7
5
xb
xw
_
xb
_
xw
2
6
6
4
3
7
7
5
þ
0
0
1
mb
1
mw
2
6
6
4
3
7
7
5
fdþ
0
0
0
kt
mw
2
6
6
4
3
7
7
5
zrð5Þ
Let the measurements available for feedback be y(t) =Cxthe output vector is
assumed to be
ytðÞ¼
ks
mb
ks
mb cs
mb
cs
mb
110 0
0100
2
43
5
€zb
sws
DTL
2
43
5ð6Þ
The system parameters of the quarter car model are obtained from ref. [10].
Vibration Control of Active Vehicle Suspension System... 391

3 Fuzzy Logic Controller Approach
This section offers a short description of the fuzzy controller that used to minimize
the vibration levels to improve the suspension performance. Fuzzy rules are used to
formulate the controller that can estimate expert reception and decision. The layout
of the FLC is shown in Fig. 2.
The control rule Si, at any time i, is NB, ... , Z, ... , PB is represented by the
linguistic descriptions (Mamdani), S1 ¼ðzbzwÞ,S2¼ð_zb_zwÞ,S3¼_zband
S4 ¼_zw. There are four fuzzy inputs (S1, S2, S3, S4) and one output ðfdÞwith
membership functions lzbzw
ðÞ,lð_zb_zwÞ,lð_
zbÞand lð_zwÞ. FLC can be
achieved by changing of universal of discourses and rule base through fuzzy to 9,
25 and 49 rules base. The fuzzy rule set is based on Table 1. Where, [NB (negative
big), NM (negative medium), NS (negative small), ZE (zero), PS (positive small),
PM (positive medium), PB (positive big)], e is the error and ce is the change of error
with respect to the time. Fuzzy Control used “Mamdani”method, the reasoning is
the “min-max”method. Two common membership functions are used; triangular
and trapezoidal. The two membership function are chosen for the input and output
variables, as shown in Fig. 3.
For instance, the linguistic control rules of the fuzzy logic controller obtained
from fuzzy control with 49 rules set used in such case are as follows:
S1 :IF S1 ¼NB AND S2 ¼NB AND S3 ¼NB AND S4 ¼NBfg
THEN ðfd¼NBÞ
S17 :IF S1 ¼NS AND S2 ¼NS AND S3 ¼NS AND S4 ¼NSfg
THEN ðfd¼NMÞ
S47 :IF S1 ¼PS OR PB AND S2 ¼PS OR PB AND S3 ¼PS OR PB AND S4 ¼PS OR PB
f g
THEN ðfd¼PBÞ
Si :IF S1;S2;S3;S4 ¼EiðÞAND ðS1;S2;S3;S4 ¼GiðÞ
fg
THEN ðfd¼BiÞ
ð6Þ
where Ei, Gi and Bi are labels of fuzzy sets representing the linguistic values
S1 ¼ðzbzwÞ,ð_
zb_
zwÞ,S3¼_
zb,S4¼_
zw, e = error(S1), ce = change of error
Fig. 1 Quarter-vehicle
suspension model
392 A. Shehata et al.

(S2) and fd= actuator force respectively, which are characterized by their mem-
bership functions. Also, the 9 and 25 rules set controller are formulated based on
the same arrangement of the presented 49 rules shown in Fig. 3.
Defuzzification is the process for mapping from a set of secondary fuzzy control
signals contained within a fuzzy output window to a non-fuzzy (crisp) control
Fig. 2 Layout of the fuzzy logic control
Table 1 Fuzzy with 49 rules set
e
ce NB NM NS ZE PS PM PB
NB NB NB NB NB NM NS ZE
NM NB NB NB NM NS ZE PS
NS NB NB NM NS ZE PS PM
ZE NB NM NS ZE PS PM PB
PS NM NS ZE PS PM PB PB
PM NS ZE PS PM PB PB PB
PB ZE PS PM PB PB PB PB
Fig. 3 Structure diagram for membership function trapmf type with 49 rules set. ae = S1, and
ce = S2. bActuator Force = fd
Vibration Control of Active Vehicle Suspension System... 393

signal. The center of region method is the most well identified defuzzification
technique, which in linguistic conditions can be pronounced as:
fdtðÞ¼Rfdlfd
ðÞdt
Rlfd
ðÞdt ð7Þ
Figure 4shows three fuzzy surfaces for the designed controllers using the
trapezoidal membership function. The other surfaces using the triangle membership
function are omitted.
Fig. 4 Fuzzy surface with (9, 25 and 49) rules set, (a,band c) respectively
394 A. Shehata et al.

