LFRT version 2.0: µ-analysis
This page describes four functions that generate from an LFR-object the input arguments of four standard Matlab functions for µ-analysis (mu, mustab, mubnd and mussv). Function lfr2muGeneration of a model with an uncertain pole close to the imaginary axis at about 10 Rd/s.
lfrs a b c A = [-1+5*a -10*(1+b);10*(1+c^2) -1-a*b*c]; B = [1+b;1*c]; C = [1 1]; D = 0; sys = abcd2lfr([A B;C D],2); sys = minlfr(sys);µ-analysis using the function mu.
frequ = logspace(0,2,20); [M,blk] = lfr2mu(sys,frequ); bnds = mu(M,blk,'wlc'); semilogx(frequ,bnds(1:20,1),'c+'); hold on semilogx(frequ,bnds(1:20,2),'g.');See figure below.
Function lfr2mubndSame as above but using an LMI-based µ upper bound.
[M,delta] = lfr2mubnd(sys,frequ); for ii = 1:length(frequ); mu2(ii) = mubnd(M{ii},delta,1e-6,'off'); end; semilogx(frequ,mu2,'rd');See figure below.
Function lfr2mussvSame as above using the function mussv of version 3 of the Robust Control Toolbox. Here we use the low precision default options.
[M,blk] = lfr2mussv(sys,frequ); [bnds2,muinfo] = mussv(M,blk); plot(bnds2); ![]()
Function lfr2mustabComputation of the stability margin (inverse of the maximum value of the µ-curve) using the function mustab (the function mustab doesn't work for this example on some platforms).
[P,delta] = lfr2mustab(sys);
[margin1,frequ0] = mustab(P,delta);
...............
Mu upper bound (peak value): 2.556e+00
Robust stability margin : 3.912e-01
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