Inverse and Series Connection - TransferFunctionModel

Question

I need to perform certain operations on individual transfer functions. As an example,

sys=StateSpaceModel[{sysA,sysB,sysC,sysD}];
Tfsys=TransferFunctionModel[sys,s];

Now I extract the required transfer functions, say $P_1$ and $P_2$

P1=SystemsModelExtract[Tfsys,{1},{1}];
P2=SystemsModelExtract[Tfsys,{1},{2}];

Now I want to perform an operation like $\Gamma=P_2 (P_1)^{-1}$. So I use

T=SystemsModelSeriesConnect[P2,Inverse[P1]];

This gives me an error saying the first argument cannot be interpreted as a polynomial matrix in SystemsModelSeriesConnect[#1,#2]

I have tried writing it as $P_2.Inverse[P_1]$ but I cannot make it accept the argument. Additionally, I would need to do a lot of algebraic operations with the TransferFunctionModel which not always can be done with commands like SystemsModelSeriesConnect,SystemsModelParallelConnect, etc.

As you would have guessed, I am not too adept with the syntax in Mathematica, so please bear with my questions.

Answer 1

I don't know, if this is what you want. But you might try this:

P1 = SystemsModelExtract[Tfsys, {1}, {1}]
P2 = SystemsModelExtract[Tfsys, {1}, {2}]

P3 = TransferFunctionModel[Inverse[P1[s]], s]

T = SystemsModelSeriesConnect[P2, P3]

How I did get this:

Documentation says:

Inverse[m] gives the inverse of a square matrix m.

And because

someTF = TransferFunctionModel[1/s, s]
someTF^-1

gives

where the first one is a transfer function model, but the second one is mixed. It's 1/someTFmodel.

You have to get the inner of your transfer function model, invert it, and put it back into a transfer function model. Helpful for this is documentation's TransferFunctionModel section "Properties & Relations":