Trevithj

Introducing John Trevithick, from New Zealand.

Coming from a background in electronics and computing, John has an interest in systems dynamics. Part-time, he is:

a tutor in maths and physics at UoA.

a small-farmer, with 1.8Ha of land near the Kaipara Harbour.

an actor, mainly stage, but with a few modest film/TV credits.

a meditator, mainly following the Theravada Buddhist tradition.

Combination of interests centers around the definitions (and confusions) of positive/negative feedback.

Feedback

Draft pages

Wikipedia:Subpages help section. Draft pages that trial different historical/example/terminology sections:

• User:Trevithj/Feedback draft of changes
• User:Trevithj/Negative feedback draft of changes
• User:Trevithj/Causal loop (disambiguation) new page to try and separate the general concept from the narrower Predestination paradox usage.

Historical Refs

Earliest

Edition 3 of The Encyclopedia Britannica, 1792:"He runs into what is termed by logicians a vicious circle."

www.etymonline.com: Inflation: Economics sense from 1844, Monetary sense of "enlargement of prices" ... first recorded 1838 in American English.Steele's "Popular Physics" schoolbook (1888) Ch1: "30. Why can not a man lift himself by pulling up on his boot-straps?"

www.etymonline.com: "chain reaction is from 1916 in physics, specific nuclear physics sense is from 1938; Chain letter recorded from 1892; usually to raise money at first..."

"St. Nicholas" magazine, vol. XXVI, April 1899: "Nine out of every ten givers are reluctant and unwilling, and are coerced into giving through the awful fear of 'breaking the chain,' so that the spirit of charity is woefully absent."

James Joyce, Ulysses, 1922:"There were others who had forced their way to the top from the lowest rung by the aid of their bootstraps."

Kunitz & Haycraft, British Authors of the Nineteenth Century, 1936:"A poet who lifted himself by his own boot-straps from an obscure versifier to the ranks of real poetry."

1865-1909

Jay (1865)

When the journal or spindle is cut ... and the carriage is about to feed back by a change of the sectional nut or burr upon the screw-shafts, the operator seizes the handle...

Cole (1866)

Heretofore ... it has been necessary to reverse the motion of the rollers, thus causing the material to travel or feed back, ...

Maxwell (1868)

A GOVERNOR is a part of a machine by means of which the velocity of the machine is kept nearly uniform, not withstanding variations in the driving-power or the resistance.

Most governors depend on the centrifugal force of a piece connected with a shaft of the machine. When the velocity increases, this force increases, and either increases the pressure of the piece against a surface or moves the piece, and so acts on a break or a valve.

...in some pieces of clockwork the moderator consists of a conical pendulum revolving within a circular case. When the velocity increases, the ball of the pendulum presses against the inside of the case, and the friction checks the increase of velocity.

In Watt's governor for steam-engines the arms open outwards, and so contract the aperture of the steam-valve.

...

...uniform motion, combined with a disturbance which may be expressed as the sum of several component motions ... of four different kinds:

(1) The disturbance may continually increase.

(2) It may continually diminish.

(3) It may be an oscillation of continually increasing amplitude.

(4) It may be an oscillation of continually decreasing amplitude

This [second and fourth] condition is mathematically equivalent to the condition that all the possible roots, and all the possible parts of the impossible roots, of a certain equation shall be negative.

Braun (1909)

...as far as possible the circuit has no feed-back into the system being investigated.

1920-1949

Espenschied (1922)

When the two one-way radio channels are merged at their two ends into a regular telephone circuit for connection to the wire network ... then there is a limit in the transmission equivalent which can be given over the radio part of the circuit ... imposed by the tendency of the two one-way channels to form a round-trip circuit by "feeding-back" from one to the other via the voice frequency connecting circuit. If the total amplification around the circuit including the voice-frequency line, exceeds the total losses in the circuit, "singing" will result. Were no line balance provided at the voice frequency terminals, then it would be impossible to operate the circuit at a zero equivalent. By setting up a balancing circuit at each end in the manner illustrated, a transmission loss is, in effect, inserted between the sending and receiving sides of the voice circuit which tends to prevent this sing-around action.

King (1923)

Use of a common grid battery, as shown, introduces a small feed-back from the second stage to the first. This feed-back may be either positive or negative, depending upon the phase relations in the intermediate transformer and may be eliminated by placing a condenser across the grid battery terminals.

Singing, which is one of the most serious troubles in amplifiers, is always due to some form of feed-back. This may be magnetic, electrostatic, or in the form of mechanical vibrations as in an amplifier having a microphone attached to the input and a receiver to the output. ... The coupling which is responsible for feed-back may be difficult to locate, but when found can usually be removed. Both retard coils and transformers may afford an easy method of coupling due to stray fields. If the coupling induces voltages which are in phase with the input voltages, it may cause singing, and if out of phase, the amplification may be seriously reduced.

