Negative feedback

For use of criticism and punishment to modify behavior, seeperformance appraisalandreinforcement.

Negative feedback(orbalancing feedback) occurs when somefunctionof the output of a system, process, or mechanism isfed backin 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 theloop gainAB is negative.

The opposite tendency — calledpositive 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 ultimatemeltdownof a nuclear reactor which has a positivetemperature coefficient of reactivity.

Whereaspositive feedbacktends to lead to instability viaexponential growth,oscillationorchaotic behavior,negative feedback generally promotes stability. Negative feedback tends to promote a settling toequilibrium,and reduces the effects of perturbations. Negativefeedback loopsin 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 andelectronic engineering,and also within living organisms,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 incontrol 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 betweensolar 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

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.

Inbiology,this process (in general,biochemical) is often referred to ashomeostasis;whereas inmechanics,the more common term isequilibrium.

Inengineering,mathematicsand the physical, and biological sciences, common terms for the points around which the system gravitates include: attractors,stablestates, eigenstates/eigenfunctions, equilibrium points, andsetpoints.

Incontrol theory,negativerefers 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.

Some authors, in particular with respect to modellingbusiness systems,usenegativeto refer to the reduction in difference between the desired and actual behavior of a system.In a psychology context, on the other hand,negativerefers to thevalenceof the feedback – attractive versus aversive, or praise versus criticism.

In contrast,positive feedbackis 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 filtersordampersfitted.

Examples

• Mercury 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 theinvisible hand of the marketmetaphor of economic theory (1776), reactions to price movements provide a feedback mechanism to matchsupplyanddemand.
• Incentrifugal governors(1788), negative feedback is used to maintain a near-constant speed of an engine, irrespective of the load or fuel-supply conditions.
• In asteering engine(1866), power assistance is applied to the rudder with a feedback loop, to maintain the direction set by the steersman.
• Inservomechanisms,thespeedor position of an output, as determined by asensor,is compared to a set value, and any error is reduced by negative feedback to the input.
• Inaudioamplifiers,negative feedback flattensfrequency response,reducesdistortion,minimises the effect of manufacturing variations in component parameters, and compensates for changes in characteristics due to temperature change.
• Inanalog computing,feedback aroundoperational amplifiersis used to generatemathematical functionssuch asaddition,subtraction,integration,differentiation,logarithm,andantilogfunctions.
• Indelta-sigmaanalog-to-digitalanddigital-to-analog converters(particularly for highqualityaudio), a negative feedback loop is used to repeatedly correct accumulatedquantization errorduring conversion.
• In aphase locked loop(1932), feedback is used to maintain a generated alternatingwaveformin a constant phase to a reference signal. In many implementations the generated waveform is the output, but when used as ademodulatorin anFMradio receiver, the error feedback voltage serves as the demodulated output signal. If there is afrequency dividerbetween the generated waveform and the phase comparator, the device acts as afrequency multiplier.
• Inorganisms,feedback enables various measures (e.g. body temperature, orblood sugarlevel) to be maintained within a desired range byhomeostaticprocesses.

Detailed implementations

Error-controlled regulation

Basic error-controlled regulator loop

See also:Control engineering,Homeostasis,andAllostasis

A regulatorRadjusts the input to a systemTso the monitored essential variablesEare held to set-point valuesSthat result in the desired system output despite disturbancesD.

One use of feedback is to make a system (sayT)self-regulatingto minimize the effect of a disturbance (sayD). Using a negative feedback loop, a measurement of some variable (for example, aprocess variable,sayE) issubtractedfrom 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.The regulator modifies the input to the systemTaccording 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.Theregulationin such systems can range from a simple 'on-off' control to a more complex processing of the error signal.

In this framework, the physical form of a signal may undergo multiple transformations. For example, a change in weather may cause a disturbance to theheatinput 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 anelectricalerror in status compared to the 'set point'S,and subsequently used by theregulator(containing a 'controller' that commandsgascontrol valves and an ignitor) ultimately to change theheatprovided by a furnace (an 'effector') to counter the initial weather-related disturbance in heat input to the house.

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.

Mathematically, the regulator signal is given by:

$\mathrm {MV(t)} =K_{p}\left(\,{e(t)}+{\frac {1}{T_{i}}}\int _{0}^{t}{e(\tau )}\,{d\tau }+T_{d}{\frac {d}{dt}}e(t)\right)$

where

$T_{i}$is theintegral time

$T_{d}$is thederivative time

Negative feedback amplifier

Main article:Negative feedback amplifier

The negative feedback amplifier was invented byHarold Stephen BlackatBell Laboratoriesin 1927, and granted a patent in 1937 (US Patent 2,102,671)"a continuation of application Serial No. 298,155, filed August 8, 1928..." ).

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

There are many advantages to feedback in amplifiers.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 canoscillate.See the article onstep response.They may even exhibitinstability.Harry NyquistofBell Laboratoriesproposed theNyquist stability criterionand theNyquist plotthat identify stable feedback systems, including amplifiers and control systems.

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

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

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

${\frac {O}{I}}={\frac {A}{1+\beta A}}\approx {\frac {1}{\beta }}\,$

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 gainAis sufficiently large.In this context, the factor (1+βA) is often called the 'desensitivity factor',and in the broader context of feedback effects that include other matters likeelectrical impedanceandbandwidth,the 'improvement factor'.

