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Negative feedback

Negative feedback (or balancing feedback) occurs when some function of the output of a system, process, or mechanism is fed back in a manner that tends to reduce the fluctuations in the output, whether caused by changes in the input or by other disturbances. A classic example of negative feedback is a heating system thermostat — when the temperature gets high enough, the heater is turned OFF. When the temperature gets too cold, the heat is turned back ON. In each case the "feedback" generated by the thermostat "negates" the trend.

A simple negative feedback system is descriptive, for example, of some electronic amplifiers. The feedback is negative if the loop gain AB is negative.

The opposite tendency — called positive feedback — is when a trend is positively reinforced, creating amplification, such as the squealing "feedback" loop that can occur when a mic is brought too close to a speaker which is amplifying the very sounds the mic is picking up, or the runaway heating and ultimate meltdown of a nuclear reactor.

Whereas positive feedback tends to lead to instability via exponential growth, oscillation or chaotic behavior, negative feedback generally promotes stability. Negative feedback tends to promote a settling to equilibrium, and reduces the effects of perturbations. Negative feedback loops in which just the right amount of correction is applied with optimum timing, can be very stable, accurate, and responsive.

Negative feedback is widely used in mechanical and electronic engineering, and also within living organisms,[1][2] and can be seen in many other fields from chemistry and economics to physical systems such as the climate. General negative feedback systems are studied in control systems engineering.

Negative feedback loops also play an integral role in maintaining the atmospheric balance in various systems on Earth. One such feedback system is the interaction between solar radiation, cloud cover, and planet temperature.

Blood glucose levels are maintained at a constant level in the body by a negative feedback mechanism. When the blood glucose level is too high, the pancreas secretes insulin and when the level is too low, the pancreas then secretes glucagon. The flat line shown represents the homeostatic set point. The sinusoidal line represents the blood glucose level.

General description edit

 
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.[3]

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.[4][5] In a psychology context, on the other hand, negative refers to the valence of the feedback – attractive versus aversive, or praise versus criticism.[6]

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 feedback require a feedback loop to operate.

However, negative feedback systems can still be subject to oscillations. This is caused by a phase shift around any loop. Due to these phase shifts the feedback signal of some frequencies can ultimately become in phase with the input signal and thus turn into positive feedback, creating a runaway condition. Even before the point where the phase shift becomes 180 degrees, stability of the negative feedback loop will become compromised, leading to increasing under- and overshoot following a disturbance. This problem is often dealt with by attenuating or changing the phase of the problematic frequencies in a design step called compensation. Unless the system naturally has sufficient damping, many negative feedback systems have low pass filters or dampers fitted.

Examples edit

 

Detailed implementations edit

Error-controlled regulation edit

 
Basic error-controlled regulator loop
 
A regulator R adjusts the input to a system T so the monitored essential variables E are held to set-point values S that result in the desired system output despite disturbances D.[1][7]

One use of feedback is to make a system (say T) self-regulating to minimize the effect of a disturbance (say D). Using a negative feedback loop, a measurement of some variable (for example, a process variable, say E) is subtracted from a required value (the 'set point') to estimate an operational error in system status, which is then used by a regulator (say R) to reduce the gap between the measurement and the required value.[8][9] The regulator modifies the input to the system T according to its interpretation of the error in the status of the system. This error may be introduced by a variety of possible disturbances or 'upsets', some slow and some rapid.[10] The regulation in such systems can range from a simple 'on-off' control to a more complex processing of the error signal.[11]

In this framework, the physical form of a signal may undergo multiple transformations. For example, a change in weather may cause a disturbance to the heat input to a house (as an example of the system T) that is monitored by a thermometer as a change in temperature (as an example of an 'essential variable' E). This quantity, then, is converted by the thermostat (a 'comparator') into an electrical error in status compared to the 'set point' S, and subsequently used by the regulator (containing a 'controller' that commands gas control valves and an ignitor) ultimately to change the heat provided by a furnace (an 'effector') to counter the initial weather-related disturbance in heat input to the house.[12]

Error controlled regulation is typically carried out using a Proportional-Integral-Derivative Controller (PID controller). The regulator signal is derived from a weighted sum of the error signal, integral of the error signal, and derivative of the error signal. The weights of the respective components depend on the application.[13]

Mathematically, the regulator signal is given by:

 

where

  is the integral time
  is the derivative time

Negative feedback amplifier edit

The negative feedback amplifier was invented by Harold Stephen Black at Bell Laboratories in 1927, and granted a patent in 1937 (US Patent 2,102,671)[14] "a continuation of application Serial No. 298,155, filed August 8, 1928 ...").[15][16]

"The patent is 52 pages long plus 35 pages of figures. The first 43 pages amount to a small treatise on feedback amplifiers!"[16]

There are many advantages to feedback in amplifiers.[17] In design, the type of feedback and amount of feedback are carefully selected to weigh and optimize these various benefits.

Advantages of negative voltage feedback in amplifiers

  1. It reduces non-linear distortion, that is, it has higher fidelity.
  2. It increases circuit stability: that is, the gain remains stable though there are variations in ambient temperature, frequency and signal amplitude.
  3. It increases bandwidth slightly.
  4. It modifies the input and output impedances.
  5. Harmonic, phase, amplitude, and frequency distortions are all reduced considerably.
  6. Noise is reduced considerably.

Though negative feedback has many advantages, amplifiers with feedback can oscillate. See the article on step response. They may even exhibit instability. Harry Nyquist of Bell Laboratories proposed the Nyquist stability criterion and the Nyquist plot that identify stable feedback systems, including amplifiers and control systems.

 
Negative feedback amplifier with external disturbance.[18] The feedback is negative if βA >0.

The figure shows a simplified block diagram of a negative feedback amplifier.

The feedback sets the overall (closed-loop) amplifier gain at a value:

 

where the approximate value assumes βA >> 1. This expression shows that a gain greater than one requires β < 1. Because the approximate gain 1/β is independent of the open-loop gain A, the feedback is said to 'desensitize' the closed-loop gain to variations in A (for example, due to manufacturing variations between units, or temperature effects upon components), provided only that the gain A is sufficiently large.[19] In this context, the factor (1+βA) is often called the 'desensitivity factor',[20][21] and in the broader context of feedback effects that include other matters like electrical impedance and bandwidth, the 'improvement factor'.[22]

If the disturbance D is included, the amplifier output becomes:

 

which shows that the feedback reduces the effect of the disturbance by the 'improvement factor' (1+β A). The disturbance D might arise from fluctuations in the amplifier output due to noise and nonlinearity (distortion) within this amplifier, or from other noise sources such as power supplies.[23][24]

The difference signal I–βO at the amplifier input is sometimes called the "error signal".[25] According to the diagram, the error signal is:

 

From this expression, it can be seen that a large 'improvement factor' (or a large loop gain βA) tends to keep this error signal small.

