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Negative feedback (orbalancing feedback) occurs when somefunction of the output of a system, process, or mechanism isfed back in a manner that tends to reduce the fluctuations in the output, whether caused by changes in the input or by other disturbances.
Whereaspositive feedback tends to instability viaexponential growth,oscillation orchaotic behavior, negative feedback generally promotes stability. Negative feedback tends to promote a settling toequilibrium, and reduces the effects of perturbations. Negativefeedback 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 inmechanical andelectronic engineering, and it is observed in many other fields including biology,[1][2] chemistry and economics. General negative feedback systems are studied incontrol systems engineering.
Negative feedback loops also play an integral role in maintaining the atmospheric balance in various climate systems on Earth. One such feedback system is the interaction betweensolar radiation,cloud cover, and planet temperature.
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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.
Inbiology, this process (in general,biochemical) is often referred to ashomeostasis; whereas inmechanics, the more common term isequilibrium.
Inengineering,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, andsetpoints.
Incontrol 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 modellingbusiness systems, usenegative 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 thevalence 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 tooscillations. 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 havelow pass filters ordampers fitted.
One use of feedback is to make a system (sayT)self-regulating to minimize the effect of a disturbance (sayD). Using a negative feedback loop, a measurement of some variable (for example, aprocess variable, sayE) issubtracted from a required value (the'set point') to estimate an operational error in system status, which is then used by aregulator (sayR) to reduce the gap between the measurement and the required value.[8][9] The regulator modifies the input to the systemT 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] Theregulation 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 theheat input to a house (as an example of the systemT) that is monitored by a thermometer as a change intemperature (as an example of an 'essential variable'E). This quantity, then, is converted by the thermostat (a 'comparator') into anelectrical error in status compared to the 'set point'S, and subsequently used by theregulator (containing a 'controller' that commandsgas control valves and an ignitor) ultimately to change theheat 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
The negative feedback amplifier was invented byHarold Stephen Black atBell 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]
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.
Negative voltage feedback in amplifiers has the following advantages; it
Though negative feedback has many advantages, amplifiers with feedback canoscillate (seeStep response of feedback amplifiers), and they may exhibitinstability.Harry Nyquist ofBell Laboratories proposed thea stability criterion and aplot to identify stable feedback systems, including amplifiers and control systems.
The figure shows a simplified block diagram of anegative 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 gainA, the feedback is said to 'desensitize' the closed-loop gain to variations inA (for example, due to manufacturing variations between units, or temperature effects upon components), provided only that the gainA 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 likeelectrical impedance andbandwidth, the 'improvement factor'.[22]
If the disturbanceD is included, the amplifier output becomes:
which shows that the feedback reduces the effect of the disturbance by the 'improvement factor' (1+βA). The disturbanceD 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 signalI–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 largeloop 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 aunilateral forward amplification block and a unilateral feedback block has significant limitations.[26] For methods of analysis that do not make these idealizations, see the articleNegative feedback amplifier.
The operational amplifier was originally developed as a building block for the construction ofanalog computers, but is now used almost universally in all kinds of applications includingaudio equipment andcontrol systems.
Operational amplifier circuits typically employ negative feedback to get a predictable transfer function. Since the open-loop gain of anop-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 andpropagation 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 feedbackvoltage division ratio β:
A real op-amp has a high but finite gainA 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]
An example of the use of negative feedback control is theballcock control of water level (see diagram), or apressure regulator. In modern engineering, negative feedback loops are found inengine governors,fuel injection systems andcarburettors. Similar control mechanisms are used in heating and cooling systems, such as those involvingair conditioners,refrigerators, orfreezers.
Some biological systems exhibit negative feedback such as thebaroreflex inblood pressure regulation anderythropoiesis. Many biological processes (e.g., in thehuman anatomy) use negative feedback. Examples of this are numerous, from the regulating of body temperature, to the regulating of bloodglucose levels. The disruption of feedback loops can lead to undesirable results: in the case ofblood glucose levels, if negative feedback fails, the glucose levels in the blood may begin to rise dramatically, thus resulting indiabetes.
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, mostendocrinehormones are controlled by aphysiologic negative feedback inhibition loop, such as theglucocorticoids secreted by theadrenal cortex. Thehypothalamus secretescorticotropin-releasing hormone (CRH), which directs theanterior pituitary gland to secreteadrenocorticotropic hormone (ACTH). In turn, ACTH directs the adrenal cortex to secrete glucocorticoids, such ascortisol. 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]
Closed systems containing substances undergoing areversible chemical reaction can also exhibit negative feedback in accordance withLe Chatelier's principle which shift thechemical equilibrium to the opposite side of the reaction in order to reduce a stress. For example, in the reaction
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 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 oftenpositive feedback is identified as a possible contributor. However, negative feedback also can play a role.[32]
In economics,automatic stabilisers are government programs that are intended to work as negative feedback to dampen fluctuations inreal GDP.
Mainstream economics asserts that the market pricing mechanism operates to matchsupply 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. HoweverNorbert Wiener wrote in 1948:
The notion of economic equilibrium being maintained in this fashion by market forces has also been questioned by numerousheterodox economists such asfinancierGeorge Soros[34] and leadingecological economist andsteady-state theoristHerman Daly, who was with theWorld Bank in 1988–1994.[35]
A basic and common example of a negative feedback system in the environment is the interaction amongcloud cover, plant growth,solar radiation, and planet temperature.[38] 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 higheralbedo, or surface reflectivity, of the Earth. As albedo increases, however, the amount of solar radiation decreases.[39] This, in turn, affects the rest of the cycle.
Cloud cover, and in turn planet albedo and temperature, is also influenced by thehydrological cycle.[40] As planet temperature increases, more water vapor is produced, creating more clouds.[41] The clouds then block incoming solar radiation, lowering the temperature of the planet. This interaction produces lesswater 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.[42]
Negative feedback as a control technique may be seen in the refinements of thewater clock introduced byKtesibios 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.[43]
Negative feedback was implemented in the 17th century.Cornelius Drebbel had builtthermostatically controlled incubators and ovens in the early 1600s,[44] andcentrifugal governors were used to regulate the distance and pressure betweenmillstones inwindmills.[45]James Watt patented a form of governor in 1788 to control the speed of hissteam engine, andJames 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.[46]
The term "feedback" was well established by the 1920s, in reference to a means ofboosting 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.[47]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 thatreduced the gain of the amplifier, in the process greatly increasing its stability and bandwidth.[48][49]
Karl Küpfmüller published papers on a negative-feedback-basedautomatic gain control system and a feedback system stability criterion in 1928.[50]
Nyquist and Bode built on Black's work to develop a theory of amplifier stability.[49]
Early researchers in the area ofcybernetics subsequently generalized the idea of negative feedback to cover any goal-seeking or purposeful behavior.[51]
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 pioneerNorbert Wiener helped to formalize the concepts of feedback control, defining feedback in general as "the chain of the transmission and return of information",[52] 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 asdegenerative,[53]self-correcting,[54]balancing,[55] ordiscrepancy-reducing[56] in place of "negative".
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.
[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.
Balancing or negative feedback counteracts and opposes change
