How do I compute the transfer matrices of the coprime factorisation?

I would like to simply calculate the 2 transfer matrices of the left coprime factorisation of a state-space system K. However, when I evaluate ncfmr to calculate this factorisation as follows (K has 2 inputs, 1 output and 3 states):

K = ss(Ak,Bk,Ck,Dk);
[GRED, redinfo] = ncfmr(K, 3);

the resulting factorisation redinfo.GL is returned as a state-space system with 3 inputs, 1 output and 3 states. What is the relationship between this system and the 2 transfer matrices of the factorisation I am looking for?

Passing an equivalent transfer function to ncfmr yields the same result. Note that I specified order 3 as that is the number of states in the original system, is this correct usage to calculate the factorisation of the original system?

Thanks!

Answer 1

[Maneet Kaur Bagga]

Hi,

As per my understanding, your originial system "K" has 2 inputs, 1 output and 3 states and the "redinfo.GL" has 3 inputs which you expected to be 2.

Referring to the MathWorks documentation of "ncfmr" function, it suggests using "reducespec" function instead for computing normalized coprime factorization. Please refer to the following code snippet to compute the factorization :

redinfo = reducespec(K, 'ncf');
GL = redinfo.GL;
ML = redinfo.ML;

For more understanding on how to use the "reducespec" function please refer to the following MathWorks documentation :

https://www.mathworks.com/help/control/ref/dynamicsystem.reducespec.html

Hope this helps!