3.7. STRUCTURED SINGULAR VALUE(µ) ANALYSIS AND SYNTHESIS 111
(a) Controller and closed loop are satisfactory so stop the iteration.
(b) The iteration has converged and the controller and closed loop are not
satisfactory. In this case the weighted design problem must be reformulated.
(c) The iteration has not yet converged. Continuewith step 6.
6. Fit rational approximations toDiand Dinv i. The function to dothis, musynfit,
is described in more detail in Section 3.7.3. A typical function invocation is,
[Dsys i,Dinvsys i]=musynfit(D i,blk,nmeas,nctrls,sensi).
7. Apply ra tional approximations to D-scales to the weighted interconnection
structure. This is equivalent to,
PD=Dsys i ∗P∗Dinvsys i.
8. Set i=i+1
9. Design an H∞controller, K i, for the interconnection structure, P D.
Ki=hinfsyn(P D,nmeas,nctrls,gamma limits).
This step is illustrated in Figure 3.9.
10. Go to step 3.
Figure3.8: µcalculationin the D-Kiteration: Step3 in the enumerated procedure. Note
that µ(Gi)≤σmax(Di*G i*Dinv i)
The above iteration uses a standard H∞design. It is possible to usethe D-Kiteration
procedure with any MIMO design procedure (H2for example).