4 Results and Discussion
The three main performance criteria in vehicle suspension design that manage the
ride comfort and vehicle stability are suspension working space (SWS), vertical
body acceleration (BA), and dynamic tire load (DTL). The BA is directly related to
the ride comfort while tire’s dynamic deformation (Zw −Zr) is required to achieve a
good vehicle stability [11]. The suspension performance is improved when the
SWS, BA, and DTL are minimized. There are four types of suspension systems
investigated in this part:
(a) Conventional passive suspension system, with damping cs¼980 Ns/m as in
reference [12];
(b) Active suspension system, with 9 rules set fuzzy for both triangular and
trapezoidal membership functions.
(c) Active suspension system, with 25 rules set fuzzy for both triangular and
trapezoidal membership functions.
(d) Active suspension system, with 49 rules set fuzzy for both triangular and
trapezoidal membership functions.
The above-mentioned performance criteria are used to calculate the performance
of the control methods to select the best method of control to obtain the actuator
force f
d
for a given time history, as described in Sect. 3. Consequently, the damping
of the conventional suspension system case is used as a reference for the com-
parisons with 3 active suspension systems proposed, noting that the value estimated
for csis typical for automotive applications [12]. There are two types of road
excitation, chosen to be very similar to the real-world road profiles, are considered
in this study. First, time responses for the bumpy road input are being introduced.
This style of road surface irregularity is one of the most encountered in actuality.
Bump road input is formulated as presented in Eq. (8).
zr¼a1cos xrt0:5ðÞðÞ
fg
;for 0:5t0:5þd
V
0;otherwise
ð8Þ
Where ais the half the bump amplitude, xr¼2pV=d,dis the width of the
bump, and Vis the vehicle velocity. In this study the values for these parameters
are, a= 0.035 m, d= 0.8 m, and V= 0.856 m/s [13]. The time history of the
suspension system reaction under road bump excitation is shown in Fig. 5. The
input of the fuzzy controller is composed of four input variables and one output
variable. The relative displacement (zb zw), relative velocity ( _zb _zw), body
velocity _zb and wheel velocity _zw are defined as the input variables while the output
variable is the controlling force based on the simulation software “Matlab/Simu-
link”. The performance of the active control scheme is illustrated through a series of
simulations. The time histories for SWS, BA, and DTL responses are shown in
Fig. 5and the Peak-To-Peak (PTP) values are shown in Fig. 6. The concluding
figures show the comparison between the controlled active suspension system using
Vibration Control of Active Vehicle Suspension System... 395

fuzzy with 9 rules set, fuzzy with 25 rules set and fuzzy with 49 rules set with both
trimf and trapmf, and the conventional passive system. From these results it is seen
that the fuzzy with 25 rules set controlled suspension can dissipate the energy due
to bump excitation very well with both trimf and trapmf, reduce the settling time,
and can improve not only ride comfort but also the vehicle stability.
The results indicate that, for the case of the fuzzy with 25 rules set control, the
response is more continuous and the maximum value is lower than in the cases of
fuzzy with 9 or 49 rules set controls for both trimf and trapmf and surely, better than
the passive suspension system. The three controlled systems, both trimf and trapmf
have the lowest peaks for the SWS, BA, and DTL, its values indicate an improved
ride comfort and vehicle stability for the system response under road bump exci-
tation. Figure 6shows a complete comparison between all controllers for the peak-
to-peak (PTP) values and their improvements percentages compared with passive
suspension system. It’s clearly shown that the 25 rules set with trapmf gives a
superior performance. Moreover, the trapmf is counted as the best method of
fuzzification and defuzzification process for SWS and BA while the trimf mem-
bership functions be in excess with DTL suspension performance.
00.5 11.5 22.5 33.5 44.5 5
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-0.04
-0.03
-0.02
-0.01
0.01
0.02
0.03
0.04
Time(sec)
Suspension working
space (m)
Time(sec)
passive
9 rules set trimf
25 rules set trimf
49 rules set trimf
passive
9 rules set trapmf
25 rules set trapmf
49 rules set trapmf
00.5 11.5 22.5 33.5 44.5 5
-3
-2
-1
0
1
2
3
Time (sec)
body acceleration (m/s
2
)
0 1 2 3 4 5
-3
-2
-1
0
1
2
3
Time (sec)Time (sec)
passive
9 rules set trimf
25 rules set trimf
49 rules set trimf
passive
9 rules set trapmf
25 rules set trapmf
49 rules set trapmf
0 1 2 3 4 5
-800
-600
-400
-200
0
200
400
600
800
Time (sec)
dynamic tyre load (N)
Suspension working
space (m)
body acceleration (m/s
2
)
dynamic tyre load (N)
0 1 2 3 4 5
-800
-600
-400
-200
0
200
400
600
800
Time (sec)
passive
9 rules set trimf
25 rules set trimf
49 rules set trimf
passive
9 rules set trapmf
25rules set trapmf
49 rules set trapmf
(a) (b)
(c) (d)
(e) (f)
Fig. 5 The time domain of system responses under road bump excitation: a,bSWS; c,dBA; e,
fDTL for both trimf and trapmf respectively
396 A. Shehata et al.

