Mathematical modelling in Matlab

Question

I am new to Matlab and I need to perform a simple task. I have an input function u(t)=2t-1 and an output function

y(t)=(-4/45)e^3t+ (1/5)e^(-2t)-1/3t-1/9

I have to find the corresponding behavior model, defined via a transfer function and then simulate the behavior model in Matlab/Simulink. I am not sure what approach I should use. What I have done so far is that I transferred the input and output function in the s-domain and then I calculated the transfer function. What does it mean to simulate the behavior model in Matlab? Can anyone please help me? I am a very beginner. Thank you very much!

Answer 1

If you've already done the Laplace transform and calculated the transfer function in s-domain, I think it means applying the transfer function to an arbitrary transient input and calculating the response.

The transfer function is based on the response due to a unit step function.

If you have an input that is something other than a unit step function (e.g. a sinusoid), you'd calculate the response as follows:

1. Transform the arbitrary input function to s-space.
2. Multiply it by the transfer function to the response in s-space.
3. Transform the response in s-space back to the time domain.

This is how Laplace transforms work.