Question

Q4) (20 pts) c(s 5) 2(s) In the control system shown in the figure, i) Express U(s) in terms of E (s). ii) Find the overall transfer function C2 and determine the characteristic equation. R(s) ii) Using Routh-Hurwitz method determine the range of values of K for stability

Answer 1

(i) E (S) 2/(s + 1) - E (S) = V (s) implies e (s) [2/s + 1 - 1] = v (s) implies (s) (2 - s - 1/s + 1) = v (s) implies v (s) = (1 - s/s + 1) E (s) (ii) E(s) = R (s) - c (s) implies (s + 1)/(1 - s) v (s) = R (s) - c (s) implies s + 1/ (1 - s) c (s)/[k/s (s + 2)] = R (s) - c (s) implies s (s - 1) (s + 2) c (s0 + c (s0/(1 - s) k = r (s) implies c (s) [s (s + 1) (s + 2) + (1 - s) k/(1 - s) k] = R (s) implies c (s)/R (s) = (1 - s) k/(s + 1) s (s + 2) + (1 - s) k \r\n g (s) = (1 - 5/1 + 5) k/(s + 2) s