idmodred (System Identification Toolbox)

Reduce the order of a model (requires the Control System Toolbox).

Syntax

MRED = idmodred(M)
MRED = idmodred(M,ORDER,'DisturbanceModel','None')

Description

This function reduces the order of any model M given as an idmodel object. The resulting reduced order model MRED is an idss model.

The function requires several routines in the Control System Toolbox.

ORDER: The desired order (dimension of the state-space representation). If ORDER = [], which is the default, a plot will show how the diagonal elements of the observability and controllability Gramians of a balanced realization decay with the order of the representation. You will then be prompted to select an order based on this plot. The idea is that such a small element will have a negligible influence on the input-output behavior of the model. It is thus suggested that an order is chosen, such that only large elements in these matrices are retained.

'DisturbanceModel': If the property DisturbanceModel is set to 'None', then an Output- Error model MRED is produced, that is, one with the Kalman gain equal to zero (see Equation (Equation 3-23) in the "Tutorial" chapter). Otherwise (default), also the disturbance model is reduced.

The function will recognize whether M is a continuous- or discrete-time model and perform the reduction accordingly. The resulting model MRED will be of the same kind in this respect as M.

Algorithm

The functions balreal and modred from the Control System Toolbox are used. The plot, in case ORDER = [], shows the vector g as returned from balreal.

Examples

Build a high order multivariable ARX model, reduce its order to 3 and compare the frequency responses of the original and reduced models.

M = arx(data,[4*ones(3,3),4*ones(3,2),ones(3,2)]);
MRED = idmodred(M,3);
bode(M,MRED)

Use the reduced order model as initial condition for a third order state-space model.

```
M2= pem(data,MRED);
```

idmodel idpoly