Control theory: Difference between revisions

Revision as of 09:14, 20 July 2025

Revision as of 05:03, 25 July 2025

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{{Use mdy dates|date=July 2016}}

'''Control theory''' is a field of [[control engineering]] and [[applied mathematics]] that deals with the [[control system|control]] of [[dynamical system]]s in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control [[Stability theory|stability]]; often with the aim to achieve a degree of [[Optimal control|optimality]].

To do this, a '''controller''' with the requisite corrective behavior is required. This controller monitors the controlled [[process variable]] (PV), and compares it with the reference or [[Setpoint (control system)|set point]] (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are [[controllability]] and [[observability]]. Control theory is used in [[control system engineering]] to design automation that have revolutionized manufacturing, aircraft, communications and other industries, and created new fields such as [[robotics]].

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Control theory dates from the 19th century, when the theoretical basis for the operation of governors was first described by [[James Clerk Maxwell]].<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 |archive-url=https://web.archive.org/web/20081219051207/http://upload.wikimedia.org/wikipedia/commons/b/b1/On_Governors.pdf |archive-date=2008-12-19 |url-status=live}}</ref> Control theory was further advanced by [[Edward Routh]] in 1874, [[Jacques Charles François Sturm|Charles Sturm]] and in 1895, [[Adolf Hurwitz]], who all contributed to the establishment of control stability criteria; and from 1922 onwards, the development of [[PID control]] theory by [[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 of Naval Engineers |year=1922 |volume=34 |pages=280–309 |issue=2 |doi=10.1111/j.1559-3584.1922.tb04958.x}}</ref>

Although athe most majordirect application of [[mathematics|mathematical]] control theory is is use in [[Control Systems Engineering|control systems engineering]], which deals(dealing with the design of [[process control]] systems for [[robotics]] and industry), othercontrol applicationstheory rangeis farroutinely beyondapplied thisto problems both the natural and [[behavioral science]]s. As the general theory of feedback systems, control theory is useful wherever feedback occurs, -making thusit controlimportant theoryto alsofields haslike applications in life sciences[[economics]], computer[[operations engineeringresearch]], sociology and the [[operationslife researchscience]]s.<ref>{{Cite web|url=https://d-nb.info/gnd/4032317-1|title=Katalog der Deutschen Nationalbibliothek (Authority control)|last=GND|website=portal.dnb.de|access-date=2024-12-21}}</ref>

==History==