Trevithj

January 2009

Welcome to Wikipedia. Although everyone is welcome to make constructive contributions to Wikipedia, at least one of your recent edits, such as the one you made to Feedback, did not appear to be constructive and has been automatically reverted by ClueBot ... <snip> ClueBot (talk) 20:32, 19 January 2009 (UTC)

Problem with Firefox during editing: characters were getting reversed. Browser wars? I was editing in Notepad and pasting into the browser to check the changes. Somehow, the lower part of the article got deleted. My bad! Trevithj (talk) 20:29, 27 January 2009 (UTC)

Regarding Electronic oscillator edit summary comment

I'd like to apologise for the comment "That was a controversial edit added by a disruptive editor who has been blocked several times." I wasn't referring to you but to Circuit dreamer, who was a principle player in a long edit conflict about introducing the term "negative resistance" into the harmonic oscillator section. I screwed up and confused the term "negative resistance" with "positive/negative feedback", the subject of your edit. In addition, although I meant "disruptive editor" to apply to CD, it looks like I was talking about you. I'd change it if I could, but I don't think there's any way of editing an edit summary. Anyway, I'm sorry for inadvertently dragging your name through the mud.    ;) --Chetvorno^TALK 23:33, 29 February 2012 (UTC)

Have responded on your talk page. Don't think edit summaries are changeable - but hardly the end of the world. No worries! Trevithj (talk) 23:51, 29 February 2012 (UTC)

Feedback Definitions and Possible Scope

There appear to be three fairly distinct usages for "feedback" (FB) in general - and for "positive feedback" (+FB) by extension.

1. loop: (A influences B, B influences A) Ashby describes the situation where two parts influence each other - where "part" can be anything from a wire to a multinational corporation. This seems the most generic definition of FB, and +FB is when the influences are self-reinforcing.
2. signal: (A (the process) influences B (the controller)) Several authors (e.g., Ramaprasad) talk about feedback as information used as basis of control. In behavioural contexts, this is often what is meant when people say "give me feedback". +FB is when A and B are moving in the same direction.
3. control: (B (the controller) influences A (the process)) This is often where the technical distinction of positive/negative FB occurs - if the controller increases the process, it is positive, else negative. Again, with +FB A and B are moving in the same direction.

Three hypothetical cases are described below: one (hopefully) uncontroversial, and the others introducing some areas of ambiguity.

• Bull market: (A=stock-price, B=investors) Price increases attract investors, which increases prices. By all three definitions above, this is +FB:

1 The entire loop is self-reinforcing -- the more prices increase, the more they increase. This example is ignoring the effect of profit-taking.

2 The signal path is positive -- the increased price results in increased investments;

3 The control action is positive -- more investments ('buy' actions) cause increased stock-price.

And the same would hold true for a Bear market: reduced prices, reduced investors etc.

• Flood-gates: (A=water-level, B=out-flow) An increasing water level in a reservoir leads to the increasing of outflow through floodgates, so as to maintain the level below maximum. Here some confusion arises in the different definitions:

1 By the loop definition, this is -FB -- increased level leads to decreased level.

2 By the signal definition, this is +FB -- the level and the outflow both increase/decrease together.

3 By the control definition, this is -FB -- increase in outflow causes decrease in level.

Some care needs to be taken with how the 'signal' is defined. Should it include the effect of the outflow in this case?

• Reverse-floodgates: As above, but assume that the signal definition now supports -FB -- increasing level will now result in decreased outflow.

1 Now the loop is an example of +FB, since rising levels lead to rising levels, and v.v.

2 As stated, the feedback connection is now negative -- increased levels cause decreased outflow.

3 The control link is unchanged. The outflow's effect on the water level remains negative.

To summarise, it is possible for one or both influences to be negative/inverting. This may lead to confusion as to how the FB should be defined. Consideration of the entire loop's effect doesn't seem to have this difficulty, but covers a lot of very different cases where signal/control descriptions are important and varied.

Nice collection of feedback stuff

You have a nice collection of feedback stuff on your user page – even Chuck Wilts, who was my rock-climbing instructor at Caltech. Dicklyon (talk) 04:29, 18 June 2014 (UTC)

Thank you. Its a small world, isn't it?Trevithj (talk) 04:40, 18 June 2014 (UTC)

Indeed; you have a copy of his book? I've got one if you need anything from it. See about him. Dicklyon (talk) 06:19, 19 June 2014 (UTC)

I don't have a copy. Does he say anything about general feedback, or history of the terms? I recall he was very detailed on process control, but I was looking for generic/historical references at the time (still am!) The rock-climbing stories very interesting - a friend's son does a lot of climbing in Yosemite, so I hear it is quite the place. Trevithj (talk) 09:08, 20 June 2014 (UTC)

Yes, thanks for asking. I just scanned and OCR'd page 1, which says:

Systems which utilize feedback for control purposes have become essential elements in modern technology. They range all the way from simple toys to our most complex automatic factories and production equipment. Feedback control is the guidance, more popularly known as "intelligence," that makes modern automation possible, and as such is in a large measure responsible for the ever-increasing productivity and rising standard of living of man. However, the science of feedback control stems not just from the importance of control systems but from the fact that the presence of feedback introduces problems that are peculiar to this class of systems. Examination of typical feedback control systems shows that they constitute a very broad group, with members that show remarkably different form and purpose. However, in spite of their great dissimilarities, they are related by one overriding feature, the use of feedback.

1-1 Definition of feedback.

