Figure shows PD control applied to an unstable plant. The gains have been computed so that the damping ratio is ζ = 0.707 and the time constant is 2.5 sec, assuming that the transfer functions of the actuator and the feedback sensor are unity. Suppose that the actuator has the transfer function
Gs(s) = 1/(Ï„s + 1)

This lag in the response of the actuator might affect the system's stability, its overshoot in response to a step input, or its 2% settling time.
a. What effect does this lag have on the system's performance if Ï„ = 0.1 sec?
b. What effect does this lag have on the system's performance if Ï„ = 1 sec?

Transcribed Image Text:

C(s) 15002 1932 Plant s +1 Controller Actuator