National Instruments 370753C-01

Chapter 5 Classical Feedback Analysis

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() s0.5+()

s2s2+()s10+()

-----------------------------------------=