Function File: [sys, x0] = arx (dat, n, …)

Function File: [sys, x0] = arx (dat, n, opt, …)

Function File: [sys, x0] = arx (dat, opt, …)

Function File: [sys, x0] = arx (dat, 'na', na, 'nb', nb)

Estimate ARX model using QR factorization.

A(q) y(t) = B(q) u(t) + e(t)

Inputs

dat

iddata identification dataset containing the measurements, i.e. time-domain signals.

n

The desired order of the resulting model sys.

…

Optional pairs of keys and values. 'key1', value1, 'key2', value2.

opt

Optional struct with keys as field names. Struct opt can be created directly or by function options. opt.key1 = value1, opt.key2 = value2.

Outputs

sys

Discrete-time transfer function model. If the second output argument x0 is returned, sys becomes a state-space model.

x0

Initial state vector. If dat is a multi-experiment dataset, x0 becomes a cell vector containing an initial state vector for each experiment.

Option Keys and Values

’na’

Order of the polynomial A(q) and number of poles.

’nb’

Order of the polynomial B(q)+1 and number of zeros+1. nb <= na.

’nk’

Input-output delay specified as number of sampling instants. Scalar positive integer. This corresponds to a call to function nkshift, followed by padding the B polynomial with nk leading zeros.

Algorithm
Uses the formulae given in [1] on pages 318-319, ’Solving for the LS Estimate by QR Factorization’. For the initial conditions, SLICOT IB01CD is used by courtesy of NICONET e.V.

References
[1] Ljung, L. (1999) System Identification: Theory for the User: Second Edition. Prentice Hall, New Jersey, USA.

Package: control