Finding plant model in SISO system. Need help

I have a problem with system identification and can't find a solution in Matlab for it.

I have a SISO system in a closed loop

with T(s)=Y(s)/U(s)=(K*G(s))/(1+K*G(s))

I collected my data (input-output), managed to found a model and the transfer function of this model (T(s) or Y(s)/U(s)). But I have to go further and have to found the plant model (G(s)). I can calculate G(s) by solving the eq. above to (G(s)=T(s)/((1-T(s))*K) (K is known). But the problem is that T(s) is pretty complicated (8th order TF) so to do it manually, it's almost impossible.

Therefore my questions: 1) Is there a command that I can use to find easily the plant model in my system?

2) Can I solve the equation with the solve function? I tried but didn't get a proper solution.

Greetings Mudi

[Ryan G]

What is the transfer function in question? How did you determine the transfer function T(s)? You should be able to define the order using the MATLAB System Identification tools.

[Mudi]

T(s) =

 3.951e12 s^2 - 4.877e13 s + 5.585e13

------------------------------------------------------------------------

 s^8 - 8.521e06 s^7 - 3.247e08 s^6 - 1.284e10 s^5 - 2.398e11 s^4 - 3.09e12 s^3 - 1.299e13 s^2 - 2.842e13 s + 3.765e13

I didn't use the identification toolbox as I already had a script written to identify the systems. But the problem is not identification of the system, it's extracting the parts.

Answer 1

[Shashank Prasanna]

If you already have the transfer functions for K and G then you can use the CONNECT and FEEDBACK function to get T without having to do it manually.

http://www.mathworks.com/help/control/ref/connect.html

http://www.mathworks.com/help/control/ref/feedback.html

HTH