# Control Systems: Root-Locus Problems

Question 1:

a) Construct the root-locus for the K > 0 for the transfer function

GH = K / [s(s+1)(s^2+7s+12)

b) If the design value for the gain is K = 6, calculate the gain margin.

c) Determine the value of the gain factor K for which the system with the above open loop transfer has closed loop poles with a damping ratio of 0.5.

Question 2:

a) Figure 2 models a pressure control system with a plant G = 1{(s+1)(s+3)] consisting of twwo lags, and PI control Gc = K(s+2)/s.

i) Sketch the loci of the closed-loop system poles for varying K.

ii) Find, reasonably accurately, the value of K for a damping ratio 0.5 for the dominating poles.

b) Plot the root loci for a system with the loop gain function (i.e. open loop transfer function).

K/[(s+2)(s+6)(s^2 + 8s + 20)

and find the limiting value of K for stability.

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#### Solution Summary

This solution provides steps to answer each of the root-locus problems.