how should i do adaptive tuning of parameter gain "K " mention in the function ?

Hello, I want to do adaptive tuning of gain K in the following code. At the starting time of tspan K should be more and at the end time of tspan it should be less. how should i do this ?

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%function

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function dz = myeqd(t,y,ti,fi)
dz = zeros(3,1);
mu=0.3;
r= sqrt(y(1)^2 + y(2)^2);
K=20;

F=interp1(ti,fi,t);
dz(1)= (mu - r^2)*y(1) - y(3)*y(2) +K*F;
dz(2) = (mu - r^2)*y(2) + y(3)*y(1);
dz(3) = (-K*F) * (y(2)/sqrt(y(1)^2 + y(2)^2));

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w1=20;
w2=30;
w3=40;
Tspan1=0:0.01:10;
Tspan2= 10.01:0.01:20;
Tspan3= 20.01:0.01:30;
fi1 = cos(2*pi*w1.*Tspan1);
fi2 = cos(2*pi*w2.*Tspan2);
fi3 = cos(2*pi*w3.*Tspan3);
Tspan = [Tspan1 Tspan2 Tspan3];
fi=[fi1 fi2 fi3];
ti=Tspan;
[T,Y]=ode45(@(t,y) myeqd(t,y,ti,fi),Tspan,[1;1;15]);
plot (T,Y(:,3),'r')

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Answer 1

[Azzi Abdelmalek]

In your function you can use t to change the value of K

K=20-t/2

Your max(tspan ) is 30, then K will change from 20 to 20-30/2

[Aniket]

Hello Azzi,

I have done for only for one time span that is 0 to 10 secs and run the simulation.

the function --- function dz = myeqd(t,y,ti,fi)

if i am using K = 20 - ti/2 , because ti = Tspan in main code.

but i am getting following error.

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In an assignment A(I) = B, the number of elements in B and I must be the same.

Error in eqd1 (line 75) dz(1)= (mu - r^2)*y(1) - y(3)*y(2) +K*F;

Error in @(t,y)eqd1(t,y,ti,fi)

Error in odearguments (line 88) f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 114) [neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Error in maincode1 (line 9) [T,Y]=ode45(@(t,y) eqd1(t,y,ti,fi),Tspan,[1;1;30]);

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why this error is coming ?

[Azzi Abdelmalek]

It's not K = 20 - ti/2 , it's

   K = 20 - t/2

[Aniket]

ok ..... but in the function t is related to Tspan ?

[Azzi Abdelmalek]

ti is a vector, each step ti is not varying, it's used to find F at time t, which vary according to tspan. And whatever is t, you just need to change the value of K. Then write

   K = 20 - t/2

[Aniket]

ok , thank you for your guidance Azzi

I will try this for more than 1 time span .