Page 149 - MATLAB an introduction with applications

134 ——— MATLAB: An Introduction with Applications

nyquist (num, den, w)
nyquist (A, B, C, D)
nyquist (A, B, C, D, w)
nyquist (A, B, C, D, iu, w) ...(3.29)
nyquist (sys)
where w is the frequency vector.
The MATLAB command involving the user-specified vector w in Eq. (3.29) computes the frequency response
at the specified frequency points.
The following MATLAB commands
[re, im,w ] = nyquist (num, den)
[re, im,w ] = nyquist (num, den, w)
[re, im,w ] = nyquist (A, B, C, D)
[re, im,w ] = nyquist (A, B, C, D, w) ...(3.30)
[re, im,w ] = nyquist (A, B, C, D, iu, w)
[re, im,w ] = nyquist (sys)
are used to obtain the frequency response of the system in the matrices re, im and w. The plot is not drawn
on the screen. The matrices re and im contain the real and imaginary parts of the frequency response of the
system, computed at the frequency points specificated in the vector w.

3.15 NICHOLS CHART
The chart consisting of the M and N loci in the log magnitude versus phase diagram is called the Nichols
chart. The G(jw) locus drawn on the Nichols chart gives both the gain characteristics and phase
characteristics of the closed loop transfer function at the same time. The Nichols chart contains curves of
constant closed loop magnitude and phase angle. The Nichols chart is symmetric about the 180° axis. The
M loci are centered about the critical point (0 dB, –180). The Nichols chart is useful in determining the
frequency response of the closed loop from that of the open loop. The Nichols chart is produced by using
the MATLAB command nichols(num, den). The command n grid creates the dotted lines that allow reading
closed-loop gain and phase from the Nichols chart. In order to customize the axes of the Nichols chart, the
MATLAB command axis is used.

3.16 GAIN MARGIN, PHASE MARGIN, PHASE CROSSOVER
FREQUENCY AND GAIN CROSSOVER FREQUENCY

The MATLAB command
[Gm, pm, wcp, wcg] = margin (sys) ...(3.31)
can be used to obtain the gain margin, phase margin, phase crossover frequency and gain crossover
frequency.
In Equation (3.31), Gm is the gain margin, pm is the phase margin, wcp is the phase crossover frequency,
and wcg is the gain crossover frequency.

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