# Negative Feedback Loop

## Explanation

Negative feedback occurs when some function of the output of a system, process, or mechanism is fed back in a manner that tends to reduce the fluctuations in the output, whether caused by changes in the input or by other disturbances. Whereas positive feedback tends to lead to instability via exponential growth or oscillation, negative feedback generally promotes stability.

Negative feedback tends to promote a settling to equilibrium, and reduces the effects of perturbations. Negative feedback loops in which just the right amount of correction is applied in the most timely manner can be very stable, accurate, and responsive.

In place of the adjective "Negative" before feedback loop, alternative terms are used, such as: degenerative, self-inhibiting, self-correcting, self-dampening, balancing, discrepancy-reducing, or centripetal.

Negative feedback is widely used in mechanical and electronic engineering, but it also occurs naturally within living organisms, and can be seen in many other fields from chemistry and economics to physical systems such as the climate. General negative feedback systems are studied in control systems engineering.

In organisms, feedback enables various measures (eg body temperature, or blood sugar level) to be maintained within precise desired ranges by homeostatic processes. 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.

Figure: Both starting points eventuate in equilibrium, during a negative feedback loop.

## Cybernetics

Early researchers in the area of cybernetics subsequently generalized the idea of negative feedback to cover any goal-seeking or purposeful behavior. All purposeful behavior may be considered to require negative feed-back. If a goal is to be attained, some signals from the goal are necessary at some time to direct the behavior.

Cybernetics pioneer Norbert Wiener helped to formalize the concepts of feedback control, defining feedback in general as "the chain of the transmission and return of information". Wiener defind negative feedback as the case when: "The information fed back to the control center tends to oppose the departure of the controlled from the controlling quantity...".

## Operant conditioning

Confusion arose after BF Skinner introduced the terms positive and negative reinforcement, both of which can be considered negative feedback mechanisms in the sense that they try to minimize deviations from the desired behavior.

In a similar context, Herold and Greller used the term "negative" to refer to the valence of the feedback: that is, cases where a subject receives an evaluation with an unpleasant emotional connotation.

## Differerence in Terminology

In biology, this process (in general, biochemical) is often referred to as homeostasis; whereas in mechanics, the more common term is equilibrium.

In engineering, mathematics and the physical, and biological sciences, common terms for the points around which the system gravitates include: attractors, stable states, eigenstates/eigenfunctions, equilibrium points, and setpoints.

In control theory, negative refers to the sign of the multiplier in mathematical models for feedback. In delta notation, −Δoutput is added to or mixed into the input.

In multivariate systems, vectors help to illustrate how several influences can both partially complement and partially oppose each other.

Some authors, in particular with respect to modelling business systems, use negative to refer to the reduction in difference between the desired and actual behavior of a system.

In a psychology context, on the other hand, negative refers to the valence of the feedback – attractive versus aversive, or praise versus criticism.

## Negative versus Positive

Negative feedback is feedback in which the system responds so as to decrease the magnitude of any particular perturbation, leading to dampening of the original signal, resulting in stabilization of the process.
In contrast, positive feedback is feedback in which the system responds so as to increase the magnitude of any particular perturbation, resulting in amplification of the original signal instead of stabilization (see: Positive Feedback Loop).

Any system in which there is positive feedback together with a gain greater than one will result in a runaway situation. Both positive and negative feedback require a feedback loop to operate.
However, some negative feedback systems can still be subject to oscillations. This is caused by the slight delays around any loop. Due to these delays the feedback signal of some frequencies can arrive one half cycle later which will have a similar effect to positive feedback and these frequencies can reinforce themselves and grow over time. This problem is often dealt with by attenuating or changing the phase of the problematic frequencies. Unless the system naturally has sufficient damping, many negative feedback systems have low pass filters or dampers fitted.

## Fields of application

### Control systems

Examples of the use of negative feedback to control its system are: thermostat control, the phase-locked loop oscillator, the ballcock control of water level, and temperature regulation in animals.

#### WC

The ballcock or float valve uses negative feedback to control the water level in a cistern of a toilette.

Figure: the ballcock control of water level via negative feedback.

#### Thermostat

A simple and practical example is a thermostat. When the temperature 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, or a freezer.

#### Biology and chemistry

Control of endocrine hormones by negative feedback. Some biological systems exhibit negative feedback such as the baroreflex in blood pressure regulation and erythropoiesis. Many biological process (e.g., in human physiology) use negative feedback. Examples of this are numerous, from the regulating of body temperature, to the regulating of blood glucose 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.

For hormone secretion regulated by the negative feedback loop: when gland X releases hormone X, this stimulates target cells to release hormone Y. When there is an excess of hormone Y, gland X "senses" this and inhibits its release of hormone X.
As shown in the figure below, most endocrine hormones are controlled by a physiologic negative feedback inhibition loop, such as the glucocorticoids secreted by the adrenal cortex. The hypothalamus secretes corticotropin-releasing hormone (CRH), which directs the anterior pituitary gland to secrete adrenocorticotropic hormone (ACTH). In turn, ACTH directs the adrenal cortex to secrete glucocorticoids, such as cortisol. Glucocorticoids not only perform their respective functions throughout the body but also negatively affect the release of further stimulating secretions of both the hypothalamus and the pituitary gland, effectively reducing the output of glucocorticoids once a sufficient amount has been released.

Figure: Stress hormone Cortisol dampens its own creation indirectly.

#### Self-organization

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

#### Economics

In economics, automatic stabilisers are government programs that are intended to work as negative feedback to dampen fluctuations in real GDP. Free market economic theorists claim that the pricing mechanism operated to match supply and demand. However Norbert Wiener wrote in 1948: "There is a belief current in many countries and elevated to the rank of an official article of faith in the United States that free competition is itself a homeostatic process... Unfortunately the evidence, such as it is, is against this simple-minded theory."