time_id - SISO least square identification

Calling Sequence

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

Parameters

• 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  arl2  armax  frep2tf  

Author

Serge Steer INRIA