Feedback

# Feedback

Overview
Feedback describes the situation when output from (or information
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...

about the result of) an event or phenomenon
Phenomenon
A phenomenon , plural phenomena, is any observable occurrence. Phenomena are often, but not always, understood as 'appearances' or 'experiences'...

in the past will influence an occurrence or occurrences of the same (i.e. same defined) event / phenomenon (or the continuation / development of the original phenomenon) in the present or future.
When an event is part of a chain of cause-and-effect
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....

that forms a circuit or loop, then the event is said to "feed back" into itself.

Feedback is also a synonym for:
• Feedback signal - the information about the initial event that is the basis for subsequent modification of the event
• Feedback loop - the causal path that leads from the initial generation of the feedback signal to the subsequent modification of the event
• Audio feedback
Audio feedback
Audio feedback is a special kind of positive feedback which occurs when a sound loop exists between an audio input and an audio output...

- the special kind of positive feedback
Positive feedback
Positive feedback is a process in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system that responds to a perturbation in a way that reduces its effect is...

that occurs when a loop exists between an audio input and output.

Feedback is a mechanism, process or signal that is looped back to control a system
System
System is a set of interacting or interdependent components forming an integrated whole....

within itself.
Discussion

Recent Discussions
Encyclopedia
Feedback describes the situation when output from (or information
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...

about the result of) an event or phenomenon
Phenomenon
A phenomenon , plural phenomena, is any observable occurrence. Phenomena are often, but not always, understood as 'appearances' or 'experiences'...

in the past will influence an occurrence or occurrences of the same (i.e. same defined) event / phenomenon (or the continuation / development of the original phenomenon) in the present or future.
When an event is part of a chain of cause-and-effect
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....

that forms a circuit or loop, then the event is said to "feed back" into itself.

Feedback is also a synonym for:
• Feedback signal - the information about the initial event that is the basis for subsequent modification of the event
• Feedback loop - the causal path that leads from the initial generation of the feedback signal to the subsequent modification of the event
• Audio feedback
Audio feedback
Audio feedback is a special kind of positive feedback which occurs when a sound loop exists between an audio input and an audio output...

- the special kind of positive feedback
Positive feedback
Positive feedback is a process in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system that responds to a perturbation in a way that reduces its effect is...

that occurs when a loop exists between an audio input and output.

## Overview

Feedback is a mechanism, process or signal that is looped back to control a system
System
System is a set of interacting or interdependent components forming an integrated whole....

within itself. Such a loop is called a feedback loop. In systems containing an input and output, feeding back part of the output so as to increase the input is positive feedback
Positive feedback
Positive feedback is a process in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system that responds to a perturbation in a way that reduces its effect is...

(regeneration); feeding back part of the output in such a way as to partially oppose the input is negative feedback
Negative feedback
Negative feedback occurs when the output of a system acts to oppose changes to the input of the system, with the result that the changes are attenuated. If the overall feedback of the system is negative, then the system will tend to be stable.- Overview :...

(degeneration).

Generally, a control system
Control system
A control system is a device, or set of devices to manage, command, direct or regulate the behavior of other devices or system.There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls...

has input from an external signal source and output to an external load; this defines a natural sense (or direction) or path of propagation of signal; the feedforward sense or path describes the signal propagation from input to output; feedback describes signal propagation in the reverse sense. When a sample of the output of the system is fed back, in the reverse sense, by a distinct feedback path into the interior of the system, to contribute to the input of one of its internal feedforward components, especially an active device or a substance that is consumed in an irreversible reaction, it is called the "feedback". The propagation of the signal around the feedback loop takes a finite time because it is causal.

The natural sense of feedforward is defined chemically by some irreversible reaction, or electronically by an active circuit element that has access to an auxiliary power supply, so as to be able to provide power gain to amplify the signal as it propagates from input to output. For example, an amplifier can use power from its controlled power reservoir, such as its battery, to provide power gain to amplify the signal; but the reverse is not possible: the signal cannot provide power to re-charge the battery of the amplifier.

Feedforward, feedback and regulation are self related. The feedforward carries the signal from source to load.

Negative feedback helps to maintain stability in a system in spite of external changes. It is related to homeostasis
Homeostasis
Homeostasis is the property of a system that regulates its internal environment and tends to maintain a stable, constant condition of properties like temperature or pH...

. For example, in a population of foxes (predators) and rabbits (prey), an increase in the number of foxes will cause a reduction in the number of rabbits; the smaller rabbit population will sustain fewer foxes, and the fox population will fall back. In an electronic amplifier
Electronic amplifier
An electronic amplifier is a device for increasing the power of a signal.It does this by taking energy from a power supply and controlling the output to match the input signal shape but with a larger amplitude...

feeding back a negative copy of the output to the input will tend to cancel distortion
Distortion
A distortion is the alteration of the original shape of an object, image, sound, waveform or other form of information or representation. Distortion is usually unwanted, and often many methods are employed to minimize it in practice...

, making the output a more accurate replica of the input signal.

Positive feedback amplifies possibilities of divergences (evolution, change of goals); it is the condition to change, evolution, growth; it gives the system the ability to access new points of equilibrium
Dynamic equilibrium
A dynamic equilibrium exists once a reversible reaction ceases to change its ratio of reactants/products, but substances move between the chemicals at an equal rate, meaning there is no net change. It is a particular example of a system in a steady state...