Although the term feedback appears to have a very simple meaning, a completely general definition is surprisingly difficult. The existence of feedback, particularly when unwanted or of incidental occurrence, is often obscure and difficult to demonstrate. Nevertheless, when feedback is deliberately used for control, its existence and nature are easily ascertained. In a simple feedback system a specific physical quantity is being controlled, and control is brought about by making an actual comparison of this quantity with its desired value and utilizing the difference to reduce the error observed. Such a system is self-correcting in the sense that any deviations from the desired performance are used to produce corrective action. Whether this action is sufficient to eliminate the error is a complicated question that will be the subject matter of a later chapter, but in any case the corrective action must be dependent upon the existence of a difference which results from a comparison process. A system of the type described above can be represented by the diagram shown in Fig. 1-1. In later chapters a systematic symbolism and nomenclature will be introduced for such diagrams, but for present

Note that he sees feedback as much broader than his own topic of feedback in control. Dicklyon (talk) 20:30, 26 June 2014 (UTC)

I also have The Origins of Feedback Control by Otto Mayr; haven't opened it for a while, but it covers the very early history in depth. Both of these are also available for moderate price at abebooks.com (or probably amazon.com). Dicklyon (talk) 20:40, 26 June 2014 (UTC)

I checked The Origins of Feedback Control. Its definition section is even more narrowly focused on error-based control. Unlike Wilts, no nod toward the wider uses of the concept. Dicklyon (talk) 17:22, 27 June 2014 (UTC)

Thanks for the quotes. I recall that Wilts was writing specifically about control, and so his terminology is feedback = negative feedback (quite common practice in that area, I've found.) I was looking for a more general definition - but he is a good reference for error-correction.

BTW, I'm wondering if Brews had a point about "different applications of negative feedback". Is there a case for a disambiguation page for these?

1. negative feedback (error-correction), involving a specific reference point
2. negative feedback (balancing) without any explicit reference point
3. negative feedback (criticism) commonly used to refer to the unpleasantness of the feedback

There is a case for 3, IMO. Not sure about 2 though - I think it is splitting hairs. Trevithj (talk) 09:34, 28 June 2014 (UTC)

I agree that 3 might be worth a separate article. The others are OK in the current article. Dicklyon (talk) 16:31, 5 July 2014 (UTC)

negative feedback without explicit reference point

Trevithj: Items 1 & 3 are clear enough. Item 2, balancing, is the rest of the universe I take it. It is perhaps the nature of any 'miscellaneous' category that it is not so clear, beyond what it doesn't include. My reading of this page and your user page quotes about feedback seem to suggest this category is empty. I'd say it includes the negative feedback amplifier, because this application does not use deviation from an established set-point. So it's not in category 1, and it seems obvious it is not in category 3. One might try to argue that the feedback loop designed to produce a gain of 1/β is a built-in set-point, but that still leaves out the other aspect of error-controlled regulation: the use of a 'gap' to govern the feedback. The departure of the gain from 1/β simply cannot happen in this circuit; the 'gap' is inherently (inevitably) zero (or as close to zero as you wish, by making the open-loop gain large enough). So regulation of a hypothetical 'gap' ("error" correction) is not an issue. Brews ohare (talk) 13:10, 14 August 2014 (UTC)

Hi Brews. I have finally had time to study your points, and I have to say I feel there is a reversal of causality at work here. To say regulation of a gap is not an issue because there is no gap is a bit like saying that a fire-prevention program isn't required because no houses have burned down. Likewise, to speak of "the simple algebra that governs this circuit" is not right - it is the circuit that governs the algebra. And finally, absence of proof is not proof of absence. A non-mention in an article (or many articles) is an invalid basis for a conclusion. It is also very easy to dispute:

"In the conventional negative feedback amplifier, it is difficult to easily correct the phase error and the amplitude error."[1]

"A feedback control system ... includes the necessary elements: the signal path, a means of sampling the output, processing of the feedback signal, and a means of reintroducing the error signal at the input."[2]

"Essential constituents of negative feedback amplifier ... input signal and feedback signal are mixed or processed to get difference or error signal to be applied to the internal or the basic amplifier."[3]

"For the feedback amplifier, an analog subtraction is achieved at the input and, to use feedback control-system notation, the output of the subtractor is an 'error signal'..."[4]

The last point I think is the telling one. I believe we are talking about different notations here, not different concepts. Trevithj (talk) 08:09, 15 August 2014 (UTC)

The term "negative feedback amplifier" that we are discussing here is the particular circuit of Black, and is not some complex circuit like Figure 9 in 1, called by these authors a "conventional negative feedback amplifier" involving an amazingly intricate input and feedback mechanism. The reference to "error signal" by Rao is used as a synonym for the difference between the input signal and the feedback signal, and is not an "error" signal in the sense of the departure of the monitored value of some essential variable from its set point. The circuit used in Breed is aimed at a feedback control system and Figure 1 includes a sampling comparator at its output. The negative feedback amplifier is an amplifier not a control device.

The "telling example", the source by Pederson, puts the term 'error signal' in quotes to suggest that the terminology is used in a special sense, and this difference is not always interpretable as an 'error'. Here this reference is treating the case where β≡1, which is the special case of a unity gain buffer where the feedback signal is the 'output', not a fraction of the output. In this application, the goal is to produce an exact copy of the input, so the difference between the input signal and the output signal is indeed an error. That is not the case when β is not 1. So I'd agree that the unity gain buffer can be seen as an example of error-controlled regulation, but that does not apply for the general case. Also, this example is unrelated to control of the gain itself, which is forced by the circuit to be 1/β≡1 regardless of feedback.

These sources do not address the basic issue that feedback does not govern gain control. That is "One might try to argue that the feedback loop designed to produce a gain of 1/β is a built-in set-point, but that still leaves out the other aspect of error-controlled regulation: the use of a 'gap' to govern the feedback. The departure of the gain from 1/β simply cannot happen in this circuit; the 'gap' is inherently (inevitably) zero (or as close to zero as you wish, by making the open-loop gain large enough). This fact of circuit topology has nothing to do with feedback or regulation. So regulation of a hypothetical 'gap' ("error" correction) is not an issue."

