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104 CHAPTER 3. FUNCTIONAL DESCRIPTION OF Xµ
Frequency
0.01 0.1 1 100.001 100
Magnitude
0.1
1
0.01
10
Sensitivity functions
Kinf
K2
Note that with the interconnection structure shown in Figure 3.7, the closed loop
transfer function from ref to e
(1) is simply Wperf*sensinf.IftheH
∞
of the resulting
closed loop system was less than one, this would guarantee that sensinf was less than
inv(Wperf) at every frequency. Note that from the above plot, this is not quite
satisfied; as we might expect because the closed loop H
∞
norm is approximately 1.17.
Now look at some step responses. Use sysic to create an unweighted interconnection
(because the weightings are only for design purposes and are not actually implemented
in the system). We create an open-loop interconnection and close the loop with starp for
each controller.
ic = sysic("plant",["ref";"ctrl"],["plant";"ref-plant"],...
"ctrl",plant)
clpinf = starp(ic,Kinf)
clp2 = starp(ic,K2)
# Examine step response
step = gstep([0:0.1:10],0,1)
yinf = clpinf*step
y2 = clp2*step
g3 = ctrlplot(yinf);
g3 = ctrlplot(y2,g3,{line
style=4});