Re: Equation Display or Problem

[Lukas Reichlin]

On 15.06.2015, at 08:18, Thomas D. Dean <address@hidden> wrote:

> 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?
> 
> Tom Dean

There's a thinko in the code above:

    a_eqn = a0/(1+s/w1)/(1+s/w2)

is equivalent (after normalization by minreal)

    a_eqn_norm = minreal (a_eqn)

to

    b_zpk = zpk ([], [-w1, -w2], a0*w1*w2)

and

    a_zpk = zpk([],[w1,w2],a0)

is equivalent to

    b_eqn = a0/(s-w1)/(s-w2)

Lukas



Transfer function 'a_eqn' from input 'u1' to output ...

                1e+05           
 y1:  --------------------------
      1e-10 s^2 + 0.000101 s + 1

Continuous-time model.

Transfer function 'a_eqn_norm' from input 'u1' to output ...

               1e+15          
 y1:  ------------------------
      s^2 + 1.01e+06 s + 1e+10

Continuous-time model.

Transfer function 'b_zpk' from input 'u1' to output ...

               1e+15          
 y1:  ------------------------
      s^2 + 1.01e+06 s + 1e+10

Continuous-time model.

Transfer function 'a_zpk' from input 'u1' to output ...

               1e+05          
 y1:  ------------------------
      s^2 - 1.01e+06 s + 1e+10

Continuous-time model.

Transfer function 'b_eqn' from input 'u1' to output ...

               1e+05          
 y1:  ------------------------
      s^2 - 1.01e+06 s + 1e+10

Continuous-time model.