For a unity feedback system with open-loop transfer function, G(s) = K(s+alpha)/(s^2 + 4s + 1):
a) Find all values of alpha such that the system is stable for K = 2.
b) If the unity feedback closes around this G(s) and an input is a unit step r(t) = 1u(t), what is the stead-state error, e_ss, as a function of alpha and K?
c) For K=2 and alpha = 1, where are the closed-loop poles?
d) For the step input, find output y(t) as a function of time, when K = 2 and alpha = 12 and y(0) = 0.
a) For a unity feedback system, the closed loop transfer function is
t(s) = G/(1 + G) = K(s + alpha) / (s^2 + 4s + 1 + K(s + alpha))
The characteristic polynomial is P(s) = s^2 ...
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