110 CHAPTER 3. FUNCTIONAL DESCRIPTION OF Xµ
mubnds2?
mubnds2 (a column vector) =
3.17155
3.17155
det(eye(4,4) - M*Delta2)?
ans (a scalar) = -2.62055e-16 + 5.82345e-17 j
3.7.2 The D-KIteration
Recall from Section 2.5 that the D-Kiteration is used as an approximation to µ
synthesis. This section discusses how Xµimplements this procedure.
The D-Kiteration procedure is as follows. The weighted design interconnection
structure is referred to as P. The successive controllersare Ki,i= 1,...andthe
successive closed loop systems are Gi,i= 1,. . . . Theblock structure is coded within
blk;nmeas is the number of controller measurements, and nctrls is the number of
controller actuators outputs.
1. Set i=1.
2. Design an initial H∞controller, K 1, for the interconnection structure, P.
K1=hinfsyn(P,nmeas,nctrls,gammalimits).
3. Form the closed loop,
Gi=starp(P,K i).
4. Calculate µ(Gi) as follows.
[bnds,Di,Dinv i,Delta i,sens i]=mu(G i,blk).
This calculation gives the D-scales for the upper bound: Di. Fig ure 3.8 illustrates
this step.
5. Compare the closed loo p to the design specifications; this will involve more than
just the calculation of µ. The user has several options at this point: