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I'm trying to evaluate the stability of discrete systems by applying the Nyquist stability criteria for discrete systems in MATLAB. I'm referring to Digital Control Analysis and Design by Charles Philips and Troy Nagle.

I need to evaluate the stability of z-transfer function as given below (from the text)

enter image description here

The Nyquist contour and curve looks like this

enter image description here

How can I get these figures in MATLAB to assess stability?

Plotting the Nyquist for the tranfer function using the nyquist feature in MATLAB gives me the following

enter image description here

Is this right? How do I assess the system stability from this?

  • I have an understanding of the theoretical concept
  • Since it does not encircle (-1,0j), does that mean this is stable?
am3
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  • If i'm not mistaken, you have to use the dynamical system as input for the `nyquist` command in Matlab not the transfer function itself. Could this be your mistake? Otherwise please provide a MWE. – Nicky Mattsson Oct 18 '17 at 09:01
  • Could you elaborate? I obtained the transfer function from dynamical system. The MATLAB page for nyquist says "nyquist(sys) creates a Nyquist plot of a dynamic system sys. This model can be continuous or discrete, and SISO or MIMO. In the MIMO case, nyquist produces an array of Nyquist plots". Here 'sys' is the transfer function. – am3 Oct 18 '17 at 09:05
  • If I try to plot your transfer function with `H = tf([0 0.368 0.264],[1 -1.368 0.368]);` and `nyquist(H)` I obtain the figure from the reference, not your matlab plot. – Nicky Mattsson Oct 18 '17 at 11:33
  • Could you post the image of the plot? – am3 Oct 18 '17 at 13:29
  • Also you're getting that plot because you're plotting a continous time signal. This code will give you a discrete signal `num = [0.368 .264]; den = [1 -1.368 0.368]; H = tf(num,den, 0.1); nyquist(H);` – am3 Oct 18 '17 at 15:20

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