How to simulate the forced response of a transfer function

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Ali Almakhmari
Ali Almakhmari 2023-9-15
回答： Sam Chak 2023-9-16
I have a transfer function G(s) = (1-s)/(s^2 + 2s+ 1) that I want to simulate while being under a forced input of u(t) = 2*cos(3t), but I am not sure how. I hope someone can help.

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采纳的回答

Star Strider
Star Strider 2023-9-15
Ran in:
Use the lsim function —
s = tf('s');
G = (1-s)/(s^2 + 2*s + 1)
G = -s + 1 ------------- s^2 + 2 s + 1 Continuous-time transfer function.
t = linspace(0, 1E+1, 1E+3);
u = @(t) 2*cos(3*t);
Gu = lsim(G,u(t),t);
figure
plot(t, u(t), ':k', 'DisplayName','u(t)')
hold on
plot(t, Gu, '-r', 'DisplayName','G(u(t))')
hold off
grid
legend('Location','best')
.

更多回答（1 个）

Sam Chak
Sam Chak 2023-9-16
Ran in:
Hi @Ali Almakhmari
The 'lsim()' command is great when the Control System Toolbox is available. Here is an alternative approach to generate the time response G(s) subject to the forced input u(t) without using the Control System Toolbox. However, it requires the Symbolic Math Toolbox. Both toolboxes are bundled in the MATLAB and Simulink Student Suite.
You can also find examples at the following links:
https://www.mathworks.com/help/symbolic/sym.laplace.html
https://www.mathworks.com/help/symbolic/sym.ilaplace.html
syms F(s) u(t);
% Forced input function
u(t) = 2*cos(3*t)
u(t) = 
U(s) = laplace(u)
U(s) = 
% Plant transfer function
G(s) = (1 - s)/(s^2 + 2*s + 1)
G(s) = 
% Convolution of two functions
F(s) = U*G
F(s) = 
% Applying the inverse Laplace transform
f(t) = ilaplace(F, s, t)
f(t) = 
% Plots
fplot(u, [0 10], ':k'), hold on, grid on
fplot(f, [0 10], 'LineWidth', 1.5), hold off
% Labels
xlabel('Time (seconds)')
ylabel('Amplitude')
legend('u(t)', 'f(t)')
title({'Time response of $G(s)$ due to input $u(t) = 2 \cos(3 t)$'}, 'Interpreter', 'LaTeX', 'FontSize', 12)

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