The unequal amplification of various frequencies arises from the presence of resonant characteristics in the circuit. This may take the form of a feed-back which discriminates in favor[sp] of certain frequencies, the feed-back not being pronounced enough to cause singing. A negative feed-back may also occur, causing a loss of efficiency over some particular frequency range.

Friis (1924)

The "feed back" or regeneration in a set is ... due to the coupling between the grid circuit and the plate circuit of the tubes through the grid-plate capacity...

If the "feed-back" action is positive, ... then the tube voltmeter reading will increase, and in order to bring it back to its former value, the resistance of the loop is increased by an amount R'... If on the other hand the "feed-back" action is negative, the resistance of the loop must be decreased in order to obtain the former value of the tube voltmeter reading.

The "feed-back" amplification K' is defined as the increase (or decrease) of signal voltage due the "feed-back" action between amplifier and its tuned input circuit. [Original emphasis. my note: Total amplification = ordinary amplification K + feedback amplification K']

Nyquist (1932)

Regeneration or feed-back is of considerable importance in many applications of vacuum tubes.

Black (1929)(1934)

However, by building an amplifier whose gain is made deliberately ... higher than necessary ... and then feeding the output back to the input in such a way as to throw away the excess gain, it has been found possible to effect extraordinary improvement in constancy of amplification and freedom from nonlinearity.

As a quantitative measure of the effect of feed-back 1/(1-μβ) will be used and the feed-back referred to as positive feed-back or negative feed-back according as the absolute value of 1/(1-μβ) is greater or less than unity. Positive feed-back increases the gain of the amplifier; negative feed-back reduces it. The term feed-back is not limited merely to those cases where the absolute value of 1/(1-μβ) is other than unity.

Black (1937)

One improvement is in lowered distortion arising in the amplifier. Another improvement is greater constancy of operation, in particular a more nearly constant gain despite variable factors such as ordinarily would influence the gain.

Hendrik_Wade_Bode (1930-1940)

• H. W. Bode A Method of Impedance Correction Bell System Technical Journal, v9: 1930
• H. W. Bode A General Theory of Electric Wave Filters Bell System Technical Journal, v14: 1935
• H. W. Bode and R. L. Dietzold Ideal Wave Filters Bell System Technical Journal, v14: 1935
• H. W. Bode Variable Equalizers Bell System Technical Journal, v17: 1938
• H. W. Bode Relations Between Attenuation and Phase in Feedback Amplifier Design Bell System Technical Journal, v19: 1940

Rosenblueth, Wiener and Bigelow (1943)

All purposeful behavior may be considered to require negative feed-back. If a goal is to be attained, some signals from the goal are necessary at some time to direct the behavior.

Positive feed-back adds to the input signals; it does not correct them. ...the behavior of an object is controlled by the margin of error at which the object stands at a given time with reference to a relatively specific goal. The feed-back is then negative...

Wiener (1948)

[Feedback is] the chain of the transmission and return of information:

Notice that the feedback [in a steam governor] tends to oppose what the system is already doing, and is thus negative.

We do not will the motions of certain muscles, and indeed we generally do not know which muscles are to be moved to accomplish a given task; we will, say, to pick up a cigarette. Our motion is regulated by some measure of the amount by which it has not yet been accomplished. The information fed back to the control center tends to oppose the departure of the controlled from the controlling quantity, but it may depend in widely differnt ways on this departure.

1950-1969

Ashby (1956).

When ... circularity of action exists between the parts of a dynamic system, then feedback can be said to exist.

Other definitions, however, are possible, and there has been some dispute as to the best... There are two main points of view that have to be considered. ...[To] those whose aim is to get an understanding of the principles behind the multitudinous special mechanisms that exhibit them ... 'feedback' exists between two parts when each affects the other...

On the other side stand the practical experimenters and constructors, who want to use the word to refer, when some forward effect from P to R can be taken for granted, to the deliberate condition of some effect back from R to P by some connexion that is physically or materially evident. They object to the mathematician's definition, pointing out that this would force them to say that feedback was present in the ordinary pendulum ... between its position and its momentum - a 'feedback' that, from the practical point of view, is somewhat mystical. To this the mathematician retorts that if feedback is to be considered present only when there is an actual wire or nerve to represent it, then the theory becomes chaotic and riddled with irrelevancies.

In fact, there need be no dispute, for the exact definition of "feedback" is nowhere important. The fact is that the concept of "feedback", so simple and natural in certain elementary cases, becomes artificial and of little use when the interconnexions between the parts become more complex. When there are only two parts joined so that each affects the other, the properties of the feedback give important and useful information about the properties of the whole. But when the parts rise to even as few as four, if every one affects the other three, then twenty circuits can be traced through them; and knowing the properties of all the twenty circuits does not give complete information about the system. Such complex systems cannot be treated as an interlaced set of more or less independent feedback circuits, but only as a whole...

