%
% Análise mu 
%
% SEM 5928 - Sistemas de Controle 
% Escola de Engenharia de São Carlos - USP
%
% Adriano Siqueira - 2016
%
%
 Uses the Mu toolbox

clear all
close all


G0=[-87.8 86.4; 108.2 -109.6];
dyn = nd2sys(1,[75 1]);
Dyn=daug(dyn,dyn);
G=mmult(Dyn,G0);

%Inversebased control

dynk=nd2sys([75 1],[1 1.e-5],0.7);
Dynk=daug(dynk,dynk);
Kinv=mmult(Dynk,minv(G0));


% Weights

wp=nd2sys([10 1],[10 1.e-5],0.5);Wp=daug(wp,wp);
wi=nd2sys([1 0.2],[0.5 1]);Wi=daug(wi,wi);

% Generalized plant P
 
systemnames = 'G Wp Wi';
inputvar = '[ydel(2); w(2) ; u(2)]';
outputvar = '[Wi; Wp; -G-w]';
input_to_G = '[u+ydel]';
input_to_Wp = '[G+w]'; 
input_to_Wi = '[u]';
sysoutname = 'P';
cleanupsysic = 'yes';
sysic;

N = starp(P,Kinv); omega=logspace(-3,3,61);
Nf = frsp(N,omega);

% mu for RP

blk =[1 1;1 1;2 2];   
[mubnds,rowd,sens,rowp,rowg] = mu(Nf,blk,'c');
muRP = sel(mubnds,':',1);
pkvnorm(muRP) %(ans=5.7726)  

% Worstcase weighted sensitivity

[delworst,muslow,musup] = wcperf(Nf,blk,1); 
musup
%musup = 44.93 for delta=1  

% mu for RS

Nrs = sel(Nf,1:2,1:2);

[mubnds,rowd,sens,rowp,rowg] = mu(Nrs,[1 1;1 1],'c');
muRS = sel(mubnds,':',1);
pkvnorm(muRS) %(ans=0.52) 

% mu for NP (= max singular value of Nnp)

Nnp=sel(Nf,3:4,3:4);
[mubnds,rowd,sens,rowp,rowg] = mu(Nnp,[2 2],'c');
muNP= sel(mubnds,':',1);
pkvnorm(muNP)  % ans =0.5

vplot('liv,m',muRP,muRS,muNP);
legend('RP','RS','NP')