How to solve this

[KSSV]

Substitute second equation into first and use ode45.

[Minh Danl]

Can i use dsolve for this math

Answer 1

[Ameer Hamza]

Following shows how to find a numerical solution. You ODEs seems stiff, therefore, I used a stiff solver (ode23s).

tspan = [0 10];
IC = [0; 0; 0];

[t, y] = ode23s(@odeFun, tspan, IC);

plot(t, y);
legend({'$\theta$', '$\dot{\theta}$', '$i(t)$'}, ...
    'FontSize', 16, 'Interpreter', 'latex', 'Location', 'best')

function dXdt = odeFun(t, X)
    J = 1;
    Kt = 0.1;
    b = 0.5;
    L = 1e-2;
    R = 10;
    V = 1;
    Ke = 0.5;
    
    % X is 3x1 vector
    % X(1) is theta, X(2) is theta_dot, X(3) = I
    
    theta = X(1);
    theta_dot = X(2);
    i = X(3);
    
    dXdt = zeros(3,1);
    dXdt(1) = X(2);
    dXdt(2) = 1/J*(Kt*i-b*theta_dot);
    dXdt(3) = 1/L*(-R*i+V-Ke*theta_dot);
end

[Minh Danl]

Thanks for your support!

[Ameer Hamza]

I am glad to be of help!

[Minh Danl]

Error using feval

Undefined function 'odeFun' for input arguments of type 'double'.

Error in odearguments (line 87)

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

Error in ode23s (line 119)

[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

:((( i have a problem

[Ameer Hamza]

How are you running the code? Have you used the odeFun() I have given in my answer? Which MATLAB release are you using?

[Minh Danl]

i'm using matlab 2014a

[Ameer Hamza]

In that case create a new file named odeFun.m in current MATLAB folder and paste the following code in it

function dXdt = odeFun(t, X)
    J = 1;
    Kt = 0.1;
    b = 0.5;
    L = 1e-2;
    R = 10;
    V = 1;
    Ke = 0.5;
    
    % X is 3x1 vector
    % X(1) is theta, X(2) is theta_dot, X(3) = I
    
    theta = X(1);
    theta_dot = X(2);
    i = X(3);
    
    dXdt = zeros(3,1);
    dXdt(1) = X(2);
    dXdt(2) = 1/J*(Kt*i-b*theta_dot);
    dXdt(3) = 1/L*(-R*i+V-Ke*theta_dot);
end