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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-K Iteration
Recall from Section 2.5 that the D-K iteration is used as an approximation to µ
synthesis. This section discusses how Xµ implements this procedure.
The D-K iteration procedure is as follows. The weighted design interconnection
structure is referred to as P. The successive controllers are K
i, i = 1,...andthe
successive closed loop systems are G
i, i = 1,.. .. The block 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.
K
1 = hinfsyn(P, nmeas,nctrls,gamma limits).
3. Form the closed loop,
G
i = starp(P,K i).
4. Calculate µ(G
i) as follows.
[bnds,D
i,Dinv i, Delta i,sens i]=mu(G i,blk).
This calculation gives the D-scales for the upper bound: D
i. Figure 3.8 illustrates
this step.
5. Compare the closed loop to the design specifications; this will involve more than
just the calculation of µ. The user has several options at this point: