Editing Proportional–integral–derivative controller (section)

==History==
[[File:Scross helmsman.jpg|thumb|Early PID theory was developed by observing the actions of [[helmsmen]] in keeping a vessel on course in the face of varying influences such as wind and sea state.]]
[[File:Pneumatische regelaar.jpg|thumb|Pneumatic PID (three-term) controller. The magnitudes of the three terms (P, I and D) are adjusted by the dials at the top.|alt=]]

===Origins===
The [[centrifugal governor]] was invented by [[Christiaan Huygens]] in the 17th century to regulate the gap between [[millstone]]s in [[windmill]]s depending on the speed of rotation, and thereby compensate for the variable speed of grain feed.<ref>{{citation|last=Hills|first=Richard L|authorlink=Richard L. Hills|title=Power From the Wind|publisher=Cambridge University Press|year=1996}}</ref><ref>{{cite book |title=Adaptive Control Processes: A Guided Tour |author=Richard E. Bellman |publisher=Princeton University Press |date=December 8, 2015 |url=https://books.google.com/books?id=iwbWCgAAQBAJ&q=%22Centrifugal+Governor%22+Huygens&pg=PA36 |isbn=9781400874668 }}</ref>

With the invention of the low-pressure stationary steam engine there was a need for automatic speed control, and [[James Watt]]'s self-designed "[[conical pendulum]]" governor, a set of revolving steel balls attached to a vertical spindle by link arms, came to be an industry standard. This was based on the millstone-gap control concept.<ref name="ben96" />

Rotating-governor speed control, however, was still variable under conditions of varying load, where the shortcoming of what is now known as proportional control alone was evident. The error between the desired speed and the actual speed would increase with increasing load. In the 19th century, the theoretical basis for the operation of governors was first described by [[James Clerk Maxwell]] in 1868 in his now-famous paper ''On Governors''. He explored the mathematical basis for control stability, and progressed a good way towards a solution, but made an appeal for mathematicians to examine the problem.<ref>{{cite journal |first=J. C. |last=Maxwell |author-link=James Clerk Maxwell |title=On Governors |date=1868 |journal=Proceedings of the Royal Society |volume=100 |url=https://upload.wikimedia.org/wikipedia/commons/b/b1/On_Governors.pdf}}</ref><ref name="ben96" />  The problem was examined further in 1874 by [[Edward Routh]], [[Charles Sturm]], and in 1895, [[Adolf Hurwitz]], all of whom contributed to the establishment of control stability criteria.<ref name="ben96" />
In subsequent applications, speed governors were further refined, notably by American scientist [[Willard Gibbs]], who in 1872 theoretically analyzed Watt's conical pendulum governor.

About this time, the invention of the [[Whitehead torpedo]] posed a control problem that required accurate control of the running depth. Use of a depth pressure sensor alone proved inadequate, and a pendulum that measured the fore and aft pitch of the torpedo was combined with depth measurement to become the [[pendulum-and-hydrostat control]]. Pressure control provided only a proportional control that, if the control gain was too high, would become unstable and go into overshoot with considerable [[instability]] of depth-holding. The pendulum added what is now known as derivative control, which damped the oscillations by detecting the torpedo dive/climb angle and thereby the rate-of-change of depth.<ref>{{cite book |last=Newpower |first=Anthony |title=Iron Men and Tin Fish: The Race to Build a Better Torpedo during World War II |publisher=Praeger Security International |year=2006 |isbn=978-0-275-99032-9}} p.&nbsp; citing {{citation |first=Edwyn |last=Gray |title=The Devil's Device: Robert Whitehead and the History of the Torpedo |location=Annapolis, MD |publisher=U.S. Naval Institute |date=1991 |page=33 |ref=none}}.</ref> This development (named by Whitehead as  "The Secret" to give no clue to its action) was around 1868.<ref>{{citation |last=Sleeman |first=C. W. |title=Torpedoes and Torpedo Warfare |date=1880 |location=Portsmouth |publisher=Griffin & Co. |pages=137&ndash;138 |url=https://archive.org/stream/torpedoestorpedo00sleerich#page/136/mode/2up/search/depth |quote=which constitutes what is termed as the secret of the fish torpedo. |ref=none}}</ref>

Another early example of a PID-type controller was developed by [[Elmer Sperry]] in 1911 for ship steering, though his work was intuitive rather than mathematically-based.<ref>{{cite web |url=http://www.building-automation-consultants.com/building-automation-history.html |title=A Brief Building Automation History |access-date=2011-04-04 |url-status=dead |archive-url=https://web.archive.org/web/20110708104028/http://www.building-automation-consultants.com/building-automation-history.html |archive-date=2011-07-08 }}</ref>

