Feedback

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For behavioural reinforcement and personal feedback, see reinforcement.
For other uses, see Feedback (disambiguation).
"...'feedback' exists between two parts when each affects the other."[1](p53, §4/11)

Feedback is the return of information about a system or process that may effect a change in the process, for example, the regulation or optimization of performance.[2] As part of a chain of cause-and-effect that forms a circuit or loop, the system is said to "feed back" into itself.

Feedback is also used as an adjective as in:

  • Feedback signal – the embodiment of feedback information in some form: electrical, neural, mechanical, chemical etc.
  • Feedback mechanism – the action or means used to act upon feedback information
  • Feedback loop – the closed path made up of the system itself and the path that transmits the feedback about the system from its origin (for example, a sensor) to its destination (for example, an actuator).

History[edit]

Self-regulating mechanisms have existed since antiquity, and the idea of feedback had started to enter economic theory in Britain by the eighteenth century, but it wasn't at that time recognized as a universal abstraction and so didn't have a name.[3]

The verb phrase "to feed back", in the sense of returning to an earlier position in a mechanical process, was in use in the US by the 1860s,[4][5] and in 1909, Nobel laureate Karl Ferdinand Braun used the term "feed-back" as a noun to refer to (undesired) coupling between components of an electronic circuit.[6]

By the end of 1912, researchers using early electronic amplifiers (audions) had discovered that deliberately coupling part of the output signal back to the input circuit would boost the amplification (through regeneration), but would also cause the audion to howl or sing.[7] This action of feeding back of the signal from output to input gave rise to the use of the term "feedback" as a distinct word by 1920.[7]

There has been over the years some dispute as to the best definition of feedback. According to Ashby (1956), mathematicians and theorists interested in the principles of feedback mechanisms prefer the definition of circularity of action, which keeps the theory simple and consistent. For those with more practical aims, feedback should be a deliberate effect via some more tangible connection.

"[Practical experimenters] 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."[1](p54)

Ramaprasad (1983) defines feedback generally as "...information about the gap between the actual level and the reference level of a system parameter" that is used to "alter the gap in some way." He emphasizes that the information by itself is not feedback unless translated into action.[8]

Types[edit]

Maintaining car speed using negative feedback. Car speed is decided by the combination of the road grade and the gasoline input. The feedback is the amount of gasoline decided by the driver upon comparing the speedometer reading to the speed limit, and adjusting the throttle (accelerator) to reduce the error observed by the driver.

Two types of feedback are termed positive feedback and negative feedback.

The terms "positive/negative" were first applied to feedback prior to WWII. The idea of positive feedback was already current in the 1920s with the introduction of the regenerative circuit.[9] Friis and Jensen (1924) described regeneration in a set of electronic amplifiers as a case where the "feed-back" action is positive in contrast to negative feed-back action, which they mention only in passing.[10] Harold Stephen Black's classic 1934 paper first details the use of negative feedback in electronic amplifiers. According to Black:

"Positive feed-back increases the gain of the amplifier, negative feed-back reduces it."[11]

According to Mindell (2002) confusion in the terms arose shortly after this:

"...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."[9](p121)

Even prior to the terms being applied, James Clerk Maxwell had described several kinds of "component motions" associated with the centrifugal governors used in steam engines, distinguishing between those that lead to a continual increase in a disturbance or the amplitude of an oscillation, and those that lead to a decrease of the same.[12]

Terminology[edit]

The terms positive and negative feedback are defined in different ways within different disciplines.

