Module 3: transfer function for multiple input and multiple output system (MIMO)

[@stephenfrey3793]

Thank you for making this video. It's good to have content that demonstrates modelling concepts with simple, accessible examples. Here is the GNU Octave version of the code (it requires a little setup ...installation of control and symbolics packages and configuration with Python and Sympy... ChatGPT is your friend):
m1 = 1; m2 = 1; k1 = 5; k2 = 5; b = 1;
syms s U;
A = [m1*s^2 + b*s + k1 + k2, -b*s - k2; -b*s - k2, m2*s^2 + b*s + k2];
B = [k1*U; 0];
x_s = A \ B;
% Substitute U with 1 to simplify the expressions
x_s = subs(x_s, U, 1);
% Extract numerator and denominator manually
[num1, den1] = numden(x_s(1));
[num2, den2] = numden(x_s(2));
% Convert symbolic expressions to numeric coefficients
num1_coeffs = double(coeffs(num1, s, 'All'));
den1_coeffs = double(coeffs(den1, s, 'All'));
num2_coeffs = double(coeffs(num2, s, 'All'));
den2_coeffs = double(coeffs(den2, s, 'All'));
% Create transfer functions
G1 = tf(num1_coeffs, den1_coeffs);
G2 = tf(num2_coeffs, den2_coeffs);
% Define the time vector and input signal
t = 0:0.1:30;
u = sin(t);
% Simulate the system response
x = lsim(G1, u, t);
y = lsim(G2, u, t);
% Plot the results
plot(t, x);
hold on;
plot(t, y);
hold off;

[@ibrahimalotaibi2399]

This is not a MIMO system. MIMO systems can not have single transfer functions and single input-output relationships. Instead, you may have G(s) from y1 to u1, y1 to u2, etc.

[@UAkronMechanicalEngineering]

You are right on this case.

[@alexandermontoyareyes6186]

Hi, maybe you could help me with an exercise on the transfer function of a circuit? 🙏