How to find the inverse transfer function of a system?

I have a system of mass (m), spring (k) and damper (c). The equation of my system in Laplace domain is: ms^2x(s)+csx(s)+kx(s)=F(s) So the transfer function of the system is: x(s)/F(s)=1/(ms^2+cs+k), where x(s)-->output and F(s)-->input. How can find the inverse transfer function of my system in which x(s) will be the input and F(s) the output and build it in simulink? (Namely, i want to find F(s)/x(s) )

Answer 1

[Robert]

Well you have a lot going on.

Do you understand the fundamentals of going back and forth between Transfer function and differential equation by hand first? In order to fully understand how to do this in matlab you need to first understand how to do it by hand.

At the end of your post you say

"(Namely, i want to find F(s)/x(s) )"

Im assuming you mean you want F(t)/X(t) because with your equation you already have F(S)/X(s)

In general F(S) is your output and X(s) is your input in 90% of books. I do know that in some books the classical mass spring dampener system is backwards. For some reason Mech people are always upside down from EE :)

Anways!!

This procedure is pretty simple Please don't forget to accept the answer so i get the credit Thanks!

clear all
close all
clc

syms k c m s

My_trasnfer_function = 1/(m*s^2+c*s+k)
pretty(My_trasnfer_function)

%Get the inverse of the trasnfer function in terms of C M and K

My_generic_trasnfer_function = ilaplace(My_trasnfer_function)

%Perhaps you would like to find the inverse
%of some potential specific
%values of K and M and C

K = [.5 2 4 6]
M = [.1 .2 .5 .9]
C = [1 2 3 4]

for p = 1:4

      My_transfer_function = subs(My_trasnfer_function,k,K(p)) % sub in a value for K from the K row Vector
      My_transfer_function = subs(My_transfer_function,m,M(p)) % sub in a value for M from the M row Vector
      My_transfer_function = subs(My_transfer_function,c,C(p)) % sub in a value for C from the C row Vector

      pretty(My_transfer_function) %Print the transfer function so you can see it nicley

      My_diff_eq =  ilaplace(My_transfer_function); %take the inverse of it
      pretty(My_diff_eq) % print it again so you can see it nicley

end