02.3 Gain Margin and Phase Margin

Let’s say, you have a gain margin of $6+0.1 dB$, what does that mean?

This means your system’s overall open-loop gain can increase by exactly 6 decibels before the closed-loop system goes unstable. In linear terms, 6 dB equates to a factor of roughly 2 (since $20log(2)=6$. This means your controller’s gain could essentially double before your system starts oscillating out of control.

This is simply the grading tolerance for your iterative “guess-and-check” process. Because finding the perfect sample rate for a mathematically exact 6.00000 dB margin is tedious, the problem is telling you that any sample rate that yields a gain margin anywhere between $5.9$ and $6.1$ is correct answer

[Gm, Pm, Wcg, Wcp] = margin(open_loop); %Wcg and Wcp is in rad/s

Gm = Gain Margin. You need to convert that to dB by 20log(Gm) Wcg = Gain Margin at phase cross-over frequency

What is phase cross-over frequency?

This is the frequency where the phase lag of your open-loop system drops to exactly -180 degrees.

What is gain cross-over frequency?

This is the frequency where the magnitude of your open-loop system crosses exactly 0 dB (a gain of 1)