MATLAB: The generalized Nyquist stability criterion
generalized nyquist criterion
Hi I am trying to plot the Nyquist plot of MIMO system. any help please
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Once you have a MIMO matrix transfer function you can generate the plot by finding the eigenvalues of the matrix as a function of frequency. A 2x2 MIMO matrix transfer function will have 2 eigenvalues at every frequency point. The imaginary vs. the real part of the two eigenvalues will yield two loci that should always connect. This is the generalized Nyquist. I include a sample code for a textbook example in Multivariable Feedback Design by Maciejowski. Example 2.7. This example is limited to 2x2 but can be extended easily to higher dimensions.
Neither bode nor bodeplot will display the slope of the bode diagram directly. You will need to calculate it manually.
One way to do this is by calculating the number of poles & zeros, and identifying the corner frequency on the bode plot, then finding the slope. This previously answered question can give you some insight on how to get the corner frequency values.
I figured it out. You could extract each input-ouput transfer function via g=tf(G.Numerator(i,j),G.Denominator(i,j)) where g is the SISO function you want and G is the original MIMO function and i,j are indeces of output and input respectively. That way when you use bode(g) you can estimate all stability margins.
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