.

For example, in an organism, most positive feedback provides for fast autoexcitation of elements of endocrine and nervous systems (in particular, in stress responses conditions) and are believed to play a key role in morphogenesis, growth, and development of organs, all processes that are, in essence, a rapid escape from the initial state. Homeostasis is especially visible in the nervous
Nervous system
The nervous system is an organ system containing a network of specialized cells called neurons that coordinate the actions of an animal and transmit signals between different parts of its body. In most animals the nervous system consists of two parts, central and peripheral. The central nervous...

and endocrine system
Endocrine system
In physiology, the endocrine system is a system of glands, each of which secretes a type of hormone directly into the bloodstream to regulate the body. The endocrine system is in contrast to the exocrine system, which secretes its chemicals using ducts. It derives from the Greek words "endo"...

s when considered at organism level. Chemical potential energy for irreversible reactions or electrical potential energy for irreversible cell-membrane current powers the feedforward sense of the process. However, in the case of morphogenesis, feedback may only be enough to explain the increase in momentum of the system, and may not be sufficient in itself to account for the movement or direction of its parts.

A public address system is an electronic amplification system with a mixer, amplifier and loudspeakers, used to reinforce a sound source, e.g., a person giving a speech, a DJ playing prerecorded music, and distributing the sound throughout a venue or building.Simple PA systems are often used in...

system is used with a microphone to amplify speech, the output from a random sound at the microphone may produce sound at a loudspeaker that reaches the microphone such as to reinforce and amplify the original signal (positive feedback), building up to a howl (of frequency dependent upon the acoustics of the hall). A similar process is used deliberately to produce oscillating electrical signals.

Feedback is distinctly different from reinforcement that occurs in learning, or in conditioned reflexes. Feedback combines immediately with the immediate input signal to drive the responsive power gain element, without changing the basic responsiveness of the system to future signals. Reinforcement changes the basic responsiveness of the system to future signals, without combining with the immediate input signal. Reinforcement is a permanent change in the responsiveness of the system to all future signals. Feedback is only transient, being limited by the duration of the immediate signal.

## Types of feedback

When feedback acts in response to an event/phenomenon, it can influence the input signal in one of two ways:
1. An in-phase feedback signal, where a positive-going wave on the input leads to a positive-going change on the output, will amplify the input signal, leading to more modification. This is known as positive feedback
Positive feedback
Positive feedback is a process in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system that responds to a perturbation in a way that reduces its effect is...

.
2. A feedback signal which is inverted, where a positive-going change on the input leads to a negative-going change on the output, will dampen the effect of the input signal, leading to less modification. This is known as negative feedback
Negative feedback
Negative feedback occurs when the output of a system acts to oppose changes to the input of the system, with the result that the changes are attenuated. If the overall feedback of the system is negative, then the system will tend to be stable.- Overview :...

.
• Note that an increase or decrease of the feedback signal here refers to the magnitude
Magnitude (mathematics)
The magnitude of an object in mathematics is its size: a property by which it can be compared as larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....

relative to the input signal's absolute value
Absolute value
In mathematics, the absolute value |a| of a real number a is the numerical value of a without regard to its sign. So, for example, the absolute value of 3 is 3, and the absolute value of -3 is also 3...

, without regard to the polarity or sign of the feedback signal. For example if the input signal changes by 100 then a change in feedback signal value from +5 to +10 is a positive feedback. If the input signal changes by -100 then a change in the feedback signal from -5 to -10 is also a positive feedback.

Positive feedback tends to increase the event that caused it, such as in a nuclear chain-reaction. It is also known as a self-reinforcing loop. An event influenced by positive feedback can increase or decrease its output/activation until it hits a limiting constraint. Such a constraint may be destructive, as in thermal runaway
Thermal runaway
Thermal runaway refers to a situation where an increase in temperature changes the conditions in a way that causes a further increase in temperature, often leading to a destructive result...

or a nuclear chain reaction
Chain reaction
A chain reaction is a sequence of reactions where a reactive product or by-product causes additional reactions to take place. In a chain reaction, positive feedback leads to a self-amplifying chain of events....

. Self-reinforcing loops can be a smaller part of a larger balancing loop, especially in biological systems such as regulatory circuits.

Negative feedback, which tends to reduce the input signal that caused it, is also known as a self-correcting or balancing loop. Such loops tend to be goal-seeking, as in a thermostat
Thermostat
A thermostat is the component of a control system which regulates the temperature of a system so that the system's temperature is maintained near a desired setpoint temperature. The thermostat does this by switching heating or cooling devices on or off, or regulating the flow of a heat transfer...

, which compares actual temperature with desired temperature and seeks to reduce the difference. Balancing loops are sometimes prone to hunting: an oscillation
Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...

caused by an excessive or delayed negative feedback signal, resulting in over-correction, wherein the signal becomes a positive feedback.

