How to plot forcing function in matlab

function [xdot]=External_input(t,x)

x1=x(1);
x2=x(2);

m=2;
g=9.8;
k=0.15;
J=0.125;
x1dot=x2;
x2dot=((m*g*k*sin(x1))-ui(t))/J;
xdot=[x1dot;x2dot];
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clc
clear all;close all

t=linspace(0,10,1000);
x0=[0 0];
[t,x,u]=ode45(@External_input,t,x0);
% x1=x(1);
% x2=x(2);
subplot(211);plot(t,x(:,1),'linewidth',2);grid on ;title('Pos')
subplot(212);plot(t,x(:,2),'linewidth',2);grid on ;title('Vel')
figure(2)
plot(t,u)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%f
function u=ui(t)
% For impulse
eps=0.1;   
if t<eps
      u=1;
  else
     u=0;
end

end %%%%%%%%%%%%%%%%%%%%%%%%%%%%5 Question is %%%%%%%%%%%%%%%%%%%%%

i also want to plot u input ,,,but i am unable to plot it ...can some one guide me how can i plot the u input forcing function (which i have written in a separate function )

thanks

Answer 1

[Siraj]

Hi! @Bilal sadiq

I understand you want to plot the "u" input forcing function along with the state variables "x1" and "x2".

You need to evaluate the "ui" function separately for each time step to get the "u" values.

Here is how you can modify your code to plot the "u" input:

function [xdot]=External_input(t,x)
    x1 = x(1);
    x2 = x(2);
    m = 2;
    g = 9.8;
    k = 0.15;
    J = 0.125;
    x1dot = x2;
    x2dot = ((m * g * k * sin(x1)) - ui(t)) / J;
    xdot = [x1dot; x2dot];
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clc;
clear all;
close all;

t = linspace(0, 10, 1000);
x0 = [0 0];
[t, x] = ode45(@External_input, t, x0);

% Calculate the u values at each time step
u = arrayfun(@ui, t);

% Plot the results
subplot(3, 1, 1);
plot(t, x(:, 1), 'linewidth', 2);
grid on;

subplot(3, 1, 2);
plot(t, x(:, 2), 'linewidth', 2);
grid on;

subplot(3, 1, 3);
plot(t, u, 'linewidth', 2);
grid on;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function u = ui(t)
    % For impulse
    eps = 0.1;
    if t < eps
        u = 1;
    else
        u = 0;
    end
end

To plot "u", I have used the "arrayfun" function. This function applies a given function to each element of an array. To learn more about it, please refer to the following link:

https://www.mathworks.com/help/matlab/ref/arrayfun.html

Hope this helps.