The feedback ... is said to be 'negative' (for it causes an eventual subtraction from the initial displacement). ... the rule may break down if applied crudely.

(Gives an example where 'positive' simply means an increase in the relative size of a value, and shows how the results make no sense.) It shows clearly that arguments based on some short cut, e.g. by showing that the feedback is positive, may not be reliable. (It shows also that feedback can be positive and yet leave the system stable; yet another example of how unsuitable is the concept of feedback outside its particular range of applicability.

Skinner (1957)

Among the conditions which alter rate of responding are some of the consequences of behavior. Operant behavior usually affects the environment and generates stimuli which "feed back" to the organism. Some feedback may have the effects identified by the layman as reward and punishment. Any consequence of behavior which is rewarding or, more technically, reinforcing, increases the probability of further responding.

Haus and Adler 1959

Wilts (1960)

Although the term feedback appears to have a very simple meaning, a completely general definition is surprisingly difficult.

...actual comparison of this [specific physical] quantity with its desired value and utilizing the difference to reduce the error observed.

It can be seen that the comparison involves in some sense a process in which the response is subtracted from the input. For this reason feedback used for control is often called negative feedback.

Johnson(1963)

Many of the patterns of information flow in a business are found to have the nature of closed loops. [This is because] any system, if it is to achieve a predetermined goal, must have available to it at all times an indication of its degree of attainment.

...inadequate or improper feedback flows may bring about a regeneration of output, leading to an oscillatory effect...

...where the delay is exactly one-half cycle ... then the corrective action is superimposed upon a deviation which at the moment is in the same direction as that of correction.

1970-1989

Herold (1977)

If the action has positive emotional connotation (makes recipient happy etc.), it is called positive feedback. If the action has negative emotional connotation (makes recipient unhappy etc.), it is called negative feedback. (as cited in Ramaprasad 1983)

Factor I - A common theme for the 10 items loading on the first factor is their valence, all representing negative feedback. Examples are being removed from a job or suffering some adverse consequence due to poor performance or receiving more or less direct indications of dissatisfaction from co-workers or the supervisor. ...

Factor II - The information conveyed in the second factor differs most notably from the first in that the items are positive in their valence.

Bennett (1979)

...the way forward towards a clear understanding and a mathematical formulation of the theory of feedback systems was through engineering: first through mechanics - the regulation of prime movers led to an understanding of stability, the positioning of heavy loads to the development of servomechanisms - and then, as difficulties of analysis of mechanical systems began to hinder further progress, through electronics, and, in particular, through the need to obtain low distortion in the amplification and transmission of telephone signals.

This phase occupied 150 years, a period extending roughly from 1790 to 1940;..

In the summer of 1912 Edwin Armstrong (1890-1964), an undergraduate at Columbia University, discovered that the gain of the [amplifier] could be increased if part of the output signal was coupled back to the input circuit.

[T]he concept of positive feedback was, as it were, in the air: it was ready to be discovered, and between 1912 and 1914 several people ... sensed the concept and in various ways attempted to make use of it.

On 6th August 1912 von Etten, Lee de Forest's assistant, had accidentally discovered that if the output of a double [amplifier] was connected to the input, the audion would howl or sing.

[Friis and Jensen] noted that R' could be positive, giving an increase in amplification, or negative, giving a decrease, but they investigated only the behaviour for R' positive.

Black's first attempts to reduce distortion in repeater amplifiers were made around 1925...

Mees (1981)

There is a tradition in control theory that one deals with a negative feedback loop in which a negative sign is included in the feedback loop...

Ramaprasad (1983)

Feedback is information about the gap between the actual level and the reference level of a system parameter which is used to alter the gap in some way.

1. The focus of feedback may be any system parameter: input, process, or output.
2. The necessary conditions for feedback are the existence of data on the reference level [and the] actual level of the parameter, and a mechanism for comparing the two to generate information about the gap between the two levels.
3. The information on the gap between the actual level and the reference level is feedback only when it is used to alter the gap.

There is often another source of confusion about the distinction between positive and negative feedback. The terms are confused with positive and negative reinforcement (Skinner, 1969). We will not discuss this in detail; suffice it to say that both positive and negative reinforcements are negative feedback mechanisms, because they try to minimize deviations from the reference level (desired behavior).

If the action triggered by feedback widens the gap between the reference and actual levels of the system parameter, the feedback is called positive feedback. On the other hand, if the action reduces the gap between the two levels, the feedback is called negative feedback.

Sadler (1989)

...the learner has to (a) possess a concept of the standard (or goal, or reference level) being aimed for, (b) compare the actual (or current) level of performance with the standard, and (c) engage in appropriate action which leads to some closure of the gap. ... It will be argued that they are necessary conditions, which must be satisfied simultaneously rather than as sequential steps.

The traditional definition of feedback is then too narrow to be of much use, and in this article a more appropriate conception is presented. It requires knowledge of the standard or goal, skills in making multicriterion comparisons, and the development of ways and means for reducing the discrepancy between what is produced and what is aimed for.