The terms negative and positive feedback can be used loosely or colloquially to describe or imply criticism and praise, respectively. This may lead to confusion with the more technically accurate terms positive and negative reinforcement, which refer to something that changes the likelihood of a future behaviour. Moreover, when used technically, negative feedback leads to stability that is, in general, considered good, whereas positive feedback can lead to unstable and explosive situations that are considered bad. Thus, when used colloquially, these terms imply the opposite desirability to that when used technically.

Negative feedback
Negative feedback
Negative feedback occurs when the output of a system acts to oppose changes to the input of the system, with the result that the changes are attenuated. If the overall feedback of the system is negative, then the system will tend to be stable.- Overview :...

was applied by Harold Stephen Black
Harold Stephen Black
Harold Stephen Black was an American electrical engineer, who revolutionized the field of applied electronics by inventing the negative feedback amplifier in 1927. To some, his invention is considered the most important breakthrough of the twentieth century in the field of electronics, since it...

to electrical amplifiers in 1927, but he could not get his idea patented until 1937. Arturo Rosenblueth
Arturo Rosenblueth
Arturo Rosenblueth Stearns was a Mexican researcher, physician and physiologist, who is known as one of the pioneers of cybernetics.- Biography:...

, a Mexican researcher and physician, co-authored a seminal 1943 paper Behavior, Purpose and Teleology that, according to Norbert Wiener
Norbert Wiener
Norbert Wiener was an American mathematician.A famous child prodigy, Wiener later became an early researcher in stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.Wiener is regarded as the originator of cybernetics, a...

(another co-author of the paper), set the basis for the new science cybernetics
Cybernetics
Cybernetics is the interdisciplinary study of the structure of regulatory systems. Cybernetics is closely related to information theory, control theory and systems theory, at least in its first-order form...

. Rosenblueth proposed that behaviour controlled by negative feedback, whether in animal, human or machine, was a determinative, directive principle in nature and human creations. This kind of feedback is studied in cybernetics
Cybernetics
Cybernetics is the interdisciplinary study of the structure of regulatory systems. Cybernetics is closely related to information theory, control theory and systems theory, at least in its first-order form...

and control theory
Control theory
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...

.

### Biology

In biological systems such as organism
Organism
In biology, an organism is any contiguous living system . In at least some form, all organisms are capable of response to stimuli, reproduction, growth and development, and maintenance of homoeostasis as a stable whole.An organism may either be unicellular or, as in the case of humans, comprise...

s, ecosystem
Ecosystem
An ecosystem is a biological environment consisting of all the organisms living in a particular area, as well as all the nonliving , physical components of the environment with which the organisms interact, such as air, soil, water and sunlight....

s, or the biosphere
Biosphere
The biosphere is the global sum of all ecosystems. It can also be called the zone of life on Earth, a closed and self-regulating system...

, most parameters must stay under control within a narrow range around a certain optimal level under certain environmental conditions. The deviation of the optimal value of the controlled parameter can result from the changes in internal and external environments. A change of some of the environmental conditions may also require change of that range to change for the system to function. The value of the parameter to maintain is recorded by a reception system and conveyed to a regulation module via an information channel. An example of this is Insulin oscillations
Insulin oscillations
The insulin concentration in blood increases after meals and gradually returns to basal levels during the next 1-2 hours. However, the basal insulin level is not stable. It oscillates with a regular period of 3-6 min. After a meal the amplitude of these oscillations increases but the periodicity...

.

Biological systems contain many types of regulatory circuits, both positive and negative. As in other contexts, positive and negative do not imply consequences of the feedback have good or bad final effect. A negative feedback loop is one that tends to slow down a process, whereas the positive feedback loop tends to accelerate it. The mirror neuron
Mirror neuron
A mirror neuron is a neuron that fires both when an animal acts and when the animal observes the same action performed by another. Thus, the neuron "mirrors" the behaviour of the other, as though the observer were itself acting. Such neurons have been directly observed in primate and other...

s are part of a social feedback system, when an observed action is "mirrored" by the brain - like a self-performed action.

Feedback is also central to the operations of gene
Gene
A gene is a molecular unit of heredity of a living organism. It is a name given to some stretches of DNA and RNA that code for a type of protein or for an RNA chain that has a function in the organism. Living beings depend on genes, as they specify all proteins and functional RNA chains...

s and gene regulatory network
Gene regulatory network
A gene regulatory network or genetic regulatory network is a collection of DNA segments in a cell whichinteract with each other indirectly and with other substances in the cell, thereby governing the rates at which genes in the network are transcribed into mRNA.In general, each mRNA molecule goes...

s. Repressor (see Lac repressor
Lac repressor
The lac repressor is a DNA-binding protein which inhibits the expression of genes coding for proteins involved in the metabolism of lactose in bacteria. These genes are repressed when lactose is not available to the cell, ensuring that the bacterium only invests energy in the production of...

