System Identification Toolbox™

oe - Estimate parameters of output-error model returning idpoly object

Syntax

m = oe(data,orders)
m = oe(data,'nb',nb,'nf',nf,'nk',nk)
m = oe(data,orders,'Property1',Value1,'Property2',Value2,...)

Description

oe returns m as an idpoly object with the resulting parameter estimates, together with estimated covariances. The parameters of the output-error model structure

are estimated using a prediction error method.

data is an iddata object containing the output-input data. Both time- and frequency-domain data are supported. Moreover, data can be an frd or idfrd frequency-response data object.

The structure information can either be given explicitly as

(...,'nb',nb,'nf',nf,'nk',nk,...)

or in the argument orders, given as

orders = [nb nf nk]

The parameters nb and nf are the orders of the output-error model and nk is the delay. Specifically,

Alternatively, you can specify the vector as

orders = mi

where mi is an initial guess at the output-error model given in idpoly format. See What Are Black-Box Polynomial Models?.

For multiple-input systems, nb, nf, and nk are row vectors with as many entries as there are input channels. Entry number i then describes the orders and delays associated with the ith input.

Continuous-Time Models

If data is continuous-time (frequency-domain) data, oe estimates a continuous-time model with transfer function

The orders of the numerator and denominator are thus determined by nb and nf just as in the discrete-time case. However, the delay nk has no meaning and should be omitted. For multiple-input systems, nb and nf are row vectors with obvious interpretation.

Properties

The structure and the estimation algorithm are affected by any property name/property value pairs that are set in the input argument list. Useful properties are 'Focus', 'InitialState', 'InputDelay', 'SearchMethod', 'MaxIter', 'Tolerance', 'LimitError', 'FixedParameter', and 'Trace'.

See Algorithm Properties, idpoly, and idmodel for details of these properties and their possible values.

oe does not support multiple-output models. Use a state-space model for this case (see n4sid and pem).

Algorithm

oe uses essentially the same algorithm as armax, with modifications to the computation of prediction errors and gradients.

Examples

Suppose fast sampled data (Ts = 0.001) is available from a plant with a bandwidth of about 500 rad/s. The data is treated as continuous-time frequency-domain data, and a model of the type

is estimated.

z = iddata(y,u,0.001);
zf = fft(z);
zf.ts = 0;
m = oe(zf,[1 3],'foc',[0 500])

See Also

n4sid

operspec(idnlarx)