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-Kiteration will be used to lower µand improve the robust performance
with respect to these objectives.
4.1.6 Fitting D-scales for the D-KIteration
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-Kiteration procedure using the Dand Dinv scaling matrices in the µcalculation
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 Dand Dinv. Two things need to be done first. TheDand Dinv matrices produced
by µare pdms and the interconnection is a state-space system. We must first fit transfer
functions to the Dand Dinv magnitude data before we can do the multiplication.