12.19. Nyquist Plots

As mentioned earlier, the Nyquist plot is a plot of magnitude |G(jω)| versus angle ∠G(jω) for the frequency range −∞<ω<∞. Nyquist plot and Nyquist stability criterion is useful for determining the stability of the closed-loop system from the open-loop frequency response without determining the closed-loop poles. The stability of a closed-loop system is determined by finding out the number of encirclements of (−1 + j0) point by the Nyquist contour of the open-loop frequency response.

In MATLAB, the commands used to obtain Nyquist plot for a continuous LTI system are:

nyquist (n,d)
nyquist (n,d,w)

where w is the user-specified frequency vector.

To obtain the real and imaginary values of transfer function at different values ...

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