  1. the altering of the gap between reference and actual values of a parameter, based on whether the gap is widening (positive) or narrowing (negative).[8]
  2. the valence of the action or effect that alters the gap, based on whether it has a happy (positive) or unhappy (negative) emotional connotation to the recipient or observer.[13]

The two definitions may cause confusion, such as when an incentive (reward) is used to boost poor performance (narrow a gap). Referring to definition 1, some authors use alternative terms, replacing 'positive/negative' with self-reinforcing/self-correcting,[14] reinforcing/balancing,[15] discrepancy-enhancing/discrepancy-reducing[16] or regenerative/degenerative[17] respectively. And for definition 2, some authors advocate describing the action or effect as positive/negative reinforcement or punishment rather than feedback.[8][18] Yet even within a single discipline an example of feedback can be called either positive or negative, depending on how values are measured or referenced.[19]

This confusion may arise because feedback can be used for either informational or motivational purposes, and often has both a qualitative and a quantitative component. As Connellan and Zemke (1993) put it:

"Quantitative feedback tells us how much and how many. Qualitative feedback tells us how good, bad or indifferent."[20](p102)

Limitations of negative and positive feedback[edit]

While simple systems can sometimes be described as one or the other type, many systems with feedback loops cannot be so easily easily designated as simply positive or negative, and this is especially true when multiple loops are present.

"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."[1](p54)

In general, many feedback systems contain mixtures of positive and negative feedback. Positive and negative feedback can dominate at different frequencies or different points in the state space of a system.

Thus some systems with feedback can have very complex behaviors such as chaotic behaviors in non linear systems, while others have much more predictable behaviors, such as are used to make and design digital systems.

The term bipolar feedback has been coined to refer to biological systems where positive and negative feedback systems can interact, the output of one affecting the input of another, and vice versa.[21]

Applications[edit]

Biology[edit]

In biological systems such as organisms, ecosystems, or the biosphere, most parameters must stay under control within a narrow range around a certain optimal level under certain environmental conditions. The deviation of the optimal value of the controlled parameter can result from the changes in internal and external environments. A change of some of the environmental conditions may also require change of that range to change for the system to function. The value of the parameter to maintain is recorded by a reception system and conveyed to a regulation module via an information channel. An example of this is Insulin oscillations.

Biological systems contain many types of regulatory circuits, both positive and negative. As in other contexts, positive and negative do not imply consequences of the feedback have good or bad final effect. A negative feedback loop is one that tends to slow down a process, whereas the positive feedback loop tends to accelerate it. The mirror neurons are part of a social feedback system, when an observed action is "mirrored" by the brain—like a self-performed action.

Feedback is also central to the operations of genes and gene regulatory networks. Repressor (see Lac repressor) and activator proteins are used to create genetic operons, which were identified by Francois Jacob and Jacques Monod in 1961 as feedback loops. These feedback loops may be positive (as in the case of the coupling between a sugar molecule and the proteins that import sugar into a bacterial cell), or negative (as is often the case in metabolic consumption).

On a larger scale, feedback can have a stabilizing effect on animal populations even when profoundly affected by external changes, although time lags in feedback response can give rise to predator-prey cycles.[22]

In zymology, feedback serves as regulation of activity of an enzyme by its direct product(s) or downstream metabolite(s) in the metabolic pathway (see Allosteric regulation).

Hypothalamo-pituitary-adrenal and gonadal axis is largely controlled by positive and negative feedback, much of which is still unknown.

In psychology, the body receives a stimulus from the environment or internally that causes the release of hormones. Release of hormones then may cause more of those hormones to be released, causing a positive feedback loop. This cycle is also found in certain behaviour. For example, "shame loops" occur in people who blush easily. When they realize that they are blushing, they become even more embarrassed, which leads to further blushing, and so on.[23]

Climate science[edit]

The climate system is characterized by strong positive and negative feedback loops between processes that affect the state of the atmosphere, ocean, and land. A simple example is the ice-albedo positive feedback loop whereby melting snow exposes more dark ground (of lower albedo), which in turn absorbs heat and causes more snow to melt.