Although the diagram illustrates the principles of the negative feedback amplifier, modeling a real amplifier as a unilateral forward amplification block and a unilateral feedback block has significant limitations.[26] For methods of analysis that do not make these idealizations, see the article Negative feedback amplifier.

Operational amplifier circuits edit

 
A feedback voltage amplifier using an op amp with finite gain but infinite input impedances and zero output impedance.[27]

The operational amplifier was originally developed as a building block for the construction of analog computers, but is now used almost universally in all kinds of applications including audio equipment and control systems.

Operational amplifier circuits typically employ negative feedback to get a predictable transfer function. Since the open-loop gain of an op-amp is extremely large, a small differential input signal would drive the output of the amplifier to one rail or the other in the absence of negative feedback. A simple example of the use of feedback is the op-amp voltage amplifier shown in the figure.

The idealized model of an operational amplifier assumes that the gain is infinite, the input impedance is infinite, output resistance is zero, and input offset currents and voltages are zero. Such an ideal amplifier draws no current from the resistor divider.[28] Ignoring dynamics (transient effects and propagation delay), the infinite gain of the ideal op-amp means this feedback circuit drives the voltage difference between the two op-amp inputs to zero.[28] Consequently, the voltage gain of the circuit in the diagram, assuming an ideal op amp, is the reciprocal of feedback voltage division ratio β:

 .

A real op-amp has a high but finite gain A at low frequencies, decreasing gradually at higher frequencies. In addition, it exhibits a finite input impedance and a non-zero output impedance. Although practical op-amps are not ideal, the model of an ideal op-amp often suffices to understand circuit operation at low enough frequencies. As discussed in the previous section, the feedback circuit stabilizes the closed-loop gain and desensitizes the output to fluctuations generated inside the amplifier itself.[29]

Areas of application edit

Mechanical engineering edit

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

An example of the use of negative feedback control is the ballcock control of water level (see diagram), or a pressure regulator. In modern engineering, negative feedback loops are found in engine governors, fuel injection systems and carburettors. Similar control mechanisms are used in heating and cooling systems, such as those involving air conditioners, refrigerators, or freezers.

Biology edit

 
Control of endocrine hormones by negative feedback.

Some biological systems exhibit negative feedback such as the baroreflex in blood pressure regulation and erythropoiesis. Many biological processes (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. As shown in the figure, 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.[30]

Chemistry edit

Closed systems containing substances undergoing a reversible chemical reaction can also exhibit negative feedback in accordance with Le Chatelier's principle which shift the chemical equilibrium to the opposite side of the reaction in order to reduce a stress. For example, in the reaction

N2 + 3 H2 ⇌ 2 NH3 + 92 kJ/mol

If a mixture of the reactants and products exists at equilibrium in a sealed container and nitrogen gas is added to this system, then the equilibrium will shift toward the product side in response. If the temperature is raised, then the equilibrium will shift toward the reactant side which, since the reverse reaction is endothermic, will partially reduce the temperature.

Self-organization edit

Self-organization is the capability of certain systems "of organizing their own behavior or structure".[31] There are many possible factors contributing to this capacity, and most often positive feedback is identified as a possible contributor. However, negative feedback also can play a role.[32]

Economics edit

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

Mainstream economics asserts that the market pricing mechanism operates to match supply and demand, because mismatches between them feed back into the decision-making of suppliers and demanders of goods, altering prices and thereby reducing any discrepancy. However Norbert Wiener wrote in 1948:

"There is a belief current in many countries and elevated to the rank of an official article of faith in the United States that free competition is itself a homeostatic process... Unfortunately the evidence, such as it is, is against this simple-minded theory."[33]

The notion of economic equilibrium being maintained in this fashion by market forces has also been questioned by numerous heterodox economists such as financier George Soros[34] and leading ecological economist and steady-state theorist Herman Daly, who was with the World Bank in 1988–1994.[35]

Environmental Science edit

 
Some effects of climate change can either enhance (positive feedbacks) or weaken (negative feedbacks) global warming.[36][37] Observations and modeling studies indicate that there is a net positive feedback to Earth's current global warming.[38]

A basic and common example of a negative feedback system in the environment is the interaction among cloud cover, plant growth, solar radiation, and planet temperature.[39] As incoming solar radiation increases, planet temperature increases. As the temperature increases, the amount of plant life that can grow increases. This plant life can then make products such as sulfur which produce more cloud cover. An increase in cloud cover leads to higher albedo, or surface reflectivity, of the Earth. As albedo increases, however, the amount of solar radiation decreases.[40] This, in turn, affects the rest of the cycle.

Cloud cover, and in turn planet albedo and temperature, is also influenced by the hydrological cycle.[41] As planet temperature increases, more water vapor is produced, creating more clouds.[42] The clouds then block incoming solar radiation, lowering the temperature of the planet. This interaction produces less water vapor and therefore less cloud cover. The cycle then repeats in a negative feedback loop. In this way, negative feedback loops in the environment have a stabilizing effect.[43]

History edit

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. 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.[44]

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

Negative feedback was implemented in the 17th century. Cornelius Drebbel had built thermostatically controlled incubators and ovens in the early 1600s,[45] and centrifugal governors were used to regulate the distance and pressure between millstones in windmills.[46] James Watt patented a form of governor in 1788 to control the speed of his steam engine, 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.[47]

The term "feedback" was well established by the 1920s, in reference to a means of boosting the gain of an electronic amplifier.[3] Friis and Jensen described this action as "positive feedback" and made passing mention of a contrasting "negative feed-back action" in 1924.[48] Harold Stephen Black came up with the idea of using negative feedback in electronic amplifiers in 1927, submitted a patent application in 1928,[15] and detailed its use in his paper of 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 and bandwidth.[49][50]

Karl Küpfmüller published papers on a negative-feedback-based automatic gain control system and a feedback system stability criterion in 1928.[51]

Nyquist and Bode built on Black's work to develop a theory of amplifier stability.[50]

Early researchers in the area of cybernetics subsequently generalized the idea of negative feedback to cover any goal-seeking or purposeful behavior.[52]

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",[53] 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...: 97 

While the view of feedback as any "circularity of action" helped to keep the theory simple and consistent, Ashby pointed out that, while it may clash with definitions that require a "materially evident" connection, "the exact definition of feedback is nowhere important".[1] Ashby pointed out the limitations of the concept of "feedback":

The concept of 'feedback', so simple and natural in certain elementary cases, becomes artificial and of little use when the interconnections between the parts become more complex...Such complex systems cannot be treated as an interlaced set of more or less independent feedback circuits, but only as a whole. For understanding the general principles of dynamic systems, therefore, the concept of feedback is inadequate in itself. What is important is that complex systems, richly cross-connected internally, have complex behaviors, and that these behaviors can be goal-seeking in complex patterns.: 54 

To reduce confusion, later authors have suggested alternative terms such as degenerative,[54] self-correcting,[55] balancing,[56] or discrepancy-reducing[57] in place of "negative".

