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feedback, arrangement for the automatic self-regulation of an electrical, mechanical, or biological system by returning part of its output as input. A simple example of feedback is provided by a governor on an engine; if the speed of the engine exceeds a preset limit, the governor reduces the supply of fuel, thus decreasing the speed. Electronic control systems employ feedback extensively. In voltage and current regulators, part of the output is used as a control input, providing self-regulation. For example, if the output becomes too great, it acts through the feedback loop to reduce itself. The use of feedback as the fundamental control mechanism for machinery occurs in automation. Living organisms possess feedback control systems of great complexity. For example, when the hand reaches for an object, information about its position is continuously fed back to the brain, both by the eyes and by position-sensing nerves in the arm; the brain uses the position information to guide the hand to the object. Such feedback can be termed voluntary, since it is to some extent under conscious control. Automatic, involuntary feedback is constantly taking place as well, controlling processes such as respiration, circulation, digestion, and maintenance of body temperature. Feedback is one of the main concerns of cybernetics. See control systems. See also biofeedback.

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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.



return action of the results of a process on the course of the process or return action of the process being controlled on the control element. Feedback is typical of regulation and control systems in living nature, society, and engineering. A distinction is made between positive and negative feedback. If the results of the process intensify the process, the feedback is positive. If the results of the process lessen its action, the feedback is negative. Negative feedback stabilizes the course of the process, while positive feedback, by contrast, usually leads to accelerated development of the process or an oscillatory process. In complex systems, for example, social or biological systems, it is difficult, sometimes even impossible, to determine the type of feedback.

Feedback can also be classified by the nature of the bodies and media through which it is carried out. For example, it can be mechanical (the negative feedback of Watt’s flyball governor in a steam engine), optical (the positive feedback of the optical resonator in a laser), and electrical. Sometimes feedback in complex systems is viewed as the transmission of information on the course of the process in order to provide a basis for developing a particular control action. In this case, the feedback is called informational. The concept of feedback as a form of interaction plays an important part in analyzing the operation and development of complex control systems in living things and society and in revealing the structure of the material unity of the world.


In automatic regulation and control systems. Feedback in automatic regulation and control systems is a connection of the output of the segment under consideration of the main control chain (or information circuit) to its input. This segment may be either the object controlled or any element (or set of elements) of the automatic system. The main control chain is an arbitrarily singled-out path of signals from the input to the output of the automatic system. Feedback forms a path for transmitting control actions to supplement the main control chain or some segment of it.

Because of feedback, the results of the operation of the automatic system can act on the input of the system or, correspondingly, on a part of the system and influence the nature of the system’s performance characteristics and the mathematical description of the motion. Such systems with closed control chains, which are called closed-loop control systems, are characterized by having both external and control input signals, the latter being produced by the object controlled and fed to the control device.

The feedback circuit (channel) may contain one or several elements that convert the output signal of the main control chain according to a given algorithm. An example of a feedback circuit is a control device (for example, an automatic regulator) that receives the output (effective) action of the object controlled as an input quantity and compares this quantity with the value prescribed by the operation algorithm. As a result of this comparison, the action of the control device on the object controlled is produced. In this way, the object of control is encompassed by the feedback circuit as a control device and the control loop is closed. This kind of feedback is ordinarily called the monitoring feedback.

Feedback is a fundamental concept of cybernetics, especially of control theory and information theory. Feedback makes it possible to control and monitor the actual state of the system being controlled—that is, in the final analysis, the results of the work of the controlling system—and to make appropriate corrections in the control algorithm. In technical systems, monitored information on the working of the object controlled passes along a feedback circuit to the operator or to an automatic control device.

Negative feedback is widely used in closed-loop automatic systems for various purposes, for example, to increase stability, improve transient processes, and reduce sensitivity. (Sensitivity is understood to mean the ratio of an infinitesimally small change in the output action to the infinitesimally small input action that causes the change.) Positive feedback intensifies the output action of an element (or system) and leads to a rise in sensitivity and, as a rule, to a decrease in stability, which often results in sustained and increasingly divergent oscillations. Positive feedback has various other effects; for example, it worsens transient processes and dynamic characteristics.

Three types of feedback are distinguished on the basis of the conversion of the control action in the feedback circuit: direct (static), differentiating (elastic), and integrating. Direct feedback contains only proportional elements, and its output action is proportional to the input action in both static and dynamic modes, within a certain frequency range. Differentiating loops contain differentiating elements (simple or isodromic) and may be astatic (vanishing with time) or static. Astatic loops occur only in dynamic mode because the input action does not participate in the mathematical model; only derivatives of the input action, which approach zero with completion of transient processes, figure in the model. Integrating feedback includes an integrating element, which accumulates incoming control actions over time.

