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enter image description here

  1. How can one know, with just looking at the Bode plots, if the closed-loop system is going to be stable or not?
  2. This closed-loop system is unstable, why?

@DSP Novice @Jake

It was my fault that the input perturbation was misplaced. enter image description here

enter image description here

Closed loop stable: Yes . Thank you.

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  • $\begingroup$ hi! This is homework without explaining any of your own attempts at this. That's explicitly off-topic here :( $\endgroup$ Mar 19, 2020 at 16:29
  • $\begingroup$ I am pretty sure the closed-loop system is stable, in the picture you provided. $\endgroup$
    – Jake
    Mar 20, 2020 at 0:14
  • $\begingroup$ Can you post the full screenshot because the system in this screenshot looks stable $\endgroup$
    – DSP Novice
    Mar 20, 2020 at 11:28

1 Answer 1

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1) To determine if a system is stable by looking at a bode plot, generally, you just need to look at two things: Gain Margin and Phase Margin.

First find the frequency at which you phase plot reaches -180 degrees. In this case, it is 18.6kHz (I am inferring this from the pictures you sent because the plot covers up this crossing). Then find the gain at that frequency, which is -51.9dB. Invert that number and you have your Gain Margin, which is 51.9dB.

Second find the frequency at which the magnitude plot hits 0dB. This would be 3.54kHz. Then find the phase at that frequency, which is -100.4 degrees.Your Phase Margin will be 180 degrees plus this number, so 79.6 degrees.

The reason we find these two numbers is because we want to find out if the system will increase over time as it oscillates. When your signal hits -180 degrees, it has finished an oscillation (-180 degrees = 180 degrees). If you have positive gain when this happens then you signal increases with every oscillation, to infinity, which is unstable.

So if your Gain and Phase Margin are positive numbers then you know you have a stable system.

2) For the above reason, you closed loop system looks stable, but there might be a part of you bode plot you are not showing/is being covered up.

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