See also edit

References edit

  1. ^ a b c W. Ross Ashby (1957). "Chapter 12: The error-controlled regulator" (PDF). Introduction to cybernetics. Chapman & Hall Ltd.; Internet (1999). pp. 219–243.
  2. ^ Robert E. Ricklefs; Gary Leon Miller (2000). "§6.1 Homeostasis depends upon negative feedback". Ecology. Macmillan. p. 92. ISBN 9780716728290.
  3. ^ a b David A. Mindell (2002). Between Human and Machine : Feedback, Control, and Computing before Cybernetics. Baltimore, MD, USA: Johns Hopkins University Press. ISBN 9780801868955.
  4. ^ Arkalgud Ramaprasad (1983). "On The Definition of Feedback". Behavioral Science. 28 (1): 4–13. doi:10.1002/bs.3830280103.
  5. ^ John D.Sterman, Business Dynamics: Systems Thinking and Modeling for a Complex World McGraw Hill/Irwin, 2000. ISBN 9780072389159
  6. ^ Herold, David M.; Greller, Martin M. (1977). "Research Notes. Feedback: The Definition of a Construct". Academy of Management Journal. 20 (1): 142–147. doi:10.2307/255468. JSTOR 255468.
  7. ^ Sudheer S Bhagade; Govind Das Nageshwar (2011). Process Dynamics and Control. PHI Learning Pvt. Ltd. pp. 6, 9. ISBN 9788120344051.
  8. ^ Charles H. Wilts (1960). Principles of Feedback Control. Addison-Wesley Pub. Co. p. 1. In a simple feedback system a specific physical quantity is being controlled, and control is brought about by making an actual comparison of this quantity with its desired value and utilizing the difference to reduce the error observed. Such a system is self-correcting in the sense that any deviations from the desired performance are used to produce corrective action.
  9. ^ SK Singh (2010). Process Control: Concepts Dynamics And Applications. PHI Learning Pvt. Ltd. p. 222. ISBN 9788120336780.
  10. ^ For example, input and load disturbances. See William Y. Svrcek; Donald P. Mahoney; Brent R. Young (2013). A Real-Time Approach to Process Control (3rd ed.). John Wiley & Sons. p. 57. ISBN 9781118684733.
  11. ^ Charles D H Williams. "Types of feedback control". Feedback and temperature control. University of Exeter: Physics and astronomy. Retrieved 2014-06-08.
  12. ^ Giannini, Alessandra; Biasutti, Michela; Verstraete, Michel M. (2008-12-01). "A climate model-based review of drought in the Sahel: Desertification, the re-greening and climate change". Global and Planetary Change. Climate Change and Desertification. 64 (3): 119–128. Bibcode:2008GPC....64..119G. doi:10.1016/j.gloplacha.2008.05.004. ISSN 0921-8181.
  13. ^ Bechhoefer, John (2005). "Feedback for Physicists: A Tutorial Essay On Control". Reviews of Modern Physics. 77 (3): 783–835. Bibcode:2005RvMP...77..783B. CiteSeerX 10.1.1.124.7043. doi:10.1103/revmodphys.77.783.
  14. ^ Black, Harold (1937-12-21). (PDF). www.eepatents.com. Archived from the original (PDF) on 2014-10-06.
  15. ^ a b James E Brittain (February 2011). "Electrical engineering hall of fame: Harold S Black" (PDF). Proceedings of the IEEE. 99 (2): 351–353. doi:10.1109/jproc.2010.2090997.
  16. ^ a b CA Desoer (August 1984). "In Memoriam: Harold Stephen Black". IEEE Transactions on Automatic Control. AC-29 (8): 673–674. doi:10.1109/tac.1984.1103645.
  17. ^ Santiram Kal (2009). "§6.3 Advantages of negative feedback amplifiers". Basic electronics: Devices, circuits and its fundamentals. PHI Learning Pvt. Ltd. pp. 193 ff. ISBN 9788120319523.
  18. ^ Marc Thomson (2006). "Figure 11-4: Classical single input, single output control loop". Intuitive Analog Circuit Design. Newnes. ISBN 9780080478753.
  19. ^ Santiram Kal (2009). "§6.3.1 Gain stability". Basic Electronics: Devices, Circuits, and IT Fundamentals. PHI Learning Pvt. Ltd. pp. 193–194. ISBN 9788120319523.
  20. ^ Marc T Thompson, p. 309
  21. ^ Thomas H Lee (2004). The Design of CMOS Radio Frequency Circuits (2nd ed.). Cambridge University Press. p. 447. ISBN 9780521835398.
  22. ^ Norbert A Malik (1995). "Improvement Factor". Electronic Circuits: Analysis simulation and design. Prentice Hall. p. 671. ISBN 9780023749100.
  23. ^ Santiram Kal (14 January 2009). "§6.3.2 Noise Reduction". Basic Electronics: Devices, Circuits and IT fundamentals. p. 194. ISBN 9788120319523.
  24. ^ SK Bhattacharya. "§5.3.3 Effect of feedback on disturbance signal". Linear Control Systems: For Punjab Technical University. ISBN 9788131759523.
  25. ^ Muhammad Rashid (2010). Microelectronic Circuits: Analysis & Design (2nd ed.). Cengage Learning. p. 642. ISBN 9780495667728.
  26. ^ Wai-Kai Chen (2005). "Chapter 13: General feedback theory". Circuit Analysis and Feedback Amplifier Theory. CRC Press. pp. 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.
  27. ^ See, for example, Figure 1.4, p. 7 Ideal op amp model in Sergio Franco (2002). Design with operational amplifiers and analog integrated circuits (3rd ed.). McGraw-Hill. ISBN 978-0078028168. or David G Nair; Sergio B Franco (2009). "Figure 16.2: The four possible op-amp configurations". In Wai-Kai Chen (ed.). Fundamentals of Circuits and Filters (The Circuits and Filters Handbook, 3rd ed.). CRC Press. pp. 16–2. ISBN 9781420058888.
