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Feedback exists between two parts when each affects the other.
[1](p53)
A feedback loop where all outputs of a process are available as causal inputs to that process
Feedback occurs when outputs of a system are routed back as inputs as part of a
chain of
cause-and-effect that forms a circuit or loop.
[2] The system can then be said to
feed back into itself. The notion of cause-and-effect has to be handled carefully when applied to feedback systems:
- "Simple causal reasoning about a feedback system is difficult
because the first system influences the second and second system
influences the first, leading to a circular argument. This makes
reasoning based upon cause and effect tricky, and it is necessary to
analyze the system as a whole." [3]
History
Self-regulating
mechanisms have existed since antiquity, and the idea of feedback had
started to enter economic theory in Britain by the eighteenth century,
but it wasn't at that time recognized as a universal abstraction and so
didn't have a name.
[4]
The verb phrase "to feed back", in the sense of
returning to an earlier position in a mechanical process, was in use in the US by the 1860s,
[5][6] and in 1909, Nobel laureate
Karl Ferdinand Braun used the term "feed-back" as a noun to refer to (undesired)
coupling between components of an electronic circuit.
[7]
By the end of 1912, researchers using early electronic amplifiers (
audions)
had discovered that deliberately coupling part of the output signal
back to the input circuit would boost the amplification (through
regeneration), but would also cause the audion to howl or sing.
[8]
This action of feeding back of the signal from output to input gave
rise to the use of the term "feedback" as a distinct word by 1920.
[8]
Over the years there has been some dispute as to the best definition of feedback. According to
Ashby (1956), mathematicians and theorists interested in the
principles of feedback mechanisms prefer the definition of
circularity of action, which keeps the theory simple and consistent. For those with more
practical aims, feedback should be a deliberate effect via some more tangible connection.
-
- "[Practical experimenters] object to the mathematician's definition,
pointing out that this would force them to say that feedback was
present in the ordinary pendulum ... between its position and its
momentum—a 'feedback' that, from the practical point of view, is
somewhat mystical. To this the mathematician retorts that if feedback is
to be considered present only when there is an actual wire or nerve to
represent it, then the theory becomes chaotic and riddled with
irrelevancies."[1](p54)
Focusing on uses in management theory, Ramaprasad (1983) defines
feedback generally as "...information about the gap between the actual
level and the reference level of a system parameter" that is used to
"alter the gap in some way." He emphasizes that the information by
itself is not feedback unless translated into action.
[9]
Types
Positive and negative feedback
Maintaining a desired system performance despite disturbance using negative feedback to reduce system error.
There are two types of feedback:
positive feedback and
negative feedback.
As an example of negative feedback, the diagram might represent a
cruise control
system in a car, for example, that matches a target speed such as the
speed limit. The controlled system is the car; its input includes the
combined torque from the engine and from the changing slope of the road
(the disturbance). The car's speed (status) is measured by a
speedometer.
The error signal is the departure of the speed as measured by the
speedometer from the target speed (set point). This measured error is
interpreted by the controller to adjust the accelerator, commanding the
fuel flow to the engine (the effector). The resulting change in engine
torque, the feedback, combines with the torque exerted by the changing
road grade to reduce the error in speed, minimizing the road
disturbance.
The terms "positive" and "negative" were first applied to feedback
prior to WWII. The idea of positive feedback was already current in the
1920s with the introduction of the
regenerative circuit.
[10] Friis and Jensen (1924) described regeneration in a set of electronic amplifiers as a case where
the "feed-back" action is positive in contrast to negative feed-back action, which they mention only in passing.