Can you address this point?

Thanks for your interest Trevith. Brews ohare (talk) 14:50, 15 August 2014 (UTC)

It is a very interesting discussion, and several points have come clear for me during it. Regards the use of a gap to govern feedback, here is my reasoning:

1. If we accept that feedback opposes/reduces change, then we have to accept that "change" is a basic part of the definition. Otherwise we will have to come up with another definition that doesn't have a synonym for "change" in it.

OK Brews ohare (talk) 12:28, 16 August 2014 (UTC)

2. If something changes, its new value and its old value are different. If we don't know the old value, we can't say for sure that there has been a change. So any change is by definition the difference between the old value and the new value.

Yes. The 'old' value is the output signal resulting from the input signal at time 't', say, the 'new' value that at a later time 't+Δt', and the change is the difference. Brews ohare (talk) 12:28, 16 August 2014 (UTC)

3. If the feedback opposes this change, it is because the old value is somehow "more correct" than the new value. If that wasn't the case, the feedback wouldn't oppose the change.

No, opposition is not based on an incorrect value, but too great a change in value. The feedback always opposes this change because the change in output must reflect a gain of 1/β, a smaller change than would occur were there no feedback. Brews ohare (talk) 12:31, 16 August 2014 (UTC)

4 If the feedback doesn't oppose this change, it is because the new value is somehow "more correct" than the old value. If that wasn't the case, the feedback would oppose the change. In all cases, if there is change, then there is a difference between two values. The feedback treats one of those values as "better" than the other, and responds accordingly. If that were not the case, the feedback wouldn't know which direction to adjust a value, or even if it should be adjusted. A gap is a synonym for a difference. Trevithj (talk) 09:10, 16 August 2014 (UTC)

No, the feedback opposes the change because the change is too large, not because the signal at one time is 'better' than that at another time. Brews ohare (talk) 12:28, 16 August 2014 (UTC)

If that were true, then a series of small changes would get ignored by the feedback. The gain could drift to a very different value if during each time period, the difference between old and new values was too small for the feedback to react. I don't think that is right.Trevithj (talk) 03:08, 17 August 2014 (UTC)

Trevith: The notion of the absolute size or smallness of the changes is not a factor, nor is drift during a particular time interval, Δt. The gain of a voltage amplifier is a ratio: "voltage gain is equal to the difference in output voltage divided by the corresponding difference in input voltage."1 In a time interval Δt let the input signal change by ΔI causing a change in output signal ΔO. The voltage gain is then G=ΔO/ΔI. The changes ΔI and ΔO can be infinitesimal, but their ratio is a finite quantity G. In the open-loop zero-feedback case this gain is G=A, a large, uncertain, variable, and nonlinear value because transistor amplifiers are not stable and reproducible and their gain is amplitude dependent. In the circuit with feedback this gain is G=1/β, a linear, stable, low value (at least compared to A). The value of β is set by the feedback network, often a resistor ratio, and β is stable because resistors are passive components that can be constructed with reproducible and invariant values that don't change significantly with the amplitude of the voltage across them or with age. The closed-loop gain is imposed upon the amplifier by the feedback, not by the feedback network that sets the value of β, and the gain is held at 1/β by the feedback through the mechanism of opposing the change in output signal to the degree necessary to reduce the gain to this value. Brews ohare (talk) 04:51, 17 August 2014 (UTC)

In other words, the gain is constant, and a change in the input will result in a proportional change in the output. Seems straight-forward enough.Trevithj (talk) 06:38, 17 August 2014 (UTC)

It could happen that the open-loop gain A drifts in the time interval Δt, for example due to heating. In fact, it could change by orders of magnitude, and it would not matter because the closed-loop gain is 1/β regardless of what happens with A, so long as A remains large. The gain is held at the set value of 1/β because the output signal variation is opposed (reduced) to achieve ΔO= (1/β)ΔI by the feedback. That is what the feedback does.Brews ohare (talk) 04:51, 17 August 2014 (UTC)

In other words, the feedback holds the gain constant. Seems simple enough. Trevithj (talk) 06:38, 17 August 2014 (UTC)

I don't want to try your patience, but if you want to go into this further, let me know. Brews ohare (talk) 04:51, 17 August 2014 (UTC)

There is one point. The comments "the feedback opposes the change because the change is too large" and "The notion of the absolute size or smallness of the changes is not a factor" seem mutually exclusive to me. Can you clarify?

The first statement is one way to say that with no feedback the gain would be very large, and not 1/β. Consequently the change in output signal without feedback must be reduced by the feedback to keep the gain at 1/β.

The second statement was a reply to your remark that the feedback would not be able to respond to small changes in output. As it is the gain that is enforced, the ratio of infinitesimal changes, the feedback is not governed by the size of these changes as such, but by the enforcement of a gain of 1/β. Naturally, for a given input signal, enforcing a gain of 1/β entails a reduction in the amplitude of the output signal that would result if feedback weren't there.