The following rules apply to systems with feedback. A proportional element encompassed by feedback remains proportional, with a new transfer ratio that is increased compared to the initial one for positive feedback and reduced for negative feedback. A static element of the first order encompassed by direct negative feedback remains a static element of the first order; the time constant and the transfer ratio change. An integrating element encompassed by direct negative feedback becomes a static element and, when encompassed by isodromic feedback, begins to respond also to the time derivative of the input action. A static element of the first order encompassed by isodromic feedback also responds to the time derivative of an input action. When a proportional element is encompassed by integrating negative feedback, a lag differentiating element results. If in this case the initial proportional element has a very large transfer ratio compared with the transfer ratio of isodromic feedback, then the element formed has characteristics close to those of a differentiating element.


Hammond, P. H. Teoriia obratnoi sviazi i ee primeneniia. Moscow, 1961. (Translated from English.)
Wiener, N. Kibernetika. Moscow, 1958. (Translated from English.)
Wiener, N. Kibernetika i obshchestvo. Moscow, 1958. (Translated from English.)
Teoriia avtomaticheskogo upravleniia, parts 1–2. Moscow, 1968–72.
Osnovy avtomaticheskogo upravleniia, 3rd ed. Moscow, 1974.


In electronic devices. Feedback in electronic devices involves the action of a signal from the output of the device on the input of the device. The electric circuit in which a signal from the output of the device is fed to the input is called the feedback circuit. The device can usually be represented in the form of an equivalent electric circuit that has two (input and output) pairs of terminals; the device can be characterized by a transfer function, which can be defined as the ratio of the voltage or current at the output pair of terminals to the voltage or current at the input pair. The transfer function Fc of a device with feedback can be determined from the formula

where F0 is the transfer function of the device without feedback, β is the transfer function of the feedback circuit, βF0 is the gain in the loop, and 1 — βFo is the feedback amount.

Classification. Feedback is classified primarily according to the type of transfer function of the feedback circuit, the relationship between the transfer functions of the feedback circuit and the device itself, the nature of the feedback circuit, and the method of connecting the feedback circuit to the input and output of the device.

A distinction is made between linear and nonlinear feedback depending on whether the transfer function of the feedback circuit is linear or nonlinear. If βF0 is a real positive number, the feedback is called positive; if βF0 is a real negative number, the feedback is called negative. For harmonic input oscillations, the nature and amount of the feedback can vary with the oscillation frequency. Such feedback is called frequency-dependent. The feedback may be positive for one frequency when the oscillations that are fed to the input of the device from the output of the feedback circuit and from outside are in phase (phase difference Δø = 0°) and it may be negative for another frequency when the oscillations are in antiphase. For a frequency for which Δø is not equal to 0° or 180°, the transfer function of the feedback circuit is a complex number; such feedback is called complex. When Δø is equal to 90°, the feedback is sometimes called (purely) reactive. If a complex feedback circuit contains a delay line—that is, if Δø is approximately proportional to the oscillation frequency—then the feedback is called a lagging (or delayed) feedback.

If the feedback is accomplished by connecting additional circuits to the device, it is called external feedback; if the feedback depends on physical phenomena that occur in the actual electronic components used in the device, it is called internal feedback. If an unwanted external feedback circuit arises, the feedback is called parasitic.

A distinction is made according to how the feedback circuits are connected to the input and output of the device. The feedback is called series feedback if the output of the feedback circuit is connected in series (Figure 1, a and b) with the signal source; the feedback is parallel if the output is in parallel with the signal source (Figure 1, c and d); and the feedback is mixed (compound) with respect to the input if the feedback circuits have a series-parallel connection with the signal source.

Figure 1. Diagrams of amplifiers with different types of feedback circuits: (a) series, current feedback; (b) series, voltage feedback; (c) parallel, current feedback; (d) parallel, voltage feedback; (1) amplifier of electrical oscillations; (2) feedback circuit (arrow shows direction of transfer of signal in feedback circuit from its input terminals to its output terminals); (Zs) impedance of signal source Es; (ZL impedance of amplifier load

A distinction is also made between voltage feedback and current feedback, depending on whether the voltage or current at the input of the feedback circuit is proportional to the voltage across the load resistance (Figure 1, b and d) or to the current through the load resistance (Figure 1, a and c). The feedback is called mixed (compound) feedback with respect to the output if there is a series-parallel connection between the feedback circuits and the load (output) resistance. Feedback in which only interference and distortions of the signal that occur in the device are transferred from the output to the input of the device is called balance feedback.

