madb.m

D-S.Kim, Y.S.Lee, W.H.Kwon, and H.S.Park, "Maximum Allowable Delay Bounds in Networked Control Syste

%------------------------------------------
% File Name : dd_nominal.m
% 侩档 : Nominal system俊 措茄 maximum 
%        allowble delay bound甫 备茄促.
%
% h = 1.8125 is the maximum for this example.
%------------------------------------------
clear all;

h= input('h = ');
%%----------------- 
%% Model Parameter
%%-----------------
% loop 1
Ra=10;
%Ra=13;
%Ra=14;
Ki=10;
Kb=0.075;
J=0.006;


%%---------------
%% System Matrix
%%---------------
A=[-Ki*Kb/(Ra*J) 0;1 0];  
B=[Ki/(Ra*J);0];
%A = [0 1; 0 -0.1]
%B = [0 ; 0.1]
R=10;
w=0.025;
Q=w*eye(2);
[K,s]=lqr(A,B,Q,R);

A1 = -B*K;




[n,n]=size(A);

%-------------------------------------
% 扁粮俊 洤带 规过
%-------------------------------------
Q=eye(2);
P = lyap((A+A1)',Q);

sig = min(eig(Q))/(2*max(abs(eig(P))));
del = sqrt(max(abs(eig(P)))/min(abs(eig(P))));
normF = norm(A1*(A+A1));
tau = sig/(del*normF);

%----------------------------
% LMI 规过
%----------------------------
setlmis([]);
%-------------------
%  LMI Variable
%-------------------
P = lmivar(1,[n 1]);
Q = lmivar(1,[n 1]);
X = lmivar(1,[n 1]);
Y = lmivar(2,[n n]);
Z = lmivar(1,[n 1]);

STAB = newlmi;

lmiterm([STAB 1 1 P],1,A,'s');
lmiterm([STAB 1 1 X],h,1);
lmiterm([STAB 1 1 Y],1,1,'s');
lmiterm([STAB 1 1 Q],1,1);

lmiterm([STAB 2 2 Q],-1,1);
lmiterm([STAB 3 3 Z],-h,1);

lmiterm([STAB 1 2 P], 1,A1);
lmiterm([STAB 1 2 Y], -1,1);
lmiterm([STAB 1 3 Z], h*A',1);
lmiterm([STAB 2 3 Z], h*A1',1);


STAB1 = newlmi;
lmiterm([-STAB1 1 1 X], 1,1);
lmiterm([-STAB1 1 2 Y], 1,1);
lmiterm([-STAB1 2 2 Z], 1,1);

STAB2 = newlmi;
lmiterm([-STAB2 1 1 P], 1,1);

delaylmi = getlmis;

[topt,xopt] = feasp(delaylmi);

P = dec2mat(delaylmi,xopt,P);
Q = dec2mat(delaylmi,xopt,Q);
X = dec2mat(delaylmi,xopt,X);
Y = dec2mat(delaylmi,xopt,Y);
Z =  dec2mat(delaylmi,xopt,Z);

sprintf('Conventional method : tau = %f ', tau)
sprintf('LMI method : tau = %f', h)
sprintf('LMI method yields %f bigger value than the conventional method', h/tau)