As I understand your reservations, they are not about how β is set, nor about the feedback enforcement of the gain, but about the mechanism of this feedback. There is a difference between error-controlled regulation and that involved here. Error control involves actually measuring the controlled parameter and using the error (departure of the measured value from the set point) to instigate correction of the measured gap. In the negative feedback amplifier the gain is not measured and 1/β subtracted to find a 'gain error' that then instigates reduction of the error. Rather, the output signal is monitored (not the gain) and set fraction β of this output is subtracted from the input which, without any error measurement, automatically (without intermediary steps) reduces the input so the output will be 1/β times larger than the signal. Brews ohare (talk) 14:48, 17 August 2014 (UTC)

See my thoughts below. Trevithj (talk) 09:01, 18 August 2014 (UTC)

The feedback response does require some time (not large), but this delay is not a factor in the analysis of how things work in principle, and in practice is simply a limitation on the frequency of signals for which it is useful. In fact, the frequency limitation in these amplifiers is usually due to the drop in open loop gain A with frequency, which sets a limit upon A/(1+βA) ≃ 1/β because, at high frequencies, A is not large enough to make this approximation valid. Brews ohare (talk) 04:56, 17 August 2014 (UTC)

A useful discussion, Brews ohare (talk) 12:31, 16 August 2014 (UTC)

Analogy

BTW, your analogy "To say regulation of a gap is not an issue because there is no gap is a bit like saying that a fire-prevention program isn't required because no houses have burned down." is wide of the mark. Inasmuch as the gain is 1/β no matter what, and there is no possibility of "fire", the analogy is to say "a fire prevention program isn't required because there is no combustible material." Brews iohare (talk) 15:04, 15 August 2014 (UTC)

Well now, the no combustible material analogy is the same as saying "if the gain is 1/β no matter what, then there is no need for a feedback loop." The gain is 1/β because of the feedback loop, just as there is no combustible material because of the fire-prevention program. Trevithj (talk) 09:10, 16 August 2014 (UTC)

I'd disagree that this is the correct alternative. Rather, the feedback loop here does not serve to set β. That is done by e.g. a resistor ratio. The feedback, rather than address the value of β, serves to oppose the change of the output signal, and by doing so, forces the closed-loop gain to be the reduced value 1/β that is predetermined by this resistor ratio, Brews ohare (talk) 12:03, 16 August 2014 (UTC)

I'm saying I don't believe the gain would stay at 1/β if there wasn't a feedback loop, regardless of how β is set. Trevithj (talk) 03:08, 17 August 2014 (UTC)

Trevith: Let's see if I understand you. I think you are in agreement that the value of β is determined by (say) a resistor ratio that is a property of the feedback network that is independent of any amplifier considerations. If not, I can provide sources about design of such networks showing how β is determined and that it is a network property that has nothing to do with feedback. Assuming this fact, your assertion is that gain of the closed loop amplifier would not be 1/β if there was no feedback loop. That assertion is beyond controversy, and we don't disagree about that. Brews ohare (talk) 04:51, 17 August 2014 (UTC)

It seems we are in full agreement. How then is it that you disagree on the "correct alternative" of the analogy? Trevithj (talk) 06:38, 17 August 2014 (UTC)

I think your analogy intends to support a role for reduction of a 'gap', the difference between a measured actual value of the gain and 1/β. No such measurement or subtraction occurs in the negative feedback amplifier, and the sometimes so-called 'error' produced by the difference between the original signal and β times the output is not the actual gain minus 1/β , so it is not a 'gap'. Moreover, unlike a 'gap', this so-called 'error' does not play the role of something to be minimized - it simply is what it is and stays that way, not the role of a 'gap' where the intent is to bring it to zero. Brews ohare (talk) 15:24, 17 August 2014 (UTC)

My analogy was intended to support a role for reduction of a 'gap', of course! But your explanations gives me food for thought. I have been crunching the numbers a bit, to get a better feel for the implications. For example (pardon my short-hand notation):

1. If the open-loop gain (A_ol)=50 and the raw input (I)=2V, the output voltage (O) should initially be 100V. Let β=0.01. The formula O = (I - β.O)A_ol yields a value of O=50V. Now either this formula is saying 100=50, or we are really talking about O_old vs O_new. So O_old=100V, and O_new=50V. But the feedback doesn't oppose this change - the feedback creates this change. Yes?
2. If I changes to 3V, then by the above formula O_new=75V. Again, the feedback doesn't oppose the change in I. The effective gain in both cases (O_new ÷ I) is 25x. Yes?
3. If A_ol changes to 60x (and I=2V as before) then O_new is 48V, and the effective gain is 24x. So a fairly large rise in open-loop gain of 20% actually results in a small fall of closed-loop gain of 4%. The change in A_ol has been opposed, and then some. Yes?

Trevithj (talk) 09:01, 18 August 2014 (UTC)

You appear to ignore the requirement βA >> 1; try A = 10⁶. It also assumes a mode of operation not actually in use, namely, the feedback is switched on and off. I suppose this is a thought experiment, but the rationale hasn't been outlined. More importantly, this arithmetic doesn't address the issue that the operation of this circuit does not involve reduction of a measured 'gap': defined as "actual gain -1/β". Brews ohare (talk) 13:23, 18 August 2014 (UTC)

Actually, I did try that. It seems that when βA >> 1 the feedback signal swamps the input. With A=500000, and all else the same, I get O_new=-4999000000V. (?!)

