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Chapter 5 Classical Feedback Analysis
© National Instruments Corporation 5-17 Xmath Control Design Module
The Nyquist plot Xmath generates is complete only for the frequencies you
specify. Ideally you would obtain a plot based on the frequency response
from ω = 0 to ω = ∞. However, a good choice of frequency range usually
comes close enough. When you have obtained the Nyquist plot from
approximately w = 0 to ∞, you can reflect it about the real axis to get a
complete plot of the open-loop frequency response from –∞ to +∞. Extend
the resulting curve, traveling clockwise, until the contour is closed. Refer
the augmented plots in Example 5-6. When you have done this, you can use
the expression Z = N + P to find the number of unstable closed-loop system
roots, Z, given the number of clockwise encirclements of the (–1/K,0) or
(–1,0) point and the number of unstable (right-half plane) poles of the
open-loop system.
For an example of how to use Nyquist plots to determine stable gains for
the closed-loop system, refer to Example 5-6.
Example 5-6 Using Nyquist Plots to Determine Stable Gains for the Closed-Loop System
By examining the Nyquist plot for your open-loop system
you can tell for what multiplicative gain values K the closed-loop system
will be unstable.
H = nyquist(sys,{Fmin=0.01,Fmax=10,npts=300});
gives you an overview of the Nyquist plot for a broad range of frequencies,
but the plot gives more information than you need about the low frequency
response and not enough about the response at higher frequencies. Refer to
Figure 5-7.
You do another Nyquist plot, this time examining the high-frequency
response more closely. Refer to Figure 5-8.
H2= nyquist(sys,{Fmin=.5,Fmax=5,npts = 150})
Gs()
s 0.5+()
s
2
s 2+()s 10+()
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