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 feedback sensor has the transfer function
Gs(s) = 1/(Ï„s + 1)
This lag in the response of the feedback elements 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 have on the system's performance if Ï„ = 1 sec?

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Cs) 24122001500 1932 Controller Plant Sensor