[Octave-bug-tracker] [bug #62292] Generic close loop formula doesn't show same result than feedback function

[Pablo Scinardo]

URL:
  <https://savannah.gnu.org/bugs/?62292>

                 Summary: Generic close loop formula doesn't show same result
than feedback function
                 Project: GNU Octave
            Submitted by: pabloscinardo
            Submitted on: lun 11 abr 2022 14:49:41 UTC
                Category: Octave Forge Package
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Incorrect Result
                  Status: None
             Assigned to: None
         Originator Name: pabloscinardo
        Originator Email: 
             Open/Closed: Open
                 Release: 6.4.0
         Discussion Lock: Any
        Operating System: Microsoft Windows

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Details:

Generic loop back formula:

             G
Sys =  --------------
         1 + G * H

It shows wrong result.

But changing the loop back formula:
             1
Sys =  --------------
         1/G + H

The result is right, the same than feedback(G,H) funcion


Follow some example on Octave 6.4.0

>> pkg load control
>> num1 =[10];

>> den1 =[1 2 10];

>> G1=tf(num1,den1)


Transfer function 'G1' from input 'u1' to output ...

            10
 y1:  --------------
      s^2 + 2 s + 10

Continuous-time model.
>> num2 =[0 5];

>> den2 =[1 5];

>> G2=tf(num1,den1)


Transfer function 'G2' from input 'u1' to output ...

            10
 y1:  --------------
      s^2 + 2 s + 10

Continuous-time model.
>> feedback(G1,G2)


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

             10 s^2 + 20 s + 100
 y1:  ---------------------------------
      s^4 + 4 s^3 + 24 s^2 + 40 s + 200

Continuous-time model.
>> G1/(1+(G1*G2))


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

             10 s^4 + 40 s^3 + 240 s^2 + 400 s + 1000
 y1:  -------------------------------------------------------
      s^6 + 6 s^5 + 42 s^4 + 128 s^3 + 520 s^2 + 800 s + 2000

Continuous-time model.
>> 1/((1/G1)+G2)

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

             10 s^2 + 20 s + 100
 y1:  ---------------------------------
      s^4 + 4 s^3 + 24 s^2 + 40 s + 200

Continuous-time model.




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