Control theory[edit]

Main article: Control theory

Feedback is extensively used in control theory, using a variety of methods including state space (controls), full state feedback (also known as pole placement), and so forth. Note that in the context of control theory, "feedback" is traditionally assumed to specify "negative feedback".[24]

Further information: PID controller

The most common general-purpose controller using a control-loop feedback mechanism is a proportional-integral-derivative (PID) controller. Heuristically, the terms of a PID controller can be interpreted as corresponding to time: the proportional term depends on the present error, the integral term on the accumulation of past errors, and the derivative term is a prediction of future error, based on current rate of change.[25]

Customer experience[edit]

Main article: Customer experience

Closed feedback loops are the primary tool used (and deployed throughout the customer lifecycle) when developing Customer Experience Management (CXM) systems. Data from all customer touchpoints including Voice of the customer (VoC) solutions used such as Incentivised Feedback Surveys is then analysed triggering intervention where necessary to initiate a customer rescue. The ultimate goal for CXM and the feedback obtained being to achieve longevity in terms of the customer lifecycle.[26]

Customer experience should be a total enterprise goal, not just the purview of the customer service team. Sales, finance, product development and other teams now all have a role in collecting customer feedback and closing the loop with customers.[27]Feedback into CXM systems includes both the individual experience in a single transaction as well as the sum of all experiences.[28]

"Any organization that cares about delivering value to its customers should care about CXM," says Kurt Carlson, associate professor of marketing at Georgetown University's McDonough School of Business. "Organizations that will benefit most are those that operate in spaces where consumers have a lot of choice and where switching costs are low."[29]

Mechanical engineering[edit]

In ancient times, the float valve was used to regulate the flow of water in Greek and Roman water clocks; similar float valves are used to regulate fuel in a carburettor and also used to regulate tank water level in the flush toilet.

The Dutch inventor Cornelius Drebbel (1572-1633) built thermostats (c1620) to control the temperature of chicken incubators and chemical furnaces. In 1745, the windmill was improved by blacksmith Edmund Lee, who added a fantail to keep the face of the windmill pointing into the wind. In 1787, Thomas Mead regulated the rotation speed of a windmill by using a centrifugal pendulum to adjust the distance between the bedstone and the runner stone (i.e., to adjust the load).

The use of the centrifugal governor by James Watt in 1788 to regulate the speed of his steam engine was one factor leading to the Industrial Revolution. Steam engines also use float valves and pressure release valves as mechanical regulation devices. A mathematical analysis of Watt's governor was done by James Clerk Maxwell in 1868.[12]

The Great Eastern was one of the largest steamships of its time and employed a steam powered rudder with feedback mechanism designed in 1866 by John McFarlane Gray. Joseph Farcot coined the word servo in 1873 to describe steam-powered steering systems. Hydraulic servos were later used to position guns. Elmer Ambrose Sperry of the Sperry Corporation designed the first autopilot in 1912. Nicolas Minorsky published a theoretical analysis of automatic ship steering in 1922 and described the PID controller.[30]

Internal combustion engines of the late 20th century employed mechanical feedback mechanisms such as the vacuum timing advance but mechanical feedback was replaced by electronic engine management systems once small, robust and powerful single-chip microcontrollers became affordable.

Electronic engineering[edit]

The simplest form of a feedback amplifier can be represented by the ideal block diagram made up of unilateral elements.[31]

The use of feedback is widespread in the design of electronic amplifiers, oscillators, and logic circuit elements. Electronic feedback systems are also very commonly used to control mechanical, thermal and other physical processes.

If the signal is inverted on its way round the control loop, the system is said to have negative feedback;[32] otherwise, the feedback is said to be positive. Negative feedback is often deliberately introduced to increase the stability and accuracy of a system by correcting or reducing the influence of unwanted changes. This scheme can fail if the input changes faster than the system can respond to it. When this happens, the lag in arrival of the correcting signal can result in over-correction, causing the output to oscillate or "hunt".[33] While often an unwanted consequence of system behaviour, this effect is used deliberately in electronic oscillators.

