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    Control Systems: Root-Locus Problems

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    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.