Page 62 - 2023-Vol19-Issue2

58 | Matrood & Nassar

TABLE III.
CONVENTIONAL PID CONTROLLER GAINS

Controller Kp Ki Kd
234
Conventional PID controller 1 175 12 215
Conventional PID controller 2 198 5

Fig. 7. Active half-car model with modified PID controller Therefore, only proportional and derivative actions pick
up system variables while the integral action works on the er-
TABLE I. ror and the system response occurs accordingly. Also, by this
RESPONSE OF PROPORTIONAL, INTEGRAL AND way the noise caused by the error signal is eliminated. Figures
DERIVATIVE CONTROLLER GAINS [19] 8 – 15 show the dynamic responses of the half-car’s outputs
for the three cases. The responses show that the settling time
Closed loop response Rise time Over- shoot Settling time Steady state error is very short which ensures high and fast passenger comfort.
Kp Decrease Increase Small change Decrease In addition, the peak overshoots are clearly damped, and good
Ki Decrease Increase Increase Eliminate reference tracking are obtained, which reflect appropriate dy-
Kd Small change Decrease Decrease Small change namic response. As a result, sufficient shock absorption and
vehicle vibration reductions are achieved. From the results,
the modified PID controller has a better performance to sup-
press both car body oscillations and suspension deflection in
comparison with conventional PID controller.

TABLE II. Value Fig. 8. Vertical body displacement
730 Kg Fig. 9. Rotational body displacement
HALF-CAR PARAMETERS [3] 2460 Kgm2
40 Kg
Parameter Description 35.5 Kg
Ms :Body mass (sprung mass) 19,960 N/m
Is :Body pitch moment of inertia 17,500 N/m
Mu f :Front wheel mass (front unsprung mass 1290 Ns/m
Mur :Rear wheel mass (rear unsprung mass) 1620 Ns/m
Kf :Front suspension stiffness 175,500 N/m
Kr :Rear suspension stiffness 175,500 N/m
Cf :Front suspension damping coefficient 1.011 m
Cr :Rear suspension damping coefficient 1.803 m
Kt f :Front tire stiffness
Ktr :Rear tire stiffness
a :Distance from vehicle center of gravity (C.G.) to front axle
b :Distance from vehicle center of gravity (C.G.) to rear axle

V. SIMULATION RESULTS AND DISCUSSION

In this section, a half-car model has been simulated in three
cases (passive, active with conventional PID controller and ac-
tive with modified PID controller) according to the mathemat-
ical modeling implemented in MATLAB/ Simulink software
to present the dynamic response. Tables III and IV show PID
gains for conventional and modified PID controllers respec-
tively. After running the simulation for five seconds, system
dynamic behavior and response to a step input reference or set
point signal can be found to show the main properties such as
rise time, overshoot, settling time and steady state error. Using
modified PID controller, the set value does not influence the
proportional and derivative parts as in the conventional PID
controller while the controller action is still affecting.