Harry Nyquist contributed the Nyquist plot for assessing the stability of feedback systems. An easier assessment, but less general, is based upon gain margin and phase margin using Bode plots (contributed by Hendrik Bode). Design to ensure stability often involves frequency compensation, one method of compensation being pole splitting.

Electronic feedback loops are used to control the output of electronic devices, such as amplifiers. A feedback loop is created when all or some portion of the output is fed back to the input. A device is said to be operating open loop if no output feedback is being employed and closed loop if feedback is being used.[34]

Negative feedback loops
When the fed-back output signal is out of phase with the input signal. This occurs when the fed-back signal is anywhere from 90° to 270° with respect to the input signal. Negative feedback can be used to correct output errors or to desensitize a system to unwanted fluctuations.[35] In feedback amplifiers, this correction is generally for waveform distortion reduction or to establish a specified gain level. A general expression for the gain of a negative feedback amplifier is the asymptotic gain model.
Positive feedback loops
When the fed-back signal is in phase with the input signal. Under certain gain conditions, positive feedback reinforces the input signal to the point where the output of the device oscillates between its maximum and minimum possible states. Positive feedback may also introduce hysteresis into a circuit. This can cause the circuit to ignore small signals and respond only to large ones. It is sometimes used to eliminate noise from a digital signal. Under some circumstances, positive feedback may cause a device to latch, i.e., to reach a condition in which the output is locked to its maximum or minimum state. This fact is very widely used in digital electronics to make bistable circuits for volatile storage of information.

The loud squeals that sometimes occurs in audio systems, PA systems, and rock music are known as audio feedback. If a microphone is in front of a loudspeaker that it is connected to, sound that the microphone picks up comes out of the speaker, and is picked up by the microphone and re-amplified. If the loop gain is sufficient, howling or squealing at the maximum power of the amplifier is possible.

Software engineering and computing systems[edit]

Feedback loops provide generic mechanisms for controlling the running, maintenance, and evolution of software and computing systems.[36] Feedback-loops are important models in the engineering of adaptive software, as they define the behaviour of the interactions among the control elements over the adaptation process, to guarantee system properties at run-time. Feedback loops and foundations of control theory have been successfully applied to computing systems.[37] In particular, they have been applied to the development of products such as IBM's Universal Database server and IBM Tivoli. From a software perspective, the autonomic (MAPE, monitor analyze plan execute) loop proposed by researchers of IBM is another valuable contribution to the application of feedback loops to the control of dynamic properties and the design and evolution of autonomic software systems.[38][39]

Social sciences[edit]

A feedback loop to control human behaviour involves four distinct stages.[40]

  1. Evidence. A behaviour must be measured, captured, and data stored.
  2. Relevance. The information must be relayed to the individual, not in the raw-data form in it was captured in, but in a context that makes it emotionally resonant.
  3. Consequence. The information must illuminate one or more paths ahead.
  4. Action. There must be a clear moment when the individual can recalibrate a behavior, make a choice, and act. Then that action is measured, and the feedback loop can run once more, every action stimulating new behaviors that inch the individual closer to their goals.

Reflexive feedback[edit]

A sociological concept that states a feedback association is created within a certain relationship whereby the subject/object that delivers a stimulus to a second subject/object, receives the stimulus back in response. This first impulse is reflected back and forth repeatedly.

Economics and finance[edit]

The stock market is an example of a system prone to oscillatory "hunting", governed by positive and negative feedback resulting from cognitive and emotional factors among market participants. For example,

  • When stocks are rising (a bull market), the belief that further rises are probable gives investors an incentive to buy (positive feedback—reinforcing the rise, see also stock market bubble); but the increased price of the shares, and the knowledge that there must be a peak after which the market falls, ends up deterring buyers (negative feedback—stabilizing the rise).
  • Once the market begins to fall regularly (a bear market), some investors may expect further losing days and refrain from buying (positive feedback—reinforcing the fall), but others may buy because stocks become more and more of a bargain (negative feedback—stabilizing the fall).

