User manual

112 CHAPTER 3. FUNCTIONAL DESCRIPTION OF Xµ

Figure 3.9: H

∞

controller design. Step 9 in the enumerated procedure

There is actually another possibility at step 5; numerical problems cause the iteration to

diverge. As γ approaches its optimal value, the numerical properties of the calculation

deteriorate. This may lead to mu(G

i) increasing as i is increased. This problem is

observed more often in systems with very lightly damped modes.

A comparison of Figures 3.8 and 3.9 will show that Dsys

i is not quite a rational

approximation to D

i. The reason is that Dsys i has as inputs, the lower outputs of P.

These are actually passed through an identity for the design of the next controller: K

(with j = i+1). In other words,

Dsys

i ≈



i 0

0 I



This identity is of dimension nmeas × nmeas and is the reason that nmeas and nctrls

must be passed to the musynfit function. Do not confuse this identity with that

corresponding to the last block in D

3.7.3 Fitting D Scales

The XµD-scale ﬁtting function is musynfit; the syntax is as follows.

[Dsys,Dinvsys] = musynfit(Dmagdata,blk,nmeas,nctrls,weight)