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Loop function, Phase margin, Gain margin, Nyquist plot

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Solution Summary

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

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1. A system has a loop function:

What is the phase margin and gain margin?
Solution
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 ...

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