35 lines
1.2 KiB
Matlab
35 lines
1.2 KiB
Matlab
function [K,alpha0,apol,p]=isstable(G,a0)
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% isstable - check whether an FOTF object is stable or not
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%
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% [K,alpha,apol]=isstable(G)
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%
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% G - an FOTF object
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% K- identifier to indicate the stability of G, returns 0, and 1
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% alpha - the common order
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% apol - all the pseudo poles of the system
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% Copyright (c) Dingyu Xue, Northeastern University, China
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% Last modified 28 March, 2017
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% Last modified 18 May, 2022
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[n0,m0]=size(G); K=1; if nargin==1, a0=0.001; end
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for i=1:n0, for j=1:m0
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g=G(i,j); a=g.den.na; a1=fix(a/a0);
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if length(a1)==1 && a1==0
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else
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[g1,alpha]=fotf2cotf(g); c=g1.den{1};
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alpha0(i,j)=alpha; p0=roots(c); kk=[];
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for k=1:length(p0)
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a=g.den.a; na=g.den.na; pa=p0(k)^(1/alpha);
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if norm(a*[pa.^na'])<1e-6, kk=[kk,k]; end
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end
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p=p0(kk); subplot(n0,m0,(i-1)*m0+j),
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plot(real(p),imag(p),'x',0,0), xm=xlim;
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if alpha<1, xm(1)=0; else, xm(2)=0; end
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apol=min(abs(angle(p))); K=K*(apol>alpha*pi/2);
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a1=tan(alpha*pi/2)*xm; a2=tan(alpha*pi)*xm;
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line(xm,a1), line(xm,-a1), line(xm,a2), line(xm,-a2)
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xlabel('Real Axis'), ylabel('Imaginary Axis')
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end, end, end
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title('Pole Map')
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end
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