Consider the control system shown in the following diagmm.

_r_(t)_~®----1 D(s) I 1 y(t) . s(s+ 1)

A Control System The controller D(s) is given by,

() , s+a Ds=l\. 2 2 .

s +w

(a) Prove that the system is capable of tracking a sinusoidal reference input, r(t) = sin(wt), with a zero steady state error.

(b) Find the range of K and a such that the closed-loop system remains stable. For the case where n = L is the closed-loop system asymplotically stable for some set of values of K?

Problem