Properties and applications. In devices with positive feedback where the loop gain ≥ 1, self-oscillations may occur; they are used in various types of electrical oscillators. Positive feedback with βF0 < 1 is used for enhancement of certain properties of a device, for example, to increase the selectivity and sensitivity of a radio receiver with regenerative reception. A very important property of negative feedback is that it brings the transfer function of the device close in value to the function that is the reciprocal of the transfer function of the feedback circuit and is stronger, the greater is the magnitude of the feedback. Therefore, it is used primarily to stabilize the parameters of a device (for example, the gain of an amplifier of electrical oscillations) and to reduce by the factor 1 — βF0 the nonlinear distortions that occur in the device. In addition to changing the transfer function, feedback changes the input and output impedances of a device with feedback. Negative parallel (series), voltage (current) feedback decreases (increases), respectively, the input and output impedance of a device with feedback. Positive feedback has the opposite effect. Complex frequency-dependent feedback is used in active electrical filters. It also makes it possible to achieve, in electrical and electronic devices, elements of electrical circuits that do not exist in the form of physical components. Examples are elements with negative capacitance and negative inductance, a gyrator (impedance converter, for example, for the conversion of capacitance into inductance) for any working frequency, and elements with electrically controlled parameters (for example, in the form of a reactance tube). Sometimes this kind of feedback is used to neutralize unwanted internal feedback in electronic components.

Figure 2. Alternating-current tube amplifier with feedback: (Uin) voltage at input of amplifier; (T) electron tube; (R) resistor in cathode circuit of tube; (L) and (C) inductance and capacitance, respectively, of oscillatory circuit in anode circuit of tube; (M) inductance coil that couples anode circuit and control grid circuit of tube; (Uout) voltage at amplifier output; (Ea) voltage of anode power supply

Several feedback circuits of different types are often used simultaneously in a single device. As an example we may cite the tube amplifier (Figure 2) with complex, frequency-dependent, parallel voltage feedback, produced by coupling inductance coil (transformer feedback) and negative series current feedback, which is realized in a resistor.

At a frequency equal to the resonance frequency of the oscillatory circuit, the transformer feedback becomes positive. If the loop gain is less than unity (considering the action of negative feedback), then the entire device operates as a regenerative amplifier in which the negative feedback stabilizes the amount of the positive feedback, thus also stabilizing the gain and pass band of the amplifier. But if the loop gain is greater than or equal to unity, then the device operates as an electrical oscillator in which the negative feedback limits current through the electron tube and improves the shape of the output oscillations, making them nearly sinusoidal.


Braude, G. V. Korrektsiia televizionnykh i impul’snykh signalov. Collection of articles. Moscow, 1967.
Tsykin, G. S. Usilitel’nye ustroistva, 4th ed. Moscow, 1971.


In biology. Regulatory systems with feedback exist at all levels of organization of life, from the molecular level to the population and biotic community. The contribution of this mechanism is particularly significant in the automatic maintenance of the constancy of the internal environment of an organism (homeostasis) and the activity of the genetic apparatus and of the endocrine and nervous systems.

Ideas of regulation according to the feedback principle appeared in biology a long time ago. The first hypothesis concerning reflex actions (R. Descartes, 17th century, G. Prochaska, 18th century) already contained the seeds of this principle. These ideas were refined by C. Bell, I. M. Sechenov, and I. P. Pavlov and later, during the 1930’s and 1940’s, by N. A. Bernshtein and P. K. Anokhin. In a more general form that is close to the present-day meaning, the principle of (negative) feedback as a general principle for all living systems was formulated (1912–24) by the Russian physiologist N. A. Belov under the name “parallel-crossed interaction”; this principle was also studied experimentally on endocrine organs by M. M. Zavadovskii, who called it “plus-minus interaction.” Belov showed that negative feedback is a general principle that aids in the attainment of equilibrium for all (not just living) systems. He, like Zavadovskii, assumed that the existence of positive feedback in living systems was impossible. The Soviet scientist A. A. Malinovskii showed that both types of feedback can exist in living systems and formulated the differences in their adaptive significance (1945–60). Outside the USSR, feedback in biology was first investigated extensively after the publication of N. Wiener’s book Cybernetics in 1948. In the USSR, during the 1950’s and 1960’s, I. I. Shmal’gauzen successfully applied the concept of feedback to population genetics.

In living systems, a distinction should be made between feedback taking the form of the mutual stimulation (positive feedback) or suppression in response to a stimulation (negative feedback), on the one hand, which allow certain though approximate evaluation, and qualitatively complex feedback, on the other hand, in which, as for example in ontogenesis, one organ promotes differentiation of a second organ, and the second, in a new stage, qualitatively determines the development of the first.

The general principles of feedback have been formulated mainly for relations of the first type. Negative feedback ensures that a system stays in stable equilibrium because an increase in the action of the control organ on the object (the organ, system, or process being regulated) causes an opposite action by the object on the control organ. The physiological meaning of negative feedback is that an increase in the regulated quantity (for example, the activity of an organ) above a certain limit produces a diminishing action from a subsystem coupled with it; a sharp decrease in the regulated quantity causes the opposite action.

