4.2. A SIMPLE FLEXIBLE STRUCTURE EXAMPLE 165
4.2.4 Robustness Analysis
The block structure has two perturbation ∆ blocks and a “performance” block. The two
voice-coil perturbations are put into a single 1×2 block as they enter the system at the
same point. Note that this is not identical to twoseparate blocks — for example a
perturbation in which both blocks have magnitude one is now longer included. The
advantage of doing this is that it give one less block in the resulting analysis and design
problem. This makes the µcalculation easier (we now have three blocks and so the
upper bound is actually equal to µ) and gives one less D-scale to be appr oximatedin the
D-Kiteration.
blk = [1,2; 1,1; 2,3]
The frequency response of the closed loop system iscalculated. Thenominal
performance test simply involves checking the H∞norm of the nominal closed loop
system. This is a maximum singular value test.
Ghinfg = freq(Ghinf,omega);
npbnds = norm(svd(Ghinfg(4:6,3:4)),inf)
Robust stability is a µtest as there are two pertubation blocks. Note that here we
calculate µwith respect to the G11 partition and use a block structure containing only
the perturbation blocks.
[rsbnds,Drs,Drsinv,Deltars,sensrs] = mu(Ghinfg(1:3,1:2),[1,2; 1,1])
Robust performance is a µtest on the entire Gmatrix.
[rpbnds,D,Dinv,Delta,sens] = mu(Ghinfg,blk)
These results are plotted. Note that µtests give bounds and in this case the upper and
lower bounds are almost indistinguishable.