Consider a closed-loop system with reference input (no feedforward control) and input disturbance. the nominal plant and controller are given by
go (s) = 2/[(s+1)(s+2)] c(s) = [(s+1)(s+2)(s+3)(s+5)]/[s(s^2 + 1)(s+100)]
if the reference input is a step function (constant) and the input disturbance is given by di = a sin(t + f).
(a) show the nominal closed-loop system is stable.
(b) show the steady-state error response of the system to a unit step reference input and an input disturbance given by di = a sin(t + f) is zero.