time_id

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