Solving system of ODEs and then get the optimum value for certain parameters.

I want to optimize fro R1 and R2 with the objective function (t_f-1.2e-6).^2+(t_t-50e-6).^2 == 0. Hereis my code that takes R1 and R2 to solve two differential eqns and give me t_f and t_t.

 function [t_f,t_t] = fun1(R1,R2)
C1 = 25e-9;
C2 = 1200e-12;
V0 = 10e3;
F = @(t,V) [((1/(R1*C1))*(V(2) - V(1)));((V(1)/(R1*C2))-(V(2)/(R1*C2))-(V(2)/(R2*C2)))];
[t1, V1]=ode45(F,[0 300e-6], [V0 0]);
Vp = max(V1(:,2));
for n=1:size((V1(:,2)),1)
    if V1(n,2) == Vp
        t_f = t1(n);
    elseif ((V1(n,2)-(Vp/2))*1e-3)^2 < 1e-5
            t_t =t1(n);
    end
end
end
Someone please help me in using optimization tools of matlab like fminsearch or ga to get the optimal values of R1 and R2.

Answer 1

[Eduard Reitmann]

I am not sure what type of input arguments the "fun1" needs, but it gives the following error when I try fun1(1,1):

Output argument "t_t" (and maybe others) not assigned during call to
"test>fun1".

Both output arguments (t_f & t_t) need to be assigned in the "fun1" function in order to solve the objective function. I made the following changes to "fun1" to assign both outputs (assume zero if not assigned):

if V1(n,2) == Vp
   t_f = t1(n);
   t_t = 0;
elseif ((V1(n,2)-(Vp/2))*1e-3)^2 < 1e-5
   t_t = t1(n);
   t_f = 0;
end

I you are happy with the modification above, this code should work theoretically.

fun = @(x) objfun(x(1),x(2));
x0 = [1;1];
options.Display = 'iter';
x = fminsearch(fun,x0,options);
R1 = x(1)
R2 = x(2)

Just remember to define this objective function (after script or separate file, depending on MATLAB version):

function fval = objfun(R1,R2)
[t_f,t_t] = fun1(R1,R2);
fval = (t_f-1.2e-6).^2 + (t_t-50e-6).^2;
end

I got the following answer (you can play with the "options" parameter to increase the accuracy of the answer):

R1 =
   1.2505e+03
R2 =
   1.3598e+03

[prabhat sonu]

Dear Reitmann,

Thanks for your valuable response. I made those changes in my code but its not serving my purpose. I know the solution of the problem, it should come like R1 = 199 & R2 = 2.5e3.

I have two differential equations that you can see in my fun1 code, The solution of which gives me different values of voltages in the range 0 to 300e-6. I want to get t_f ( i.e time instant at which the voltage is maximum) and t_t (i.e time instant at which voltage is half its maximum value). Then I want to to optimize for R1 and R2 with the objective function (t_f-1.2e-6).^2+(t_t-50e-6).^2 == 0.

So now i think you got my point, so please try to give me some hint/solution so that i can get my desired value.

[Eduard Reitmann]

I would rewrite your fun1 code to:

function [t_f,t_t,t,V] = fun1(R1,R2)
C1 = 25e-9;
C2 = 1200e-12;
V0 = 10e3;
F = @(t,V) [((1/(R1*C1))*(V(2) - V(1)));((V(1)/(R1*C2))-(V(2)/(R1*C2))-(V(2)/(R2*C2)))];
[t, V]=ode45(F,[0 300e-6], [V0 0]);
V = V(:,2);
[Vmax,imax] = max(V);
t_f = t(imax);
ihalf = find(V>=Vmax/2,1,'last');
t_t = t(ihalf);
end

The execution code should then be:

fun = @(x) objfun(x(1),x(2));
x0 = [100;100];
options.Display = 'iter';
options.TolX = 1e-20;
x = fminsearch(fun,x0,options);
R1 = x(1)
R2 = x(2)
[t_f,t_t,t,V] = fun1(R1,R2);
figure
plot(t,V,t_f,max(V),'*',t_t,max(V)/2,'*')
t_f
t_t

With the objective function:

function [fval,t,V] = objfun(R1,R2)
[t_f,t_t,t,V] = fun1(R1,R2);
fval = (t_f-1.2e-6).^2 + (t_t-50e-6).^2;
end

Using initial conditions R1=100 and R2=100, I get:

R1 =
   2.6172e+03
R2 =
  191.7561

This gives a function value of 3.84394e-36 instead of 1.6731e-14 for R1=199 and R2=2.5e3, i.e. more optimized answer.

[prabhat sonu]

Thanks a lot.