1990-2009

Senge (1990)

[Feedback is] any reciprocal flow of influence ... every influence is both cause and effect.

Levine (1992)

However, after scrutinizing the statistical properties of the structural equations, the members of the committee assured themselves that it is possible to have a significant positive feedback loop when using standardized scores, and a negative loop when using real scores.

Richardson (1995)

...some define a loop to be positive if it gives "divergent behavior." Graham (1977) finds problems with that characterization and suggests instead that a loop be called positive if its open-loop steady state gain is greater than one. Richmond delightfully exposed our confusions by describing a well-meaning professor trying to explain to a concerned student: "Positive loops are … er, well, they give rise to exponential growth … or collapse … but only under certain conditions … under other conditions they behave like negative feedback loops…" He concluded that the nicest way out of the confusion is to define a positive loop to be a goal-seeking loop whose goal continually "runs off in the direction of the search" (Richmond 1980). Some, of course, ignore all the subtleties and obtain loop polarities simply by counting negative links (Richardson and Pugh 1981).

If the resulting change in the inflow rate is in the opposite direction to the change dx, then sign(dx/dx) is negative and the polarity of the loop is negative by both our intuitive and formal definitions.

Bhattacharyya (2000?)

Mindell (2000)

At Bell Laboratories from 1927 to 1940, the legend goes, Black, Harry Nyquist, and Hendrik Bode laid the foundations of feedback control that engineers then applied to all types of closed-loop systems, from servomechanisms to thermostats, fire control systems to automatic computers. More than other contemporary narratives of control systems such as automatic pilots or servomechanisms, this story of feedback earned a place in engineering legend and college textbooks. It produced design methods and graphical techniques that carry their author's names (the Bode plot, the Nyquist diagram) and earned telephone engineering a claim to priority in feedback history. Feedback theory, moreover, formed the basis of cybernetics, systems theory, and a host of other post-World War II information sciences, so Black's invention is hailed as a foundation of the information age.

Feedback is indeed a fundamental concept in twentieth-century technology, and the Bell Labs feedback theorists did lay critical foundations for it. But the origin myth effaces its sources. It skips over the inventors themselves and the ways in which their backgrounds and prior experience influenced their work. It reveals little about the concrete problems these men worked on when they produced their solutions. The story also removes feedback theory from its engineering culture, that of the telephone network between the world wars. Black's version also does not account for the relationship of his feedback amplifiers to prior traditions of governors and self-regulating machinery.

Sterman (2000)

• In common parlance the term "feedback" has come to serve as a euphemism for criticizing others, as in "the boss gave me feedback on my presentation." This use of feedback is not what we mean in system dynamics. Further, "positive feedback" does not mean "praise" and "negative feedback" does not mean "criticism". Positive feedback denotes a self-reinforcing process, and negative feedback denotes a self-correcting one. ... Telling someone your opinion does not constitute feedback unless they act on your suggestions and thus lead you to revise your view.
• Oscillation is the third fundamental mode of behavior observed in dynamic systems. Like goal-seeking behavior, oscillations are caused by negative feedback loops. ... In an oscillatory system, the state of the system constantly overshoots its goal or equilibrium state, reverses, then undershoots, and so on. The overshooting arises from the presence of significant time delays in the negative loop.

Carver (2001)

• In a negative feedback system, the change in output is aimed at countering any deviation of the input function from the reference value. There are several ways to say this, all of which mean the same thing: the change in output is aimed at reducing the discrepancy between input and reference value, at causing the former to conform to the latter. It's an attempt to create input information that's not discriminable from the standard. It isn't behavior for the sake of behavior, but behavior in the service of creating and maintaining a desired perception.
• If the time lag isn't taken into account, the system continues to register a discrepancy long after it has executed the output needed to counter the initially sensed error.
• A positive feedback loop ... is a discrepancy amplifying system. These loops create movement away from the reference value.
• The loop has two sources of information, the input function and the reference value. It should be apparent that both sources are important - indeed, both are necessary for a feedback loop to exist and to function.

Mindell (2002)

Today the adjective negative in the term negative feedback means that the feedback signal subtracts from the input signal rather than adding to it (i.e., the sign of the feedback signal is reversed). In analogy to James Watt’s flyball governor on a steam engine when the engine speeds up, the spinning balls slow it down, and when the balls spin slower, they speed up the engine. Hence the feedback is negative.

