Solving a system with embedded differential and non-differential equations

I was trying to resolve this system for md and mq with this answer as a reference.

This is my code:

function dX=fun(t,X)
%constants
f=50;
ws=2*pi*f;
Ls=15e-3;
Rs=1;
Rcdc=500;
Cdc=500e-6;
Vs=220*sqrt(2);
Vsd=220*sqrt(3);
ipv=10
fp=0.96

%7 ecuaciones, 3 diferenciales.
%en el sistema, Vq=0, por lo que no se agrega al sistema de ec.
%X(1)=id X(2)=iq X(3)=Vdc
dX(1)=ws*X(2) + Vsd/Ls - Rs*X(1)/Ls - cos(theta)*md/Ls;
dX(2)=-ws*X(1) -  Rs*X(2)/Ls -    sin(theta)*mq/Ls;
dX(3)=(X(1)*md+X(2)*mq)/Cdc  +   ipv/Cdc   -   X(3)/(Cdc*Rcdc); 
md=sqrt(3/2)*M*cos(theta)
mq=sqrt(3/2)*M*sin(theta)
M=sqrt(3/2)*sqrt((mq^2)+(md^2))
fp=X(1)/X(2);

%Definition of dX
dX=[dX(1);dX(2);dX(3)];
end

tSpan = [0 5];
initial=[.01; .01; .01];
     
%X(1)=id X(2)=iq X(3)=theta X(4)=Vdc X(5)=md X(6)=mq X(7)=M

[t,x]=ode45(@difsyssolve,tSpan,initial);
id=x(:,1);
iq=x(:,2);
theta=x(:,3);
Vdc=x(:,4);
md=x(:,5);
mq=x(:,6);
M=x(:,7);


figure
plot(t,Vdc)
xlabel('tiempo')
ylabel('vdc')

And it gives me the following error:

Unrecognized function or variable 'theta'.

Error in difsyssolve (line 19)

dX(1)=ws*X(2) + Vsd/Ls - Rs*X(1)/Ls - theta*md/Ls;

Error in odearguments (line 92)

f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 107)

odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

Error in test (line 6)

[t,x]=ode45(@difsyssolve,tSpan,initial);

I don´t know how to define theta, and how to solve the system.

Can you help me?

Thank you in advance.

[Torsten]

What is X(4) ? You only have three odes that you define.

md, mq and M have to be explicitly calculated from this system (after you tell us what X(4) is) :

md=sqrt(3/2)*M*cos(X(4))
mq=sqrt(3/2)*M*sin(X(4))
M=sqrt(3/2)*sqrt((mq^2)+(md^2))
fp=X(1)/X(2);

You cannot just add equations and hope MATLAB will somehow solve for them:

[Marcelo García Olavarría]

You're right! I edited it now. It still gives me errors. "Unrecognized function or variable 'theta'."

Edit: I typed X(4) by mistake. It should be "theta". I don't know how to define it, and I don't know how to solve the system.

I just have those 7 equations, 3 of them being odes. Don't know how to proceed.

[Torsten]

If you knew M and theta, you could solve for md and mq, and you could solve the three odes.

But with M and theta unknown, your system cannot be solved (at least not numerically).

[Marcelo García Olavarría]

Ok! that's helpful. Maybe I have built my system incorrectly.

Thank you.

Answer 1

[Steven Lord]

I assume you've written this function in a file named difsyssolve.m and that your call to ode45 is not in that same file?

function dX=fun(t,X)
%constants
f=50;
ws=2*pi*f;
Ls=15e-3;
Rs=1;
Rcdc=500;
Cdc=500e-6;
Vs=220*sqrt(2);
Vsd=220*sqrt(3);
ipv=10
fp=0.96
%7 ecuaciones, 3 diferenciales.
%en el sistema, Vq=0, por lo que no se agrega al sistema de ec.
%X(1)=id X(2)=iq X(3)=Vdc
dX(1)=ws*X(2) + Vsd/Ls - Rs*X(1)/Ls - cos(theta)*md/Ls;
% Snip the rest

On this line of code you try to use something named theta. Where in your function do you define a variable by that name? If you haven't defined that variable, MATLAB will check for a function named theta that it can call with 0 input arguments and 1 output argument. If it can't, MATLAB will throw an error.

Looking at the rest of your code, I think you probably want something like this in your diffsyssolve.m file. [Though you would need to change x to X.]

theta=x(:,3);

[Marcelo García Olavarría]

Yes, I have another file that contains my function, called difsyssolve.m. Theta is another variable like md, mq or M, but I don´t know how to define it.

[Marcelo García Olavarría]

Also, I couldn´t find another example of a solution for a system with differential and non-differential equations besides the one wich I attached in my post.

Answer 2

[Joel Van Sickel]

you need to create and define the variable theta in your function before you use it.

[Marcelo García Olavarría]

Could you give me an example please? I really don't know how to create it or define it. I tried with syms, but I guess that's incorrect.