[11] Harold Stephen Black's classic 1934 paper first details the use of negative feedback in electronic amplifiers. According to Black:
- "Positive feed-back increases the gain of the amplifier, negative feed-back reduces it."[12]
According to Mindell (2002) confusion in the terms arose shortly after this:
- "...Friis and Jensen had made the same distinction Black used
between 'positive feed-back' and 'negative feed-back', based not on the
sign of the feedback itself but rather on its effect on the amplifier’s
gain. In contrast, Nyquist and Bode, when they built on Black’s work,
referred to negative feedback as that with the sign reversed. Black had
trouble convincing others of the utility of his invention in part
because confusion existed over basic matters of definition."[10](p121)
Even prior to the terms being applied,
James Clerk Maxwell had described several kinds of "component motions" associated with the
centrifugal governors used in steam engines, distinguishing between those that lead to a continual
increase in a disturbance or the amplitude of an oscillation, and those that lead to a
decrease of the same.
[13]
Terminology
The terms positive and negative feedback are defined in different ways within different disciplines.
- the altering of the gap between reference and actual values of a parameter, based on whether the gap is widening (positive) or narrowing (negative).[9]
- the valence of the action or effect that alters the gap, based on whether it has a happy (positive) or unhappy (negative) emotional connotation to the recipient or observer.[14]
The two definitions may cause confusion, such as when an incentive
(reward) is used to boost poor performance (narrow a gap). Referring to
definition 1, some authors use alternative terms, replacing
positive/negative with
self-reinforcing/self-correcting,
[15] reinforcing/balancing,
[16] discrepancy-enhancing/discrepancy-reducing[17] or
regenerative/degenerative[18] respectively. And for definition 2, some authors advocate describing the action or effect as positive/negative
reinforcement or
punishment rather than feedback.
[9][19]
Yet even within a single discipline an example of feedback can be
called either positive or negative, depending on how values are measured
or referenced.
[20]
This confusion may arise because feedback can be used for either
informational or
motivational purposes, and often has both a
qualitative and a
quantitative component. As Connellan and Zemke (1993) put it:
-
- "Quantitative feedback tells us how much and how many. Qualitative feedback tells us how good, bad or indifferent."[21](p102)
Limitations of negative and positive feedback
While
simple systems can sometimes be described as one or the other type,
many systems with feedback loops cannot be so easily designated as
simply positive or negative, and this is especially true when multiple
loops are present.
-
- "When there are only two parts joined so that each affects the
other, the properties of the feedback give important and useful
information about the properties of the whole. But when the parts rise
to even as few as four, if every one affects the other three, then
twenty circuits can be traced through them; and knowing the properties
of all the twenty circuits does not give complete information about the
system."[1](p54)
Other types of feedback
In
general, feedback systems can have many signals fed back and the
feedback loop frequently contain mixtures of positive and negative
feedback where positive and negative feedback can dominate at different
frequencies or different points in the state space of a system.
The term bipolar feedback has been coined to refer to biological
systems where positive and negative feedback systems can interact, the
output of one affecting the input of another, and vice versa.
[22]
Some systems with feedback can have very complex behaviors such as
chaotic behaviors
in non-linear systems, while others have much more predictable
behaviors, such as those that are used to make and design digital
systems.
Feedback is used extensively in digital systems. For example, binary
counters and similar devices employ feedback where the current state and
inputs are used to calculate a new state which is then fed back and
clocked back into the device to update it.
Applications
Biology
In
biological systems such as
organisms,
ecosystems, or the
biosphere,
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.
Biological systems contain many types of regulatory circuits, both positive and negative. As in other contexts,
positive and
negative do not imply that the feedback causes
good or
bad
effects. A negative feedback loop is one that tends to slow down a
process, whereas the positive feedback loop tends to accelerate it. The
mirror neurons 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
genes and
gene regulatory networks.
Repressor (see
Lac repressor) and
activator proteins are used to create genetic
operons, which were identified by
Francois Jacob and
Jacques Monod 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).
On a larger scale, feedback can have a stabilizing effect on animal
populations even when profoundly affected by external changes, although
time lags in feedback response can give rise to
predator-prey cycles.
[23]
In
zymology,
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).
The
hypothalamic–pituitary–adrenal axis is largely controlled by positive and negative feedback, much of which is still unknown.
In
psychology, 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 people who blush
easily. When they realize that they are blushing, they become even more
embarrassed, which leads to further blushing, and so on.
