Chapter 5 Classical Feedback Analysis
© National Instruments Corporation 5-7 Xmath Control Design Module
For an example of frequency response of a simple system, refer to
Example 5-2.
Given the single-input, single-output open-loop plant in Figure 5-3, where
U(s) and Y(s) are the frequency domain input and output, respectively, you
can examine its response characteristics and see how you can improve them
using the frequency-response based control design functions in this chapter.
Figure 5-3. Representation of the Open-Loop System
Example 5-2 Frequency Response of a Simple System
You can create the system directly in transfer function form:
sys = system(polynomial(-0.5),
polynomial([0,0,-2,-10]));
and then obtain the frequency response directly:
H = freq(sys,{Fmin = 0.01,Fmax = 10,npts = 150});
freq( ) also can be called with a predefined vector of frequency points,
or you can specify that phase tracking be used to compute frequency points
between the minimum and maximum frequencies. The number of
frequency points used with tracking will vary. To illustrate:
H = freq(sys,{Fmin=0.01,Fmax=10,track,delta=.5});
size(H)
ans (a row vector) = 1 1 335
The dynamics of this system are adequately reflected in both frequency
responses. However, systems having more closely-placed pole and zero
locations are good candidates to use with the track keyword.
Bode Frequency AnalysisWhile freq( ) provides you directly with the frequency response, other
tools in the Control Design module can give you more insight into what the
open- and closed-loop frequency responses of a system imply about the
system behavior. Bode plots of system frequency response are useful
U(s) Y(s)
(s + 0.5)
s2(s + 2)(s + 10)