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# time_id

SISO least square identification

### Syntax

[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

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