George Soros used the word reflexivity, to describe feedback in the financial markets and developed an investment theory based on this principle.

The conventional economic equilibrium model of supply and demand supports only ideal linear negative feedback and was heavily criticized by Paul Ormerod in his book The Death of Economics, which, in turn, was criticized by traditional economists. This book was part of a change of perspective as economists started to recognise that chaos theory applied to nonlinear feedback systems including financial markets.

World-system development[edit]

The hyperbolic growth of the world population observed till the 1970s has recently been correlated to a non-linear second-order positive feedback between the demographic growth and technological development that can be spelled out as follows: technological growth—increase in the carrying capacity of land for people—demographic growth—more people—more potential inventors—acceleration of technological growth—accelerating growth of the carrying capacity—the faster population growth—accelerating growth of the number of potential inventors—faster technological growth—hence, the faster growth of the Earth's carrying capacity for people, and so on.[41]

Education[edit]

In the majority of universities, teachers decide learning objectives and feedbacks to students.[42] Learners have different conceptions of learning activities and preconceptions about hierarchy in education. Some may look up to instructors as experts in the field and take to heart most of the things instructors say. This is the subject of study in the field of "formative feedback" or "formative assessment".

Types of reinforcement that operate in student assessment[43]
Reinforcement Example
Confirmation Your answer was correct.
Corrective Your answer was incorrect. The correct answer was Jefferson.
Explanatory Your answer was incorrect because Carter was from Georgia; only Jefferson called Virginia home.
Diagnostic Your answer was incorrect. Your choice of Carter suggests some extra instruction on the home states of past presidents might be helpful.
Elaborative Your answer, Jefferson, was correct. The University of Virginia, a campus rich with Jeffersonian architecture and writings, is sometimes referred to as "Mr. Jefferson's University".

A different application of feedback in education is the system for "continuous improvement" of engineering curricula monitored by the Accreditation Board for Engineering and Technology (ABET).[44]

Government[edit]

Examples of feedback in government are:

Email administration[edit]

Main article: Feedback loop (email)

A mechanism to alert the purported sender of an email with information about the email.

In organizations[edit]

As an organization seeks to improve its performance, feedback helps it to make required adjustments. Feedback motivates many people in the work place. People who receive negative or positive feedback must decide how to apply it to their job. Joseph Folkman says that to find the greatest level of success in an organization, working with other people, a person should learn how to accept any kind of feedback, analyze it in the most constructive manner possible, and use it to further impact future decision making.[45]

Sterman (2000, p 14) makes the point that the use of the term feedback in organizations can sometimes be misleading.

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.[15]

Examples of feedback in organizations:

In Psychology[edit]

One application of feedback in psychology, education, and organizations is feedback intervention; defined as "actions taken by (an) external agent(s) to provide information regarding some aspect(s) of one's task performance."[46] Despite common beliefs that such feedback is typically effective, Kluger & DeNisi (1996) reported a meta-analysis that showed that in 38% of the experiments published between 1905 and 1992, feedback caused a decline in performance.[46] Moreover, the decline in performance was not related to whether the feedback was positive or negative (i.e., encouraging or critical). This result was explained with Higgins' Regulatory focus theory. Specifically, positive feedback seems to improve motivation and performance when people are promotion-focused (doing things out of a desire; working on a task requiring creativity.) Whereas negative feedback improves performance when people are prevention-focused (doing things out of an obligation; working on a task requiring vigilance.)[47]

See also[edit]

References[edit]

