%
% Cálculo das Barreiras de Estabilidade e de Desempenho - veja arquivo Aula8_ExemploLQG.doc
%
% SEM 5928 - Sistemas de Controle 
% Escola de Engenharia de São Carlos - USP
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% Adriano Siqueira - 2016
%

clear;
close all
A=[ 0 0 0 0 0 0;
    0 0 0 0 0 0;
    0.14 -0.12 -0.02 0.005 2.4 -32;
    0.36 -8.6 -0.014 0.44 -1.3 -30;
    0.35 0.009 0 0.018 -6 1.2;
    0 0 0 0 1 0];
B=[1 0;
    0 1;
    0 0;
    0 0;
    0 0;
    0 0];
C=[0 0 0 1 0 0;
    0 0 0 0 0 57.3];
D=[0 0; 0 0];

sysG=ss(A,B,C,D);
w=logspace(-2,3,100);

alfar = 20*log10(1/0.10);
alfad = 20*log10(1/0.10);
alfas = 20*log10(1/0.15);

aux=[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0];
b=0;
w_=i*w;
for j=1:100,
    inverro(j)= 100000;
    for i=1:10
        gr=tf(625, [1 50*aux(i) 625]);
        sysGr=series(gr,eye(2));
        sysGR=series(sysG,sysGr);
        [AR,BR,CR,DR]=ssdata(sysGR);

        G = C*inv(w_(j)*eye(size(A))-A)*B-D;
        GR = CR*inv(w_(j)*eye(size(AR))-AR)*BR-DR;
        E = (GR - G)*inv(G);
        S = svd(E);
        aux3= 1/(S(1));
        if aux3 <= inverro(j),
            inverro(j) = aux3;
        end;

    end;

end;
semilogx(w,20*log10(inverro),'r');
hold on;


w=linspace(0.01,0.5,1000);
semilogx(w,alfar,'r.');
t=linspace(-10,alfar);
semilogx(0.5,t,'r.');

w=linspace(0.01,0.7,1000);
semilogx(w,alfas,'r.');
t=linspace(-10,alfas);
semilogx(0.7,t,'r.');

grid;
title('Barreiras de desempenho e estabilidade');
xlabel('frequência');
ylabel('dB');

save barreira inverro