) and activator protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

s are used to create genetic operon
Operon
In genetics, an operon is a functioning unit of genomic DNA containing a cluster of genes under the control of a single regulatory signal or promoter. The genes are transcribed together into an mRNA strand and either translated together in the cytoplasm, or undergo trans-splicing to create...

s, which were identified by Francois Jacob
François Jacob
François Jacob is a French biologist who, together with Jacques Monod, originated the idea that control of enzyme levels in all cells occurs through feedback on transcription. He shared the 1965 Nobel Prize in Medicine with Jacques Monod and André Lwoff.-Childhood and education:François Jacob is...

and Jacques Monod
Jacques Monod
Jacques Lucien Monod was a French biologist who was awarded a Nobel Prize in Physiology or Medicine in 1965, sharing it with François Jacob and Andre Lwoff "for their discoveries concerning genetic control of enzyme and virus synthesis"...

in 1961 as feedback loops. These feedback loops may be positive (as in the case of the coupling between a sugar molecule and the proteins that import sugar into a bacterial cell), or negative (as is often the case in metabolic consumption).

Any self-regulating natural process involves feedback and/or is prone to hunting. A well-known example in ecology
Ecology
Ecology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...

is the oscillation of the population of snowshoe hare
Snowshoe Hare
The Snowshoe Hare , also called the Varying Hare, or Snowshoe Rabbit, is a species of hare found in North America. It has the name "snowshoe" because of the large size of its hind feet and the marks its tail leaves. The animal's feet prevent it from sinking into the snow when it hops and walks...

s due to predation from lynx
Lynx
A lynx is any of the four Lynx genus species of medium-sized wildcats. The name "lynx" originated in Middle English via Latin from Greek word "λύγξ", derived from the Indo-European root "*leuk-", meaning "light, brightness", in reference to the luminescence of its reflective eyes...

es.

In zymology
Fermentation (biochemistry)
Fermentation is the process of extracting energy from the oxidation of organic compounds, such as carbohydrates, using an endogenous electron acceptor, which is usually an organic compound. In contrast, respiration is where electrons are donated to an exogenous electron acceptor, such as oxygen,...

, feedback serves as regulation of activity of an enzyme by its direct product(s) or downstream metabolite(s) in the metabolic pathway (see Allosteric regulation
Allosteric regulation
In biochemistry, allosteric regulation is the regulation of an enzyme or other protein by binding an effector molecule at the protein's allosteric site . Effectors that enhance the protein's activity are referred to as allosteric activators, whereas those that decrease the protein's activity are...

).

The hypothalamic-pituitary-adrenal axis , also known as thelimbic-hypothalamic-pituitary-adrenal axis and, occasionally, as the hypothalamic-pituitary-adrenal-gonadotropic axis, is a complex set of direct influences and feedback interactions among the hypothalamus, the pituitary gland ,...

The gonad is the organ that makes gametes. The gonads in males are the testes and the gonads in females are the ovaries. The product, gametes, are haploid germ cells. For example, spermatozoon and egg cells are gametes...

al axis is largely controlled by positive and negative feedback, much of which is still unknown.

In psychology
Psychology
Psychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...

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

### Climate science

The climate system is characterized by strong positive and negative feedback
Negative feedback
Negative feedback occurs when the output of a system acts to oppose changes to the input of the system, with the result that the changes are attenuated. If the overall feedback of the system is negative, then the system will tend to be stable.- Overview :...

loops between processes that affect the state of the atmosphere, ocean, and land. A simple example is the ice-albedo positive feedback
Ice-albedo feedback
Ice-albedo feedback is a positive feedback climate process where a change in the area of snow-covered land, ice caps, glaciers or sea ice alters the albedo. This change in albedo acts to reinforce the initial alteration in ice area...

loop whereby melting snow exposes more dark ground (of lower albedo
Albedo
Albedo , or reflection coefficient, is the diffuse reflectivity or reflecting power of a surface. It is defined as the ratio of reflected radiation from the surface to incident radiation upon it...

), which in turn absorbs heat and causes more snow to melt.

### Control theory

Feedback is extensively used in control theory
Control theory
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...

, using a variety of methods including state space (controls)
State space (controls)
In control engineering, a state space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations...

, full state feedback
Full state feedback
Full state feedback , or pole placement, is a method employed in feedback control system theory to place the closed-loop poles of a plant in pre-determined locations in the s-plane. Placing poles is desirable because the location of the poles corresponds directly to the eigenvalues of the system,...

(also known as pole placement), and so forth.
The most common general-purpose controller
Controller (control theory)
In control theory, a controller is a device which monitors and affects the operational conditions of a given dynamical system. The operational conditions are typically referred to as output variables of the system which can be affected by adjusting certain input variables...

using a control-loop feedback mechanism is a proportional-integral-derivative
PID controller
A proportional–integral–derivative controller is a generic control loop feedback mechanism widely used in industrial control systems – a PID is the most commonly used feedback controller. A PID controller calculates an "error" value as the difference between a measured process variable and a...

(PID) controller. Heuristically, the terms of a PID controller can be interpreted as corresponding to time: the proportional term depends on the present error, the integral term on the accumulation of past errors, and the derivative term is a prediction of future error, based on current rate of change.

### Mechanical engineering

In ancient times, the float valve was used to regulate the flow of water in Greek and Roman water clock
Water clock
A water clock or clepsydra is any timepiece in which time is measured by the regulated flow of liquid into or out from a vessel where the amount is then measured.Water clocks, along with sundials, are likely to be the oldest time-measuring instruments, with the only exceptions...

s; similar float valves are used to regulate fuel in a carburettor and also used to regulate tank water level in the flush toilet
Flush toilet
A flush toilet is a toilet that disposes of human waste by using water to flush it through a drainpipe to another location. Flushing mechanisms are found more often on western toilets , but many squat toilets also are made for automated flushing...

