Page 61 - 2023-Vol19-Issue2

57 | Matrood & Nassar

Where; u(t): Control force, e(t): Tracking error, r(t): Desired
output, e(t) = r(t) – y(t), y(t): Actual output, Kp: Proportional
gain, Ki: Integral gain, and Kd: Derivative gain.

Fig. 3. Block diagram of conventional PID controller [24]

Fig. 5. Simulink block diagram of passive linear half-car
model

Fig. 4. Block diagram of modified PID controller [24] Referring to the Simulink block diagram of passive half-
car model, the vertical and angular displacement of the sprung
IV. SIMULINK MODELING mass as well as the displacement of the unsprung masses and
the suspension deflection are obtained. With the assist of
The block diagram of a passive half car model is shown MATLAB/Simulink software environment, the mathematical
in Fig. 5. This model was built in the MATLAB/Simulink model of the entire active half-car model with the conventional
environment. A step function is used to excite the system as and modified PID controllers are shown in Figures 6 and 7
an external source to represent the road profile. The forward respectively. The controller gains Kp, Ki and Kd are found
linear velocity (v) of the vehicle when it crossed over a road by applying trial-and-error tuning method and Table I. The
profile of 0.1 m height was 45 km/h. The time delay between parameters of the half-car model used for simulation are listed
the front and the rear wheels is calculated using the following in Table II.
formula as 0.225 second [6]:

Timedelay = (a + b)/v (11)

When the system is activated, the hydraulic actuator forces are Fig. 6. Active half-car model with conventional PID
generated and applied to the passive system with the imple- controller
mentation of both modified and conventional PID controllers.
In this study, the vertical displacement of the front body (Zs f )
and rear body (Zsr) are used as feedback signals to the con-
trollers, the desired performance of these variables are set to
improve system dynamic response.