Interactive animation while solving ODE

I am using ode45 to solve a system representing the inverted pendulum and its control. I am using the solution to plot the system in the form of an animation using the position x and the angle of the pendulum ϕ.

I would like to add new functionalities to this simulation, such as an external disturbance. I have been able to successfully code this functionality by changing the code, but it is static, i.e. I need to define the disturbance before calling ode45. Is there a way to solve / integrate this system in real time? I mean, I'd like to keep solving the system continuously, without defining a time range previously. This way, the user might disturb the system whenever he wants and the system will respond accordingly.

Answer 1

[Jan]

You can use the event function to trigger an external event:

Opt   = odeset('Events', @yourEvent);
t0    = 0;
tEnd  = 1000;
y0    = [0,0];
Param = 17;
while t0 < tEnd
    yourFcn = @(t,y) yourFcn(t, y, Param);
    [time, pos] = ode45(yourFcn, [t0, tEnd], y0, Opt);
    t0 = time(end);
    y0 = pos(end, :);
    Param = ???  % Adjust the parameter like you want.
end

And your event function:

function [value, isterminal, direction] = yourEvent(t, y)
persistent P
if nargin == 0
    P = 1;
    return;
end

drawnow;
if isempty(P)
    value      = 0;
    isterminal = 0;
    direction  = 0;
else
    value      = -1;
    isterminal = 1;
    direction  = 0;
    P          = [];
end
end

Now ODE45 calls yourEvent with 2 inputs every time. But you can call this function from a timer callback also without input arguments. Then the persistent variable P is used as a flag, which stops the integration in the next time step. This allows the main loop while t0<tEnd to modify the parameters used inside the function to be integrated, or maybe the current velocities or positions.

The drawnow is important, because without it, Matlab does not evaluate the other callbacks.

[Ankith Anil Das]

Hi!

Would it be possibe to show me an example with such an eventFunction implementation. Also, what do you mean by "timer callback also without input arguments" and how do you set it up with events function ?

Thank you so much

[Jan]

The posted code contains such an example already.