Phase Margin Problems
Problem Freq6P02Int

        For this problem set you will need to open a simulator that will let you see the Bode' plot for these system.  If you click here, you can get to the Phase Margin Bode' Plot tool.  Click here for the instructions for the tool.  (You can leave the Bode' plot tool and the instructions open in separate windows.)  Then work on the following problems which you can answer best using the Bode' plot tool.

Problem 1

        What is the phase margin for a gain of 2.0?

Enter your answer - in degrees - in the box below, then click the button to submit your answer.  You will get a grade on a 0 (completely wrong) to 100 (perfectly accurate answer) scale.

Your grade is:

Problem 2

        For a gain of 1.0, what is the closed loop steady state error?

Enter your answer in the box below, then click the button to submit your answer.  You will get a grade on a 0 (completely wrong) to 100 (perfectly accurate answer) scale.

Your grade is:

Things to note

        In this problem there is a resonant peak and some interesting things can happen.  Enter a gain of 1.2, and then note that there are three zero-db crossings.  One occurs around f = .15 Hz, and there the frequency response is going down.  Then at f = .35 the frequency response rises and goes from below zero db to above zero db.  Finally, the frequency response bends down again - after the resonant peak - and crosses zero db at f = 0.5.  What is happening here?  The only way you can tell what is happening is to look at the Nyquist plot.