MATLAB: How to fix matrices while using ssest

parametersssest

Hey everyone,

I try to estimate the A-matrix out of a data set constisting of the states and the human input. The other matrices B C D are given, so I want to fix them while using the command ssest.

Code:

A = NaN*ones(n); B = [1; zeros(n-1,1)]; C = eye(n); D = zeros(n,1); K = zeros(n);
dt= 0.01;
n=3;
q0= zeros(n,2);
sys_initial = idss(A,B,C,D,K,q0(:,1),dt);
sys_initial.Structure.B.Free = false;
sys_initial.Structure.C.Free = false;
sys_initial.Structure.D.Free = false;
sys_initial.Structure.K.Free = false;
sys_ssest     = ssest(data,sys_initial);

The problem is, that the matrices B and C in sys_ssest change their values but this should not happen. Even bounding with

sys_initial.Structure.B.Minimum = B;
sys_initial.Structure.C.Minimum = C;
sys_initial.Structure.B.Maximum = B;
sys_initial.Structure.C.Maximum = C;

did not help at all. How can I solve this problem?

Thank you in advance!

Best Answer

Problem solved by removing the factor NaN in matrix A

Related Solutions

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

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

MATLAB: How do you extract the state space model from ssest()

sys1 is a discrete-time state space model.

If you want to compare the results with sys2, replace your code with:

%% Extract the A, B, C, and D matricies from sys1 to to put the state space model in a ss class
sys2 = ss(sys1.A,sys1.B,sys1.C,sys1.D,sys1.Ts);

You should obtain similar plots for both sys1 and sys2.

Best Answer

Related Solutions

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

MATLAB: How do you extract the state space model from ssest()

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