Page 60 - 2023-Vol19-Issue2

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Is? = aKf (Zs - Zu f - a? ) + aCf (Z?s - Z?u f - a? ) (2)
- bKr(Zs - Zur + b? ) - bCr(Z?s - Z?ur + b?? )
Mu f Z¨u f = Kf (Zs - Zu f - a? ) (3)
+ Cf (Z?s - Z?u f - a? ) - Kt f (Zu f - Zr f )
MurZ¨ur = Kr(Zs - Zur + b? ) (4)
+ Cr(Z?s - Z?ur + b? ) - Ktr(Zur - Zrr)
For active suspension system shown in Fig. 2, the hydraulic
actuator forces Fa1 and Fa2 at the front and rear suspension
system are generated respectively. Therefore, equations of
motion can be written [8]:
MsZ¨s = -Kf (Zs - Zu f - a? ) - Cf (Z?s - Z?u f - a? )
- Kr(Zs - Zu f + b? ) -Cr(Z?s - Z?ur - b?? ) + Fa1 + Fa2
(5) then the signals feedback to a reference point to compare a
Is? = aKf (Zs - Zu f - a? ) + aCf (Z?s - Z?u f - a? )
- bKr(Zs - Zur + b? ) (6)
- bCr(Z?s - Z?ur + b?? ) - aFa1 + bFa2
Mu f Z¨u f = Kf (Zs - Zu f - a? ) + Cf (Z?s - Z?u f - a?()7)
- Kt f (Zu f - Zr f ) - Fa1
MurZ¨ur = Kr(Zs - Zur + b? ) + Cr(Z?s - Z?ur + b? ) (8)
- Ktr(Zur - Zrr) - Fa2
Where;
Zs f : sprung mass displacement at front body(Zs - a? )
Zsr : sprung mass displacement at rear body(Zs + b? )
Zs : sprung mass displacement
Zu f : unsprung mass displacement at front body
Zur : unsprung mass displacement at rear body
Zr f : road input to front wheel
Zrr : road input to rear wheel
? : vehicle rotational movement (rad)
Fa1 : front actuator force (Newton)
Fa2: rear actuator force (Newton)
Matrood & Nassar
Fig. 2. Active half-car model
III. CONTROL METHOD
The suspension system electronic control was designed in a
way that the damping energy can be improved against different
road disturbances like bumps or potholes. The suspension
control system relies on a control unit to control the operation
of the hydraulic actuator. In Fig. 2, suitable sensors located
on the car body send signals reflected road disturbances and
specific actual signal with the set point. Accordingly, the
control unit can moderate the output variables to acceptable
ranges. In this study, two different types of PID (Proportional-
Integral-Derivative) controllers are used to control a half-car
model. The first type of PID controller is a conventional
PID controller as shown in Fig. 3. This controller can be
represented in time domain by the following equation [24]:
u(t) = Kpe(t) + Ki te(t)dt + Kd(de(t)/dt) (9)
The second type of PID controller is shown in Fig. 4.
This controller is a modified form of the conventional PID
controller and can be formed by moving the proportional and
derivative parts from the main forward path to the feedback
path to operate on a measured signal y(t). In the meantime,
keeping the integral part in the main forward path to operate
on error e(t). In result, the controller is converted to an I-PD
controller form [25].
The modified PID controller has the ability to eliminate
the kick of error or impulse function that associated with using
the conventional PID controller generated at the time the set
point change [24],[26]. Thus, a preferred tracking reference
can be obtained by using the modified PID controller [27].
The time domain equation of the modified PID controller is
given by [24]:
u(t) = -Kpy(t) + Ki te(t)dt - Kd(de(t)/dt) (10)