The second type of road excitation was a random road profile selected from ref.
[12] and described mathematically as;
_
xrþqVxr¼Vwnð9Þ
where, w
n
is white noise with the intensity 2r2qV, qis the road irregularity
parameter, and r2is the covariance of road irregularity. In random road excitation,
the values of road surface irregularity (q=0.45m
−1
and r2= 300 mm
2
) were
selected assuming that the vehicle moves on the paved road with the constant speed
V = 20 m/s, as in reference [13]. Isolate the vehicle body from the road disturbances
also to reduce the resonance peak of the body mass proximity to 1 Hz; it is
important to improve the ride comfort, which is a sensitive frequency of the human
body. Furthermore, to improve vehicle stability, it is important to maintain the tire
in contact with the road surface and therefore reduce the resonance peak proximity
at 10 Hz, which is the resonance frequency of the wheel [14]. In view of these
considerations, the results obtained from the excitation described by Eq. (9) are
presented in the frequency domain. The modulus of the Fast Fourier Transform
(FFT) of the SWS, BA and DTL over the range 0–16 Hz are shown in Fig. 7. The
FFT was suitably scaled and smoothed by curve fitting as done in [12–15]. The
lowest resonance peaks in the body and the wheel can be achieved using the
projected 25 rules set fuzzy control strategy. These figures indicate that the
Fig. 6 Percentage improvements in PTP values for the controlled systems compared to passive
system for road disturbance excitation
Vibration Control of Active Vehicle Suspension System... 397

technique of the fuzzy controlled system with 25 rules set, especially for trimf,
dissipate the energy gained through the given road excitation in an excellent manner
and thus, improves the SWS. On the other hand, the 49 rules set, for both trimf and
trapmf achieves a significant improvement not only in terms of BA, which relates to
the ride comfort, but also in DTL, which relates to the vehicle stability.
5 Conclusion
Control performance criteria were studied in the time domain and frequency domain
to assessed the suspension effectiveness under bump and random road disturbance.
The study implemented the 9, 25 and 49 rules set technique for the fuzzy controller
of the active suspension system. From the time domain results, it had been con-
cluded that these rules set can decrease the settling time and can improve ride
comfort and vehicle stability over a conventional passive system. Comparing the
number of rules set for the fuzzy controller for both trimf, trapmf implied that the 25
rules set improved SWS, BA and DTL over the 9 and even 49 rules set technique.
Furthermore, frequency domain comparison between the three forms of fuzzy
0.035
(a) (b)
(c) (d)
(e) (f)
0.03
0.025
0.02
0.015
0.01
0.005
0
2.4
2.2
1.8
1.6
1.4
1.2
0.8
0.6
0.4
1
2
2 4 6 8 10 12 14
Frequency (Hz) Frequency (Hz)
Frequency (Hz) Frequency (Hz)
Frequency (Hz) Frequency (Hz)
16
20
700
650
600
550
500
450
400
350
300
250
200
46810121416
2
04
681012
14 16
700
650
600
550
500
450
400
350
300
250
200
2
04
6810
12 14 16
2.4
2.2
1.8
1.6
1.4
1.2
0.8
0.6
0.4
1
2
20 4 6 8 10 12 14 1
6
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
2 4 6 8 10 12 14 1
6
Suspension Working
dynamic tyre load(N)
vertical body
acceleration (m/s2)
vertical body
acceleration (m/s2)dynamic tyre load(N)
Suspension Working
Space(m)
Space(m)
Passive
9 rules set trimf
25 rules set trimf
49 rules set trimf
Passive
9 rules set trimf
25 rules set trimf
49 rules set trimf
Passive
9 rules set trimf
25 rules set trimf
49 rules set trimf
Passive
9 rules set trimf
25 rules set trimf
49 rules set trimf
Passive
9 rules set trimf
25 rules set trimf
49 rules set trimf
Passive
9 rules set trimf
25 rules set trimf
49 rules set trimf
Fig. 7 The frequence domain responses under random road excitation: a,bSWS; c,dBA; e,
fDTL for both trimf and trapmf respectively
398 A. Shehata et al.

controllers, clarifies that the 49 rules set technique with trimf or trapmf achieved a
significant improvement in BA and DTL. Moreover, the 25 rules set technique
overcomes the 49 technique in SWS over the frequency domain. This is in addition
to the improved dynamic criteria in time domain.
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