Question

(9 pts) If a system whose Unilateral Laplace Transform is: H(s)--is put into a closed loop with a proportional gain feedback K. S-0.3 (3 pts) Write the transfer function of the closed loop system a. b. (3 pts) What would the gain of the system need to be for the system to be marginally stable (i.e. at s = 0)? (3 pts) What would the gain of the system need to be for the system to have a time constant of 1/10th of a second? c.

Answer 1

H(s) = 1/s - 0.3 feedback gain = k closed loop transfer function = H(s)/1 + k H(s) = 1/s - 0.3/1 + k/s -0. 3 = 1/s + k - 0.3 = (1/k - 0.3)/(1 + s (1/k - 0.3)) marginally stable = (s = 0) k - 0.3 = 0 k = 0.3 k = 0.3 gain needed k = 0.3 time constant = 1/k - 0.3 = 1/10 k - 0.3 = 10 k = 10.3 the gain needed k = 10. 3