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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. Continue with step 6.
6. Fit rational approximations to D
i and Dinv i. The function to do this, 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,sens i).
7. Apply rational approximations to D-scales to the weighted interconnection
structure. This is equivalent to,
P
D = Dsys i ∗ P ∗ Dinvsys i.
8. Set i=i+1
9. Design an H
∞
controller, K i, for the interconnection structure, P D.
K
i = hinfsyn(P D,nmeas, nctrls,gamma limits).
This step is illustrated in Figure 3.9.
10. Go to step 3.
Figure 3.8: µ calculation in the D-K iteration: Step 3 in the enumerated procedure. Note
that µ(G
i) ≤ σ
max
(D i*G i*Dinv i)
The above iteration uses a standard H
∞
design. It is possible to use the D-K iteration
procedure with any MIMO design procedure (H
2
for example).