MATLAB: How to use arbitrary relationships of nominator/denominator while trying to estimating a transfer function? (idtf and tfest)

System Identification Toolbox

How to use arbitrary relationships of nominator/denominator while trying to estimating a transfer function? (idtf)

I would like to provide relationships like the following:

init_sys.Structure.Numerator(1) = init_sys.Structure.Denominator(1)
init_sys.Structure.Numerator(2) = init_sys.Structure.Denominator(2)* init_sys.Structure.Denominator(3)

Best Answer

As you can see in the documentation of 'tfest' only the following is possible by directly declaring this as an input to the function:

https://mathworks.com/help/ident/ref/tfest.html

init_sys

Linear system that configures the initial parameterization of sys.

You obtain init_sys by either performing an estimation using measured data or by direct construction.

If init_sys is an idtf model, tfest uses the parameters and constraints defined in init_sys as the initial guess for estimating sys. Use the Structure property of init_sys to configure initial guesses and constraints for the numerator, denominator, and transport lag. For example:

To specify an initial guess for the numerator of init_sys, set init_sys.Structure.Numerator.Value to the initial guess.
To specify constraints for the numerator of init_sys:
Set init_sys.Structure.Numerator.Minimum to the minimum numerator coefficient values
Set init_sys.Structure.Numerator.Maximum to the maximum numerator coefficient values
Set init_sys.Structure.Numerator.Free to indicate which numerator coefficients are free for estimation

If init_sys is not an idtf model, the software first converts init_sys to a transfer function. tfest uses the parameters of the resulting model as the initial guess for estimation.

If opt is not specified, and init_sys was obtained by estimation, then the estimation options from init_sys.Report.OptionsUsed are used.

So are there any other ways to implement this?

This is not possible directly. We only allow bounds on parameters, not arbitrary relationships. For that, you will need to use grey box models. Basically you need to write a function that converts your desired free parameters into state-space matrices.

See these examples:

https://www.mathworks.com/help/ident/ug/estimating-coefficients-of-odes-to-fit-given-solution.html

https://www.mathworks.com/help/ident/ug/estimate-complex-conjugate-poles-and-zeros-using-grey-box-model.html

Related Solutions

MATLAB: How to force tfest to estimate the process with “only real poles”

TFEST cannot guarantee real poles.

If you can work with <=3 poles and <=1 zero, try PROCEST. This is a process model estimator.
Otherwise, consider a grey-box formulation where your parameters are the real poles. See for example:

https://www.mathworks.com/help/ident/ug/estimate-complex-conjugate-poles-and-zeros-using-grey-box-model.html

The downside to using grey-box approach is that you will need to initialize the parameter values manually; the software will not do that for you. You can run TFEST and use the poles of the resulting model to may be take a guess at the initial real pole values for grey-box estimation.

MATLAB: How to set a limit to the coefficient of the estimated transfer function in the System Identification app

The GUI for transfer function estimation does not support parameter constraints, but it's possible in command-line, without using grey-box modeling.

More details are at

https://www.mathworks.com/help/ident/ug/imposing-constraints-on-model-parameter-values.html

For example, given the data

u = randn(200,1);
y = randn(200,1);
ts = 0.1;
z = iddata(y,u,ts);
% Generate an initial model, perhaps by unconstrained initialization, prior knowledge, or random system. 
Gtf = tfest(z,2,0); % unconstrained initialization
Gtf.Structure.Numerator.Minimum = 0; % Constrain the numerator coefficient to be positive 
Gtf.Structure.Numerator.Value = 1e-4; % Give a + numerator guess
Gtf = tfest(z,Gtf); % Refine the initial model estimate

Best Answer

Related Solutions

MATLAB: How to force tfest to estimate the process with “only real poles”

MATLAB: How to set a limit to the coefficient of the estimated transfer function in the System Identification app

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