.

In 1745, the windmill was improved with by blacksmith Edmund Lee who added a fantail
Windmill fantail
A Fantail is a small windmill mounted at right angles to the sails, at the rear of the windmill, and which turns the cap automatically to bring it into the wind. The fantail was patented in 1745 by Edmund Lee, a blacksmith working at Brockmill Forge near Wigan, England, and perfected on mills...

to keep the face of the windmill pointing into the wind. In 1787, Thomas Mead
Thomas Francis Mead was an Australian politician, elected as a member of the New South Wales Legislative Assembly representing the seat of Hurstville for the Liberal Party...

regulated the rotation speed of a windmill by using a centrifugal pendulum to adjust the distance between the bedstone and the runner stone (i.e., to adjust the load).

The use of the centrifugal governor
Centrifugal governor
A centrifugal governor is a specific type of governor that controls the speed of an engine by regulating the amount of fuel admitted, so as to maintain a near constant speed whatever the load or fuel supply conditions...

by James Watt
James Watt
James Watt, FRS, FRSE was a Scottish inventor and mechanical engineer whose improvements to the Newcomen steam engine were fundamental to the changes brought by the Industrial Revolution in both his native Great Britain and the rest of the world.While working as an instrument maker at the...

in 1788 to regulate the speed of his steam engine
Steam engine
A steam engine is a heat engine that performs mechanical work using steam as its working fluid.Steam engines are external combustion engines, where the working fluid is separate from the combustion products. Non-combustion heat sources such as solar power, nuclear power or geothermal energy may be...

was one factor leading to the Industrial Revolution
Industrial Revolution
The Industrial Revolution was a period from the 18th to the 19th century where major changes in agriculture, manufacturing, mining, transportation, and technology had a profound effect on the social, economic and cultural conditions of the times...

. Steam engines also use float valves and pressure release valves as mechanical regulation devices. A mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...

of Watt's governor was done by James Clerk Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...

in 1868.

The Great Eastern
SS Great Eastern
SS Great Eastern was an iron sailing steam ship designed by Isambard Kingdom Brunel, and built by J. Scott Russell & Co. at Millwall on the River Thames, London. She was by far the largest ship ever built at the time of her 1858 launch, and had the capacity to carry 4,000 passengers around the...

was one of the largest steamships of its time and employed a steam powered rudder with feedback mechanism designed in 1866 by J.McFarlane Gray. Joseph Farcot coined the word servo
Servomechanism
thumb|right|200px|Industrial servomotorThe grey/green cylinder is the [[Brush |brush-type]] [[DC motor]]. The black section at the bottom contains the [[Epicyclic gearing|planetary]] [[Reduction drive|reduction gear]], and the black object on top of the motor is the optical [[rotary encoder]] for...

in 1873 to describe steam-powered steering systems. Hydraulic servos were later used to position guns. Elmer Ambrose Sperry
Elmer Ambrose Sperry
Elmer Ambrose Sperry was a prolific inventor and entrepreneur, most famous as co-inventor, with Herman Anschütz-Kaempfe of the gyrocompass.Sperry was born at Cincinnatus, New York, United States of America...

of the Sperry Corporation
Sperry Corporation
Sperry Corporation was a major American equipment and electronics company whose existence spanned more than seven decades of the twentieth century...

designed the first autopilot
Autopilot
An autopilot is a mechanical, electrical, or hydraulic system used to guide a vehicle without assistance from a human being. An autopilot can refer specifically to aircraft, self-steering gear for boats, or auto guidance of space craft and missiles...

in 1912. Nicolas Minorsky published a theoretical analysis of automatic ship steering in 1922 and described the PID controller
PID controller
A proportional–integral–derivative controller is a generic control loop feedback mechanism widely used in industrial control systems – a PID is the most commonly used feedback controller. A PID controller calculates an "error" value as the difference between a measured process variable and a...

.

Internal combustion engines of the late 20th century employed mechanical feedback mechanisms such as the vacuum timing advance but mechanical feedback was replaced by electronic engine management systems
Engine control unit
An engine control unit is a type of electronic control unit that determines the amount of fuel, ignition timing and other parameters an internal combustion engine needs to keep running...

once small, robust and powerful single-chip microcontroller
Microcontroller
A microcontroller is a small computer on a single integrated circuit containing a processor core, memory, and programmable input/output peripherals. Program memory in the form of NOR flash or OTP ROM is also often included on chip, as well as a typically small amount of RAM...

s became affordable.

### Electronic engineering

The main applications of feedback in electronics
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

are in the designs of amplifiers, oscillators, and logic circuit elements.

The processing and control of feedback is engineered into many electronic devices
Electronic component
An electronic component is a basic electronic element and may be available in a discrete form having two or more electrical terminals . These are intended to be connected together, usually by soldering to a printed circuit board, in order to create an electronic circuit with a particular function...

and may also be embedded in other technologies.

