Using `feedback` with feedback gains argument

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In the feedback.m documentation (both help and online documentation), I'm only seeing examples where two state space / transfer function models must be provided.
For example -- in documentation, I see feedback(sys1, sys2, ...). However, I seem to be able to instead provide feedback(sys1, k) where k is a feedback gain (vector for SISO systems).
I guess my question is - is feedback(sys, k) doing what I think it's doing?
  1 Comment
Mathieu NOE
Mathieu NOE on 12 Nov 2020
probably yes
the two examples below gives the same closed loop tf
G = tf([2 5 1],[1 2 3],'inputname',"torque",'outputname',"velocity");
C = tf([1],[1]); % unitary gain
% Use feedback to create the negative feedback loop using G and C.
sys = feedback(G,C,-1)
% equivalent to :
sys = feedback(G,1) % ! assumed neg feedback here

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Answers (1)

Ameer Hamza
Ameer Hamza on 12 Nov 2020
A scalar 'k' is also a static gain transfer function. So you are correct; in your case, 'k' is the same as negative feedback gain.

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