Also, if we don't assume the feedback is switched on and off, how do we calculate O_old? I'm assuming that the feedback signal takes a finite amount of time to get around the circuit, and that it isn't clairvoyant. In effect, it is off first time around. Trevithj (talk) 20:03, 18 August 2014 (UTC)

The algebra shows that for an input signal I, the signal going into A following the subtraction of the feedback is I–βO = I–βA/(1+βA)I = I/(1+βA). If this signal is feed into A, the output is O=A I/((1+βA). In other words the gain is G=A/((1+βA) the standard expression which is ≈ (1/β) for large A. Brews ohare (talk) 22:09, 18 August 2014 (UTC)

Ah, that makes the numbers behave. Thank you. Point 3 above still holds: big changes in A_ol result in much smaller changes in A_cl. Trevithj (talk) 09:14, 19 August 2014 (UTC)

Although the negative feedback amplifier does result in a gain of 1/β, I imagine you will agree that the achievement of this goal by this circuit does not in itself imply that it achieves this result by the mechanism of error-controlled regulation? 1, Ashby: Chapter 12: The error-controlled regulator, pp. 219 ff Brews ohare (talk) 14:09, 18 August 2014 (UTC)

Interesting first source. I will study. Trevithj (talk) 20:03, 18 August 2014 (UTC)

As pointed out by your source, David Mindell, Black's patents and Bell Labs documents do not mention any error-controlled regulatory devices despite the fact that these systems were well-known at the time, going back before Minorsky's automatic pilot for ships used in 1923. 2 Prior to Minorsky's work "some acute observers...noted that the best human operators ... used both anticipation, backing off the power as the controlled variable approached the set-point, and small, slow adjustments when the error persisted. Sperry tried to incorporate these ideas into his devices... In 1922, Nicholas Minorsky presented a clear analysis of the control involved in position control systems and formulated a control law that we now refer to as three-term or PID control." 3

A cynic might suggest that the Bell Labs avoidance of mention of the PID controller was a deliberate act to enforce their patent claims and avoid any challenges that it was a variant of the established art. However, my opinion is that there is no connection. Brews ohare (talk) 15:58, 18 August 2014 (UTC)

There are probably other explanations for the non-mention. I'm trying to track down a complete copy of Mindell, to see what his full argument is. Will advise.Trevithj (talk) 20:03, 18 August 2014 (UTC)

Trevith: Although of some historical interest, tracking this down will settle nothing. The issue has to be faced that in any published analysis of the math behind this circuit, there is no 'gap' of the form (actual gain -1/β) measured in the circuit, and no error-controlled regulation based upon reduction of such an error is used in any of the analyses. That is a perfectly understandable reason why the Bell Labs writings don't bring up feedback controllers that use error controlled regulation. Brews ohare (talk) 22:16, 18 August 2014 (UTC)

I agree there is no gap of the form (actual gain -1/β). There is a gap of the form (I - βO) though. And that gap changes if A_ol changes.

I'm finding Mindell quite informative. Bell Labs' silence may be because the connection between the two approaches was not fully worked out at that time. Trevithj (talk) 09:14, 19 August 2014 (UTC)

Trevith: You can choose to call (I - βO) a "gap", although I don't think any source does that. Some sources call it an "error". However, no source, and probably not you either, claim that (I - βO) involves an "error" serving the same function as the error in error-correcting regulation. The difference I–βO is given by:

$I-\beta O=I\left(1-\beta {\frac {O}{I}}\right)={\frac {I}{1+\beta A_{OL}}}$

and is therefore fixed by the (arbitrary) input I and the invariant values of β and A_OL, and is not 'adjusted' as a matter of circuit operation. Naming (I - βO) a "gap" with the idea in mind of pointing out similarities with the "gap" in error-controlled regulation suggests a non-existent parallel. In particular, (I - βO) is not corrected or minimized. Instead it reduces the output so the gain will be 1/β. I've included this point in the negative feedback amplifier subsection.

Your exploration of numerical examples appears new to you, but it is described in detail in algebraic terms by Santiram Kal (2009). "§6.3 Advantages of negative feedback amplifiers". Basic electronics: Devices, circuits and its fundamentals. PHI Learning Pvt. Ltd. pp. 193 ff. ISBN 9788120319523..

From an historical review, you hope to show that Black did not connect his work to existing uses of feedback, not because the connection was weak or missing, but because he was just unaware of Sperry's (1911) ship-steering mechanism "that incorporated PID control and automatic gain adjustment to compensate for the disturbances when the sea conditions changed" and the 1922 presentation by Minorsky of a "clear analysis of the control involved in position control and formulation [of] a control law that we now refer to as three-term or PID control."1 Of course, Black may have been ignorant of the major uses of feedback in his day, although in my experience (admittedly decades later), Bell Labs' patent attorneys would have been on top of it in minutes. It seems highly improbable to me that Black's patents would withstand legal challenge by those fully aware of PID control had there been a clear parallel with the negative feedback amplifier. In fact, the delay in granting Black's patents, according to Black, was not that his amplifier was nothing new, just a variant of the recognized art, but was due to the patent office's belief that the idea was bogus and would not work.Proc IEEE, p. 352 In any event, even supposing such challenges occurred and were shot down it wouldn't prove anything except that patent disputes occurred, so some folks thought they were similar, while others disagreed.

I'd say that the above argument about (I–βO) shows beyond any dispute that this "error" has nothing to with "error" as something the amplifier circuit attempts to reduce, and makes a clear distinction between Black's use of feedback and its use in error-controlled regulation. Nonetheless, the literature is replete with blurry confusion of the negative feedback amplifier with error-controlled regulation, based in part upon failure to distinguish between different uses of the word "error", and a muddy reliance upon verbalization of the goals of feedback, unsupported by solid examination of the mechanisms for achieving those goals.

It appears rather likely that you will reach the conclusion that the operation of the negative feedback amplifier is indeed an example of error-controlled regulation, even if no source makes that claim. It seems likely that you will hold that there are indeed some differences, but they are minor and inessential and the basic idea is not "negative feedback" but, more specifically, "error control" (somehow conceived) exercised via negative feedback.

I'd suggest the situation is best handled by going back to the proposed "opposition-to-change" formulation of negative feedback that (a) apples very generally (not restricted to electronics or homeostasis, nor indeed, error control), and (b) is sourced, and leave resolution of these systems' degree of similarity to the reader when they have perused the subsections on error-controlled regulation and on the negative feedback amplifier. Brews ohare (talk) 15:31, 19 August 2014 (UTC)

Negative feedback is feedback that opposes change.

