Fixing parameters when estimation of transfer function

I am working on a closed loop control of a robotic arm. I have input data and output data and would like to find the transfer function. It is a MISO system and i am using tfest to find the transfer function. However, when I estimate the transfer function, I would like to put conditions on the denominator such that the denominators of all three transfer functions are the same. How do i fix two different parameters to be the same in the transfer function while estimation? this is my code.

num={[1],[2 3],[3 5 2 3]};
den={[1 2 3 0],[1 2 3 0],[1 2 3 0]};
sys_init=idtf(num,den);
sys=tfest(soliddrive,sys_init);

I couldnt specify that sys_init.structure(1,1).Denominator=sys_init.structure(1,2).Denominator while estimation. How can this be done?

Answer 1

[Sebastian Castro]

There is a setpar function that lets you set whether or not the variables are free.

For example, to have only the first 3 parameters in your model be modifiable:

>> sys_init_mod = setpar(sys_init,'free',[zeros(16,1);ones(3,1)])

For more info, check out https://www.mathworks.com/help/ident/ref/idparametricsetpar.html

- Sebastian

[Narayanan V Baradwaj]

Hi. This is to fix the variable to a fixed number. Is it possible to make the denominator of 3 transfer functions of a MISO system same? Because if I set it as fixed, it doesn't change the value

[Sebastian Castro]

Oh... my bad, I don't think you can do that with tfest.

Only way I could think about that is to use the Optimization Toolbox functionality such as fmincon and write the constraint function in yourself...

- Sebastian