Negative feedback

Negative feedback

Overview
Negative feedback occurs when the output of a system
System
System is a set of interacting or interdependent components forming an integrated whole....

 acts to oppose changes to the input of the system, with the result that the changes are attenuated. If the overall feedback
Feedback
Feedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...

 of the system is negative, then the system will tend to be stable.

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.
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Encyclopedia
Negative feedback occurs when the output of a system
System
System is a set of interacting or interdependent components forming an integrated whole....

 acts to oppose changes to the input of the system, with the result that the changes are attenuated. If the overall feedback
Feedback
Feedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...

 of the system is negative, then the system will tend to be stable.

Overview


In many physical and biological systems, qualitatively different influences can oppose each other. For example, in biochemistry, one set of chemicals drives the system in a given direction, whereas another set of chemicals drives it in an opposing direction. If one, or both of these opposing influences are non-linear, equilibrium point(s) result.

In biology
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

, this process (generally biochemical
Biochemistry
Biochemistry, sometimes called biological chemistry, is the study of chemical processes in living organisms, including, but not limited to, living matter. Biochemistry governs all living organisms and living processes...

) is often referred to as 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...

; whereas in mechanics
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....

, the more common term is equilibrium
Mechanical equilibrium
A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....

.

In engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

, mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 and the physical and biological sciences, common terms for the points around which the system gravitates include: attractors, stable
Stability theory
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions...

 states, eigenstates/eigenfunctions, equilibrium points, and setpoint
Setpoint
Setpoint is the target value that an automatic control system, for example PID controller, will aim to reach. For example, a boiler control system might have a temperature setpoint, that is a temperature the control system aims to attain....

s.

Negative refers to the sign of the multiplier in mathematical models for feedback. In delta notation, output 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.

In contrast, 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...

 is feedback in which the system responds so as to increase the magnitude of any particular perturbation, resulting in amplification of the original signal instead of stabilization. Any system where there is a net positive feedback will result in a runaway situation. Both positive and negative feedback require a feedback loop to operate.

Negative feedback is used to describe the act of reversing any discrepancy between desired and actual output.

Mechanical engineering


Negative feedback was first implemented in the 16th Century with the invention 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...

. Its operation is most easily seen in its use 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...

 to control 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...

. Two heavy balls on an upright frame rotate at the same speed as the engine. As their speed increases they move outwards due to the centrifugal force. This causes them to lift a mechanism which closes the steam inlet valve and the engine slows. When the speed of the engine falls too far, the balls will move in the opposite direction and open the steam valve.

Control systems


Examples of the use of negative feedback to control its system are: 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...

 control, phase-locked loop
Phase-locked loop
A phase-locked loop or phase lock loop is a control system that generates an output signal whose phase is related to the phase of an input "reference" signal. It is an electronic circuit consisting of a variable frequency oscillator and a phase detector...

, hormonal regulation (see diagram above), and temperature regulation in animals.

A simple and practical example is 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...

. When the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 in a heated room reaches a certain upper limit the room heating is switched off so that the temperature begins to fall. When the temperature drops to a lower limit, the heating is switched on again. Provided the limits are close to each other, a steady room temperature is maintained. Similar control mechanisms are used in cooling systems, such as an air conditioner, a refrigerator
Refrigerator
A refrigerator is a common household appliance that consists of a thermally insulated compartment and a heat pump that transfers heat from the inside of the fridge to its external environment so that the inside of the fridge is cooled to a temperature below the ambient temperature of the room...

, or a freezer.

Biology and chemistry


Some biological systems exhibit negative feedback such as the baroreflex
Baroreflex
The baroreflex or baroreceptor reflex is one of the body's homeostatic mechanisms for maintaining blood pressure. It provides a negative feedback loop in which an elevated blood pressure reflexively causes heart rate to decrease therefore causing blood pressure to decrease; likewise, decreased...

 in blood pressure
Blood pressure
Blood pressure is the pressure exerted by circulating blood upon the walls of blood vessels, and is one of the principal vital signs. When used without further specification, "blood pressure" usually refers to the arterial pressure of the systemic circulation. During each heartbeat, BP varies...

 regulation and erythropoiesis
Erythropoiesis
Erythropoiesis is the process by which red blood cells are produced. It is stimulated by decreased O2 in circulation, which is detected by the kidneys, which then secrete the hormone erythropoietin...

