Negative feedback

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Simple feedback model. The feedback is negative if AB < 0

Negative feedback occurs when the result of a process influences the operation of the process itself in such a way as to reduce changes. Negative feedback tends to make a system self-regulating; it can produce stability and reduce the effect of fluctuations. Negative feedback loops in which just the right amount of correction is applied in the most timely manner can be very stable, accurate, and responsive.

In systems controlled by a negative feedback loop, a measurement of some variable is compared with a required value to estimate the current error, which is then used to reduce the gap between the measurement and the required value,[1] as well as to counter the effects of unpredictable influences from the system's environment.

Negative feedback is widely used in mechanical and electronic engineering, but it also occurs naturally within living organisms, and can be seen in many other fields from chemistry and economics to social behaviour and the climate. For example, negative feedback as a control technique may be seen in the refinements of the water clock introduced by Ktesibios of Alexandria in the 3rd century BCE and in the steam engine governor patented by James Watt in 1788. The mathematical principles were first worked out by Harold S. Black at Bell Telephone Laboratories in 1933[2][3] as the basis for electronic systems. General negative feedback systems are studied mathematically in control systems engineering.


Self-regulating mechanisms have existed since antiquity, and were used to maintain a constant level in the reservoirs of water clocks as early as 200 BCE.[4] Cornelius Drebbel had built thermostatically-controlled incubators and ovens in the early 1600s,[5] James Watt employed centrifugal governors to regulate the speed of steam engines, and James Clerk Maxwell in 1868 described "component motions" associated with these governors that lead to a decrease in a disturbance or the amplitude of an oscillation.[6]

The general idea of feedback was well established by the 1920s, in reference to a means of boosting the gain of an electronic amplifier.[7] Friis and Jensen described this action as "positive feedback" and made passing mention of a contrasting "negative feed-back action" in 1924.[8] Harold Stephen Black detailed the use of negative feedback in electronic amplifiers in 1934, where he defined negative feedback as a type of coupling that reduced the gain of the amplifier, in the process greatly increasing its stability.[2] Nyquist and Bode built on Black’s work to develop a theory of amplifier stability, but chose to define "negative" as applying to the polarity of the loop (rather than the effect on the gain), which gave rise to some confusion over basic definitions.[7]

Early researchers in the area of cybernetics subsequently generalised the idea of negative feedback to cover any goal-seeking or purposeful behavior.[9]

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.

Cybernetics pioneer Norbert Wiener helped to formalize the concepts of feedback control, defining feedback in general as "the chain of the transmission and return of information",[10] and negative feedback as the case when:

The information fed back to the control center tends to oppose the departure of the controlled from the controlling quantity...(p97)

While the view of feedback as any "circularity of action" helped to keep the theory simple and consistent, Ashby pointed out that it can clash with definitions in other fields that require "a more tangible connexion."[11]

[The] practical experimenters and constructors ... 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.(p54)

Further confusion arose after BF Skinner introduced the terms positive and negative reinforcement,[12] both of which can be considered negative feedback mechanisms in the sense that they try to minimize deviations from the desired behavior.[1] In a similar context, Herold and Greller used the term "negative" to refer to the valence of the feedback: that is, cases where a subject receives an evaluation with an unpleasant emotional connotation.[13]

A common theme for the 10 items [in the feedback analysis] 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.

To reduce confusion, later authors have suggested alternative terms such as degenerative,[14] self-correcting,[15] balancing,[16] or discrepancy-reducing[17] in place of "negative".


Feedback loops in the human body

In many physical and biological systems, qualitatively different influences can oppose each other. For example, in biochemistry, one set of chemicals drives the system in a given direction, whereas another set of chemicals drives it in an opposing direction. If one or both of these opposing influences are non-linear, equilibrium point(s) result.

In biology, this process (in general, biochemical) is often referred to as homeostasis; whereas in mechanics, the more common term is equilibrium.

In engineering, mathematics and the physical, and biological sciences, common terms for the points around which the system gravitates include: attractors, stable states, eigenstates/eigenfunctions, equilibrium points, and setpoints.

In control theory, negative refers to the sign of the multiplier in mathematical models for feedback. In delta notation, −Δoutput is added to or mixed into the input. In multivariate systems, vectors help to illustrate how several influences can both partially complement and partially oppose each other.[7]

Some authors, in particular with respect to modelling business systems, use negative to refer to the reduction in difference between the desired and actual behavior of a system.[1][16] While in a psychology context, negative refers to the valence of the feedback - how unhappy it makes the recipient.[13]

In contrast, positive feedback is feedback in which the system responds so as to increase the magnitude of any particular perturbation, resulting in amplification of the original signal instead of stabilization. Any system in which there is positive feedback together with a gain greater than one will result in a runaway situation. Both positive and negative feedbacks require a feedback loop to operate.


Mechanical engineering[edit]

The fly-ball governor is an early example of negative feedback.

Negative feedback was first implemented in the 16th Century with the invention of the centrifugal governor. Its operation is most easily seen in its use by James Watt to control the speed of his steam engine. Two heavy balls on an upright frame rotate at the same speed as the engine. As their speed increases they swing up and outwards due to centrifugal force. This causes them to lift a mechanism that closes the steam inlet valve, and the engine slows. When the speed of the engine falls too far, the balls will fall by gravity and open the steam valve.

Control systems[edit]

The ballcock or float valve uses negative feedback to control the water level in a cistern.

