MATLAB: Simulink Linear Analysis Pole/Zero Plots

linear analysispole-zero mapsimulink

Attached is the Simulink file I'm having problems with. I have this system controlled by a PID controller which gives me the desired response on 'Scope1'. Now I want to do some plots using "Analysis -> Control Design -> Linear Analysis…".

Here I get my bode and step responses plot, but when I go to the "I/O Pole/Zero Map" all the poles and zeros are on the right side (real positive values) which means the system is unstable and it seems to be contradictory from the step and bode plot that shows an stable system. Am I missing or misinterpreting anything? Here are the bode and step plots I get:

And this is the I/O Pole/Zero Map:

Best Answer

Based on the staircase step response, looks like your system is discrete.

This means that stability is inside the unit circle (circle of radius 1), which it is :)

- Sebastian

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I get the same Bode plots. What's different about yours? Also, you can do this with one Bode command

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Think about what a root locus plot actually is. It plots the locations of the roots (pole locations) in the complex plane as a function of some parameter, for example controller gain. So you can make a simple loop which varies the parameter. For each pass through the loop, solve for the n (in your case 4) eigenvalues and plot them. Note the standard plot command in MATLAB will plot a complex value with the x axis as the real part and y axis as the imaginary part. So at each pass through the loop, if your poles (eigenvalues) are given by the vector v, you could just use the command plot(v,'*'), which would put a star (asterisk) at each pole location. Use the command hold on before entering the loop, and hold off after leaving the loop so it won't get erased as you build up the plot.

Best Answer

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