What Defines the Open Loop Transfer Function in Control Systems?

[dhruv.tara]

Homework Statement

Reading my text I see the definition of open loop transfer function as GH and closed loop as G/1+GH

I cannot understand the def. of open loop t/r func. Shouldn't it be just G?
(B/w with open loop I understand that there is no feedback...)

Homework Equations

The Attempt at a Solution

 

[MisterX]

Yes, I think typically G would be called the open loop transfer function.

 

[gneill]

The open loop transfer function may have gain G as well as some 'filtering' embodied in H.

A closed loop system can have 'filtering' elements in both the forward path and the feedback path. When such a system is simplified mathematically the entire thing can be rendered into the 'canonical' form G/(1 + GH), where H subsumes all of the disparate filtering elements that may be involved.

 

[dhruv.tara]

@gneill... I don't understand your explanation.

Also one more thing, we usually do all our plots with open loop configuration while we actually use the closed loop configuration... like in Bode plot or polar plots? Why don't we use the closed loop configurations to get those plots?

Also something aside from the topic, my book mentions that open loop systems are more stable than closed loop systems while I have been taught the other way round (by my college teachers)
My teacher told me that book could be talking only about positive feedback systems and not the negative ones.
However I suspect that it maybe because in the closed loop system the system's pole are more sensitive (or rather just became sensitive) to the open loop gain (not transfer function) K... and as far as I have understood these systems K is a not a very trustworthy quantity... Am I right? Or am I missing something?

 

[dhruv.tara]

And by the way thanks for your help guys :)

 

[gneill]

@gneill... I don't understand your explanation.

Also one more thing, we usually do all our plots with open loop configuration while we actually use the closed loop configuration... like in Bode plot or polar plots? Why don't we use the closed loop configurations to get those plots?

Also something aside from the topic, my book mentions that open loop systems are more stable than closed loop systems while I have been taught the other way round (by my college teachers)
My teacher told me that book could be talking only about positive feedback systems and not the negative ones.
However I suspect that it maybe because in the closed loop system the system's pole are more sensitive (or rather just became sensitive) to the open loop gain (not transfer function) K... and as far as I have understood these systems K is a not a very trustworthy quantity... Am I right? Or am I missing something?

The actual implementation of a control loop may have a filter in the forward path and another in the feedback path. For purposes of analysis the two can be combined mathematically to create a single overall filter block (see attached).

The open loop response is handy because it's a simple form that permits you to completely characterize the transfer function and its response to various inputs (impulse, step, etc.), and the closed loop response is easily obtained from it mathematically. Consider it an analysis "convention".

Regarding stability, while it is true that an open loop configuration is not subject to oscillation or "hunting" (where the output ends up continuously seeking to match its goal and
'missing' due to either measurement errors or overzealous adjustment stepsize), the accuracy of the output response is entirely dependent on having the gain set exactly right for the desired response to the input. This is difficult to achieve and can require frequent calibration to compensate for component value drift, operating conditions, etc.

A properly designed control loop with feedback is inherently more accurate and stable, and is not nearly so sensitive to component aging and operating conditions. If the design places the poles inadvisedly, well, it's just asking for trouble!

 

[dhruv.tara]

okk... :) thanks a lot.. I get most of it now... :D

One more thing that bugged me is that in control why do we take impulse, step and ramp as basic signals? I thought that we shall rather be interested in sin function response for a particular frequency and then a complete bode plot or something alike for the complete picture.

I read a little about Fourier analysis and how it can model almost any function in terms of periodic sin functions and hence sin gets ideal for electric(al) people to study about it.

I know that text mentions that the 3 inputs impulse, step and ramp can be considered as basic building block of most inputs, but I just need to be convinced a little more about that... (according to me shouldn't sin be rather a building block)

 

[gneill]

okk... :) thanks a lot.. I get most of it now... :D

One more thing that bugged me is that in control why do we take impulse, step and ramp as basic signals? I thought that we shall rather be interested in sin function response for a particular frequency and then a complete bode plot or something alike for the complete picture.

I read a little about Fourier analysis and how it can model almost any function in terms of periodic sin functions and hence sin gets ideal for electric(al) people to study about it.

I know that text mentions that the 3 inputs impulse, step and ramp can be considered as basic building block of most inputs, but I just need to be convinced a little more about that... (according to me shouldn't sin be rather a building block)

Quite often in systems where control loops are used the signals found will in fact end up being steps, impulses, ramps, or combinations of them. Switches closing or opening, position sensors triggering, steadily increasing or decreasing measures, sudden loads applied, and so on.

Sine and cosine functions are also "building blocks", and very handy when the signals involved are periodic and can be represented by sine and cosine series (Fourier analysis). But the impulse, step, and ramp often match real-life situations quite readily.

 

[dhruv.tara]

Okk... Thanks a lot... I get it... I thinks ;)