To explore the performance of a proportional-plus-derivative controller on a second-order system, let G p (s) =
Question:
To explore the performance of a proportional-plus-derivative controller on a second-order system, let Gp(s) = 1/(s(s + 1)) be the transfer function of the plant and Gc(s) = K1 + K2s be the controller.
(a) Find the transfer function H(s) = Y(s)/X(s) of a negative feedback system with Gc(s) and Gp(s) in the feed forward path and unity in the feedback. The input and the output of the feedback system are x(t) and y(t) with Laplace transforms X(s) and Y(s).
(b) Suppose (i) K1 = K2 = 1; (ii) K2 = 0, K1 = 1, and (iii) K1 = 1, K2 = 0. For each of these cases indicate the new location of the poles and zeros, and the corresponding steady-state responses due to x(t) = u(t). Comparing the absolute value of the steady-state error |ε(t)|= |yss(t)−1|for the three cases, which of (i)–(iii) gives the largest error?
Step by Step Answer:
a The feedforward transfer function is so that b i K 1 ...View the full answer
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