System Identification Toolbox

Polynomial Black-Box Models: The idpoly Model

The general input-output form (3-19)

(3-43)

is defined by the five polynomials A(q), B(q), C(q), D(q), and F(q). These are represented in the standard MATLAB format for polynomials. Polynomial coefficients are stored as row vectors ordered by descending powers. For example, the polynomial

is represented as

• A = [1 a1 a2 ...  an]
  

Delays in the system are indicated by leading zeros in the polynomial. For example, the ARX model

(3-44)

is represented by the polynomials

• A = [1 -1.5 0.7]
  B = [0 0 2.5 0.9]
  

The idpoly representation of (3-43) is now created by the command

• m = idpoly(A,B,C,D,F,lam,T)
  

lam is here the variance of the white noise source and T is the sampling interval. Trailing arguments can be omitted for default values. The system (3-44) can for example be represented by

• m = idpoly([1 -1.5 0.7],[0 0 2.5 0.9])
  

In the multi-input case (3-41) B and F are matrices, whose row number k corresponds to the k-th input. The command idpoly can also be used to define time-continuous systems. See Function Reference for details.

When m is defined, the polynomials and their orders can be easily retrieved and changed, as in

• m.a % for the A-polynomial
  roots(m.a)
  m.a(3)=0.95
  

Defining Model Structures

Multivariable ARX Models: The idarx Model