Modern Control System Theory and Design, 2nd Edition

6.6.  NYQUIST DIAGRAMS USING MATLAB[7]

In the previous section, several Nyquist diagrams were illustrated which were hand drawn. They were based on the transformation of the contour drawn in the s-plane to the G(s)H(s) plane. In this section, the MATLAB utility used for obtaining the Nyquist diagram is identified, and it is applied.

A.  Drawing Nyquist Diagrams of Systems Defined by Transfer Functions

If the system is defined by a transfer function, the Control System Toolbox command which determines the Nyquist plot is:

nyquist.

The Nyquist diagram can be used with polynomial transfer functions, defined as G(s) = num(s)/den(s) where “num” and “den” contain the polynomial coefficients, if invoked with three right-hand arguments as follows

[re,im] = nyquist(num,den,w)

where

re       = real part on the Nyquist diagram

im      = imaginary part on the Nyquist Diagram

num   = row matrix format representing the numerator of the polynomial

den    = row matrix format representing the denominator of the polynomial

w       = frequency in rad/sec.

As shown in the previous section on the Nyquist diagram, it will occasionally go to infinity. Without special precautions in the MATLAB program, an erroneous Nyquist plot may occur. We can avoid this with MATLAB by specifying the finite area we want plotted. This will be illustrated next.

Let us consider the Nyquist diagram of a unity feedback control system whose forward transfer function is given by

Since the Nyquist diagram goes to infinity, ...