Question about Transfer Function Analysis
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.