Control system - open loop transfer function and open loop gain

Click For Summary

Discussion Overview

The discussion revolves around the concepts of open loop transfer function and open loop gain within control systems. Participants explore the definitions, relationships, and implications of these terms, particularly in the context of frequency response and stability.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants question whether there is a difference between open loop transfer function and open loop gain, suggesting that some authors use the terms interchangeably.
  • One participant proposes a specific transfer function, y = Acos(xt + θ), and inquires about the implications for gain, particularly if the open loop gain varies with frequency.
  • It is noted that a transfer function provides both gain and phase shift at any given frequency, with gain being a primary component.
  • Participants discuss the possibility of obtaining negative values from the transfer function due to phase shifts, with one asserting that this is indeed possible.
  • Another participant provides an example using H(s) = 1/s² to illustrate how a phase shift of 180 degrees can result in a negative gain.
  • Clarifications are made regarding the definitions of loop gain, indicating that it typically refers to the product of the forward gain and feedback factor in a feedback loop.

Areas of Agreement / Disagreement

Participants express differing views on whether open loop transfer function and open loop gain are distinct concepts or interchangeable. The discussion remains unresolved, with multiple competing interpretations presented.

Contextual Notes

There are limitations regarding the definitions and assumptions surrounding the terms used, as well as the implications of phase shifts on stability and gain. The discussion does not resolve these complexities.

lazyaditya
Messages
176
Reaction score
7
control system -- open loop transfer function and open loop gain

Is there any difference between open loop transfer function and open loop gain ?
 
Physics news on Phys.org


What if the transfer function was

y = Acos(xt + θ)

where θ was a phase shift.

What would the gain be?

What if the open loop gain varies with frequency?
 


A transfer function gives gain and phase shift at any given frequency. Gain is the first part of that.
 


Does this mean that transfer function can provide with negative value due to phase shift !
 


lazyaditya said:
Is there any difference between open loop transfer function and open loop gain ?
I think you will find some authors make no distinction, both terms equating to G(s)H(s).
 


lazyaditya said:
Does this mean that transfer function can provide with negative value due to phase shift !
There has to be a negative sign somewhere in the loop over the frequency band of interest*, either in G(s) or else H(s), otherwise your loop gain will be +ve and when the loop is closed the system will be unstable.
 


lazyaditya said:
Does this mean that transfer function can provide with negative value due to phase shift !

Most assuredly yes.

Consider H(s) = 1/s2. Letting s = jω you get a gain of -1/ω2, in other words a phase shift of 180 degrees.

(This is two integrators in cascade FYI).
 


NascentOxygen said:
I think you will find some authors make no distinction, both terms equating to G(s)H(s).

That would be the loop gain since H(s) is normally in the feedback path :)

Open loop transfer function and open loop gain are almost used interchangeably. It's assumed to be the 'A' part (or 'G' part) of your standard feedback loop diagram.

Loop gain is the gain after making one lap around the feedback loop from the output of the summer to the input of the summer and is Aβ (or GH) of your standard feedback loop diagram.
 


aralbrec said:
NascentOxygen said:
I think you will find some authors make no distinction, both terms equating to G(s)H(s)
That would be the loop gain since H(s) is normally in the feedback path
Correct. ... equating both to G(s).
 

Similar threads

Root Locus of Negative Feedback System
  • · Replies 3 ·
Replies
3
Views
3K
Which data set should I trust more?
  • · Replies 1 ·
Replies
1
Views
2K
Oven controller block diagram, transfer function and temperature calcs
  • · Replies 24 ·
Replies
24
Views
5K
Engineering Analyzing the output impedance and open loop gain of a IC-741 Op-Amp
  • · Replies 2 ·
Replies
2
Views
3K
Engineering What is wrong in this 2nd order transfer function?
  • · Replies 2 ·
Replies
2
Views
2K
Engineering Review of Concepts: Air Recycling Systems (closed-loop/open-loop)
  • · Replies 2 ·
Replies
2
Views
2K
Control System Gain design problem
  • · Replies 4 ·
Replies
4
Views
2K
INA Frequency Response: Gain, Circuit & Open Loop Explained
  • · Replies 10 ·
Replies
10
Views
2K
Control theory: process given, PID settings
  • · Replies 4 ·
Replies
4
Views
3K
Open loop transfer function help
  • · Replies 4 ·
Replies
4
Views
2K