Output Error Method for parameter estimation

Dear Matlab community,

I have the following state space model :

The model is defined with : 5 states (X),1 input (U), and 2 outputs (Y)

Hence the matrices are of the following dimensions:

-

This makes a total of 49 parameters.

I have the data that come from testing and are given in the attached .mat file as an iddata object.

Now, i would like to perform system identification to fit the model to the measured output, using the output error method. And finally get the values of the parameters.

I have tried to use the oe() function included in the system identification toolbox, but it doesn't seem to do what i want. Is there anybody who can help me ? Do you know other methods to get the parameters of the fitted model ? Has anyone good experience with system identification ?

Thank you for your time !

Answer 1

[Star Strider]

I would use the ssest function:

D = load('dat.mat');
dat = D.dat;

sys = ssest(dat, 5);

A = sys.A
B = sys.B
C = sys.C
D = sys.D

those being:

A =
  -9.8108e-03  -1.7520e-02   2.2364e-02   9.7365e-03   3.0023e-01
  -8.5323e-02  -1.5350e-01  -1.7269e+00   7.8601e-02   5.1336e-01
  -4.6620e-02   1.4686e+00  -9.1005e+00   1.7038e+00   1.8151e+00
   1.7951e-02  -3.4105e-01  -2.9225e+00  -5.5039e+00   7.5581e+01
   2.7352e-02   4.1784e-01   4.0000e+00  -4.2111e+01  -6.9225e+01

B =
   1.1602e-05
   7.3110e-06
  -9.9022e-04
   5.3061e-03
   1.5000e-02

C =
  -1.7279e+03   1.3914e+03  -1.3506e+01  -7.0445e-02  -1.4056e-01
   2.8143e+04   9.0494e+02  -1.6417e+00  -1.9433e+01  -4.8266e+00

D =
     0
     0

with:

figure
compare(dat, sys)

producing:

.

[M.Many]

Thanks for the reply, I more or less got the same result with systemIdentification GUI and i was looking for the name of the function and then there was your answer ! I can see that the estimated model doesn't fit that well to the data. So I will try to get a validation dataset for a better fit. Thanks again !!

[M.Many]

Do you know if there is a way to get the bias parameters with the ssest function ?

[Star Strider]

As always, my pleasure!

I’m not certain what ‘bias parameters’ are in this context, so I can’t specifically address that. There are a number of options and name-value pair arguments to get additional information from the model and the estimation procedure, all described in the documentation.