  28. ^ a b G. Schitter; A. Rankers (2014). "§6.3.4 Linear amplifiers with operational amplifiers". The Design of High Performance Mechatronics. IOS Press. p. 499. ISBN 9781614993681.
  29. ^ Walter G Jung (2005). "Noise gain (NG)". Op Amp Applications Handbook. Newnes. pp. 12 ff. ISBN 9780750678445.
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  31. ^ William R. Uttal (2014). Psychomythics: Sources of Artifacts and Misconceptions in Scientific Psychology. Psychology Press. pp. 95 ff. ISBN 9781135623722.
  32. ^ Scott Camazine; Jean-Louis Deneubourg; Nigel R Franks; James Sneyd; Guy Theraulaz; Eric Bonabeau (2003). "Chapter 2: How self-organization works". Self-organization in biological systems. Princeton University Press. pp. 15 ff. ISBN 9780691116242.
  33. ^ Cybernetics: Or Control and Communication in the Animal and the Machine p.158
  34. ^ Goeroge Soros, The Alchemy of Finance
  35. ^ Herman Daly, Steady State Economics
  36. ^ "The Study of Earth as an Integrated System". nasa.gov. NASA. 2016. from the original on November 2, 2016.
  37. ^ Fig. TS.17, Technical Summary, Sixth Assessment Report (AR6), Working Group I, IPCC, 2021, p. 96. from the original on July 21, 2022.
  38. ^ Stocker, Thomas F.; Dahe, Qin; Plattner, Gian-Kaksper (2013). IPCC AR5 WG1. Technical Summary (PDF). (PDF) from the original on 16 July 2023. See esp. TFE.6: Climate Sensitivity and Feedbacks at p. 82.
  39. ^ Charlson, Robert J.; Lovelock, James E.; Andreae, Meinrat O.; Warren, Stephen G. (1987). "Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate". Nature. 326 (6114): 655–661. Bibcode:1987Natur.326..655C. doi:10.1038/326655a0. ISSN 1476-4687. S2CID 4321239.
  40. ^ Winton, Michael (2006). "Amplified Arctic climate change: What does surface albedo feedback have to do with it?". Geophysical Research Letters. 33 (3): L03701. Bibcode:2006GeoRL..33.3701W. doi:10.1029/2005GL025244. ISSN 1944-8007.
  41. ^ Stephens, Graeme L. (2005). "Cloud Feedbacks in the Climate System: A Critical Review". Journal of Climate. 18 (2): 237–273. Bibcode:2005JCli...18..237S. doi:10.1175/JCLI-3243.1. ISSN 0894-8755. S2CID 16122908.
  42. ^ Jickells, T. D.; An, Z. S.; Andersen, K. K.; Baker, A. R.; Bergametti, G.; Brooks, N.; Cao, J. J.; Boyd, P. W.; Duce, R. A.; Hunter, K. A.; Kawahata, H. (2005). "Global Iron Connections Between Desert Dust, Ocean Biogeochemistry, and Climate". Science. 308 (5718): 67–71. Bibcode:2005Sci...308...67J. doi:10.1126/science.1105959. ISSN 0036-8075. PMID 15802595. S2CID 16985005.
  43. ^ Giannini, Alessandra; Biasutti, Michela; Verstraete, Michel M. (2008). "A climate model-based review of drought in the Sahel: Desertification, the re-greening and climate change". Global and Planetary Change. Climate Change and Desertification. 64 (3): 119–128. Bibcode:2008GPC....64..119G. doi:10.1016/j.gloplacha.2008.05.004. ISSN 0921-8181.
  44. ^ Breedveld, Peter C (2004). "Port-based modeling of mechatronic systems". Mathematics and Computers in Simulation. 66 (2): 99–128. CiteSeerX 10.1.1.108.9830. doi:10.1016/j.matcom.2003.11.002.
  45. ^ "Tierie, Gerrit. Cornelis Drebbel. Amsterdam: HJ Paris, 1932" (PDF). Retrieved 2013-05-03.
  46. ^ Hills, Richard L (1996). Power From the Wind. Cambridge University Press. ISBN 9780521566865.
  47. ^ Maxwell, James Clerk (1868). "On Governors" (PDF). Proceedings of the Royal Society of London. 16: 270–283. doi:10.1098/rspl.1867.0055. S2CID 51751195 – via Wikimedia.
  48. ^ Friis, H. T.; Jensen, A. G. (1924). "High Frequency Amplifiers". Bell System Technical Journal. 3 (2): 181–205. doi:10.1002/j.1538-7305.1924.tb01354.x.
  49. ^ Black, H.S. (January 1934). "Stabilized Feedback Amplifiers" (PDF). Bell System Tech. J. 13 (1): 1–18. doi:10.1002/j.1538-7305.1934.tb00652.x. Retrieved January 2, 2013.
  50. ^ a b Stuart Bennett (1993). "Chapter 3: The electronic negative feedback amplifier". A history of control engineering 1930-1955. Institution of Electrical Engineers. pp. 70 ff. ISBN 9780863412806.
  51. ^ C. Bissell (2006). "Karl Kupfmuller, 1928: an early time-domain, closed-loop, stability criterion" (PDF). IEEE Control Systems Magazine: 115–116, 126.
  52. ^ Rosenblueth, Arturo, Norbert Wiener, and Julian Bigelow. "Behavior, purpose and teleology." Philosophy of science 10.1 (1943): 18-24.
  53. ^ 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.
  54. ^ Hermann A Haus and Richard B. Adler, Circuit Theory of Linear Noisy Networks, MIT Press, 1959
  55. ^ Peter M. Senge (1990). The Fifth Discipline: The Art and Practice of the Learning Organization. New York: Doubleday. p. 424. ISBN 978-0-385-26094-7.
  56. ^ Helen E. Allison; Richard J. Hobbs (2006). Science and Policy in Natural Resource Management: Understanding System Complexity. Cambridge University Press. p. 205. ISBN 9781139458603. Balancing or negative feedback counteracts and opposes change
  57. ^ Carver, Charles S.; Scheier, Michael F. (2001-05-07). On the Self-Regulation of Behavior. ISBN 9780521000994.

