Scilab Website | Contribute with GitLab | Mailing list archives | ATOMS toolboxes
Scilab Online Help
5.5.1 - English

Change language to:
Français - 日本語 - Português - Русский

Please note that the recommended version of Scilab is 2024.0.0. This page might be outdated.
See the recommended documentation of this function

Scilab Help >> CACSD (Computer Aided Control Systems Design) > armax1

armax1

armax identification

Calling Sequence

[arc,resid]=armax1(r,s,q,y,u [,b0f])

Arguments

y

output signal

u

input signal

r,s,q

auto regression orders with r >=0, s >=-1.

b0f

optional parameter. Its default value is 0 and it means that the coefficient b0 must be identified. if bof=1 the b0 is supposed to be zero and is not identified

arc

is tlist with type "ar" and fields a, b, d, ny, nu, sig

a

is the vector [1,a1,...,a_r]

b

is the vector [b0,......,b_s]

d

is the vector [1,d1,....,d_q]

sig

resid=[ sig*echap(1),....,];

Description

armax1 is used to identify the coefficients of a 1-dimensional ARX process:

A(z^-1)y= B(z^-1)u + D(z^-1)sig*e(t)
e(t) is a 1-dimensional white noise with variance 1.
A(z)= 1+a1*z+...+a_r*z^r; ( r=0 => A(z)=1)
B(z)= b0+b1*z+...+b_s z^s ( s=-1 => B(z)=0)
D(z)= 1+d1*z+...+d_q*z^q  ( q=0 => D(z)=1)

for the method, see Eykhoff in trends and progress in system identification) page 96. with

z(t)=[y(t-1),..,y(t-r),u(t),...,
      u(t-s),e(t-1),...,e(t-q)]

and

coef= [-a1,..,-ar,b0,...,b_s,d1,...,d_q]'
y(t)= coef'* z(t) + sig*e(t).

a sequential version of the AR estimation where e(t-i) is replaced by an estimated value is used (RLLS). With q=0 this method is exactly a sequential version of armax

Examples

a = [1, -2.851, 2.717, -0.865];
b = [0, 1, 1, 1];
d = [1, 0.7, 0.2];
ar = armac(a, b, d, 1, 1, 1);
disp(_("Simulation of an ARMAX process:"));
disp(ar);

n = 300;
u = -prbs_a(n, 1, int([2.5,5,10,17.5,20,22,27,35]*100/12));
zd = narsimul(ar, u);

// using now armax1 : colored noise identification
// you can test the same example with
[arc1, resid] = armax1(3,3,2,zd(1:n),u,1);
disp(arc1);

Important notice

In Scilab versions up to 4.1.2 the returned value in arc.sig is the square of sig square. To be conform with the help, the display of arma models and the armax function, starting from Scilab-5.0 version the returned arc.sig is sig.

Report an issue
<< armax CACSD (Computer Aided Control Systems Design) arsimul >>

Copyright (c) 2022-2023 (Dassault Systèmes)
Copyright (c) 2017-2022 (ESI Group)
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Thu Oct 02 13:46:49 CEST 2014