A closed-loop control system is shown in Figure P2.50. (a) Determine the transfer function T(s) = Y(s)/R(s).

Question:

A closed-loop control system is shown in Figure P2.50.
(a) Determine the transfer function T(s) = Y(s)/R(s).
(b) Determine the poles and zeros of T(s).
(c) Use a unit step input, R(s) = l/s, and obtain the partial fraction expansion for Y(s) and the value of the residues.
(d) Plot y(t) and discuss the effect of the real and complex poles of T(s). Do the complex poles or the real poles dominate the response?
(e) Predict the final value of y(t) for the unit step input.