Help with Inverse Laplace Transform Function

If I run the following code, I get an answer.

 n = 5; 
ku = 1; 
syms s; 
HDs = (ku^n)/(s*(ku+s)^n);
sim_data = ilaplace(HDs,s,0.1);

sim_data = 1 - (265241*exp(-1/10))/240000;

However, if n is a decimal, such as 5.1, the inverse laplace function doesn't work.

   n = 5.1; 
     ku = 1; 
     syms s 
     HDs = (ku^n)/(s*(ku+s)^n)
     sim_data = ilaplace(HDs,s,0.1)

sim_data = ilaplace(1/(s*(s + 1)^(51/10)), s, 1/10)

I need to be able to calculate the inverse laplace transform for decimal values of n. Please help.

Answer 1

[Aveek Podder]

Hi,

The ilaplace function computes the analytic closed inverse Laplace form of a transfer function. It seems that mathematically a closed inverse Laplace form for this function cannot be found out, so ilaplace function is returning the input transfer function.

There is a community submission at MathWorks File Exchange which numerically approximates an inverse Laplace transform for any function of "s". I will encourage you to have a look at the submission. However, in case you have any query regarding the submission you have to get in touch with the owner of the submission.

https://www.mathworks.com/matlabcentral/fileexchange/39035-numerical-inverse-laplace-transform/

Answer 2

[Walter Roberson]

For positive ku and n, and non-negative t, the inverse laplace apparently works out as

((-1-n)*igamma(1+n, ku*t)+ku^n*t^n*exp(-ku*t)*(1+n)+gamma(2+n))/gamma(2+n)