. Many biological process (e.g., in the human anatomy
Human anatomy
Human anatomy is primarily the scientific study of the morphology of the human body. Anatomy is subdivided into gross anatomy and microscopic anatomy. Gross anatomy is the study of anatomical structures that can be seen by the naked eye...

) use negative feedback. Examples of this are numerous, from the regulating of body temperature, to the regulating of blood glucose
Glucose
Glucose is a simple sugar and an important carbohydrate in biology. Cells use it as the primary source of energy and a metabolic intermediate...

 levels. The disruption of feedback loops can lead to undesirable results: in the case of blood glucose levels, if negative feedback fails, the glucose levels in the blood may begin to rise dramatically, thus resulting in diabetes
Diabetes mellitus
Diabetes mellitus, often simply referred to as diabetes, is a group of metabolic diseases in which a person has high blood sugar, either because the body does not produce enough insulin, or because cells do not respond to the insulin that is produced...

.

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.

Economics


In economics, automatic stabilisers are government programs which work as negative feedback to dampen fluctuations in real GDP
Real GDP
Real Gross Domestic Product is a macroeconomic measure of the value of output economy adjusted for price changes . The adjustment transforms the money-value measure, called nominal GDP, into an index for quantity of total output...

.

Electronic amplifiers



The negative feedback amplifier was invented 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...

 at Bell Laboratories in 1927, and patented by him in 1934. Fundamentally, all electronic devices (e.g. vacuum tube
Vacuum tube
In electronics, a vacuum tube, electron tube , or thermionic valve , reduced to simply "tube" or "valve" in everyday parlance, is a device that relies on the flow of electric current through a vacuum...

s, bipolar transistors, MOS transistors
MOSFET
The metal–oxide–semiconductor field-effect transistor is a transistor used for amplifying or switching electronic signals. The basic principle of this kind of transistor was first patented by Julius Edgar Lilienfeld in 1925...

) exhibit some nonlinear behavior. Negative feedback corrects this by trading unused gain for higher linearity (lower distortion). An amplifier with too large an open-loop gain, possibly in a specific frequency range, will additionally produce too large a feedback signal in that same range. This feedback signal, when subtracted from the original input, will act to reduce the original input, also by "too large" an amount. This "too small" input will be amplified again by the "too large" open-loop gain, creating a signal that is "just right". The net result is a flattening of the amplifier's gain over all frequencies (desensitising). Though much more accurate, amplifiers with negative feedback can become unstable if not designed correctly, causing them to oscillate. Harry Nyquist
Harry Nyquist
Harry Nyquist was an important contributor to information theory.-Personal life:...

 of Bell Laboratories managed to work out a theory about how to make this behaviour stable.

Negative feedback is used in this way in many types of amplification systems to stabilize and improve their operating characteristics (see e.g., operational amplifiers).

See also


  • Asymptotic gain model
  • Biofeedback
    Biofeedback
    Biofeedback is the process of becoming aware of various physiological functions using instruments that provide information on the activity of those same systems, with a goal of being able to manipulate them at will...

  • 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...

  • 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...

  • Global Warming
    Global warming
    Global warming refers to the rising average temperature of Earth's atmosphere and oceans and its projected continuation. In the last 100 years, Earth's average surface temperature increased by about with about two thirds of the increase occurring over just the last three decades...

  • Nyquist stability criterion
    Nyquist stability criterion
    When designing a feedback control system, it is generally necessary to determine whether the closed-loop system will be stable. An example of a destabilizing feedback control system would be a car steering system that overcompensates -- if the car drifts in one direction, the control system...

  • Perceptual Control Theory
    Perceptual control theory
    Perceptual control theory is a model of the psychological and behavioral processes occurring within living beings, including humans. It demonstrates that animals are goal-driven, purposeful entities rather than automata repeating conditioned responses to external stimuli or computers planning...

  • 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...

  • Stability criterion
  • Step response
    Step response
    The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from...