Sources

Brews ohare (talk) 15:54, 19 August 2014 (UTC)

Initial conclusions

This discussion was initiated by the hypothesis that the negative feedback amplifier does not use error-controlled regulation. The null hypothesis is of course that it does use error-controlled regulation. While I can't say we can clearly reject the null hypothesis (yet), the search has been most informative and serves to reaffirm something I have suspected for a while: the negative feedback amplifier is a more complicated example than it seems! Even its inventor had trouble explaining the essential concepts, and I am beginning to see why.

I'm going to try and outline what I see as some of those complications here. In particular, there are two terms that I have found problematic. Some discussions (hopefully not this one) tend to lump them together, or be ambiguous in their usage.

1. "Input". Actually, there are two inputs: raw input $I$; post-summation input $I_{2}$.
2. "Gain". Actually there are three "gains": overall gain ${\frac {O}{I}}$; actual gain ${\frac {O}{I_{2}}}$; desired gain ${\frac {1}{\beta }}$.

The feedback keeps the overall gain close to the desired gain by adjusting the actual gain - not that straight-forward, especially considering that A_ol isn't altered by any of this.

The other variables in the system can be derived from three variables: I, A_ol and β. β is fixed, so the feedback responds to changes in I and A_ol. Changes in I don't affect the overall gain, because the feedback changes I₂ (and so actual gain) in direct proportion to the changes. Changes in A_ol have some affect on overall gain, but relatively little. These two responses are difficult to untangle.

From an error-control POV, it seems at first glance that β is the reference value, because it is fixed. But then the essential variable is O. Does that make -βO the error signal? If so, what use does the summation component serve? On second glance, error-control would expect the reference and the measured values to be compared (in the summation component). But that would make -βO the measured value, I the reference value, and I₂ the error value. While perhaps feasible, it is confusing to regard I as a reference.

So even if this could be made to work, the error-control approach is evidently an uncomfortable fit. The suggestion to go with a higher-level concept common to both makes a lot of sense. We may perhaps split hairs as to whether "opposes change" or "reduces change" is the more generic term, but I feel that the proposed wording has it right. Trevithj (talk) 09:20, 23 August 2014 (UTC)

It seems we agree to use the "opposes-change" wording. Will you support that change as the lead sentence?

That change being the only effect upon WP, there isn't too much profit in further analysis here unless you wish to take up the sub-section on the negative feedback amplifier?

In any event, I suggest we change the lead sentence as proposed above including the four sources, and then we can continue to discuss the sub-section on the amplifier. What say you? Brews ohare (talk) 17:04, 23 August 2014 (UTC)

Hi Trevithj: This action seems to be a no-brainier. Any reason to delay? Brews ohare (talk) 15:33, 26 August 2014 (UTC)

I've brought this correction up on the Talk page. Brews ohare (talk) 16:58, 26 August 2014 (UTC)

Hi Brews: pardon delay - work issues needed attention. Yes, I support the proposed changes to the first sentence, and the first two points in the rationale. Re the third point: I'm more inclined to avoid the negative feedback amplifier completely in the lede, if possible. Getting into details of its operation in any form tends to cause arguments, largely driven by confusion around terms. Trevithj (talk) 07:10, 27 August 2014 (UTC)

The section below provides three possible ways error correction can work, and what eliminates them as candidates for the negative feedback amplifier. The source linked in the proposed change demonstrates in general terms that what does apply is desensitization to changes and that analysis (which is the same as Kal's for the feedback amplifier) does not involve error controlled regulation. If you have qualms remaining, can you identify them? Brews ohare (talk) 12:04, 27 August 2014 (UTC)

Or, is your aim simply strategic? Brews ohare (talk) 12:15, 27 August 2014 (UTC)

Mainly strategic. The distinction between error-control and desensitization is not easy to communicate. It is best left to a sub-section or the dedicated page, which can do it justice. If the amplifier features in the lede, it will continue to attract debate that clouds the main issue of generic definition.

Also, while "error" may be too narrow a term here, it is difficult to discuss "change" without some sort of reference point. So best to stick to examples with clear and agreed-upon reference points. Thermostats or steam governors would do a better job, IMO. Trevithj (talk) 19:43, 27 August 2014 (UTC)

Apparently you are correct in thinking understanding the amplifier is too much for many. Of course, if they stuck to sources, the problem of dissuading them from erroneous opinions would be avoided. As things stand, this article will have a wrong statement of what is negative feedback, and will give the impression that it is limited to error-controlled regulation.

This unfortunate situation would not happen if WP policy on sources were observed. But that is not going to happen here, and WP is stuck with inaccuracy. Brews ohare (talk) 01:36, 28 August 2014 (UTC)

In fairness, using words like 'hokum' and 'nonsense' are unlikely to encourage agreement! Try for a more charitable approach here. You asked for opinions on the new text, and you received them. Great - that is better than being ignored. Trevithj (talk) 02:17, 28 August 2014 (UTC)

Quite right, calling a spade a spade is not tactful. However, these interchanges have failed completely to address the sources and their analyses, so whether that is different from ignoring them is debatable. I've now tried since early June to get the sources addressed with nothing to show for it but insults. Too bad, eh? That's WP when policies on sources are replaced by editors repeating personal opinions. In a few cases, the issue may be that a bit of algebra is simply not a skill, so the sources cannot be understood. Brews ohare (talk) 02:43, 28 August 2014 (UTC)

Your lack of participation here and lack of comment on the examples below may indicate a lapse of interest or reservations that linger. In any event, it appears likely that a failure to act earlier will lead to the introductory sentence in negative feedback remaining in error indefinitely. Brews ohare (talk) 15:28, 29 August 2014 (UTC)

My lack of participation is due mainly to time constraints. However, I am working my way through Mindell and Kal. I think Kal is being a little imprecise when he says that "the gain of the feedback amplifier is entirely determined by the feedback network." The formula he provides shows that for large values of $A\beta$, the gain is almost entirely determined so. And he is talking about the overall gain $A_{f}$, not the actual gain.

