# control system -- open loop transfer function and open loop gain

by lazyaditya
Tags: control, function, gain, loop, transfer
 P: 110 Is there any difference between open loop transfer function and open loop gain ?
 P: 2,525 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?
 PF Patron HW Helper P: 3,798 A transfer function gives gain and phase shift at any given frequency. Gain is the first part of that.
P: 110

## control system -- open loop transfer function and open loop gain

Does this mean that transfer function can provide with negative value due to phase shift !
HW Helper
P: 4,192
 Quote by lazyaditya 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).
HW Helper
P: 4,192
 Quote by lazyaditya 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.
PF Patron
HW Helper
P: 3,798
 Quote by lazyaditya 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).
P: 296
 Quote by NascentOxygen 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.
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P: 4,192
Quote by aralbrec
 Quote by NascentOxygen 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).

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