Re: Equation Display or Problem

[Thomas D. Dean]

On 06/15/15 02:59, Tatsuro MATSUOKA wrote:
> ----- Original Message -----
>
> > From: Thomas D. Dean
> > To: help-octave
> > Cc:
> > Date: 2015/6/15, Mon 15:18
> > Subject: Equation Display or Problem
> >
> > Back to my previous problem.  I expected to bet the same system from either the
> > zpk or equation representation.  But, they are different
> >
> > octave:1869> clear all
> > octave:1870> a0 = 1e5;
> > octave:1871> w1 = 1e4;
> > octave:1872> w2 = 1e6;
> > octave:1873> s = tf('s');
> > octave:1874> a_eqn = a0/(1+s/w1)/(1+s/w2)
> >
> > Transfer function 'a_eqn' from input 'u1' to output ...
> >                  1e+05
> > y1:  --------------------------
> >        1e-10 s^2 + 0.000101 s + 1
> > Continuous-time model.
> >
> > octave:1875> a_zpk = zpk([],[w1,w2],a0)
> >
> > Transfer function 'a_zpk' from input 'u1' to output ...
> >                 1e+05
> > y1:  ------------------------
> >        s^2 - 1.01e+06 s + 1e+10
> > Continuous-time model.
> >
> > octave:1876> a_eqn(w1)
> > ans =  4.9495e+04 - 5.0495e+04i
> > octave:1877> a_zpk(w1)
> > ans =  4.9495e-06 + 5.0495e-06i
> >
> > Is this correct?  What am I doing wrong?
>
>
> I am not familiar with control theory but I did experiments.
>
> Why did you define "a_eqn" as "a0/(1+s/w1)/(1+s/w2)"?
> instead of help
> a_eqn = a0/(s+w1)/(s+w2)

According to Mathworks and others, the open loop gain of an op amp with 
poles w1 and w2 is

s = tf('s');
a_eqn = a0/( (1+s/w1) * (1+s/w2) )

> > > a_eqn = a0/(s+w1)/(s+w2)
>
> Transfer function 'a_eqn' from input 'u1' to output ...
>
>                  1e+005
>   y1:  --------------------------
>        s^2 + 1.01e+006 s + 1e+010
>
> > >   a_eqn(w1)
> ans = 4.9495e-006 - 5.0495e-006i
>
> > > a_zpk = zpk([],[w1,w2],a0)
>
> Transfer function 'a_zpk' from input 'u1' to output ...
>
>                  1e+005
>   y1:  --------------------------
>        s^2 - 1.01e+006 s + 1e+010
>
> > >   a_zpk(w1)
> ans = 4.9495e-006 + 5.0495e-006i
>
> The sign of coefficient of first order in s is different.
> Thus a_eqn(w1) and a_zpk(w1) are complex conjugate
>
> > > help zpk
>   Function File: SYS = zpk (SYS)
>
>   <snip>
>   Create transfer function model from zero-pole-gain data.
>
>   "zero-pole-gain"
> Are not this correct?
> a_zpk = zpk([],[-w1,-w2],a0)
>
>
>
> Tatsuro