External links edit

  • "Physiological Homeostasis". biology online: answers to your biology questions. Biology-Online.org. 30 January 2020.

negative, feedback, criticism, punishment, modify, behavior, performance, appraisal, reinforcement, balancing, feedback, occurs, when, some, function, output, system, process, mechanism, back, manner, that, tends, reduce, fluctuations, output, whether, caused,. For use of criticism and punishment to modify behavior see performance appraisal and reinforcement Negative feedback or balancing feedback occurs when some function of the output of a system process or mechanism is fed back in a manner that tends to reduce the fluctuations in the output whether caused by changes in the input or by other disturbances A classic example of negative feedback is a heating system thermostat when the temperature gets high enough the heater is turned OFF When the temperature gets too cold the heat is turned back ON In each case the feedback generated by the thermostat negates the trend A simple negative feedback system is descriptive for example of some electronic amplifiers The feedback is negative if the loop gain AB is negative The opposite tendency called positive feedback is when a trend is positively reinforced creating amplification such as the squealing feedback loop that can occur when a mic is brought too close to a speaker which is amplifying the very sounds the mic is picking up or the runaway heating and ultimate meltdown of a nuclear reactor Whereas positive feedback tends to lead to instability via exponential growth oscillation or chaotic behavior negative feedback generally promotes stability Negative feedback tends to promote a settling to equilibrium and reduces the effects of perturbations Negative feedback loops in which just the right amount of correction is applied with optimum timing can be very stable accurate and responsive Negative feedback is widely used in mechanical and electronic engineering and also within living organisms 1 2 and can be seen in many other fields from chemistry and economics to physical systems such as the climate General negative feedback systems are studied in control systems engineering Negative feedback loops also play an integral role in maintaining the atmospheric balance in various systems on Earth One such feedback system is the interaction between solar radiation cloud cover and planet temperature Blood glucose levels are maintained at a constant level in the body by a negative feedback mechanism When the blood glucose level is too high the pancreas secretes insulin and when the level is too low the pancreas then secretes glucagon The flat line shown represents the homeostatic set point The sinusoidal line represents the blood glucose level Contents 1 General description 2 Examples 3 Detailed implementations 3 1 Error controlled regulation 3 2 Negative feedback amplifier 3 3 Operational amplifier circuits 4 Areas of application 4 1 Mechanical engineering 4 2 Biology 4 3 Chemistry 4 4 Self organization 4 5 Economics 4 6 Environmental Science 5 History 6 See also 7 References 8 External linksGeneral description edit nbsp Feedback loops in the human bodyIn 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 Doutput 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 3 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 4 5 In a psychology context on the other hand negative refers to the valence of the feedback attractive versus aversive or praise versus criticism 6 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 feedback require a feedback loop to operate However negative feedback systems can still be subject to oscillations This is caused by a phase shift around any loop Due to these phase shifts the feedback signal of some frequencies can ultimately become in phase with the input signal and thus turn into positive feedback creating a runaway condition Even before the point where the phase shift becomes 180 degrees stability of the negative feedback loop will become compromised leading to increasing under and overshoot following a disturbance This problem is often dealt with by attenuating or changing the phase of the problematic frequencies in a design step called compensation Unless the system naturally has sufficient damping many negative feedback systems have low pass filters or dampers fitted Examples editMercury thermostats circa 1600 using expansion and contraction of columns of mercury in response to temperature changes were used in negative feedback systems to control vents in furnaces maintaining a steady internal temperature In the invisible hand of the market metaphor of economic theory 1776 reactions to price movements provide a feedback mechanism to match supply and demand In centrifugal governors 1788 negative feedback is used to maintain a near constant speed of an engine irrespective of the load or fuel supply conditions In a steering engine 1866 power assistance is applied to the rudder with a feedback loop to maintain the direction set by the steersman In servomechanisms the speed or position of an output as determined by a sensor is compared to a set value and any error is reduced by negative feedback to the input In audio amplifiers negative feedback flattens frequency response reduces distortion minimises the effect of manufacturing variations in component parameters and compensates for changes in characteristics due to temperature change In analog computing feedback around operational amplifiers is used to generate mathematical functions such as addition subtraction integration differentiation logarithm and antilog functions In delta sigma analog to digital and digital to analog converters particularly for high quality audio a negative feedback loop is used to repeatedly correct accumulated quantization error during conversion In a phase locked loop 1932 feedback is used to maintain a generated alternating waveform in a constant phase to a reference signal In many implementations the generated waveform is the output but when used as a demodulator in an FM radio receiver the error feedback voltage serves as the demodulated output signal If there is a frequency divider between the generated waveform and the phase comparator the device acts as a frequency multiplier In organisms feedback enables various measures e g body temperature or blood sugar level to be maintained within a desired range by homeostatic processes nbsp Detailed implementations editError controlled regulation edit nbsp Basic error controlled regulator loopSee also Control engineering Homeostasis and Allostasis nbsp A regulator R adjusts the input to a system T so the monitored essential variables E are held to set point values S that result in the desired system output despite disturbances D 1 7 One use of feedback is to make a system say T self regulating to minimize the effect of a disturbance say D Using a negative feedback loop a measurement of some variable for example a process variable say E is subtracted from a required value the set point to estimate an operational error in system status which is then used by a regulator say R to reduce the gap between the measurement and the required value 8 9 The regulator modifies the input to the system T according to its interpretation of the error in the status of the system This error may be introduced by a variety of possible disturbances or upsets some slow and some rapid 10 The regulation in such systems can range from a simple on off control to a more complex processing of the error signal 11 In this framework the physical form of a signal may undergo multiple transformations For example a change in weather may cause a disturbance to the heat input to a house as an example of the system T that is monitored by a thermometer as a change in temperature as an example of an essential variable E This quantity then