MATLAB: Solving A System of Equations Using ODE45

ode45

So I was having trouble solving differential equations in ODE45. The system is as follows:

I was not sure how to proceed since the first equation contains an integral of the V_dot(t). Any help would be greatly appreciated.

Best Answer

You have two coupled ODEs for V_p and x. If you want to apply numerical methods (ODE15S, e.g.) for the solution, I don't see a problem.

Maybe starting at t=0 is not a good idea since powers of t appear in the denominator when you solve the first equation for xdot.

Best wishes

Torsten.

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MATLAB: ODE solver for coupled equations

See if this helps:

...
iLoad   = vC/Rload;
dxdt = zeros(7,1);
dxdt(1,:) = (x*(Vs - vC) + y*(-vj1 - dxdt(2) - vC))/L;      % diL/dt  
...

MATLAB: Can I use the ode45 solver for the state update in a unscented Kalman filter

You cannot use the ode45 function directly in the above example code as it will output integrated function values for all the time points instead of a single time-step value as required here. However, you can implement single-step updates of higher order methods such as Runge-Kutta ( https://en.wikipedia.org/wiki/Runge%2525E2%252580%252593Kutta_methods ) instead of the Euler method for better accuracy.

ode45 function itself uses an explicit Runge-Kutta formula, the Dormand-Prince pair (refer to the documentation page https://www.mathworks.com/help/matlab/ref/ode45.html#bu0200e-1)

You can find more information on other ODE integration methods related to this here https://blogs.mathworks.com/cleve/2014/05/26/ordinary-differential-equation-solvers-ode23-and-ode45/

Best Answer

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MATLAB: ODE solver for coupled equations

MATLAB: Can I use the ode45 solver for the state update in a unscented Kalman filter

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