[24]
Climate science
The climate system is characterized by strong positive and negative
feedback loops between processes that affect the state of the
atmosphere, ocean, and land. A simple example is the
ice-albedo positive feedback loop whereby melting snow exposes more dark ground (of lower
albedo), which in turn absorbs heat and causes more snow to melt.
Control theory
Feedback is extensively used in control theory, using a variety of methods including
state space (controls),
full state feedback
(also known as pole placement), and so forth. Note that in the context
of control theory, "feedback" is traditionally assumed to specify
"negative feedback".
[25]
The most common general-purpose
controller using a control-loop feedback mechanism is a
proportional-integral-derivative
(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.
[26]
Mechanical engineering
In ancient times, the
float valve was used to regulate the flow of water in Greek and Roman
water clocks; similar float valves are used to regulate fuel in a
carburettor and also used to regulate tank water level in the
flush toilet.
The Dutch inventor
Cornelius Drebbel
(1572-1633) built thermostats (c1620) to control the temperature of
chicken incubators and chemical furnaces. In 1745, the windmill was
improved by blacksmith Edmund Lee, who added a
fantail to keep the face of the windmill pointing into the wind. In 1787,
Thomas Mead
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 by
James Watt in 1788 to regulate the speed of his
steam engine was one factor leading to the
Industrial Revolution. Steam engines also use float valves and pressure release valves as mechanical regulation devices. A
mathematical analysis of Watt's governor was done by
James Clerk Maxwell in 1868.
[13]
The
Great Eastern was one of the largest steamships of its time and employed a steam powered rudder with feedback mechanism designed in 1866 by
John McFarlane Gray.
Joseph Farcot coined the word
servo in 1873 to describe steam-powered steering systems. Hydraulic servos were later used to position guns.
Elmer Ambrose Sperry of the
Sperry Corporation designed the first
autopilot in 1912.
Nicolas Minorsky published a theoretical analysis of automatic ship steering in 1922 and described the
PID controller.
[27]
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 once small, robust and powerful single-chip
microcontrollers became affordable.
Electronic engineering
The simplest form of a feedback amplifier can be represented by the
ideal block diagram made up of
unilateral elements.
[28]
The use of feedback is widespread in the design of
electronic
amplifiers, oscillators, and stateful logic circuit elements such as
flip-flops and counters. Electronic feedback systems are also very
commonly used to control mechanical, thermal and other physical
processes.
If the signal is inverted on its way round the control loop, the system is said to have
negative feedback;
[29] otherwise, the feedback is said to be
positive. Negative feedback is often deliberately introduced to increase the
stability
and accuracy of a system by correcting or reducing the influence of
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 can result in overcorrection, causing the output
to
oscillate or "hunt".
[30] While often an unwanted consequence of system behaviour, this effect is used deliberately in electronic oscillators.
Harry Nyquist contributed the
Nyquist plot 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). Design to ensure stability often involves
frequency compensation, one method of compensation being
pole splitting.
Electronic feedback loops are used to control the output of
electronic devices, such as
amplifiers. A feedback loop is created when all or some portion of the output 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.
[31]
When two or more amplifiers are cross-coupled using positive feedback, complex behaviors can be created. These
multivibrators are widely used and include:
-
- astable circuits, which act as oscillators
- monostable circuits, which can be pushed into a state, and will return to the stable state after some time
- bistable circuits, which have two stable states that the circuit can be switched between
Negative feedback
A
Negative feedback occurs when the fed-back output signal has a relative
phase of 180° with respect to the input signal (upside down). This
situation is sometimes referred to as being
out of phase, but
that term also is used to indicate other phase separations, as in "90°
out of phase". Negative feedback can be used to correct output errors or
to desensitize a system to unwanted fluctuations.
[32] In feedback amplifiers, this correction is generally for waveform
distortion reduction
[citation needed] or to establish a specified
gain level. A general expression for the gain of a negative feedback amplifier is the
asymptotic gain model.
Positive feedback
Positive
feedback occurs 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
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. This fact is very widely used in
digital electronics to make
bistable circuits for volatile storage of information.
