time_id — SISO least square identification
[H [,err]]=time_id(n,u,y)
order of transfer
one of the following
a vector of inputs to the system
if y is an impulse response
if y is a step response.
vector of response.
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.
||y - impuls(H,npt)||^2, where impuls(H,npt) are the npt first coefficients of impulse response of H
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
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