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