It was not until 1922, however, that a formal control law for what we now call PID or three-term control was first developed using theoretical analysis, by [[Russian American]] engineer [[Nicolas Minorsky]].<ref>{{cite journal |last=Minorsky |first=Nicolas |author-link=Nicolas Minorsky |title=Directional stability of automatically steered bodies |journal=Journal of the American Society for Naval Engineers |year=1922 |volume=34 |pages=280–309 |issue=2 |doi=10.1111/j.1559-3584.1922.tb04958.x}}</ref> Minorsky was researching and designing automatic ship steering for the US Navy and based his analysis on observations of a [[helmsman]]. He noted the helmsman steered the ship based not only on the current course error but also on past error, as well as the current rate of change;<ref>{{Harvnb|Bennett|1993|loc = [https://books.google.com/books?id=VD_b81J3yFoC&pg=PA67 p. 67]}}</ref> this was then given a mathematical treatment by Minorsky.<ref name="ben96">{{cite journal
| journal = IEEE Control Systems Magazine
| volume = 16
| issue = 3
| last = Bennett
| first = Stuart
| title = A brief history of automatic control
| year = 1996
| url = http://ieeecss.org/CSM/library/1996/june1996/02-HistoryofAutoCtrl.pdf
| pages = 17–25
| doi = 10.1109/37.506394
| access-date = 2014-08-21
| archive-url = https://web.archive.org/web/20160809050823/http://ieeecss.org/CSM/library/1996/june1996/02-HistoryofAutoCtrl.pdf
| archive-date = 2016-08-09
| url-status = dead
}}</ref>
His goal was stability, not general control, which simplified the problem significantly. While proportional control provided stability against small disturbances, it was insufficient for dealing with a steady disturbance, notably a stiff gale (due to [[#Steady-state error|steady-state error]]), which required adding the integral term. Finally, the derivative term was added to improve stability and control.

Trials were carried out on the [[USS New Mexico (BB-40)|USS ''New Mexico'']], with the controllers controlling the ''[[angular velocity]]'' (not the angle) of the rudder. PI control yielded sustained yaw (angular error) of ±2°. Adding the D element yielded a yaw error of ±1/6°, better than most helmsmen could achieve.<ref>{{cite book
| publisher = IET
| isbn = 978-0-86341-047-5
| last = Bennett
| first = Stuart
| title = A history of control engineering, 1800-1930
|date=June 1986
| pages = [https://books.google.com/books?id=1gfKkqB_fTcC&pg=PA142 142–148]
}}</ref>

The Navy ultimately did not adopt the system due to resistance by personnel. Similar work was carried out and published by several others{{who|date=December 2023}} in the 1930s.{{citation needed|date=December 2023}}

===Industrial control===
[[File:Nozzle and flapper proportional controller.png|thumb|Proportional control using nozzle and flapper high gain amplifier and negative feedback]]
The wide use of feedback controllers did not become feasible until the development of wideband high-gain amplifiers to use the concept of [[negative feedback]]. This had been developed in telephone engineering electronics by [[Harold Stephen Black|Harold Black]] in the late 1920s, but not published until 1934.<ref name="ben96" /> Independently, Clesson E Mason of the Foxboro Company in 1930 invented a wide-band pneumatic controller by combining the [[nozzle and flapper]] high-gain pneumatic amplifier, which had been invented in 1914, with negative feedback from the controller output. This dramatically increased the linear range of operation of the nozzle and flapper amplifier, and integral control could also be added by the use of a precision bleed valve and a bellows generating the integral term. The result was the "Stabilog" controller which gave both proportional and integral functions using feedback bellows.<ref name="ben96" /> The integral term was called ''Reset''.<ref>{{citation|last=Shinskey|first=F Greg|title=The power of external-reset feedback|publisher=Control Global|year=2004|url=https://classes.engineering.wustl.edu/2009/spring/che433/2009-LAB/Control%20Theory/external-reset.pdf}}</ref>  Later the derivative term was added by a further bellows and adjustable orifice.

From about 1932 onwards, the use of wideband pneumatic controllers increased rapidly in a variety of control applications. Air pressure was used for generating the controller output, and also for powering process modulating devices such as diaphragm-operated control valves.  They were simple low maintenance devices that operated well in harsh industrial environments and did not present explosion risks in [[Electrical equipment in hazardous areas|hazardous locations]]. They were the industry standard for many decades until the advent of discrete electronic controllers and [[distributed control system]]s (DCSs).

With these controllers, a pneumatic industry signaling standard of {{cvt|3|-|15|psi|bar|1}} was established, which had an elevated zero to ensure devices were working within their linear characteristic and represented the control range of 0-100%.

[[File:DTK4848V01.jpg|thumb|Typical setup for temperature controlling process. From left to right: [[resistance thermometer]], Delta DTK4848V01 temperature controller with PID function, a [[solid-state relay]]]]

In the 1950s, when high gain electronic amplifiers became cheap and reliable, electronic PID controllers became popular, and the pneumatic standard was emulated by 10-50 mA and 4–20 mA [[current loop]] signals (the latter became the industry standard). Pneumatic field actuators are still widely used because of the advantages of pneumatic energy for control valves in process plant environments.
[[File:Analogue control loop evolution.png|thumb|Showing the evolution of analog control loop signaling from the pneumatic to the electronic eras]]
[[File:Smart current loop positioner.png|thumb|Current loops used for sensing and control signals. A modern electronic "smart" valve positioner is shown, which will incorporate its own PID controller.]]

Most modern PID controls in industry are implemented as [[computer software]] in DCSs, [[programmable logic controller]]s (PLCs), or discrete [[compact controller]]s.

===Electronic analog controllers===
Electronic analog PID control loops were often found within more complex electronic systems, for example, the head positioning of a [[disk drive]], the power conditioning of a [[power supply]], or even the movement-detection circuit of a modern [[seismometer]]. Discrete electronic analog controllers have been largely replaced by digital controllers using [[microcontrollers]] or [[FPGA]]s to implement PID algorithms. However, discrete analog PID controllers are still used in niche applications requiring high-bandwidth and low-noise performance, such as laser-diode controllers.<ref name="Toptica">{{cite web|url = http://www.toptica.com/fileadmin/user_upload/Articles_Application_Notes/toptica_AP_1012_laser_locking_2012.pdf|last = Neuhaus|first = Rudolf|title = Diode Laser Locking and Linewidth Narrowing|access-date = June 8, 2015}}</ref>