x(t+1) = A x(t) + B u(t) + K e(t)
y(t) = C x(t) + D u(t) + e(t)
The SITB supports two kinds of parametrizations of state-space models: Black box, free parametrizations and parametrizations tailor made to the application.
To estimate a state space model, select Parametric Models in the pop-up menu Estimate in the ident window. In the dialog that opens, choose State space as the model structure, and enter the desired order. The delays from the different inputs u can be entered within square brackets. The default values of the delays are all 1. This means that the D-matrix is fixed to zero. The estimation of the initial state x(0) is goverend by the pop-up menu Initial State in the Parametric Model window.
The Order editor handles options to fix K to zero in the black box case, as well as entering the delays from the input(s)
The order editor also gives the possibility to choose two variables that may
have an influence on the quality of the N4SID estimated. This estimate is also used
to initialize the PEM estimate. The N4sid Options are
By entering a vector (e.g. 1:10), all orders will be computed
using a preliminary method, and you will have to choose order(s) based on
information in a special graph. You can also use the button
Order selection to fill out the Model order field with a default
model order range.
There are two basic methods for the estimation: PEM and N4SID
There are a number of structure options that can be reached in the Order Editor:
By fixing the matrix K to zero, an Output Error method is obtained.
The search for a minimum is controlled by a number of options. These are
accessed from the Options button in the
Iteration control... dialog.
The quality of the resulting estimates may significantly depend on the
N4sid Options N4Weight and N4Horizon
See the commands PEM and N4SID in the manual for more information.
To use them in conjunction with ident, define the appropriate structure in the MATLAB
command line and enter its variable name in the Orders: edit box of the Parametric
Models dialog. If desired, select the appropriate iteration options for PEM by
pressing the Iteration control... button.
(file iduiss.htm)
Note that in the black box case, there is a special feature to select the
model order by entering a vector (like 1:10) for the model order. You can
push the Order selection button to fill out the model order field in
this case.
You can enter any variable name in the N4Horizon field, that will be evaluated in
the workspace to give the desired option.
Black Box State-space Models
Estimating Black Box State-space Models
Tailor-made State-space Models