is converted by the thermostat a comparator into an electrical error in status compared to the set point S and subsequently used by the regulator containing a controller that commands gas control valves and an ignitor ultimately to change the heat provided by a furnace an effector to counter the initial weather related disturbance in heat input to the house 12 Error controlled regulation is typically carried out using a Proportional Integral Derivative Controller PID controller The regulator signal is derived from a weighted sum of the error signal integral of the error signal and derivative of the error signal The weights of the respective components depend on the application 13 Mathematically the regulator signal is given by M V t K p e t 1 T i 0 t e t d t T d d d t e t displaystyle mathrm MV t K p left e t frac 1 T i int 0 t e tau d tau T d frac d dt e t right nbsp where T i displaystyle T i nbsp is the integral time T d displaystyle T d nbsp is the derivative timeNegative feedback amplifier edit Main article Negative feedback amplifier The negative feedback amplifier was invented by Harold Stephen Black at Bell Laboratories in 1927 and granted a patent in 1937 US Patent 2 102 671 14 a continuation of application Serial No 298 155 filed August 8 1928 15 16 The patent is 52 pages long plus 35 pages of figures The first 43 pages amount to a small treatise on feedback amplifiers 16 There are many advantages to feedback in amplifiers 17 In design the type of feedback and amount of feedback are carefully selected to weigh and optimize these various benefits Advantages of negative voltage feedback in amplifiers It reduces non linear distortion that is it has higher fidelity It increases circuit stability that is the gain remains stable though there are variations in ambient temperature frequency and signal amplitude It increases bandwidth slightly It modifies the input and output impedances Harmonic phase amplitude and frequency distortions are all reduced considerably Noise is reduced considerably Though negative feedback has many advantages amplifiers with feedback can oscillate See the article on step response They may even exhibit instability Harry Nyquist of Bell Laboratories proposed the Nyquist stability criterion and the Nyquist plot that identify stable feedback systems including amplifiers and control systems nbsp Negative feedback amplifier with external disturbance 18 The feedback is negative if bA gt 0 The figure shows a simplified block diagram of a negative feedback amplifier The feedback sets the overall closed loop amplifier gain at a value O I A 1 b A 1 b displaystyle frac O I frac A 1 beta A approx frac 1 beta nbsp where the approximate value assumes bA gt gt 1 This expression shows that a gain greater than one requires b lt 1 Because the approximate gain 1 b is independent of the open loop gain A the feedback is said to desensitize the closed loop gain to variations in A for example due to manufacturing variations between units or temperature effects upon components provided only that the gain A is sufficiently large 19 In this context the factor 1 bA is often called the desensitivity factor 20 21 and in the broader context of feedback effects that include other matters like electrical impedance and bandwidth the improvement factor 22 If the disturbance D is included the amplifier output becomes O A I 1 b A D 1 b A displaystyle O frac AI 1 beta A frac D 1 beta A nbsp which shows that the feedback reduces the effect of the disturbance by the improvement factor 1 b A The disturbance D might arise from fluctuations in the amplifier output due to noise and nonlinearity distortion within this amplifier or from other noise sources such as power supplies 23 24 The difference signal I bO at the amplifier input is sometimes called the error signal 25 According to the diagram the error signal is Error signal I b O I 1 b O I I 1 b A b D 1 b A displaystyle text Error signal I beta O I left 1 beta frac O I right frac I 1 beta A frac beta D 1 beta A nbsp From this expression it can be seen that a large improvement factor or a large loop gain bA tends to keep this error signal small Although the diagram illustrates the principles of the negative feedback amplifier modeling a real amplifier as a unilateral forward amplification block and a unilateral feedback block has significant limitations 26 For methods of analysis that do not make these idealizations see the article Negative feedback amplifier Operational amplifier circuits edit Main article Operational amplifier applications nbsp A feedback voltage amplifier using an op amp with finite gain but infinite input impedances and zero output impedance 27 The operational amplifier was originally developed as a building block for the construction of analog computers but is now used almost universally in all kinds of applications including audio equipment and control systems Operational amplifier circuits typically employ negative feedback to get a predictable transfer function Since the open loop gain of an op amp is extremely large a small differential input signal would drive the output of the amplifier to one rail or the other in the absence of negative feedback A simple example of the use of feedback is the op amp voltage amplifier shown in the figure The idealized model of an operational amplifier assumes that the gain is infinite the input impedance is infinite output resistance is zero and input offset currents and voltages are zero Such an ideal amplifier draws no current from the resistor divider 28 Ignoring dynamics transient effects and propagation delay the infinite gain of the ideal op amp means this feedback circuit drives the voltage difference between the two op amp inputs to zero 28 Consequently the voltage gain of the circuit in the diagram assuming an ideal op amp is the reciprocal of feedback voltage division ratio b V out R 1 R 2 R 1 V in 1 b V in displaystyle V text out frac R text 1 R text 2 R text 1 V text in frac 1 beta V text in nbsp A real op amp has a high but finite gain A at low frequencies decreasing gradually at higher frequencies In addition it exhibits a finite input impedance and a non zero output impedance Although practical op amps are not ideal the model of an ideal op amp often suffices to understand circuit operation at low enough frequencies As discussed in the previous section the feedback circuit stabilizes the closed loop gain and desensitizes the output to fluctuations generated inside the amplifier itself 29 Areas of application editMechanical engineering edit See also Control systems and Control engineering nbsp The ballcock or float valve uses negative feedback to control the water level in a cistern An example of the use of negative feedback control is the ballcock control of water level see diagram or a pressure regulator In modern engineering negative feedback loops are found in engine governors fuel injection systems and carburettors Similar control mechanisms are used in heating and cooling systems such as those involving air conditioners refrigerators or freezers Biology edit See also Counterregulatory hormone and Homeostasis nbsp Control of endocrine hormones by negative feedback Some biological systems exhibit negative feedback such as the baroreflex in blood pressure regulation and erythropoiesis Many biological processes 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 As shown in the figure 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 30 Chemistry edit Closed systems containing substances undergoing a reversible chemical reaction can also exhibit negative feedback in accordance with Le Chatelier s principle which shift the chemical equilibrium to the opposite side of the reaction in order to reduce a stress For example in the reaction N2 3 H2 2 NH3 92 kJ molIf a mixture of the reactants and products exists at equilibrium