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matlabodedifferential-equations
Teo Protoulis
Teo Protoulis

Reputation: 203

Change value of variable at each time step - Matlab ODE function

I have the following system of differential equations to simulate in a .m file:

function dx = odefun(t,x)
    % display(x(1));
    % y = 5; 
    dx = [x(2); - y - 3*x(2) - 2*x(1)];
end

I am simulating the system running another .m file with the code below:

[t,x] = ode45(@odefun, [0 10], [0;0]);
% display(x(:,1));
plot(t,x(:,1));

My problem is that I want the value of y parameter, which happens to be the output of my system, to change in each time step while the ode(...) function is executing. I tried by sending another argument like this: 

[t,x] = ode45(@odefun, [0 10], [0;0], [some_elements]);
function dx = odefun(t,x,y)

but I get the error: Not enough input arguments. Truth is that I want y parameter to take one value at each time step from a vector with a hundred elements. Any help would be greatly appreciated.

Upvotes: 1

Views: 2714

Answers (2)

Teo Protoulis
Teo Protoulis

Reputation: 203

For those interested I post here the way I finally managed to get what I want. I have a 1x100 vector representing the input to a system and I want to take back a 1x100 vector consisting of the values of the output of my system. I wanted one value as output for each value of my input. 

global f    
t = 0.1:0.1:10.0;
f = @create_signal;

[t,x] = ode45(@odefun, t, [0;0]);

and the odefun function is like this:

function dx = odefun(t,x)
    global f
    m = 15;
    b = 0.2;
    k = 2;
    u = f(t);

    dx = [x(2); u/m - (b/m)*x(2) - (k/m)*x(1)];

end

and lastly the function that creates the values of the input:

function u = create_signal(t)

    u = 5*sin(t) + 10.5;

end

I applied the create function handle feature of MATLAB. Here is the link of mathworks help: https://www.mathworks.com/help/matlab/matlab_prog/creating-a-function-handle.html

Upvotes: 0

PilouPili
PilouPili

Reputation: 2699

Not tested on Matlab but just to help and mainly wrapped up from https://fr.mathworks.com/help/matlab/ref/ode45.html#bu00_4l_sep_shared-options ODE with Time-Dependent Terms

function dx = odefun(t,x,y,yt)
    f = interp1(yt,y,t);
    dx = [x(2); - f - 3*x(2) - 2*x(1)];
end

%define your array (or even function) y(yt)
yt = 0.0:0.1:10.0;
y = array; % array being your array of input values. (should contain the corresponding value for 0.0:0.1:10.0

[t,x] = ode45(@(t,x) odefun(t,x,y,yt), [0.0 10.0], [0;0]);

or try the following if you want specific time steps included in your result :

[t,x] = ode45(@(t,x) odefun(t,x,y,yt), yt, [0;0]);

You can also do, to be sure to have your solution corresponding to 0.0:0.1:10.0,

x100 = interp1(t,x,yt);

Upvotes: 0

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