If the signal is inverted on its way round the control loop, the system is said to have negative feedback; otherwise, the feedback is said to be positive. Negative feedback is often deliberately introduced to increase the stability
BIBO stability
In electrical engineering, specifically signal processing and control theory, BIBO stability is a form of stability for linear signals and systems that take inputs. BIBO stands for Bounded-Input Bounded-Output...

and accuracy of a system by correcting unwanted changes. This scheme can fail if the input changes faster than the system can respond to it. When this happens, the lag in arrival of the correcting signal results in unintended positive feedback, causing the output to oscillate
Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...

or "hunt". Oscillation is usually an unwanted consequence of system behaviour.

Harry Nyquist
Harry Nyquist
Harry Nyquist was an important contributor to information theory.-Personal life:...

contributed the Nyquist plot
Nyquist plot
A Nyquist plot is a parametric plot of a transfer function used in automatic control and signal processing. The most common use of Nyquist plots is for assessing the stability of a system with feedback. In Cartesian coordinates, the real part of the transfer function is plotted on the X axis. The...

for assessing the stability of feedback systems. An easier assessment, but less general, is based upon gain margin and phase margin using Bode plots (contributed by Hendrik Bode
Hendrik Wade Bode , was an American engineer, researcher, inventor, author and scientist], of Dutch ancestry. As a pioneer of modern control theory and electronic telecommunications he revolutionized both the content and methodology of his chosen fields of research.He made important contributions...

). Design to ensure stability often involves frequency compensation
Frequency compensation
In electrical engineering, frequency compensation is a technique used in amplifiers, and especially in amplifiers employing negative feedback. It usually has two primary goals: To avoid the unintentional creation of positive feedback, which will cause the amplifier to oscillate, and to control...

, one method of compensation being pole splitting
Pole splitting
Pole splitting is a phenomenon exploited in some forms of frequency compensation used in an electronic amplifier. When a capacitor is introduced between the input and output sides of the amplifier with the intention of moving the pole lowest in frequency to lower frequencies, pole splitting causes...

.

The high-pitched squeal that sometimes occurs in audio systems, PA systems, and rock music
Rock music
Rock music is a genre of popular music that developed during and after the 1960s, particularly in the United Kingdom and the United States. It has its roots in 1940s and 1950s rock and roll, itself heavily influenced by rhythm and blues and country music...

is known as audio feedback
Audio feedback
Audio feedback is a special kind of positive feedback which occurs when a sound loop exists between an audio input and an audio output...

. If a microphone is in front of a speaker that it is connected to, the noise put into the microphone will come out of the speaker. Since the microphone is in front of the speaker, the original sound (now coming from the speaker) goes back into the microphone. This happens over and over, getting louder each time. This process produces the squeal.

Electronic feedback loops: They are used to control the output of electronic
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

devices, such as amplifiers. A feedback loop is created when all or some portion of the output from an electronic device is fed-back to the input. A device is said to be operating open loop if no output feedback is being employed and closed loop if feedback is being used. Electronic feedback loops take two forms: negative feedback
Negative feedback
Negative feedback occurs when the output of a system acts to oppose changes to the input of the system, with the result that the changes are attenuated. If the overall feedback of the system is negative, then the system will tend to be stable.- Overview :...

loops and positive feedback
Positive feedback
Positive feedback is a process in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system that responds to a perturbation in a way that reduces its effect is...

loops.

Negative feedback loops: They exist when the fed-back output signal is out of phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

with the input signal. This occurs when the fed-back signal is anywhere from 90° to 270° with respect to the input signal. Negative feedback is generally used to correct output errors or to lower device output gain to a pre-determined level. In feedback amplifiers, this correction is generally for waveform distortion
Distortion
A distortion is the alteration of the original shape of an object, image, sound, waveform or other form of information or representation. Distortion is usually unwanted, and often many methods are employed to minimize it in practice...

reduction or to establish a specified gain
Gain
In electronics, gain is a measure of the ability of a circuit to increase the power or amplitude of a signal from the input to the output. It is usually defined as the mean ratio of the signal output of a system to the signal input of the same system. It may also be defined on a logarithmic scale,...

level. A general expression for the gain of a negative feedback amplifier is the asymptotic gain model.

Positive feedback loops: They occur when the fed-back signal is in phase with the input signal. Under certain gain conditions, positive feedback reinforces the input signal to the point where the output of the device oscillates between its maximum and minimum possible states. Positive feedback may also introduce hysteresis
Hysteresis
Hysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately...

into a circuit. This can cause the circuit to ignore small signals and respond only to large ones. It is sometimes used to eliminate noise from a digital signal. Under some circumstances, positive feedback may cause a device to latch, i.e., to reach a condition in which the output is locked to its maximum or minimum state.

### Software engineering and computing systems

Feedback loops provide generic mechanisms for controlling the running, maintenance, and evolution of software and computing systems. Feedback-loops are important models in the engineering of adaptive software, as they define the behaviour of the interactions among the control elements over the adaptation process, to guarantee system properties at run-time. Feedback loops and foundations of control theory has been successfully applied to computing systems. In particular, they have been applied to the development of products such as IBM's Universal Database server
IBM DB2
The IBM DB2 Enterprise Server Edition is a relational model database server developed by IBM. It primarily runs on Unix , Linux, IBM i , z/OS and Windows servers. DB2 also powers the different IBM InfoSphere Warehouse editions...

and IBM Tivoli. From a software perspective, the autonomic (MAPE, Monitor Analyze Plan Execute) loop proposed by researchers of IBM is another valuable contribution to the application of feedback loops to the control of dynamic properties and the design and evolution of autonomic software systems.