With positive feedback, information of an increase in the regulated quantity elicits a reaction in a coupled subsystem that ensures a further increase of this quantity. In highly organized animals, the normal activity of the central nervous system always includes feedback as an essential condition. Thus, any action by an animal, for example, pursuit of prey, is accompanied both by impulses that travel from the central nervous system to the muscles (running, catching the prey) and by return signals from the sense organs (vision, proprioceptors) that enable the animal to take account of the results of his efforts and to correct them in the course of events.

Self-regulation of the vital activities is also caused by feedback. Thus, a rise in arterial pressure above the norm is perceived by special receptors (for example, the baroreceptors of the carotid sinus), which signal this fact to the vasomotor centers of the nervous system. This causes centrifugal impulses that lead to a decrease in pressure (see). This process is an example of the negative feedback most often observed in stable living systems. Most regulatory systems in animals and plants function according to this principle. Positive feedback is predominant during the period of embryonic development.

Many processes in ecology, for example, the regulation of population dynamics, are also based on positive and negative feedback. Thus, the predator-prey system considered by the Italian mathematician V. Volterra is a special case of negative feedback. An increase in the number of prey promotes intensified reproduction of predators; on the other hand, an increase in the number of predators leads to a reduction in the number of prey. A balance is maintained in nature in this way; however, because of the delay in reproduction of animals, the approach to a balance assumes the form of waves of life—wide fluctuations in the number of animals around an average level.

At the molecular level, the enormous number of enzyme reactions that occur simultaneously in a living cell are regulated by the feedback principle. This complex, interrelated system is coordinated by changing (1) the activity of the enzymes or (2) the rate of enzyme synthesis. In the first situation, negative feedback is brought about by inhibitors and positive feedback by stimulators; in the second situation, the effectors bring about feedback.

Combinations of positive and negative feedback cause an alternation of physiological states, for example, sleep and wakefulness. A study of the curve of development of noninfectious pathological processes, such as trophic ulcers, hypertension, manic-depressive psychosis, and epilepsy, makes it possible to establish the most likely type of feedback that lies at the basis of the illness and to limit the study of its etiology and pathogenesis to mechanisms of a definite category. As the most highly refined self-regulating systems, living things offer a wealth of different types of feedback. The study of these types is very productive for investigating biological phenomena and determining their specificity.


Malinovskii, A. A. “Tipy upravliaiushchikh biologicheskikh sistem i ikh prisposobitel’noe znachenie.” In the collection Problemy kibernetiki, no. 4. Moscow, 1961. Pages 151–81.
Reguliatornye mekhanizmy kletki. Moscow, 1964. (Translated from English.)
Petrushenko, L. A. Printsip obratnoi sviazi. Moscow, 1967.
Wiener, N. Kibernetika ili upravlenie i sviaz’ v zhivotnom i mashine. Moscow, 1968. (Translated from English.)
Shmal’gauzen, I. I. Kiberneticheski voprosy biologii. Novosibirsk, 1968.


The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.


In a stepwise reaction, the formation of a substance in one step that affects the rate of a previous step.
The return of a portion of the output of a circuit or device to its input.
(science and technology)
The control of input as a function of output by returning a portion of the output to the input.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.


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There would be additional input signals if there is a mismatch between actual control movement and the desired control movement.
i. The transmission of aerodynamic forces on control surfaces or rotor blades to cockpit controls as also the transmission of cockpit control forces to the aircraft control surfaces or rotor blades.
ii. A process in an electrical circuit or control system in which some energy from output of the system or circuit is fed back into the input. A system using a feedback system is called a closed-loop system.
iii. The return of a portion of the output of a device to the input. Positive feedback adds to the input, and negative feedback subtracts from the input.
iv. Information, such as progress or results, returned to an originating source.
An Illustrated Dictionary of Aviation Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved


a. the return of part of the output of an electronic circuit, device, or mechanical system to its input, so modifying its characteristics. In negative feedback a rise in output energy reduces the input energy; in positive feedback an increase in output energy reinforces the input energy
b. that part of the output signal fed back into the input
2. the whistling noise so produced
a. the effect of the product of a biological pathway on the rate of an earlier step in that pathway
b. the substance or reaction causing such an effect, such as the release of a hormone in a biochemical pathway
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005


Part of a system output presented at its input. Feedback may be unintended. When used as a design feature, the output is usually transformed by passive components which attenuate it in some manner; the result is then presented at the system input.

Feedback is positive or negative, depending on the sign with which a positive change in the original input reappears after transformation. Negative feedback was invented by Black to stabilise vacuum tube amplifiers. The behaviour becomes largely a function of the feedback transformation and only minimally a function of factors such as transistor gain which are imperfectly known.

Positive feedback can lead to instability; it finds wide application in the construction of oscillators.

Feedback can be used to control a system, as in feedback control.
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