How to determine stability of transfer function from Nyquist?

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Ali Almakhmari 2023-9-14

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https://ww2.mathworks.cn/matlabcentral/answers/2021126-how-to-determine-stability-of-transfer-function-from-nyquist

评论： Sam Chak 2023-9-14

Hello guys. I have hundreds of transfer functions that I am asked to determine if they are stable or not using the Nyquist criteria specifically. I am used to doing this by using the nyquistplot command and analyze the plot. But its impossible to do this for each of the hundreds of transfer functions I have to go through. So is there a way to automate this process? Can anyone suggest any other approach?

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Sam Chak 2023-9-14

Hi Ali, show us two examples (one is stable, another is not) of how you assess the stability from a single MATLAB Nyquist PLOT with some measures, and then we will see how to automate your steps for the hundreds.

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Answer 1

William Rose 2023-9-14

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@Ali Almakhmari,

The answer depends on the form of the transfer functions which you have. Do you have hundreds of polynomials G(s)H(s), with particular coefficients for each one? Or do you have hundreds of images of Nyquist plots, without numeric data? Or do you have hundreds of tables of frequency and real and imaginary parts of G(s)H(s)? Or do you have a .mat file containing hundreds of "sys" objects?

The Matlab command

nyquist(sys)

draws a plot. Use

[re,im,wout] = nyquist(sys)

to get the vectors for the frequency response, whic you could use to assess stability.

This page has potentially useful suggestions for algorithms to determine stability of a transfer function using the Nyquist plot. It includes references to Matlab commands.