Sinusoidal steady state response to sinusoidal input

So I have a transfer function of a feedback system,

>> yd

yd =

   s^3 + 202 s^2 + 401 s + 200
  ------------------------------
  s^3 + 202 s^2 + 20401 s + 1e06

Of which I'd like to look at the sinusoidal steady state response to the disturbance d(t) = sin(130t).

How do you do this in matlab? I'm well aware of how to get a step or impulse response, but not a sinusoidal response.

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Star Strider]

Use the lsim function:

% num = s^3 + 202 s^2 + 401 s + 200
% den = s^3 + 202 s^2 + 20401 s + 1e06

n = [1  202  401  200];
d = [1  202  20401  1E+6];

sys = tf(n,d);                                      % Define LTI System

t = linspace(0, 100, 1000);                         % Time Vector
u = sin(130*t);                                     % Forcing Function
y = lsim(sys, u, t);                                % Calculate System Response

figure(1)
plot(t, y)
grid

[thiago rech]

Thanks for your comment, it helped me figure out how to test some systems for a school project. Can you also do that for systems in state space?

[Star Strider]

My pleasure!

Yes.

The lsim function will work for any valid system object.

[Max Agarwal]

here 130 is omega??

[Star Strider]

@Max Agarwal —

It is the frequency in radians/time_unit.

Answer 2

[Abdulhakim]

If you know the Laplace transform of the input you can exploit the fact that the impulse function in the s-domain is equal to 1. Here is how:

For a system with input and output

Since

impulse(G*R) is actually the output in the time domain .

The laplace transform for

num = [1 202 401 200];
den = [1 202 20401 10^6];
G = tf(num,den)
SIN = tf(130,[1 0 130^2]);
C = G*SIN
impulse(C)