Page 59 - 2023-Vol19-Issue2

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designed an optimal vibration controller for vehicle active
suspension systems. A. Pati et al. [5] designed a controller for
a half car suspension system based on sliding mode control
using proportional-integral-derivative (PID) sliding surface.
Puneet Gandhi et al. [6] used a half car active suspension
model with 4 degrees of freedom with different controllers
such as proportional, integral and derivative, linear quadratic
regulator, fuzzy and adaptive neuro fuzzy inference system.
Sangzhi Zhu et al. [7] developed a new hydraulically intercon-
nected suspension with the using of fuzzy, PID and optimal
linear quadratic regulator controllers to control vehicle body’s
roll motion. Daniel Rodriguez - Guevara et al. [8] proposed a
novel linear parameter varying (LPV) state-space (SS) model
with a fictional input to represent nonlinear half-car active sus-
pension system. H. Khodadadi and H. Ghadiri [9] used PID,
fuzzy logic and H controllers to control the car suspension sys-
tem based on half car. Also, a self-tuning PID controller based
on fuzzy logic is developed to improve the performance of the
system. J. E. Ekoru and J. O. Pedro [10] used an inner PID
hydraulic actuator force control loop, in combination with an
outer PID suspension deflection control loop, to control a non-
linear half-car. Yanghai Nan et al. [11] proposed a fuzzy logic
control strategy for active half car suspension system which is
utilized to generate counterforce to isolate vibration from the
rough ground. Ahmet Yildiz [12] considered a non-linear sus-
pension design for half vehicle model by using particle swarm
optimization technique for optimizing the vehicle vibrations.
Y. Susatio et al. [13] utilized direct synthesis method for tun-
ing PID controller gains to reduce vibration on passenger seat
caused by change in road surface profile or disturbance. L.
C. Felix-Herran et al. [14] designed and applied a fuzzy-H
control, improved with weighting functions to a novel model
of a one-half semi active suspension. G. I. Mustafa et al. [15]
presented an optimized sliding mode controller for vibration
control of active half-car suspension systems. Muhammad
A. Khan et al. [16] used feedback linearization and linear
quadratic regulator controller with a half-car model. Jimoh
O. Pedro and Nyiko Baloyi [17] designed a direct adaptive
neural network controller to control a nonlinear half car sus-
pension system and improve ride comfort. Mohammed H.
Abushaban et al. [18] proposed a new fuzzy control strategy
for a half-car active suspension system. M. Avesh and R. Sri-
vastava [19] proposed using PID controller with an active half
car suspension system to improve ride comfort to passengers
and improve the stability of vehicle. L.V. Gopala Rao and
S. Narayanan [20] studied the performance of half car model
with optimal sky-hook damper suspension and compared it
with the performance of half car model with LQR control.
Wenkui Lan and Erdong Ni [21] applied fuzzy-PID controller
to a half car suspension system to enhance ride comfort by
reducing the body acceleration and pitch angle. Ayman H.
Matrood & Nassar
Mohamed et al. [22] designed and studied linear quadratic reg-
ulator optimal control and PID classic control to achieve half
car performance such as ride comfort and road stability. Jian
Wu and Zhiyuan Liu [23] presented a novel controller design
for half-cars suspension magneto-rheological by introducing
a piecewise control approximation model.
In this study, a linear half-car model in MATLAB/ Simulink
software is being used to compare the performance of a modi-
fied PID controller versus conventional PID controller. The
model dynamic characteristics, stability of the vehicle, the
quality of shock absorption and the reduction of oscillations
and vibrations have been investigated.
II. MATHEMATICAL MODELING
The half-car model used in this study is a four degree of
freedom system. The model consists of a vehicle body with
front and rear suspension elements and wheels as shown in
Fig. 1. To derive equations of motion for the passive half-car
suspension system, the following assumptions are considered,
as below:
Pitch angle (? ) is small, springs and dampers are linear,
tires have only stiffness with no damping property, the effect
of friction is neglected, and the tires are always in contact
with the road surface.
Fig. 1. Passive half-car model
By applying Newton’s second law of motion, dynamic
equations for the half-car model can be represented as follow,
taking into consideration that the static equilibrium point is
the origin for the displacement of the mass center and the
angular displacement of the car body:
MsZ¨s = -Kf (Zs - Zu f - a? ) - Cf (Z?s - Z?u f - a? )(1)
- Kr(Zs - Zu f + b? ) - Cr(Z?s - Z?ur - b?? )