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Transfer Function Analysis for a Unity Feedback System

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.

Solution Preview

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 ...

Solution Summary

This solution includes formulas and explanation in an attached Word document. The student will be able to understand work and complete calculations on their own with this guide. 212 words.