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 γapproaches its optimal value,the numerical properties of the calculation
deteriorate. This may lead to mu(G i) increasing as iis increased. This problem is
observed more oftenin systems with very lightly damped modes.
A comparison of Figures 3.8 and3.9 will show that Dsys iis not quite a r ational
approximation to Di. 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: Kj
(with j = i+1). In other words,
Dsys i≈Di0
0I.
This identity is of dimension nmeas×nmeas and is thereason that nmeas and nctrls
must be passed to the musynfit function. Do not confuse this identity with that
corresponding to the last block in Di.
3.7.3 Fitting DScales
The XµD-scale fitting function is musynfit; the syntax is as follows.
[Dsys,Dinvsys] = musynfit(Dmagdata,blk,nmeas,nctrls,weight)