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    Loop function, Phase margin, Gain margin, Nyquist plot

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    1. A system has a loop function:

    What is the phase margin and gain margin?
    First, we find the frequency so that the magnitude equals to one.

    Solving the above equation, we get rad/sec.

    The phase of the system at 1.47 rad/sec is - 147.5 deg. Therefore, the phase margin is 32.5 deg.

    Then, to find gain margin, we find the frequency such that the imaginary of magnitude equals to zero as follows:

    The imaginary part of is ...

    Solution Summary

    The loop function, phase margin, gain margin and Nyquist plot is examined.