  1. ^ a b c W. Ross Ashby (1957). An introduction to cybernetics. Chapman & Hall.  See also: Google books, ISBN 9781258693817
  2. ^ Christopher G. Morris, ed. (1992). Academic Press Dictionary of Science and Technology. Academic Press Inc. p. 812. ISBN 0122004000. 
  3. ^ Otto Mayr (1989). Authority, liberty, & automatic machinery in early modern Europe. Johns Hopkins University Press. ISBN 0-8018-3939-4. 
  4. ^ "Heretofore ... it has been necessary to reverse the motion of the rollers, thus causing the material to travel or feed back, ..." HH Cole, "Improvement in Fluting-Machines", US Patent 55,469 (1866) accessed 23 Mar 2012.
  5. ^ "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..." JM Jay, "Improvement in Machines for Making the Spindles of Wagon-Axles", US Patent 47,769 (1865) accessed 23 Mar 2012.
  6. ^ "...as far as possible the circuit has no feed-back into the system being investigated." [1] Karl Ferdinand Braun, "Electrical oscillations and wireless telegraphy", Nobel Lecture, 11 December 1909. Retrieved 19 Mar 2012.
  7. ^ a b Stuart Bennett (1979). A history of control engineering, 1800-1930. Stevenage; New York: Peregrinus for the Institution of Electrical Engineers. ISBN 0-906048-07-9.  [2]
  8. ^ a b c Arkalgud Ramaprasad, "On The Definition of Feedback", Behavioral Science, Volume 28, Issue 1. 1983. Online PDF last accessed 16 March 2012.
  9. ^ a b David A. Mindell (2002). Between Human and Machine : Feedback, Control, and Computing before Cybernetics.. Baltimore, MD, USA: Johns Hopkins University Press. 
  10. ^ Friis,H.T., and A.G.Jensen. "High Frequency Amplifiers" Bell System Technical Journal 3 (April 1924):181-205.
  11. ^ H.S. Black, "Stabilized feed-back amplifiers", Electrical Engineering, vol. 53, pp. 114–120, Jan. 1934.
  12. ^ a b Maxwell, James Clerk (1868). On Governors 16. Proceedings of the Royal Society of London. pp. 270–283. 
  13. ^ Herold, David M., and Martin M. Greller. "Research Notes. FEEDBACK THE DEFINITION OF A CONSTRUCT." Academy of management Journal 20.1 (1977): 142-147.
  14. ^ Peter M. Senge (1990). The Fifth Discipline: The Art and Practice of the Learning Organization. New York: Doubleday. p. 424. ISBN 0-385-26094-6. 
  15. ^ a b John D.Sterman, Business Dynamics: Systems Thinking and Modeling for a Complex World McGraw Hill/Irwin, 2000. ISBN 978-0-07-238915-9
  16. ^ Charles S. Carver, Michael F. Scheier: On the Self-Regulation of Behavior Cambridge University Press, 2001
  17. ^ Hermann A Haus and Richard B. Adler, Circuit Theory of Linear Noisy Networks, MIT Press, 1959
  18. ^ BF Skinner, The Experimental Analysis of Behavior, American Scientist, Vol. 45, No. 4 (SEPTEMBER 1957), pp. 343-371
  19. ^ "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." Ralph L. Levine, Hiram E. Fitzgerald. Analysis of dynamic psychological systems: methods and applications, ISBN 978-0306437465 (1992) page 123
  20. ^ Thomas K. Connellan and Ron Zemke, "Sustaining Knock Your Socks Off Service" AMACOM, 1 July 1993. ISBN 0-8144-7824-7
  21. ^ Alta Smit, Arturo O'Byrne (2011). "Bipolar feedback". Introduction to Bioregulatory Medicine. Thieme. p. 6. ISBN 9783131469717. 
  22. ^ CS Holling. "Resilience and stability of ecological systems". Annual Review of Ecology and Systematics 4:1-23. 1973
  23. ^ Scheff, Thomas (2009-09-02). "The Emotional/Relational World". Psychology Today. Retrieved 2013-07-10. 
  24. ^ "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..." A.I.Mees, "Dynamics of Feedback Systems", New York: J. Wiley, c1981. ISBN 0-471-27822-X. p69
  25. ^ Araki, M., PID Control 
