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140 CHAPTER 4. DEMONSTRATION EXAMPLES
1 10 100 10000.1 10000
0.6
0.8
1
1.2
1.4
1.6
0.4
1.8
Max. singular value and mu comparison
max. singular value
mu upper bound
mu lower bound
Note that µ(g1g) is not less than one at all frequencies — we have not met the design
objectives. A D-K iteration will be used to lower µ and improve the robust performance
with respect to these objectives.
4.1.6 Fitting D-scales for the D-K Iteration
In some cases the H
∞
controller is adequate for our purposes. It is not necessarily the
controller which gives the best robust performance for our system — it essentially
ignores the structure in the perturbations.
The D-K iteration procedure using the D and Dinv scaling matrices in the µ calculation
to set up an H
∞
problem which will usually give better robust performance.
The first step is to pre and post multiply the interconnection, (himat
ic in this case)
with D and Dinv. Two things need to be done first. The D and Dinv matrices produced
by µ are pdms and the interconnection is a state-space system. We must first fit transfer
functions to the D and Dinv magnitude data before we can do the multiplication.