Question 9.16: Use MATLAB to find the inverse transform f(t) of the followi......
Use MATLAB to find the inverse transform f(t) of the following function:
F(s) = \frac{(s + 100)²}{(s + 50)²(s + 200)}
The following MATLAB code using the ilaplace function will find the desired waveform:
Script File
syms t s
F = (s+100)^2/(s+50)^2/(s+200);
f = ilaplace(F)
pretty (f )
MATLAB returns the following answer:
f =
(5∗exp(-50∗t))/9 + (4∗exp(-200∗t))/9 + (50∗t∗exp(-50∗t))/3
The pretty function helps MATLAB express the answer in a more recognizable form.
[latex]\frac{5 exp(-50 t)}{9} + \frac{4 exp(-200 t)}{9} + \frac{50 t exp(-50 t)}{3}[/latex]
Or, written in a more common way
f(t) = \frac{5}{9}e^{−50t} + \frac{4}{9}e^{−200t} + \frac{50t}{3}e^{−50t}
Web Appendix D contains additional examples using MATLAB to compute the Laplace transform of a waveform or to take the inverse of a transform to find the waveform.