I am also pondering one question related to the formula: $I-BO=I\left(1-\beta {\frac {O}{I}}\right)={\frac {I}{1+BA}}$ which I'm interpreting as: $I_{2}={\frac {I}{1+\beta A_{ol}}}$ which seems uncontroversial.

But anyway, I'm putting my limited time onto following this, but probably won't comment on the talk page until things cool down.Trevithj (talk) 22:41, 29 August 2014 (UTC)

Initial conclusions 2

Trevithj: If I is the input signal and O is the output signal, the gain is O/I , and the algebra from the block diagram then insists the gain is :

${\frac {O}{I}}={\frac {A}{1+BA}}.\$

for any size of BA and there are no loopholes to say this is 'mainly' the gain. So I don't know what 'mainly' means in your remark. Perhaps you mean that the gain is not determined by the feedback value B? I think Kal means the gain is determined by the feedback circuit in the general case, and of course is 1/B if A is large enough. As you say, this is the overall gain, the closed-loop gain, but it is also the actual gain. I don't know what you mean by suggesting the actual and the closed-loop gain are different things.

Re "'mainly' the gain", I mean that there is a difference between $A_{f}={\frac {1}{\beta }}$ and $A_{f}\approx {\frac {1}{\beta }}$. The A term doesn't quite go away.

Re "actual", I mean that the actual gain is: $A={\frac {O}{I-\beta O}}$, as opposed to the overall gain: $A_{f}={\frac {O}{I}}$.

I defined these terms at the top of the previous section, you will recall. Trevithj (talk) 09:49, 3 September 2014 (UTC)

On mainly the gain. Yes, the closed-loop gain is A/(1+BA) and this is only approximately 1/B. However, no matter of principle regrading the role of feedback is involved here, and the closed-loop gain can be brought to have no distinction of consequence from 1/B by making the open-loop gain large. Brews ohare (talk) 18:31, 8 September 2014 (UTC)

On actual gain. Expressing the open-loop gain as O/(I–BO) suggests that somehow this gain is a dependent variable dependent upon the output O, which is emphatically not the case. The gain A is determined by the open-loop gain hardware and design, and has nothing to do with the circuit or its operation. It is O that is the dependent variable O = AI/(1+BA). Brews ohare (talk) 18:31, 8 September 2014 (UTC)

I agree that the formula for the input to the A block, I-BO is not controversial, being simple algebra. Its value I/(1+BA) is determined by I, B, and A, and determines O as AI/(1+AB). I interpret GliderMaven's difficulties with all this stem from his confusion with error-controlled regulation. He thinks that the analysis of Kal is erroneous because it omits mention of adjusting deviation from a setpoint and so, in his view, misses the entire point of feedback. What GliderMaven misses is that his conception of feedback is only one form, and because all published analyses disagree with him that this form applies here, that should give him pause. Although one could take it that the feedback network implied a setpoint value for B there is no measurement of a 'gap' (by some invisible 'thermostat'), and no minimization or closing of a 'gap' by some (invisible) regulator. As Kal shows, desensitization to fluctuations can be achieved differently. Brews ohare (talk) 05:23, 30 August 2014 (UTC)

A minor correction: in the discussion with Glidermaven (and above), you describe A as "invariant". But it isn't, as Kal and Bhattacharya both point out.Trevithj (talk) 09:49, 3 September 2014 (UTC)

Essential variables

Ashby's "essential variable" is one parameter (perhaps of a set) that determines the state of the system. The output O is not such a variable. For example, in some systems, there is no output, such as homeostatic systems that serve only to control the state of the system by setting the essential variables to their set point. Examples might be blood pressure, or body temperature where the only 'output' is a reaction that reduces the departure of the system from its proper condition. For process control, on the other hand, the process may convert some 'input' to some product 'output' and the output is a result of the system state. For example, a bottle washer accepts input as dirty bottles, output as clean bottles, and the essential variables might be water pressure, water temperature, and amount of soap sprayed on the bottles. The setpoints are established empirically or using some analytical model, departures are measured and trigger correction, constituting feedback, That kind of system is close to the amplifier, where the input is a signal (dirty bottle) and the output is a larger signal (clean bottle), and the result depends upon β, arguably an essential variable (like pressure, temperature, etc.). However, β is not controllable, so there is no error control on β and we just hope the feedback network doesn't wander off base. If βA is small, however, the output signal does depend upon A, and A is not predictable. Unfortunately perhaps, the negative feedback amplifier has no mechanism to monitor A, nor to affect its essential variables. So there is no error control involving A.

One can imagine a more elaborate bottle washer in which the output did affect the system: that could happen if the setpoints were adjusted depending upon how clean the bottles are. So some optical assessment of 'clean' could be measured at the output and sent to an algorithm relating 'clean' to temperature, pressure, and quantity of soap, and the setpoints adjusted. Perhaps that would automate the system to deal with different species of 'dirty', maybe just a classification like 'tough to clean - use a power wash cycle' and 'easy to clean - use a rinse cycle'. This use of the output to control system operation seems to introduce something different from the notion of an 'essential variable' because a property of the output (how 'clean' it is) is a product characteristic, not itself a system parameter. However, the amplifier does not fit this situation because no setpoint adjustments occur. In particular, the output signal doesn't affect β or A, and so is not used to change the internal state of the amplifier.

