I have this system: $$\frac{(s+2)^2}{s(s-4)^2}$$
To calculate phase and magnitude margins, I used the margins function on matlab, and it says that the phase margin is 112º. When evaluating the phase of the transfer function on the crossover frequency, I get -428º.
The only way I found to get the same result as matlab, is to add 360º ass well as the 180º that you normally add to get the phase margin.
- When is it ok to add those 360º?
- Why does matlab not add 360º when tracing the phase bode plot?(plot goes from -450º to -90º
- Is this in any way related to minimun phase systems?
Best Answer
You can always add or subtract a multiple of 360°. I think it is easier to see why when drawing the Nyquist diagram.
However in this case the closed-loop will not be stable because the open-loop is unstable (two poles at $s = 4$) and there are no encirclements of the minus one point in the Nyquist diagram. Since one normally only talks about margins when the system is stable, you could say that this system has no margins.