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3.6. H
2
AND H
∞
ANALYSIS AND SYNTHESIS 99
Figure 3.7: Weighted design interconnection structure: p
In order to set up the design problem, we consider ref as an unknown input and the
tracking error (input to k ), and the actuator signal, u, as outputs to be minimized.
These outputs are weighted with the weights Wperf and Wact respectively. The weighted
interconnection structure for design, p, is illustrated in Figure 3.7.
A more realistic problem would also include weighted noise on the measurement signal,
y. We could also weight the ref input and add weighted disturbances to the plant input
or output.
# Create weights
Wperf = 100/makepoly([100,1],"s")
Wact = makepoly([0.5,0.05],"s")/makepoly([0.05,1],"s")
Wperfg = freq(Wperf,omega)
Wactg = freq(Wact,omega)
g00 = ctrlplot(Wperfg,{logmagplot});
g00 = ctrlplot(Wactg,g00,{logmagplot,line
style=4});
g00 = plot(g00,{title="Weighting functions",...
legend=["Wperf";"Wact"],!grid})?