Your current 'slider_1eqn.m' regenerates the entire time vector 'tspan' and input signal arrays every time it’s called by 'ode45' for a single 't' value. You should rather precompute the input signals ('Y' and 'sdot') once in the script file, interpolate them inside the function for the current 't', and then plug those values into the ODE equations.
Here's the updated MATLAB code:
clear; clc;
% Parameters
n = 5;
Vo = 200e-9;
tr = 2e-3;
tf = 4e-6;
td = 1e-3;
tt = tr + tf + td;
tspan = 0:1e-4:n*tt;
% Input signal generation
Y = zeros(size(tspan));
sdot = zeros(size(tspan));
for i = 1:numel(tspan)
modt = mod(tspan(i), tt);
if modt < tr
Y(i) = Vo * modt / tr;
sdot(i) = Vo / tr;
elseif modt < tr + tf
Y(i) = Vo * (tr - modt) / tf + Vo;
sdot(i) = -Vo / tf;
else
Y(i) = 0;
sdot(i) = 0;
end
end
% Pack Y and sdot into a struct
input.Y = Y;
input.sdot = sdot;
input.tspan = tspan;
% ODE solver call with extra input
[t, x] = ode45(@(t, x) slider_1eqn(t, x, input), tspan, [0 0 0 0]);
% Plot results
figure;
plot(t, x(:,3), 'r', 'LineWidth', 2); hold on;
plot(t, x(:,1), 'b');
grid on;
legend('y_2', 'y_1');
xlabel('Time (s)');
ylabel('Displacement');
function f = slider_1eqn(t, x, input)
% System parameters
k = 20;
c = 70e-3;
m2 = 1.2e-3;
m1 = 37e-3;
g = 9.81;
F = m2 * g;
% Interpolate Y and sdot for current t
Y_now = interp1(input.tspan, input.Y, t);
sdot_now = interp1(input.tspan, input.sdot, t);
% System of equations
f = zeros(4,1);
f(1) = x(2);
f(2) = (-c/m1)*(x(2) - sdot_now) + (-k/m1)*(x(1) - Y_now) - (F/m1);
f(3) = x(4);
f(4) = (c/m2)*(x(4) - sdot_now) + (k/m2)*(x(3) - Y_now);
end
You may refer to the below MathWorks documentation links to know more about the same:
- Parameterizing Functions: https://www.mathworks.com/help/matlab/math/parameterizing-functions.html
- ode45: https://www.mathworks.com/help/matlab/ref/ode45.html
I hope this helps!
