Chapter 5 Classical Feedback Analysis
© National Instruments Corporation 5-15 Xmath Control Design Module
The result is shown in Figure 5-5.
Figure 5-5. nichols( ) Gain-Phase Plot
Nyquist Stability Analysis
Nyquist analysis is a frequency domain method for examining system
performance of dynamic systems. Nyquist plots typically consist of the real
part of the frequency response plotted against the imaginary part of the
response. Nyquist plots are particularly useful in that they indicate the
stability of a closed-loop system, given an open-loop system which
includes a gain, K (it may be unity).
Nyquist’s stability criterion derives from Cauchy’s principle, which states
that a contour integral of a complex function will evaluate to zero as long
as the contour does not contain a singularity of that function [ChB84]. The
frequency response is the complex function in this case, and the contour
over which it is evaluated and plotted is determined by the frequency range
of the response.
Nyquist’s stability criterion states that the number of clockwise
encirclements of the –1 point on the real axis by the plot is equal to the
number of unstable closed-loop poles minus the number of unstable
open-loop poles. This criterion can be used to determine how many
encirclements are required for closed-loop stability. For example, if the