The loud squeals that sometimes occurs in
audio systems,
PA systems, and
rock music are known as
audio feedback.
If a microphone is in front of a loudspeaker that it is connected to,
sound that the microphone picks up comes out of the speaker, and is
picked up by the microphone and re-amplified. If the
loop gain is sufficient, howling or squealing at the maximum power of the amplifier is possible.
Oscillator
An
electronic oscillator is an
electronic circuit that produces a periodic,
oscillating electronic signal, often a
sine wave or a
square wave.
[33][34] Oscillators convert
direct current (DC) from a power supply to an
alternating current
signal. They are widely used in many electronic devices. Common
examples of signals generated by oscillators include signals broadcast
by
radio and
television transmitters, clock signals that regulate computers and
quartz clocks, and the sounds produced by electronic beepers and
video games.
[33]
Oscillators are often characterized by the
frequency of their output signal:
- A low-frequency oscillator (LFO) is an electronic oscillator that generates a frequency below ≈20 Hz. This term is typically used in the field of audio synthesizers, to distinguish it from an audio frequency oscillator.
- An audio oscillator produces frequencies in the audio range, about 16 Hz to 20 kHz.[34]
- An RF oscillator produces signals in the radio frequency (RF) range of about 100 kHz to 100 GHz.[34]
Oscillators designed to produce a high-power AC output from a DC supply are usually called
inverters.
There are two main types of electronic oscillator: the linear or harmonic oscillator and the nonlinear or
relaxation oscillator.
[34][35]
Latches and flip-flops
An SR latch, constructed from a pair of cross-coupled
NOR gates.
A latch or a
flip-flop is a
circuit
that has two stable states and can be used to store state information.
They typically constructed using feedback that crosses over between two
arms of the circuit, to provide the circuit with a state. The circuit
can be made to change state by signals applied to one or more control
inputs and will have one or two outputs. It is the basic storage element
in
sequential logic. Latches and flip-flops are fundamental building blocks of
digital electronics systems used in computers, communications, and many other types of systems.
Latches and flip-flops are used as data storage elements. Such data storage can be used for storage of
state, and such a circuit is described as
sequential logic. When used in a
finite-state machine,
the output and next state depend not only on its current input, but
also on its current state (and hence, previous inputs). It can also be
used for counting of pulses, and for synchronizing variably-timed input
signals to some reference timing signal.
Flip-flops can be either simple (transparent or opaque) or
clocked
(synchronous or edge-triggered). Although the term flip-flop has
historically referred generically to both simple and clocked circuits,
in modern usage it is common to reserve the term
flip-flop exclusively for discussing clocked circuits; the simple ones are commonly called
latches.
[36][37]
Using this terminology, a latch is level-sensitive, whereas a
flip-flop is edge-sensitive. That is, when a latch is enabled it becomes
transparent, while a flip flop's output only changes on a single type
(positive going or negative going) of clock edge.
Software
Feedback
loops provide generic mechanisms for controlling the running,
maintenance, and evolution of software and computing systems.
[38]
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
have been successfully applied to computing systems.
[39] In particular, they have been applied to the development of products such as
IBM's Universal Database server 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.
[40][41]
User interface design
Feedback is also a useful design principle for designing
user interfaces.
Video feedback
Video feedback is the
video equivalent of
acoustic feedback. It involves a loop between a
video camera input and a video output, e.g., a
television screen or
monitor. Aiming the camera at the display produces a complex video image based on the feedback.
[42]
Social sciences
Economics and finance
The
stock market is an example of a
system prone to oscillatory "hunting", governed by positive and negative feedback resulting from
cognitive and emotional factors among market participants. 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); but the increased price of the shares, and the knowledge that there must be a peak after which the market falls, 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 used the word
reflexivity, to describe feedback in the financial markets and developed an
investment theory based on this principle.
The conventional
economic equilibrium model of
supply and demand supports only ideal linear negative feedback and was heavily criticized by
Paul Ormerod in his book
The Death of Economics,
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 applied to nonlinear feedback systems including financial markets.
