Categories &
Functions List
Function Reference: arx
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’.
Uses SLICOT IB01CD
for initial conditions,
Copyright (c) 1996-2025, SLICOT, available under the BSD 3-Clause
(License and Disclaimer).
References
- Ljung, L. (1999) System Identification: Theory for the User: Second Edition. Prentice Hall, New Jersey, USA.
Source Code: arx
T = 1;
N = 30;
G = tf ([1 2 ], [1 -1 1 -0.5], T);
u = 2*rand(N,1) - 1;
e = 0.01*randn (N,1);
y = lsim (G, u) + e;
dat = iddata (y, u, T);
G_I = arx (dat, 3); # filter form (poly in z^(-1), inputs u and e)
G_I = G_I(1,1);
close (clf());
lsim (G, G_I, u);
title ("Simulation of original G and indentified system G_I")