In Black’s time, however, even the specific-sounding term negative feed back had yet to acquire a stable definition. The idea of positive feedback had become current in the 1920s with the introduction of the regenerative amplifier. Positive feedback, or regeneration, in a radio amplifier increased the sensitivity of a receiving tube by sending a wave back through an amplifier many times. Black insisted that his “negative feedback” referred to the opposite of regeneration: gain was reduced, not increased. Yet in the analogous steam-engine governor Black’s sense of negative means that the power required to spin the balls reduces the power output of the engine (as opposed to the balls’ triggering an action that slows it)—hardly a significant effect for a steam engine. In their 1924 paper, Friis and Jensen had made the same distinction Black used between “positive feed-back” and “negative feed-back,” based not on the sign of the feedback itself but rather on its effect on the amplifier’s gain. In contrast, Nyquist and Bode, when they built on Black’s work, referred to negative feedback as that with the sign reversed. Black had trouble convincing others of the utility of his invention in part because confusion existed over basic matters of definition.

Misunderstanding also arose over the critical idea of stability. Dickieson recalled why those concerned with singing in amplifiers did not take Black seriously: "Harold did not even approach the question of stability - he simply assumed that it did not sing." Actually, Black was deeply concerned with stability: his first published paper on his amplifier appeared in 1934 with the title "Stabilized Feedback Amplifiers." But for Black, stability referred not to freedom from oscillation but to the long-term behavior of components in the telephone network. Life in the network exposed a telephone repeater to a harsh world, and Black sought to insulate the signal from the brutal reality. He wanted to use feedback to stabilize the characteristics of the amplifier over time. ...

Allison & Hobbs (2006)

Balancing or negative feedback counteracts and opposes change

Aström & Murray(2008)

• A dynamical system is a system whose behavior changes over time, often in response to external stimulation or forcing. The term feedback refers to a situation in which two (or more) dynamical systems are connected together such that each system influences the other and their dynamics are thus strongly coupled. Simple causal reasoning about a feedback system is difficult because the first system influences the second and the second system influences the first, leading to a circular argument. This makes reasoning based on cause and effect tricky, and it is necessary to analyze the system as a whole. A consequence of this is that the behavior of feedback systems is often counterintuitive, and it is therefore necessary to resort to formal methods to understand them.
• The principle of feedback is simple: base correcting actions on the difference between desired and actual performance.
• One of the key uses of feedback is to provide robustness to uncertainty. By measuring the difference between the sensed value of a regulated signal and its desired value, we can supply a corrective action. If the system undergoes some change that affects the regulated signal, then we sense this change and try to force the system back to the desired operating point. This is precisely the effect that Watt exploited in his use of the centrifugal governor on steam engines.

Beerei(2009)

A negative or self-correcting feedback loop describes system behavior that opposes change

2010+

Impey(2011)

In negative feedback, a signal fed back into a system is reduced or cancelled so that change is minimized

Overview

Alternative definitions of feedback:

• measurement: when information about a gap is used to change the gap. This requires a reference value and an actual value to define the gap. This maybe relates more to the "practical experimenters" above, but emphasis may be more on information rather than pathway.
• mechanism: when performance results are used to guide motivation. As per information, but with the emphasis on the mechanism or way of altering the performance.
• macro: when two parts influence each other. Each "part" may be a system or causal chain of arbitrary size. Refers to the entire loop.

The terms positive/negative as applied to feedback have varying usage in different contexts:

1. Context of the gap. Positive feedback results in the original gap being widened (change is reinforced), while negative feedback leads to the gap being narrowed (change is opposed). Also referred to as reinforcing/balancing loops or as discrepancy enlarging/reducing respectively. Here, negative feedback is considered goal-seeking.
2. Context of the mechanism. Feedback often defines the mechanism used to alter the gap (the information about the gap is assumed). "Positive" refers to the use of encouragement or reward to alter the gap, vs. the "negative" use of reprimand/punishment (or no reward). These are also (and more accurately?) termed positive/negative reinforcement. "Negative" can also apply to with-holding a reward. One author[who?] said it also described removing an unpleasant consequence - I suspect that is plain wrong!
3. Context of the actual value. Feedback is sometimes used to define the actual value, and a reference value is assumed - especially in performance appraisals. "Positive/negative" are used to convey "correct/incorrect" signals - so error correction is implied. Although much of the issue in this area has to do with aligning the reference value of assessor to assessee, so the giving of feedback is more effective. Given that the reference is a bit of a black box for both parties, this is non-trivial.

Some possible reasons for the above: as a practicality of early control theory, measuring the mechanism was difficult - whereas the results tended to be clear and unambiguous. In psychology, it is the details of the mechanism that attracts much attention, and goal-seeking (*negative) feedback is often assumed. in performance evaluation, the reference value of "good" performance can be hard to pin down, and may differ between the assessor and the assessed - and again goal-seeking feedback* is often assumed.

Feedback amplifier diagram

"The feedback is negative if the loop gain AB is negative."

System analysis of the feedback amplifier diagram. A system requires at least one of {input, process, output}. Looking at the diagram, I can see it as representing:

1. One system with three processes {A,B,+} and 5 arrows representing 3 outputs and 4 inputs.
2. Two sub-systems, where {A} is the system being controlled, and {B,+} is the control system.
3. Two sub-systems, where {A,+} is the system being controlled, and {B} is the control system.
4. Two sub-systems, where {A,B} is the system being controlled, and {+} is the control system.
5. Three sub-systems, where {B} simply processes the feedback signal but doesn't do any direct controlling.