If the disturbanceDis included, the amplifier output becomes:

$O={\frac {AI}{1+\beta A}}+{\frac {D}{1+\beta A}}\,$

which shows that the feedback reduces the effect of the disturbance by the 'improvement factor' (1+βA). The disturbanceDmight 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.

The difference signalI–βOat the amplifier input is sometimes called the "error signal".According to the diagram, the error signal is:

${\text{Error signal}}=I-\beta O=I\left(1-\beta {\frac {O}{I}}\right)={\frac {I}{1+\beta A}}-{\frac {\beta D}{1+\beta A}}\.$

From this expression, it can be seen that a large 'improvement factor' (or a largeloop gainβA) 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 blockand a unilateral feedback block has significant limitations.For methods of analysis that do not make these idealizations, see the articleNegative feedback amplifier.

Operational amplifier circuits

Main article:Operational amplifier applications

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

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 includingaudioequipment andcontrol systems.

Operational amplifier circuits typically employ negative feedback to get a predictable transfer function. Since the open-loop gain of anop-ampis 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. 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.Consequently, the voltage gain of the circuit in the diagram, assuming an ideal op amp, is the reciprocal of feedbackvoltage divisionratio β:

$V_{\text{out}}={\frac {R_{\text{1}}+R_{\text{2}}}{R_{\text{1}}}}V_{\text{in}}\!={\frac {1}{\beta }}V_{\text{in}}\,$.

A real op-amp has a high but finite gainAat 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.

Areas of application

Mechanical engineering

See also:Control systemsandControl engineering

Theballcockor float valve uses negative feedback to control the water level in a cistern.

An example of the use of negative feedback control is theballcockcontrol of water level (see diagram), or apressure regulator.In modern engineering, negative feedback loops are found inengine governors,fuel injectionsystems andcarburettors.Similar control mechanisms are used in heating and cooling systems, such as those involvingair conditioners,refrigerators,orfreezers.

Biology

See also:Counterregulatory hormoneandHomeostasis

Control of endocrine hormones by negative feedback.

Some biological systems exhibit negative feedback such as thebaroreflexinblood pressureregulation 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 bloodglucoselevels. 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, mostendocrinehormonesare controlled by aphysiologicnegative feedback inhibition loop, such as theglucocorticoidssecreted by theadrenal cortex.Thehypothalamussecretescorticotropin-releasing hormone (CRH),which directs theanterior pituitary glandto 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.

Chemistry

Closed systems containing substances undergoing areversible chemical reactioncan also exhibit negative feedback in accordance withLe Chatelier's principlewhich shift thechemical equilibriumto 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

Main articles:Self-organizationandEmergence

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

Economics

In economics,automatic stabilisersare government programs that are intended to work as negative feedback to dampen fluctuations inreal GDP.

Mainstream economicsasserts 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 Wienerwrote 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."

The notion of economic equilibrium being maintained in this fashion by market forces has also been questioned by numerousheterodoxeconomists such asfinancierGeorge Sorosand leadingecological economistandsteady-state theoristHerman Daly,who was with theWorld Bankin 1988–1994.

Environmental Science

Someeffects of climate changecan either enhance (positive feedbacks) or weaken (negative feedbacks) global warming.

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.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.This, in turn, affects the rest of the cycle.

Cloud cover, and in turn planet albedo and temperature, is also influenced by thehydrological cycle.As planet temperature increases, more water vapor is produced, creating more clouds.The clouds then block incoming solar radiation, lowering the temperature of the planet. This interaction produces lesswater vaporand 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.

History

Negative feedback as a control technique may be seen in the refinements of thewater clockintroduced byKtesibiosof 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.

Thefly-ball governoris an early example of negative feedback.

Negative feedback was implemented in the 17th century.Cornelius Drebbelhad builtthermostatically controlledincubators and ovens in the early 1600s,andcentrifugal governorswere used to regulate the distance and pressure betweenmillstonesinwindmills.James Wattpatented a form of governor in 1788 to control the speed of hissteam engine,andJames Clerk Maxwellin 1868 described "component motions" associated with these governors that lead to a decrease in a disturbance or the amplitude of an oscillation.

The term "feedback"was well established by the 1920s, in reference to a means ofboosting the gainof an electronic amplifier.Friis and Jensen described this action as "positive feedback" and made passing mention of a contrasting "negative feed-back action" in 1924.Harold Stephen Blackcame up with the idea of using negative feedback in electronic amplifiers in 1927, submitted a patent application in 1928,and detailed its use in his paper of 1934, where he defined negative feedback as a type of coupling thatreducedthe gain of the amplifier, in the process greatly increasing its stability and bandwidth.

Karl Küpfmüllerpublished papers on a negative-feedback-basedautomatic gain controlsystem and a feedback system stability criterion in 1928.

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

Early researchers in the area ofcyberneticssubsequently generalized the idea of negative feedback to cover any goal-seeking or purposeful behavior.

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 Wienerhelped to formalize the concepts of feedback control, defining feedback in general as "the chain of the transmission and return of information",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...

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

To reduce confusion, later authors have suggested alternative terms such asdegenerative,self-correcting,balancing,ordiscrepancy-reducingin place of "negative".

See also

• Asymptotic 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 changePages displaying short descriptions of redirect targets
• 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– Psychological theory
• Positive feedback– Feedback loop that increases an initial small effect
• Stability criterion
• Step response– Time behavior of a system controlled by Heaviside step functions

External links

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