How can I use the coupled system of matrices (ODE45) using a frequency span?

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Keith Grey 2020-6-11

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关闭： MATLAB Answer Bot 2021-8-20

I haven't found much information in the Documentation addressing a case like this, so I'm unsure of where to even begin.

The following system of equations is put into matrix notation (presumably correctly done).

I'm trying to use ODE45 to solve and plot this system on a frequency span of 50 to 200 Hz.

% Matrices shown above (Corresponding x1 values 1st column & x2 in the 2nd.)
f = 50:1:200; % Frequency (Hz)
A = [23.3 0; 0 240];
B = [-5926 4566; -11133 4566];
C = [-4 0.39; 0.39 -1.34];
D = [0; -1(2 * pi * f)];

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Answer 1

Ameer Hamza 2020-6-12

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There is no 'f' term in this system of ODE. Following shows how to solve this using ode45

t = linspace(0, 10, 1000); % solve the equation for t in [0, 10]
ic = [0; 0; 0; 0]; % initial condition
[t, y] = ode45(@(t, x) odeFun(t, x), t, ic);
subplot(2,2,1)
plot(t, y(:,1))
title('x1')
subplot(2,2,2)
plot(t, y(:,2))
title('x2')
subplot(2,2,3)
plot(t, y(:,3))
title('x1dot')
subplot(2,2,4)
plot(t, y(:,4))
title('x2dot')
function dxdt = odeFun(t, x)
    % x(1)=>x1, x(2)=>x2, x(3)=>x1', x(4)=>x2'
    dxdt = zeros(4, 1);
    dxdt(1) = x(3);
    dxdt(2) = x(4);
    dxdt(3) = 1/23.3*(5926*x(3) - 4566*x(4) + 4*x(1) - 0.39*x(2));
    dxdt(3) = 1/240*(-4566*x(3) + 11133*x(4) - 0.39*x(1) + 1.34*x(2) - 1);
end