The overall system {A,B,+} has only one input and one output that cross the system boundaries. Most of the subsystems above have only one input and one output. We could argue that {A} has two outputs, but I don't think that distinction serves any useful purpose here, or it would have involved its own 'splitter' process.

Systems that include process {+} have two inputs. That makes these systems interesting, since this is where some sort of comparison is being made. In terms of semantics, it is important to note which input we mean: without qualification of some sort, I would understand input to mean the arrow leading in from the external environment, and output to mean the arrow that leads out to the external environment.

If we accept for now the idea that negative feedback is always about using a fed-back output to negate an input, it seems that the {+} process is the key point to this definition, and it highlights some of the confusion of terms: one of the inputs to {+} is the fed-back output, and the output from {+} is the modified input in question. It seems that input/output is expressed in terms of the system being controlled, and not in terms of the system doing the controlling. Yet it is the controlling system that defines feedback.

Gain

Another confusion is around gain. Black talked about using feedback to 'throw away some of the gain'. Actually the feedback throws away some of the input. The effective gain of the whole system (1) is reduced, but the actual gain of the amplifier component {A} is not changed. Only what it amplifies is changed.

So is it gain control? If we think of the diagram in terms of (3) above, then yes - the gain of the controlled system {A,+} is changed. Otherwise, we say that it is the input to {A} that is being controlled.

Ambiguity of terms

Ambiguity of the term "positive"

1. increasing or positioning: to "posit" or "lay down". (The original sense/etymology, and the one used here regards feedback.)
2. desirable or pleasant. Not necessarily harmless.
3. beneficial in some way. Not necessarily pleasant.
4. higher than some point of reference. To move "in a positive direction" is to move somehow "upward".
5. confident or definite.

Ambiguity of the term "negative" is simply the converse of the above, except for the last definition. Here "negative" tends to mean null or empty; a non-result.

Confusion seems to arise around the use of "positive" to mean "beneficial", "desirable" or "higher", rather than the intended use of "accumulative/increasing". This is distinct from meaning 4, since we are talking about a gap or displacement, an absolute value. Negative feedback also has its confusions - here maybe due to a finer distinction between "reducing" and "negating", as well as the "undesired/harmful" implications. Also distinct from meaning 4 - a movement to close a gap is valid from either "direction".

Ambiguity of the term "stable"

1. a ladder leaning against a wall is said to be stable.
2. a step-ladder standing in an open space is said to be stable.

Are these the same? In the first case, is the wall is stable, or the ladder?

Confusion arises as to whether a parameter influenced by positive feedback becomes stable when it comes up against a limit - like a ladder against a wall. Is this the same as a parameter that resists perturbations due to negative feedback? Does the limit count as negative feedback?

Using "equilibrium" in definitions

Equilibrium: "The condition of a system in which competing influences are balanced, resulting in no net change." Newton's first law may contradict this ... balanced influences may result in constant change, as in "a body in motion tends to stay in motion."

Is using "equilibrium" as a reference point to define types of feedback maybe a case of circular reasoning? (Ironic!) It seems to be a tautology: "An imbalance of influences will cause divergences from a condition of balanced influences." Or: "an imbalance is not balanced". Or maybe "positive feedback causes a net change which diverges from no net change."

Also, "no net change" with respect to what? There is always a reference point involved.

Use of "loop gain" as basis of definition

If this refers to the entire loop, it seems a useful definition. I break the loop somewhere arbitrarily, put a signal or input into one end and see what comes out the other. If it is inverted, the loop is "negative". If it is bigger, |gain| > 1. That seems to work. If this refers only to the feedback path, then there are issues... but maybe this only applies in cases where we can assume the forward path has gain=1. What about when we are interested in gain as the thing to be controlled? The (1-AB) formulation? Hmm.

Examples of confusion

• Feedback in the sense of soliciting opinions, or receiving criticism. This only counts as feedback in the above definition if the opinion/criticism leads to a modification of behaviour. Possible confusion with "positive/negative reinforcement".
• Audio feedback: The increase in the volume of the resulting howl is a good example of positive feedback - the louder the speaker, the more the microphone picks up. However, the howl itself is due to oscillations within the audio system. There seem to be multiple reference points here - the gain of the amplifier should have nothing to do with the frequency of the signal amplified. Possibly, oscillations may be better explained by (delayed) negative feedback - i.e., the value of interest is the current through the speakers, not the gain of the amp.
• Amplifier gain: Often used as a 'general' feedback model - the output is used to cancel some of the input. Great if what we're regulating is the gain (ratio of in:out) but largely meaningless outside that context. What is the output of a freezer? (See below)
• Stability and Dampening:[7] It seems that negative stability and negative damping are both caused by positive feedback (and v.v). Terminology! Argh!
• Number line/Axis: Movement on a number line (or real line) is conventionally positive if to the right. A real number value is positive if positioned to the right of the zero. But positive feedback could move a value either right or left, away from the equilibrium point. So positive refers to an increase in the absolute distance of the value from the reference point (often zero). The same holds for multiple dimensions - the euclidean distance (displacement) from the origin (equilibrium point) is the scalar of interest as far as feedback is concerned.

