A car active suspension system adds an active hydraulic actuator in parallel with the passive damper and

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A car active suspension system adds an active hydraulic actuator in parallel with the passive damper and spring to create a dynamic impedance that responds to road variations. The block diagram of Figure P5.36 depicts such an actuator with closed-loop control.

In the figure, Kt is the spring constant of the tire, MUS is the wheel mass, r is the road disturbance, x1 is the vertical car displacement, x3 is the wheel vertical displacement, ω2= Kt/MUS is the natural frequency of the unsprung system and ε is a filtering parameter to be judiciously chosen (Lin, 1997). Find the two transfer functions of interest:

a. X3(s)/R(s)

b. X1(s)/R(s)

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