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Gilles
Gilles
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I have an open-loop system function $L(s)$ and its Bode plot is

enter image description here

As MATLAB says, it is stable if we close the loop with unitary feedback. I thought that, seeing the Bode plots one could tell if the closed-loop system would be stable if the $0dB$$0\textrm{ dB}$ crossing occured at a lower frequency than the $-180°$ crossing. I made the Blode plots for $0.01L(s)$ and got the following:

enter image description here

Now the closed-loop system would be stable too, but this time the $0dB$$0\textrm{ dB}$ crossing occurs at a lower frequency than the $-180°$ crossing. Nevertheless, in both cases the closed-loop system turns out to be stable.

Then I made the Bode plots for $0.1L(s)$ and got this:

enter image description here

And now the closed-loop system is unstable.

So, my question is: how can one know, with just looking at the Bode plots, if the closed-loop system is going to be stable or not?

I have an open-loop system function $L(s)$ and its Bode plot is

enter image description here

As MATLAB says, it is stable if we close the loop with unitary feedback. I thought that, seeing the Bode plots one could tell if the closed-loop system would be stable if the $0dB$ crossing occured at a lower frequency than the $-180°$ crossing. I made the Blode plots for $0.01L(s)$ and got the following:

enter image description here

Now the closed-loop system would be stable too, but this time the $0dB$ crossing occurs at a lower frequency than the $-180°$ crossing. Nevertheless, in both cases the closed-loop system turns out to be stable.

Then I made the Bode plots for $0.1L(s)$ and got this:

enter image description here

And now the closed-loop system is unstable.

So, my question is: how can one know, with just looking at the Bode plots, if the closed-loop system is going to be stable or not?

I have an open-loop system function $L(s)$ and its Bode plot is

enter image description here

As MATLAB says, it is stable if we close the loop with unitary feedback. I thought that, seeing the Bode plots one could tell if the closed-loop system would be stable if the $0\textrm{ dB}$ crossing occured at a lower frequency than the $-180°$ crossing. I made the Blode plots for $0.01L(s)$ and got the following:

enter image description here

Now the closed-loop system would be stable too, but this time the $0\textrm{ dB}$ crossing occurs at a lower frequency than the $-180°$ crossing. Nevertheless, in both cases the closed-loop system turns out to be stable.

Then I made the Bode plots for $0.1L(s)$ and got this:

enter image description here

And now the closed-loop system is unstable.

So, my question is: how can one know, with just looking at the Bode plots, if the closed-loop system is going to be stable or not?

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Tendero
Tendero
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Analyze stability of a closed-loop system with Bode

I have an open-loop system function $L(s)$ and its Bode plot is

enter image description here

As MATLAB says, it is stable if we close the loop with unitary feedback. I thought that, seeing the Bode plots one could tell if the closed-loop system would be stable if the $0dB$ crossing occured at a lower frequency than the $-180°$ crossing. I made the Blode plots for $0.01L(s)$ and got the following:

enter image description here

Now the closed-loop system would be stable too, but this time the $0dB$ crossing occurs at a lower frequency than the $-180°$ crossing. Nevertheless, in both cases the closed-loop system turns out to be stable.

Then I made the Bode plots for $0.1L(s)$ and got this:

enter image description here

And now the closed-loop system is unstable.

So, my question is: how can one know, with just looking at the Bode plots, if the closed-loop system is going to be stable or not?