Confusion from Assumptions about positive/negative:

• That the reference point is zero and that the parameter value is always a positive number (increase in param value = increase in gap = positive feedback)
• That the reference point is the desired value and the gap is an error value (decreasing the gap is desirable and so 'positive')
• That the mechanism of adjusting the gap is the significant part, not the gap itself (reward is 'positive', punishment is 'negative')

---

Target-shooting example: where Bob the shooter is practising hitting the bullseye of a target, and being fed back a score based on each group of shots. Bob wants to get as high a score as possible, which means grouping the shots as close to the bullseye as possible. Let's assume Bob is improving.

1. in cybernetic sense, this is negative feedback since the gap between actual shot and bullseye is closing.
2. in psychology sense, this is positive feedback since the shooter is being rewarded for his accuracy.
3. in electronics sense, this doesn't apply since the output (accuracy?) isn't directly cancelling any input signal, and no phase-shifts are involved except by analogy.

Freezer-thermostat example: where a freezer is kept below (say) 10°C, not by monitoring output ("coldness" leakage?) but by measuring the internal state (temperature). If temp rises, the compressor is switched on (input increases) to lower it again. This is negative feedback, even though temp_increase = input_increase, because input_increase = temp_decrease. The loop as a whole is self-cancelling.

Notes re Valence

It seems that the use of "positive/negative" to mean pleasant/unpleasant is considered poor usage across many disciplines. In Reinforcement, which deals with the pleasant/unpleasant aspect, "positive/negative" is used to indicate the presence or absence of a stimulus, not its valence. In Management Theory, several authors are pushing for the Systems view (reinforcing/opposing change) and are openly critical of the valence usage. John_Sterman comes to mind, and maybe Jay_Wright_Forrester? Ramaprasad sort of avoids the issue.

Oscillation generalised

Investigating the idea that all oscillation can be described as "hunting" or corrective overshoot.

Some counter-arguments involve phase-shift, or instability. User:Nigelj's example of a shaft position control system is very interesting. "The sense of an amplifier had been wired reversed - causing very strong positive feedback instead of the expected negative FB. ...[This] made the system oscillate violently"--Nigelj 22:58, 8 March 2012 (UTC)

Some points to ponder:

1. would the above system have oscillated violently (or at all) if the shaft wasn't spinning? No dispute that PF gave rise to the 'violent' bit.
2. If we bring phase-shift into the mix, aren't we assuming a phase already exists to be shifted? That is, the oscillation is already there. Needs thought, esp. related to Regenerative circuit.
3. And if we now have x and y dimensions to consider, how do we define "positive" movement? Possibly as "away from the origin" vs "to the right/upward".
4. Ditto the above point re x and y dimensions, how do we define "positive" value? Try "displacement from the origin" vs "to the right of/above zero".

In the sense that PF can reinforce a very small existing oscillation until it is noticeable, we could say that PF "gives rise" to osc. Is that "causing" osc?

Looking a bit closer at what is meant by "causing": PF can be a contributory cause of the oscillation. What about being a necessary or sufficient cause? Necessary seems unlikely - oscillation doesn't necessarily imply PF (e.g., pendulums, hunting, etc). Sufficient? Well, no - PF doesn't guarantee oscillations.

Is there possible confusion between delayed NF and PF? Since both can be said to reinforce a value... Momentum pushes a pendulum past the equilibrium point. BUT not through feedback - a body in motion tends to stay in motion.

A possible counter-argument comes from the LC circuit. The circle of cause-and-effect seems to consist of 4 negative/inverting connections. Which means the net circuit is positive!

Related Dilemma(s)

Aim is to (A) improve wikipedia article(s) related to oscillation. Needs are to (B) avoid ambiguous or unclear statements, and (C) include common & important phenomena.

• if (B) then exclude PF as cause of oscillation - neither necessary nor sufficient cause, and positive is confusing in different contexts.
• if (C) then include PF as cause of oscillation - is an important contributory cause (counteracts damping, may kick off oscillation, definite cause of increasing & destructive oscillation).

Theory of constraints notes

Core Conflict Cloud

The Core Conflict Cloud is an Evaporating Cloud that emerges from analysis of a Current Reality Tree (CRT), one of the Thinking Processes. The CRT provides a way for analyzing many system or organizational problems at once, treating them as symptoms of a single core problem. If an easy solution to such a core problem has not already been implemented, it is likely there is some conflict in the organization that is blocking implementation. The role of the Core Conflict Cloud is to address the inherent conflict that prevents sorting the core conflict out.