### Social sciences

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

#### Reflexive feedback

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

#### Economics and finance

A system
System
System is a set of interacting or interdependent components forming an integrated whole....

prone to hunting (oscillating) is the stock market
Stock market
A stock market or equity market is a public entity for the trading of company stock and derivatives at an agreed price; these are securities listed on a stock exchange as well as those only traded privately.The size of the world stock market was estimated at about \$36.6 trillion...

, which has both positive and negative feedback mechanisms. This is due to cognitive and emotional factors belonging to the field of behavioural finance. For example,
• When stocks are rising (a bull market), the belief that further rises are probable gives investors an incentive to buy (positive feedback - reinforcing the rise, see also stock market bubble
Stock market bubble
A stock market bubble is a type of economic bubble taking place in stock markets when market participants drive stock prices above their value in relation to some system of stock valuation....

); but the increased price of the shares
Stock
The capital stock of a business entity represents the original capital paid into or invested in the business by its founders. It serves as a security for the creditors of a business since it cannot be withdrawn to the detriment of the creditors...

, and the knowledge
Knowledge
Knowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...

that there must be a peak after which the market will fall, ends up deterring buyers (negative feedback - stabilizing the rise).
• Once the market begins to fall regularly (a bear market), some investors may expect further losing days and refrain from buying (positive feedback - reinforcing the fall), but others may buy because stocks become more and more of a bargain (negative feedback - stabilizing the fall).

George Soros
George Soros
George Soros is a Hungarian-American business magnate, investor, philosopher, and philanthropist. He is the chairman of Soros Fund Management. Soros supports progressive-liberal causes...

used the word reflexivity
Reflexivity (social theory)
Reflexivity refers to circular relationships between cause and effect. A reflexive relationship is bidirectional with both the cause and the effect affecting one another in a situation that does not render both functions causes and effects...

,
to describe feedback in the financial markets and developed an investment
Investment
Investment has different meanings in finance and economics. Finance investment is putting money into something with the expectation of gain, that upon thorough analysis, has a high degree of security for the principal amount, as well as security of return, within an expected period of time...

theory based on this principle.

The conventional economic equilibrium
Economic equilibrium
In economics, economic equilibrium is a state of the world where economic forces are balanced and in the absence of external influences the values of economic variables will not change. It is the point at which quantity demanded and quantity supplied are equal...

model of supply and demand
Supply and demand
Supply and demand is an economic model of price determination in a market. It concludes that in a competitive market, the unit price for a particular good will vary until it settles at a point where the quantity demanded by consumers will equal the quantity supplied by producers , resulting in an...

supports only ideal linear negative feedback and was heavily criticized by Paul Ormerod
Paul Ormerod
Paul Ormerod is a Lancastrian economist who is currently researching complexity, complex systems, nonlinear feedback, the boom and bust cycle of business and economic competition...

in his book "The Death of Economics
The Death of Economics
The Death of Economics is a book written by Paul Ormerod. According to the author the title does not imply that the study of economies is not of great importance but rather it argues that conventional economics offers a misleading view of how the world operates and needs to be replaced.The book is...

", which, in turn, was criticized by traditional economists. This book was part of a change of perspective as economists started to recognise that Chaos Theory
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

applied to nonlinear feedback systems including financial markets.

#### World-system development

The hyperbolic growth
Hyperbolic growth
When a quantity grows towards a singularity under a finite variation it is said to undergo hyperbolic growth.More precisely, the reciprocal function 1/x has a hyperbola as a graph, and has a singularity at 0, meaning that the limit as x \to 0 is infinity: any similar graph is said to exhibit...

of the world population
World population
The world population is the total number of living humans on the planet Earth. As of today, it is estimated to be  billion by the United States Census Bureau...

observed till the 1970s has recently been correlated to a non-linear second-order positive feedback between the demographic growth and technological development that can be spelled out as follows: technological growth - increase in the carrying capacity
Carrying capacity
The carrying capacity of a biological species in an environment is the maximum population size of the species that the environment can sustain indefinitely, given the food, habitat, water and other necessities available in the environment...

of land for people - demographic growth - more people - more potential inventors - acceleration of technological growth - accelerating growth of the carrying capacity - the faster population growth - accelerating growth of the number of potential inventors - faster technological growth - hence, the faster growth of the Earth's carrying capacity for people, and so on.

#### Education

Learners have different conceptions of learning activities, and preconceptions about hierarchy in education. Some may look up to instructors as experts in the field and take to heart most of the things instructors say.
Thus, it is believed that spending a fair amount of time and effort thinking about how to respond to students may be a worthwhile time investment.
The Educational research literature on formative feedback also referred to as formative assessment
Formative assessment
Formative assessment is a range of formal and informal assessment procedures employed by teachers during the learning process in order to modify teaching and learning activities to improve student attainment. It typically involves qualitative feedback for both student and teacher that focuses on...

was reviewed recently by V. Shute.

