Home / Control Systems / Inverse Laplace Transform of a Transfer Function Using Matlab

Inverse Laplace Transform of a Transfer Function Using Matlab

Want create site? Find Free WordPress Themes and plugins.

In this topic, we will find out how to calculate inverse Laplace of a transfer function using Matlab.

Let’s find out Inverse Laplace of the following function

\[X(s)\frac{10{{s}^{2}}+20s+40}{{{s}^{3}}+12{{s}^{2}}+47s+60}=\frac{Numerator}{Denumerator}\]

Let’s write a little code in Matlab now:

%% % Calculate Inverse Laplace of a function using Matlab
%Let's write numerator and denumerator from the given transfer function
num = [10 20 40]; % Numerator Coefficients
den = [1 12 47 60]; %Denumerator Coefficients
 
% "residue" command is used to do Partial Fraction Operation &;
% returns "residue", and "Poles" and direct term of the partial fraction
% expansion
% Write "help residue" in Maltab GUI to get better insight
[Residue,Poles,Direct_Term] = residue(num,den)

Results:

Here, we get the following results:

Residue =

   95.0000

 -120.0000

   35.0000

Poles =

   -5.0000

   -4.0000

   -3.0000

Direct_Term =

     []

Using above mentioned results, let’s write the partial fraction expansion of the function X(s)

\[X(s)=\frac{95}{s+5}-\frac{120}{s+4}+\frac{35}{s+3}\]

From partial fraction expression, we can easily write the inverse Laplace transform as:

$x(t)=95{{e}^{-5t}}-120{{e}^{-4t}}+35{{e}^{-3t}}$

In order to convert partial fraction expansion back to the original function, we can use the following Matlab command:

\[[b,a]\text{ }=\text{ }residue(r,p,k)\]

Here, we have b (coefficients for numerator) and a (coefficients for denumerator) to write the function like X(s).

Did you find apk for android? You can find new Free Android Games and apps.

About Ahmad Faizan

Mr. Ahmed Faizan Sheikh, M.Sc. (USA), Research Fellow (USA), a member of IEEE & CIGRE, is a Fulbright Alumnus and earned his Master’s Degree in Electrical and Power Engineering from Kansas State University, USA.

Leave a Reply