The role of the Core Conflict Cloud is to explain the existence of the majority of the UDEs and the inherent conflict that prevents sorting them out.

..if an easy solution [to a core problem] has not already been implemented, it is likely there is some conflict in the organization that is blocking implementation.

Notes1: UDEs/TP

Ref: Ref:

In TOC, [problems] are referred to as symptoms or undesirable effects (UDEs) given that there is something more fundamental, the core problem, causing these symptoms.

The process of [analysing a core problem] usually begins with a list of symptoms, called "Undesirable Effects", or UDEs in the jargon of the Thinking Processes. (UDE is pronounced you-dee.)

[The Thinking Processes (TP) are] a suite of logic tools to help managers address business problems in general... [They] act as guides for the decision-making process as well as representations of logic. ... The TP were developed to facilitate beneficial change ... [and] guide the user to find answers to basic questions relating to the change sequence...

"refered to by some as the Conflict Resolution Diagram (CRD)"(Handbook page635, refering to:)

he general process for applying an EC to problem solving is described by Cohen (2010) as follows:

1. Identify the type of problem.

Notes2: 3-cloud technique

Others have developed a revised method of constructing the CRT, called the three UDE EC approach. Houle and Burton-Houle (1998) describe a series of four steps to construct a new CRT:

1. Identify a list of UDEs.
2. Generate three ECs from the list of UDEs.
3. Construct a generic EC from the three ECs, thus identifying the likely core conflict.
4. Build a CRT that starts with the core conflict, and harnesses the logic and pictorial representation of the generic EC.

In order to build the CRT, a counter clockwise rotated generic EC is used as the base of the CRT. Several authors (Cooper and Loe, 2000; Chaudhari and Mukhopadhyay, 2003; Reid and Cormier, 2003; Shoemaker and Reid, 2005; Bourke et al., 2005) use the three-cloud approach to identify a conflict. A detailed explanation is provided by Reid and Cormier (2003) and Shoemaker and Reid (2005).

Even though proponents of the three-cloud approach suggest that it is a less time consuming method of building a CRT than the traditional approach, the review demonstrates that both approaches have been much in use. Furthermore, it may not be appropriate to combine/develop one generic EC from three ECs when one EC is nested or embedded in the other EC.

...

The EC method (Goldratt, 1990) was designed to address conflict or dilemma situations viewed as trade-off situations where there is no acceptable compromise. The EC provides alternative insightful ways of viewing the dilemma and provides an approach leading to alternative ways to resolve the conflict. The search for solutions to “evaporate” the dilemma can be done in several ways. Ideas for solutions (termed “injections” in TOC) could be generated by examining the conflict cloud directly, or by methodically surfacing assumptions and then seeking to invalidate them.

Unlike the trees, the EC has a set format with five boxes. The practitioner identifies two opposing wants, that represent the conflict, the need that each want is trying to satisfy, and a common objective or goal that both needs are trying to fulfil. Then the practitioner surfaces the assumptions that underlie the connections between objectives and needs, needs and wants, and in the process, uncovers the reasons for the conflict that exists in their reality and prevents them from achieving the desired objective. This direct conflict is often the same as that underlying the CRT, and in fact forms the base of the new-style CRT.

A significant recent extension of the cloud method is in the development of a generic cloud (or core conflict cloud), which is used to form the base of the new-style CRT. The generic cloud is created from merging three individual clouds, each of which is based on a single UDE. If the generic cloud derived is identified correctly, then the existence of the UDEs stems from this generic conflict, which hypothesis is verified by checking whether all of the UDEs can be connected using If-Then logic to the generic cloud. If there are "outlier" UDEs that are relevant to the subject matter but which cannot be linked back to the hypothesised generic conflict, then the cloud is not generic enough and is revised before continuing to draw up the new-style CRT.

Notes3: TOC

"...the 80-20 rule is correct only when when there are no interdependencies between the elements of the system. The more interdependencies (and the bigger the variability), the more extreme the situation becomes... Using Pareto's vocabulary, one might say that in organizations 0.1 percent of the elements dictate 99.9 percent of the result."(Goldratt, 2010)

"7/15. Laws of Nature. First we can notice that the existence of any invariant over a set of phenomena implies a constraint, for its existence implies that the full range of variety does not occur. The general theory of invariants is thus a part of the theory of constraints.

"Further, as every law of nature implies the existence of an invariant, it follows that every law of nature is a constraint. Thus, the Newtonian law says that, of the vectors of planetary positions and velocities which might occur, e.g. written on paper (the larger set), only a smaller set will actually occur in the heavens; and the law specifies what values the elements will have. From our point of view, what is important is that the law excludes many positions and velocities, predicting that they will never be found to occur."(Ashby 1956)