Consider the plant with transfer function Gp(s) =[s(s+1)]-1, which is placed in the unity feedback configuration with compensator
Gc(s) =KP + Kω(s2 +ω2)-1
(a) Provided the system is stable and Kω > 0,show that the steady-state error is zero for the sinusoidal reference input r(t) = sin(ωt).
Now, assuming ω = 1....
(b) With Kω= 0, find the range of KP forwhich the closed loop system is stable. Fix a value KP > 0 for which stability holds, andindicate your selection on a root locus plot.
(c) Fix the value KP > 0 selected in (b), and obtaina root locus plot with respect to Kω using Matlab. Can you find a valueKω > 0 for which the closed loop system is stable? Discuss how you might modify your design based on your conclusions.