Some general types of reinforcement that can be used in many types of student assessment are:

A different application of feedback in education is the system for "continuous improvement" of engineering curricula monitored by the Accreditation Board for Engineering and Technology
Accreditation Board for Engineering and Technology
ABET, Inc., formerly the Accreditation Board for Engineering and Technology, is a non-profit organization that accredits post-secondary education programs in applied science, computing, engineering, and technology...

(ABET).

#### Government

Examples of feedback in government are:
• Elections
• Mass media
Mass media
Mass media refers collectively to all media technologies which are intended to reach a large audience via mass communication. Broadcast media transmit their information electronically and comprise of television, film and radio, movies, CDs, DVDs and some other gadgets like cameras or video consoles...

• Revolution
Revolution
A revolution is a fundamental change in power or organizational structures that takes place in a relatively short period of time.Aristotle described two types of political revolution:...

• Curfews
• Surveys
Statistical survey
Survey methodology is the field that studies surveys, that is, the sample of individuals from a population with a view towards making statistical inferences about the population using the sample. Polls about public opinion, such as political beliefs, are reported in the news media in democracies....

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

#### In organizations

As an organization
Organization
An organization is a social group which distributes tasks for a collective goal. The word itself is derived from the Greek word organon, itself derived from the better-known word ergon - as we know organ - and it means a compartment for a particular job.There are a variety of legal types of...

seeks to improve its performance, feedback helps it to make required adjustments. Feedback serves as motivation for many people in the work place. When one receives either negative or positive feedback, they decide how they will apply it to his or her job. Joseph Folkman says that to find the greatest level of success in an organization, working with other people, a person should learn how to accept any kind of feedback, analyze it in the most positive manner possible, and use it to further impact future decision making.

Examples of feedback in organizations:
• Financial audit
Financial audit
A financial audit, or more accurately, an audit of financial statements, is the verification of the financial statements of a legal entity, with a view to express an audit opinion...

• Performance appraisal
Performance appraisal
A performance appraisal, employee appraisal, performance review, or development discussion is a method by which the job performance of an employee is evaluated typically by the corresponding manager or supervisor. A performance appraisal is a part of guiding and managing career development...

• Shareholders' meeting
• Marketing research
Marketing research
Marketing research is "the function that links the consumer, customer, and public to the marketer through information — information used to identify and define marketing opportunities and problems; generate, refine, and evaluate marketing actions; monitor marketing performance; and improve...

• 360-degree feedback
360-degree feedback
In human resources or industrial/organizational psychology, 360-degree feedback, also known as multi-rater feedback, multisource feedback, or multisource assessment, is feedback that comes from all around an employee. "360" refers to the 360 degrees in a circle, with an individual figuratively in...

• Walkout
Walkout
In labor disputes, a walkout is a labor strike, the act of employees collectively leaving the workplace as an act of protest.A walkout can also mean the act of leaving a place of work, school, a meeting, a company, or an organization, especially if meant as an expression of protest or disapproval.A...

• Lockout
Lockout (industry)
A lockout is a work stoppage in which an employer prevents employees from working. This is different from a strike, in which employees refuse to work.- Causes :...

• Negative feedback
Negative feedback
Negative feedback occurs when the output of a system acts to oppose changes to the input of the system, with the result that the changes are attenuated. If the overall feedback of the system is negative, then the system will tend to be stable.- Overview :...

• Positive feedback
Positive feedback
Positive feedback is a process in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system that responds to a perturbation in a way that reduces its effect is...

• Audio feedback
Audio feedback
Audio feedback is a special kind of positive feedback which occurs when a sound loop exists between an audio input and an audio output...

• Cybernetics
Cybernetics
Cybernetics is the interdisciplinary study of the structure of regulatory systems. Cybernetics is closely related to information theory, control theory and systems theory, at least in its first-order form...

• Feed-forward
Feed-forward
Feed-forward is a term describing an element or pathway within a control system which passes a controlling signal from a source in the control system's external environment, often a command signal from an external operator, to a load elsewhere in its external environment...

• Feedback passivation
Feedback passivation
In nonlinear control, feedback passivation is the use of feedback to convert a nonpassive dynamical system into a passive one....

• Interaction
Interaction
Interaction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction, as opposed to a one-way causal effect...

• Low-key feedback
Low-key feedback
In human-computer interaction, low-key feedback is a type of output that takes a background role by being very subtle, sometimes nearly imperceptible. Physical machines often provide rich low-key feedback as a byproduct of their design...

• Negative feedback amplifier
• Optical feedback
Optical feedback
Optical feedback is the optical equivalent of acoustic feedback. A simple example is the feedback that occurs when a loop exists between an optical input, e.g., a video camera, and an optical output, e.g., a television screen or monitor...

• Perverse incentive
Perverse incentive
A perverse incentive is an incentive that has an unintended and undesirable result which is contrary to the interests of the incentive makers. Perverse incentives are a type of unintended consequences.- Examples :...

• Resonance
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...

• Stability criterion
• Tactile
• Unintended consequence
Unintended consequence
In the social sciences, unintended consequences are outcomes that are not the outcomes intended by a purposeful action. The concept has long existed but was named and popularised in the 20th century by American sociologist Robert K. Merton...