time_id

SISO least square identification

Calling Sequence

[H [,err]]=time_id(n,u,y)

Arguments

:n order of transfer : :u one of the following

:u1 a vector of inputs to the system : :”impuls” if y is an impulse response : :”step” if y is a step response. :

: :y vector of response. : :H rational function with degree n denominator and degree n-1

numerator if y(1)==0 or rational function with degree n denominator and numerator if y(1)<>0.

: :err ||y - impuls(H,npt)||^2, where impuls(H,npt) are the npt

first coefficients of impulse response of H

:

Description

Identification of discrete time response. If y is strictly proper ( y(1)=0) then time_id computes the least square solution of the linear equation: Den*y-Num*u=0 with the constraint coeff(Den,n):=1. if y(1)~=0 then the algorithm first computes the proper part solution and then add y(1) to the solution

Examples

z=`poly`_(0,'z');
h=(1-2*z)/(z^2-0.5*z+5)
rep=[0;`ldiv`_(h('num'),h('den'),20)]; //impulse response
H=time_id(2,'impuls',rep)
//  Same example with flts and u
u=`zeros`_(1,20);u(1)=1;
rep=`flts`_(u,`tf2ss`_(h));        //impulse response
H=time_id(2,u,rep)
//  step response
u=`ones`_(1,20);
rep=`flts`_(u,`tf2ss`_(h));     //step response.
H=time_id(2,'step',rep)
H=time_id(3,u,rep)    //with u as input and too high order required

See Also

• imrep2ss state-space realization of an impulse response
• arl2 SISO model realization by L2 transfer approximation
• armax armax identification
• frep2tf transfer function realization from frequency response