Re: Equation Display or Problem

[Tatsuro MATSUOKA]

----- 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)


>> 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