A third possibility has occurred to me in which feedback from the output affects the input. An example would be a bottle washer where the monitoring of 'clean' at the output is used to adjust the orientation of bottles entering the washer, or perhaps to adjust the conveyer speed (neither of which is under jurisdiction of the essential variables pressure, temperature, or amount of soap). The amplifier might be thought of this way, as the output seems to change the input as suggested by I-βO. However, with the amplifier there is no monitoring of the output signal to see whether it meets some criterion (like 'clean' or 'not clean'). In particular, the output signal amplitude is not monitored to see if it is 1/β times the input signal. The setting of the gain by the feedback network is determined by circuit topology as the response to the (so-called) 'error' I/(1+βA). That is to say, not by adaptation to the output signal, but set by the input signal I and the internal fixed values of β and A. One could imagine a more sophisticated amplifier, but it wouldn't be the simple negative feedback amplifier under discussion.

The upshot is this: none of these forms of error control apply. These points may be clear to you already. I apologize for any belaboring. Brews ohare (talk) 22:57, 23 August 2014 (UTC)

Cybernetics

Thanks for your prompt provision of full details for one of the reviews at Cybernetics:_Or_Control_and_Communication_in_the_Animal_and_the_Machine, plus the addition of a couple more excellent references. Good work also on the (bizarrely troublesome) discussions at Negative feedback. DaveApter (talk) 10:22, 3 September 2014 (UTC)

Glad to help. This is a surprisingly difficult area in which to find consensus, and passions abound! Cybernetics:_Or_Control_and_Communication_in_the_Animal_and_the_Machine is a valuable resource, IMO. Trevithj (talk) 21:08, 4 September 2014 (UTC)

Negative feedback

Hi Trevith: I am taken aback by your support of the suppression of this discussion with Dicklyon. Of course, I understand your position is that the error signal S_e=S_i./(1+βA), although determined by the variables S_i., A and β, is not determined separately from the feedback circuit because you believe these parameters are themselves not determined by the signal source, the open-loop amplifier and the feedback network operated in isolation from the feedback circuit. This contention does not square with Rashid's customary textbook formulation, his Eqs. 10.1-10.3, but there it is.

Dicklyon has a more specific view of the failure of the textbook formulation, that although the 'input-only' form of the error signal is in fact decided by variables whose values can be found externally, a different point is that the form S_e=S_i./(1+βA) rests upon the basic assumption that the gain A of the open-loop amplifier is defined by S_o=A S_i, and this definition is inapplicable within a more general view of the feedback amplifier (more general than Rashid's and other textbook formulations), especially where noise is considered that can result in an output even with no input. This viewpoint appears possible, although so far completely unsourced, so I don't understand why you do not support its discussion. Brews ohare (talk) 17:04, 1 November 2014 (UTC)

One of two things is happening here, professor.

1. the other editors on this page are conspiring (for reasons unknown) to suppress your views
2. the other editors on this page are reacting to your perceived attempts to suppress their views

You decide which of these is the most likely. Trevithj (talk) 18:57, 2 November 2014 (UTC)

A simple explanation is that they really just don't care about this point. Inasmuch as DaveApter's lead sentence is adequately ambiguous and the subsections on the negative feedback amplifier (1,2) and upon error-controlled regulation are sufficiently clear, the motivation for continuing this discussion for me is really one of developing a general approach acceptable to you and Dick and compatible with sources. Dick eventually will reach a suitable understanding. GliderMaven and Johnunique aren't interested and just want things over with. Brews ohare (talk) 19:13, 2 November 2014 (UTC)

What do you mean by "a suitable understanding"? Trevithj (talk) 20:55, 2 November 2014 (UTC)

I mean a formulation of Dick's ideas supported by sources. I suspect that Kal's or Bhattacharya's treatment of noise introduced inside the feedback loop might work. Brews ohare (talk) 21:44, 2 November 2014 (UTC)

Hmm. You do understand why sources have the authority that they do, right? Trevithj (talk) 18:20, 3 November 2014 (UTC)

Trevith, I don't know what your question is about. It sounds a lot like an assertion of some kind, and not a question. To make clear why I think these sources could be a formulation of Dick's ideas, notice that the introduction of noise inside the feedback loop changes the input-output equation, part of Dick's commentary. Brews ohare (talk) 20:31, 3 November 2014 (UTC)

My point of concern is this: it appears that there is something you are working very hard at not seeing. Trevithj (talk) 07:16, 4 November 2014 (UTC)

Trevith, if you have really a "point of concern" you might explain it, eh? If your concern is about the treatment of feedback in the literature, I've pointed out a possible treatment of Dick's concerns by sources (rather than the gut feeling of editors). It seems possible that the 'something' you refer to is the implications of error-control for the negative feedback amplifier: according to sources so far presented, there aren't any. The concept of error control in the sense of minimizing a measured 'gap' just isn't used. Brews ohare (talk) 17:05, 4 November 2014 (UTC)

I realize you want to insert minimization of a measured 'gap' into the understanding of the negative feedback amplifier, but so far this desire is unsupported by any source analyzing this amplifier. What the sources all agree upon is the use of feedback in these amplifiers to desensitize them, to make their operation largely independent of the presence of variations of various kinds without attempting to minimize them. So, A -> A/(1+βA), insensitive to any ΔA, regardless of its nature or origin. That desensitization is accomplished by using feedback to change the functional dependence of amplification so it generically is less affected in principle by variations, rather than combatting variations by explicitly monitoring such variations and adjusting operation to reduce them. In a crude analogy, this use of feedback is like a wide-spectrum vaccine that prevents many types of infection, rather than coping with the individual symptoms of any one of them after a particular infection is contracted. Brews ohare (talk) 16:24, 5 November 2014 (UTC)

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