Ece 382 homework determine the gain crossover frequency the

Question

Homework -

(I) Consider the compensator-design problem for a feedback control system shown with

G(s) = {10/s(s+2)(s+10)}.

The system is working in a noise-free environment. The desired design specifications of the compensated system are:

(1) Phase margin is ≥ 45?

(2) Gain margin is ≥ 10 dB

(3) Static error constant K_v is 15 sec^-1

(A) Determine the gain crossover frequency, the phase crossover frequency, the gain margin, and the phase margin of the uncompensated system.

(B) Design a lead compensator G_c(s) such that the overall system satisfies the desired design specifications. Does the compensated system satisfy the desired design specifications? Discuss the performance of the compensated system.

(C) Design a lag compensator G_c(s) for the uncompensated system. Does the compensated system satisfy the desired design specifications? Discuss the performance of the compensated system.

(II) If the open-loop transfer function of the above system has changed to

G(s) = {10/s(s+5)}

and the desired design specifications are specified as follow:

(1) Phase margin is ≥ 50?

(2) Gain margin is ≥ 10 dB

(3) Static error constant K_v is 20 sec^-1.

(A) Determine the gain crossover frequency, the phase crossover frequency, the gain margin, and the phase margin of the uncompensated system.

(B) Design a lead compensator G_c(s) such that the overall system satisfies the desired design specifications. Does the compensated system satisfy the desired design specifications? Discuss the performance of the compensated system.

(C) Design a lag compensator G_c(s) for the uncompensated system. Does the compensated system satisfy the desired design specifications? Discuss the performance of the compensated system.