Examples of the use of negative feedback to control its system are: thermostat control, phase-locked loop, hormonal regulation (see diagram above), and temperature regulation in animals.

A simple and practical example is a thermostat. When the temperature in a heated room reaches a certain upper limit, the room heating is switched off so that the temperature begins to fall. When the temperature drops to a lower limit, the heating is switched on again. Provided the limits are close to each other, a steady room temperature is maintained. Similar control mechanisms are used in cooling systems, such as an air conditioner, a refrigerator, or a freezer.

Biology and chemistry[edit]

Most endocrine hormones are controlled by a physiologic negative feedback inhibition loop, such as the glucocorticoids secreted by the adrenal cortex. The hypothalamus secretes corticotropin-releasing hormone (CRH), which directs the anterior pituitary gland to secrete adrenocorticotropic hormone (ACTH). In turn, ACTH directs the adrenal cortex to secrete glucocorticoids, such as cortisol. Glucocorticoids not only perform their respective functions throughout the body but also negatively affect the release of further stimulating secretions of both the hypothalamus and the pituitary gland, effectively reducing the output of glucocorticoids once a sufficient amount has been released.[18]

Some biological systems exhibit negative feedback such as the baroreflex in blood pressure regulation and erythropoiesis. Many biological process (e.g., in the human anatomy) use negative feedback. Examples of this are numerous, from the regulating of body temperature, to the regulating of blood glucose levels. The disruption of feedback loops can lead to undesirable results: in the case of blood glucose levels, if negative feedback fails, the glucose levels in the blood may begin to rise dramatically, thus resulting in diabetes.

For hormone secretion regulated by the negative feedback loop: when gland X releases hormone X, this stimulates target cells to release hormone Y. When there is an excess of hormone Y, gland X "senses" this and inhibits its release of hormone X.


In economics, automatic stabilisers are government programs that work as negative feedback to dampen fluctuations in real GDP.

Electronic amplifiers[edit]

The negative feedback amplifier was invented by Harold Stephen Black at Bell Laboratories in 1927, and patented by him in 1934. Fundamentally, all electronic devices (e.g., vacuum tubes, bipolar transistors, MOS transistors) exhibit some nonlinear behavior. Negative feedback corrects this by trading unused gain for higher linearity (lower distortion). An amplifier with too large an open-loop gain, possibly in a specific frequency range, will also produce too large a feedback signal in that same range. This feedback signal, when subtracted from the original input, will act to reduce the original input, also by "too large" an amount. This "too small" input will be amplified again by the "too large" open-loop gain, creating a signal that is "just right". The net result is a flattening of the amplifier's gain over all frequencies (desensitising). Though much more accurate, amplifiers with negative feedback can become unstable if not designed correctly, causing them to oscillate. Harry Nyquist of Bell Laboratories managed to work out a theory about how to make this behaviour stable.

Negative feedback is used in this way in many types of amplification systems to stabilize and improve their operating characteristics (see e.g., operational amplifiers).

See also[edit]


  1. ^ a b c Arkalgud Ramaprasad, On The Definition of Feedback, Behavioral Science, Volume 28, Issue 1. 1983. Accessed on 16-03-2012.
  2. ^ a b Black, H.S. (January 1934). "Stabilized Feedback Amplifiers". Bell System Tech. J. (American Telephone & Telegraph) 13 (1): 1–18. Retrieved January 2, 2013. 
  3. ^ Bennett, Stuart (1993). A History of Control Engineering: 1930-1955. IET. p. 70. ISBN 0863412998. 
  4. ^ Breedveld, Peter C. "Port-based modeling of mechatronic systems." Mathematics and Computers in Simulation 66.2 (2004): 99-128.
  5. ^ "Tierie, Gerrit. Cornelis Drebbel. Amsterdam: HJ Paris, 1932.". Retrieved 2013-05-03. 
  6. ^ Maxwell, James Clerk (1868). On Governors 16. Proceedings of the Royal Society of London. pp. 270–283. 
  7. ^ a b c David A. Mindell (2002). Between Human and Machine : Feedback, Control, and Computing before Cybernetics.. Baltimore, MD, USA: Johns Hopkins University Press. 
  8. ^ Friis,H.T., and A.G.Jensen. "High Frequency Amplifiers" Bell System Technical Journal 3 (April 1924):181-205.
  9. ^ Rosenblueth, Arturo, Norbert Wiener, and Julian Bigelow. "Behavior, purpose and teleology." Philosophy of science 10.1 (1943): 18-24.
  10. ^ Norbert Wiener Cybernetics: Or Control and Communication in the Animal and the Machine. Cambridge, Massachusetts: The Technology Press; New York: John Wiley & Sons, Inc., 1948.
  11. ^ W. Ross Ashby, "An introduction to cybernetics", Chapman & Hall, London, 1956. - Internet (1999)
  12. ^ BF Skinner, The Experimental Analysis of Behavior, American Scientist, Vol. 45, No. 4 (SEPTEMBER 1957), pp. 343-371
  13. ^ a b 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. ^ Hermann A Haus and Richard B. Adler, Circuit Theory of Linear Noisy Networks, MIT Press, 1959
  15. ^ 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. 
  16. ^ 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
  17. ^ Charles S. Carver, Michael F. Scheier: On the Self-Regulation of Behavior Cambridge University Press, 2001
  18. ^ Raven, PH; Johnson, GB. Biology, Fifth Edition, Boston: Hill Companies, Inc. 1999. page 1058.

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