switched system with time delay

please to help me. plot the switched system with time delay in matlab, but code is error???

function ddestat

tau=[0.2];

tspan = [0 400];

history = [0.333,0,083];

T = [];

Y = [];

Z=[];

IE = 1;

ti=6;

while IE == 1

options = ddeset('Events',@switched);

[Thelp,Yhelp,Zhelp,TE,YE,ZE,IE]= dde23(@ddefun ,tau,history,tspan,options,ti);

history=YE;

tau=ZE;

t0=TE;

ti=TE+9;

plot(Thelp(:),Yhelp(:,1),'g','LineWidth',1)

hold on

% plot(Thelp(:),Yhelp(:,2),'g','LineWidth',1)

% hold on

%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[Thelp,Yhelp,Zhelp,TE,YE,ZE,IE]= dde23(@ddefunn , tau, history,tspan,options,ti);

history=YE;

tau=ZE;

t0=TE;

ti=TE+9;

plot(Thelp(:),Yhelp(:,1),'k','LineWidth',1)

hold on

%plot(Thelp(:),Yhelp(:,2),'k','LineWidth',1)

%hold on

end

end

function v = ddefun(t,y,ti,Z) % equation being solved

ylag1 = Z(:,1);

v=zeros(2,1);

v(1) = y(2)+0.08*ylag1(1)+0.02*ylag1(2)+0.125*ylag1(1)^2+0.12*ylag1(2)^2;

v(2)= y(1)+0.04*ylag1(1)+0.05*ylag1(2)+0.25*sin(y(1));

end

function v = ddefunn(t,y,ti,Z) % equation being solved

ylag1=Z(:,1);

v=zeros(2,1);

v(1) = -3*y(1)+2*y(2)+0.05*ylag1(1)+0.02*ylag1(2)+0.25*y(1)*y(2);

v(2)= 2*y(1)-3*y(2)+0.03*ylag1(1)+0.07*ylag1(2)+0.125*ylag1(2)^2+0.25*y(2);

end

%-------------------------------------------

function [value,isterminal,direction] = events(t,y,ti,Z)

value = t-ti; isterminal = 1;

direction = 1;

end

Answer 1

[Mahesh Taparia]

Hi Amani,

There are some bugs in your code which needs to be fixed in order to run the script.

1. Variable history should be 1X2 vector, you have created 1X3.
2. In function ddefun/ ddefunn you have defined ylag1 as a scalar value, but you are using as a vector.
3. Function dde23 returns structure not an array. So, update the parameters as per your formula by taking the variables from struct.

For your reference you can see a modified version of your code, it may not be correct because you have to update the parameters which are stored in ‘vb’.

Run this script by putting break points in the code and update the parameters.

function vc= ddestat
tau=[0.2];
tspan = [0 400];
history = [0.333,0.083];
T = [];
Y = [];
Z=[];
IE = 1;
ti=6;
 
while IE == 1 
    
        options = ddeset('Events',@switched);   
        vb= dde23(@ddefun ,tau,history,tspan,ti);
      %[Thelp,Yhelp,Zhelp,TE,YE,ZE,IE]= dde23(@ddefun ,tau,history,tspan,options,ti);
        history=vb.history;
%         tau=ZE;   %%%%%%%% UPDATE the new parameters 
%          t0=TE;
%          ti=TE+9;
%       plot(Thelp(:),Yhelp(:,1),'g','LineWidth',1)
%       hold on
%      %   plot(Thelp(:),Yhelp(:,2),'g','LineWidth',1)
      %  hold on
         %%%%%%%%%%%%%%%%%%%%%%%%%%%%
         %[Thelp,Yhelp,Zhelp,TE,YE,ZE,IE]= dde23(@ddefunn , tau, history,tspan,options,ti);
         vc= dde23(@ddefunn , tau, history,tspan,ti);
%          history=YE;
%          tau=ZE;
%          t0=TE;
%          ti=TE+9;
%       plot(Thelp(:),Yhelp(:,1),'k','LineWidth',1)
%         hold on
        %plot(Thelp(:),Yhelp(:,2),'k','LineWidth',1)
        %hold on
end
end 
function v = ddefun(t,y,ti,Z) % equation being solved
ylag1 =[6 6]; %%%taken as example put correct value 
v=zeros(2,1);
v(1) = y(2)+0.08*ylag1(1)+0.02*ylag1(2)+0.125*ylag1(1)^2+0.12*ylag1(2)^2; 
v(2)= y(1)+0.04*ylag1(1)+0.05*ylag1(2)+0.25*sin(y(1));

end
 
function v = ddefunn(t,y,ti,Z) % equation being solved
ylag1=[6 6];%%%%taken as example put correct value 
v=zeros(2,1);
 
v(1) = -3*y(1)+2*y(2)+0.05*ylag1(1)+0.02*ylag1(2)+0.25*y(1)*y(2);
v(2)= 2*y(1)-3*y(2)+0.03*ylag1(1)+0.07*ylag1(2)+0.125*ylag1(2)^2+0.25*y(2);
end
%-------------------------------------------
function [value,isterminal,direction] = events(t,y,ti,Z)
value = t-ti;     isterminal = 1;   
direction = 1;
 end

Hope it will helps.

Answer 2

[amani alsulami]

Thanks