in a sealed container and nitrogen gas is added to this system then the equilibrium will shift toward the product side in response If the temperature is raised then the equilibrium will shift toward the reactant side which since the reverse reaction is endothermic will partially reduce the temperature Self organization edit Main articles Self organization and Emergence Self organization is the capability of certain systems of organizing their own behavior or structure 31 There are many possible factors contributing to this capacity and most often positive feedback is identified as a possible contributor However negative feedback also can play a role 32 Economics edit In economics automatic stabilisers are government programs that are intended to work as negative feedback to dampen fluctuations in real GDP Mainstream economics asserts that the market pricing mechanism operates to match supply and demand because mismatches between them feed back into the decision making of suppliers and demanders of goods altering prices and thereby reducing any discrepancy However Norbert Wiener wrote in 1948 There is a belief current in many countries and elevated to the rank of an official article of faith in the United States that free competition is itself a homeostatic process Unfortunately the evidence such as it is is against this simple minded theory 33 The notion of economic equilibrium being maintained in this fashion by market forces has also been questioned by numerous heterodox economists such as financier George Soros 34 and leading ecological economist and steady state theorist Herman Daly who was with the World Bank in 1988 1994 35 Environmental Science edit nbsp Some effects of climate change can either enhance positive feedbacks or weaken negative feedbacks global warming 36 37 Observations and modeling studies indicate that there is a net positive feedback to Earth s current global warming 38 A basic and common example of a negative feedback system in the environment is the interaction among cloud cover plant growth solar radiation and planet temperature 39 As incoming solar radiation increases planet temperature increases As the temperature increases the amount of plant life that can grow increases This plant life can then make products such as sulfur which produce more cloud cover An increase in cloud cover leads to higher albedo or surface reflectivity of the Earth As albedo increases however the amount of solar radiation decreases 40 This in turn affects the rest of the cycle Cloud cover and in turn planet albedo and temperature is also influenced by the hydrological cycle 41 As planet temperature increases more water vapor is produced creating more clouds 42 The clouds then block incoming solar radiation lowering the temperature of the planet This interaction produces less water vapor and therefore less cloud cover The cycle then repeats in a negative feedback loop In this way negative feedback loops in the environment have a stabilizing effect 43 History editNegative 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 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 44 nbsp The fly ball governor is an early example of negative feedback Negative feedback was implemented in the 17th century Cornelius Drebbel had built thermostatically controlled incubators and ovens in the early 1600s 45 and centrifugal governors were used to regulate the distance and pressure between millstones in windmills 46 James Watt patented a form of governor in 1788 to control the speed of his steam engine 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 47 The term feedback was well established by the 1920s in reference to a means of boosting the gain of an electronic amplifier 3 Friis and Jensen described this action as positive feedback and made passing mention of a contrasting negative feed back action in 1924 48 Harold Stephen Black came up with the idea of using negative feedback in electronic amplifiers in 1927 submitted a patent application in 1928 15 and detailed its use in his paper of 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 and bandwidth 49 50 Karl Kupfmuller published papers on a negative feedback based automatic gain control system and a feedback system stability criterion in 1928 51 Nyquist and Bode built on Black s work to develop a theory of amplifier stability 50 Early researchers in the area of cybernetics subsequently generalized the idea of negative feedback to cover any goal seeking or purposeful behavior 52 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 53 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 97 While the view of feedback as any circularity of action helped to keep the theory simple and consistent Ashby pointed out that while it may clash with definitions that require a materially evident connection the exact definition of feedback is nowhere important 1 Ashby pointed out the limitations of the concept of feedback The concept of feedback so simple and natural in certain elementary cases becomes artificial and of little use when the interconnections between the parts become more complex Such complex systems cannot be treated as an interlaced set of more or less independent feedback circuits but only as a whole For understanding the general principles of dynamic systems therefore the concept of feedback is inadequate in itself What is important is that complex systems richly cross connected internally have complex behaviors and that these behaviors can be goal seeking in complex patterns 54 To reduce confusion later authors have suggested alternative terms such as degenerative 54 self correcting 55 balancing 56 or discrepancy reducing 57 in place of negative See also editAsymptotic gain model Biofeedback Gaining awareness of biological processes Control theory Branch of engineering and mathematics Cybernetics Transdisciplinary field concerned with regulatory and purposive systems Climate change feedback Feedback related to climate change Nyquist stability criterion Graphical method of determining the stability of a dynamical system Open loop controller Control system whose input is independent of output Perceptual control theory model of behaviorPages displaying wikidata descriptions as a fallback Positive feedback Feedback loop that increases an initial small effect Stability criterion Step response Time behavior of a system controlled by Heaviside step functionsReferences edit a b c W Ross Ashby 1957 Chapter 12 The error controlled regulator PDF Introduction to cybernetics Chapman amp Hall Ltd Internet 1999 pp 219 243 Robert E Ricklefs Gary Leon Miller 2000 6 1 Homeostasis depends upon negative feedback Ecology Macmillan p 92 ISBN 9780716728290 a b David A Mindell 2002 Between Human and Machine Feedback Control and Computing before Cybernetics Baltimore MD USA Johns Hopkins University Press ISBN 9780801868955 Arkalgud Ramaprasad 1983 On The Definition of Feedback Behavioral Science 28 1 4 13 doi 10 1002 bs 3830280103 John D Sterman Business Dynamics Systems Thinking and Modeling for a Complex World McGraw Hill Irwin 2000 ISBN 9780072389159 Herold David M Greller Martin M 1977 Research Notes Feedback The Definition of a Construct Academy of Management Journal 20 1 142 147 doi 10 2307 255468 JSTOR 255468 Sudheer S Bhagade Govind Das Nageshwar 2011 Process Dynamics and Control PHI Learning Pvt Ltd pp 6 9 ISBN 9788120344051 Charles H Wilts 1960 Principles of Feedback Control Addison Wesley Pub Co p 1 In a simple feedback system a specific physical quantity is being controlled and control is brought about by making an actual comparison of this quantity with its desired value and utilizing the difference to reduce the error observed Such a system is self correcting in the sense that any deviations from the desired performance are used to produce corrective action SK Singh 2010 Process