Phase margin, overshoot and Q-factor

Well, not much text here really: Imagine a second-order system. We use it in a feedback configuration. Dependent on how well the poles and zeros are separated the phase margin will vary.

Assuming that the beta factor (feedback factor) is unity enables us to normalize and visualize the impact of phase margin, overshoot and Q-factor in this simple video.

If you want to see the result for a phase margin of say 37 degrees, just jump to 37 seconds into the movie (https://youtu.be/Rs3JZLZRyxQ?t=37) , for 62 jump to 62s (https://youtu.be/Rs3JZLZRyxQ?t=62), etc…

Magic? No, not really… just a few lines of MATLAB code.