  26. ^ Jamie Snape (2014-08-21). "Customer Experience Management (CXM / CEM)". 
  27. ^ Jennifer Lonoff Schiff (2012-06-13). "Why CXM Is the Next Step in Customer Interaction". 
  28. ^ Chuck Schaeffer. "CXM is the Next Category in the CRM Evolution". 
  29. ^ Jennifer Lonoff Schiff (2012-06-13). "Why CXM Is the Next Step in Customer Interaction". 
  30. ^ Minorsky, Nicolas (1922). "Directional stability of automatically steered bodies". J. Amer. Soc of Naval Engineers 34: 280–309. 
  31. ^ Wai-Kai Chen (2005). "Chapter 13: General feedback theory". Circuit Analysis and Feedback Amplifier Theory. CRC Press. p. 13-1. ISBN 9781420037272. "[In a practical amplifier] the forward path may not be strictly unilateral, the feedback path is usually bilateral, and the input and output coupling networks are often complicated." 
  32. ^ Santiram Kal (2009). Basic Electronics: Devices, Circuits and IT Fundamentals. PHI Learning Pvt. Ltd. p. 191. ISBN 9788120319523. "If the feedback signal reduces the input signal, i.e. it is out of phase with the input [signal], it is called negative feedback." 
  33. ^ With mechanical devices, hunting can be severe enough to destroy the device.
  34. ^ P. Horowitz & W. Hill, The Art of Electronics, Cambridge University Press (1980), Chapter 3, relating to operational amplifiers.
  35. ^ For an analysis of desensitization in the system pictured, see S.K Bhattacharya (2011). "§5.3.1 Effect of feedback on parameter variations". Linear Control Systems. Pearson Education India. pp. 134–135. ISBN 9788131759523. "The parameters of a system ... may vary... The primary advantage of using feedback in control systems is to reduce the system's sensitivity to parameter variations." 
  36. ^ H. Giese, Y. Brun, J. D. M. Serugendo, C. Gacek, H. Kienle, H. Müller, M. Pezzè, and M. Shaw (2009). "Engineering self-adaptive and self-managing systems". Springer-Verlag. 
  37. ^ J. L. Hellerstein, Y. Diao, S. Parekh, and D. M. Tilbury (2004). Feedback Control of Computing Systems. John Wiley & Sons. 
  38. ^ J. O. Kephart and D. M. Chess (2003). "The vision of autonomic computing". 
  39. ^ H. A. Müller, H. M. Kienle, and U. Stege, (2009). "Autonomic computing: Now you see it, now you don’t—design and evolution of autonomic software systems". 
  40. ^ Thomas, Goetz (19 June 2011). "Harnessing the power of Feedback Loops". Wired Magazine (Wired Magazine). Retrieved 20 June 2011. 
  41. ^ Introduction to Social Macrodynamics by Andrey Korotayev et al.
  42. ^ J. Scott Armstrong (2012). "Natural Learning in Higher Education". Encyclopedia of the Sciences of Learning. 
  43. ^ Fleming, M., & Levie, W.H. (1993). Instructional message design: principles from the behavioral and cognitive sciences (Second Edition ed.). Englewood Cliffs NJ: Educational Technology Publications. ISBN 0-87778-253-9. 
  44. ^ Accreditation provides you with a structured mechanism to assess and improve the quality of your program: The two-loop feedback diagram
  45. ^ Folkman, Joseph R. The Power of Feedback. 1st ed. New Jersey: John Wiley & Sons Inc., 2006. Print.
  46. ^ a b Kluger, A. N., & DeNisi, A. (1996). The effects of feedback interventions on performance: A historical review, a meta-analysis, and a preliminary feedback intervention theory. Psychological Bulletin, 119, 254-284.
  47. ^ Van Dijk, D., & Kluger, A. N. (2011). Task type as a moderator of positive/negative feedback effects on motivation and performance: A regulatory focus perspective. Journal of Organizational Behavior, 32, 1084-1105. doi: 10.1002/job.725

Further reading[edit]