Control Concepts Dynamics And Applications PHI Learning Pvt Ltd p 222 ISBN 9788120336780 For example input and load disturbances See William Y Svrcek Donald P Mahoney Brent R Young 2013 A Real Time Approach to Process Control 3rd ed John Wiley amp Sons p 57 ISBN 9781118684733 Charles D H Williams Types of feedback control Feedback and temperature control University of Exeter Physics and astronomy Retrieved 2014 06 08 Giannini Alessandra Biasutti Michela Verstraete Michel M 2008 12 01 A climate model based review of drought in the Sahel Desertification the re greening and climate change Global and Planetary Change Climate Change and Desertification 64 3 119 128 Bibcode 2008GPC 64 119G doi 10 1016 j gloplacha 2008 05 004 ISSN 0921 8181 Bechhoefer John 2005 Feedback for Physicists A Tutorial Essay On Control Reviews of Modern Physics 77 3 783 835 Bibcode 2005RvMP 77 783B CiteSeerX 10 1 1 124 7043 doi 10 1103 revmodphys 77 783 Black Harold 1937 12 21 U S Patent 2 102 671 Wave Translation System PDF www eepatents com Archived from the original PDF on 2014 10 06 a b James E Brittain February 2011 Electrical engineering hall of fame Harold S Black PDF Proceedings of the IEEE 99 2 351 353 doi 10 1109 jproc 2010 2090997 a b CA Desoer August 1984 In Memoriam Harold Stephen Black IEEE Transactions on Automatic Control AC 29 8 673 674 doi 10 1109 tac 1984 1103645 Santiram Kal 2009 6 3 Advantages of negative feedback amplifiers Basic electronics Devices circuits and its fundamentals PHI Learning Pvt Ltd pp 193 ff ISBN 9788120319523 Marc Thomson 2006 Figure 11 4 Classical single input single output control loop Intuitive Analog Circuit Design Newnes ISBN 9780080478753 Santiram Kal 2009 6 3 1 Gain stability Basic Electronics Devices Circuits and IT Fundamentals PHI Learning Pvt Ltd pp 193 194 ISBN 9788120319523 Marc T Thompson p 309 Thomas H Lee 2004 The Design of CMOS Radio Frequency Circuits 2nd ed Cambridge University Press p 447 ISBN 9780521835398 Norbert A Malik 1995 Improvement Factor Electronic Circuits Analysis simulation and design Prentice Hall p 671 ISBN 9780023749100 Santiram Kal 14 January 2009 6 3 2 Noise Reduction Basic Electronics Devices Circuits andITfundamentals p 194 ISBN 9788120319523 SK Bhattacharya 5 3 3 Effect of feedback on disturbance signal Linear Control Systems For Punjab Technical University ISBN 9788131759523 Muhammad Rashid 2010 Microelectronic Circuits Analysis amp Design 2nd ed Cengage Learning p 642 ISBN 9780495667728 Wai Kai Chen 2005 Chapter 13 General feedback theory Circuit Analysis and Feedback Amplifier Theory CRC Press pp 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 See for example Figure 1 4 p 7 Ideal op amp model in Sergio Franco 2002 Design with operational amplifiers and analog integrated circuits 3rd ed McGraw Hill ISBN 978 0078028168 or David G Nair Sergio B Franco 2009 Figure 16 2 The four possible op amp configurations In Wai Kai Chen ed Fundamentals of Circuits and Filters The Circuits and Filters Handbook 3rd ed CRC Press pp 16 2 ISBN 9781420058888 a b G Schitter A Rankers 2014 6 3 4 Linear amplifiers with operational amplifiers The Design of High Performance Mechatronics IOS Press p 499 ISBN 9781614993681 Walter G Jung 2005 Noise gain NG Op Amp Applications Handbook Newnes pp 12 ff ISBN 9780750678445 Raven PH Johnson GB Biology Fifth Edition Boston Hill Companies Inc 1999 page 1058 William R Uttal 2014 Psychomythics Sources of Artifacts and Misconceptions in Scientific Psychology Psychology Press pp 95 ff ISBN 9781135623722 Scott Camazine Jean Louis Deneubourg Nigel R Franks James Sneyd Guy Theraulaz Eric Bonabeau 2003 Chapter 2 How self organization works Self organization in biological systems Princeton University Press pp 15 ff ISBN 9780691116242 Cybernetics Or Control and Communication in the Animal and the Machine p 158 Goeroge Soros The Alchemy of Finance Herman Daly Steady State Economics The Study of Earth as an Integrated System nasa gov NASA 2016 Archived from the original on November 2 2016 Fig TS 17 Technical Summary Sixth Assessment Report AR6 Working Group I IPCC 2021 p 96 Archived from the original on July 21 2022 Stocker Thomas F Dahe Qin Plattner Gian Kaksper 2013 IPCC AR5 WG1 Technical Summary PDF Archived PDF from the original on 16 July 2023 See esp TFE 6 Climate Sensitivity and Feedbacks at p 82 Charlson Robert J Lovelock James E Andreae Meinrat O Warren Stephen G 1987 Oceanic phytoplankton atmospheric sulphur cloud albedo and climate Nature 326 6114 655 661 Bibcode 1987Natur 326 655C doi 10 1038 326655a0 ISSN 1476 4687 S2CID 4321239 Winton Michael 2006 Amplified Arctic climate change What does surface albedo feedback have to do with it Geophysical Research Letters 33 3 L03701 Bibcode 2006GeoRL 33 3701W doi 10 1029 2005GL025244 ISSN 1944 8007 Stephens Graeme L 2005 Cloud Feedbacks in the Climate System A Critical Review Journal of Climate 18 2 237 273 Bibcode 2005JCli 18 237S doi 10 1175 JCLI 3243 1 ISSN 0894 8755 S2CID 16122908 Jickells T D An Z S Andersen K K Baker A R Bergametti G Brooks N Cao J J Boyd P W Duce R A Hunter K A Kawahata H 2005 Global Iron Connections Between Desert Dust Ocean Biogeochemistry and Climate Science 308 5718 67 71 Bibcode 2005Sci 308 67J doi 10 1126 science 1105959 ISSN 0036 8075 PMID 15802595 S2CID 16985005 Giannini Alessandra Biasutti Michela Verstraete Michel M 2008 A climate model based review of drought in the Sahel Desertification the re greening and climate change Global and Planetary Change Climate Change and Desertification 64 3 119 128 Bibcode 2008GPC 64 119G doi 10 1016 j gloplacha 2008 05 004 ISSN 0921 8181 Breedveld Peter C 2004 Port based modeling of mechatronic systems Mathematics and Computers in Simulation 66 2 99 128 CiteSeerX 10 1 1 108 9830 doi 10 1016 j matcom 2003 11 002 Tierie Gerrit Cornelis Drebbel Amsterdam HJ Paris 1932 PDF Retrieved 2013 05 03 Hills Richard L 1996 Power From the Wind Cambridge University Press ISBN 9780521566865 Maxwell James Clerk 1868 On Governors PDF Proceedings of the Royal Society of London 16 270 283 doi 10 1098 rspl 1867 0055 S2CID 51751195 via Wikimedia Friis H T Jensen A G 1924 High Frequency Amplifiers Bell System Technical Journal 3 2 181 205 doi 10 1002 j 1538 7305 1924 tb01354 x Black H S January 1934 Stabilized Feedback Amplifiers PDF Bell System Tech J 13 1 1 18 doi 10 1002 j 1538 7305 1934 tb00652 x Retrieved January 2 2013 a b Stuart Bennett 1993 Chapter 3 The electronic negative feedback amplifier A history of control engineering 1930 1955 Institution of Electrical Engineers pp 70 ff ISBN 9780863412806 C Bissell 2006 Karl Kupfmuller 1928 an early time domain closed loop stability criterion PDF IEEE Control Systems Magazine 115 116 126 Rosenblueth Arturo Norbert Wiener and Julian Bigelow Behavior purpose and teleology Philosophy of science 10 1 1943 18 24 Norbert Wiener Cybernetics Or Control and Communication in the Animal and the Machine Cambridge Massachusetts The Technology Press New York John Wiley amp Sons Inc 1948 Hermann A Haus and Richard B Adler Circuit Theory of Linear Noisy Networks MIT Press 1959 Peter M Senge 1990 The Fifth Discipline The Art and Practice of the Learning Organization New York Doubleday p 424 ISBN 978 0 385 26094 7 Helen E Allison Richard J Hobbs 2006 Science and Policy in Natural Resource Management Understanding System Complexity Cambridge University Press p 205 ISBN 9781139458603 Balancing or negative feedback counteracts and opposes change Carver Charles S Scheier Michael F 2001 05 07 On the Self Regulation of Behavior ISBN 9780521000994 External links edit Physiological Homeostasis biology online answers to your biology questions Biology Online org 30 January 2020 Retrieved from https en wikipedia org w index php title Negative feedback amp oldid 1179911836, wikipedia, wiki, book, books, library,

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