frep2tf - transfer function realization from frequency response

Calling Sequence

[h [,err]]=frep2tf(frq,repf,dg [,dom,tols,weight])

Parameters

• frq : vector of frequencies in Hz.
• repf : vector of frequency response
• dg : degree of linear system
• dom : time domain ('c' or 'd' or dt)
• tols : a vector of size 3 giving the relative and absolute tolerance and the maximum number of iterations (default values are rtol=1.e-2; atol=1.e-4, N=10).
• weight : vector of weights on frequencies
• h : SISO transfer function
• err : error (for example if dom='c' sum(abs(h(2i*pi*frq) - rep)^2)/size(frq,*))

Description

Frequency response to transfer function conversion. The order of h is a priori given in dg which must be provided. The following linear system is solved in the least square sense.

 weight(k)*(n( phi_k) - d(phi_k)*rep_k)=0, k=1,..,n
   

where phi_k= 2*%i*%pi*frq when dom='c' and phi_k=exp(2*%i*%pi*dom*frq if not. If the weight vector is not given a default penalization is used (when dom='c').

A stable and minimum phase system can be obtained by using function factors.

Examples

s=poly(0,'s');
h=syslin('c',(s-1)/(s^3+5*s+20))
frq=0:0.05:3;repf=repfreq(h,frq);
clean(frep2tf(frq,repf,3))

Sys=ssrand(1,1,10); 
frq=logspace(-3,2,200);
[frq,rep]=repfreq(Sys,frq);  //Frequency response of Sys
[Sys2,err]=frep2tf(frq,rep,10);Sys2=clean(Sys2)//Sys2 obtained from freq. resp of Sys
[frq,rep2]=repfreq(Sys2,frq); //Frequency response of Sys2
xbasc();bode(frq,[rep;rep2])   //Responses of Sys and Sys2
[sort(trzeros(Sys)),sort(roots(Sys2('num')))]  //zeros
[sort(spec(Sys('A'))),sort(roots(Sys2('den')))] //poles

dom=1/1000; // Sampling time 
z=poly(0,'z');
h=syslin(dom,(z^2+0.5)/(z^3+0.1*z^2-0.5*z+0.08))
frq=(0:0.01:0.5)/dom;repf=repfreq(h,frq);
[Sys2,err]=frep2tf(frq,repf,3,dom);
[frq,rep2]=repfreq(Sys2,frq); //Frequency response of Sys2
xbasc();plot2d1("onn",frq',abs([repf;rep2])');

 

See Also

imrep2ss  arl2  time_id  armax  frfit