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第16行： − Although control systems of various types date back to antiquity, a more formal analysis of the field began with a dynamics analysis of the [[centrifugal governor]], conducted by the physicist [[James Clerk Maxwell]] in 1868, entitled ''On Governors''.<ref name="Maxwell1867">{{cite journal|author=Maxwell, J.C.|year=1868|title=On Governors|journal=Proceedings of the Royal Society of London|volume=16|pages=270–283|doi=10.1098/rspl.1867.0055|jstor=112510|doi-access=free}}<!--| accessdate = 2008-04-14--></ref> A centrifugal governor was already used to regulate the velocity of windmills.<ref>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.302.5633&rep=rep1&type=pdf Control Theory: History, Mathematical Achievements and Perspectives | E. Fernandez-Cara1 and E. Zuazua]</ref> Maxwell described and analyzed the phenomenon of [[self-oscillation]], in which lags in the system may lead to overcompensation and unstable behavior. This generated a flurry of interest in the topic, during which Maxwell's classmate, [[Edward John Routh]], abstracted Maxwell's results for the general class of linear systems.<ref name=Routh1975>{{cite book+ − + − Although control systems of various types date back to antiquity, a more formal analysis of the field began with a dynamics analysis of the centrifugal governor, conducted by the physicist James Clerk Maxwell in 1868, entitled On Governors. A centrifugal governor was already used to regulate the velocity of windmills. Maxwell described and analyzed the phenomenon of self-oscillation, in which lags in the system may lead to overcompensation and unstable behavior. This generated a flurry of interest in the topic, during which Maxwell's classmate, Edward John Routh, abstracted Maxwell's results for the general class of linear systems.<ref name=Routh1975>{{cite book − − 虽然各种类型的控制系统可以追溯到古代，一个更加正式的领域分析开始于离心式调速器的动力学分析，由物理学家詹姆斯·克拉克·麦克斯韦在1868年进行，题为统治者。离心式调速器已经被用来调节风车的速度。麦克斯韦描述并分析了自激振荡现象，其中系统的滞后可能导致系统的过度补偿和不稳定行为。这引起了人们对这个话题的浓厚兴趣，在这期间，Maxwell 的同学，爱德华·约翰·劳思，抽象出了 Maxwell 关于线性系统的一般类别的结果。 1975{ cite book − − − | author = Routh, E.J. − − 作者: 劳斯 e.j。 − − |author2=Fuller, A.T. − − − 2 Fuller，a.t. − − − | year = 1975 − − 1975年 − − | title = Stability of motion − − − 运动的稳定性 − − − | publisher = Taylor & Francis − − 出版商泰勒弗朗西斯集团 − − | isbn = − − + − | isbn+ − + − − − }}</ref> Independently, Adolf Hurwitz analyzed system stability using differential equations in 1877, resulting in what is now known as the Routh–Hurwitz theorem.<ref name=Routh1877>{{cite book − − 阿道夫 · 赫尔维茨在1877年独立地用微分方程分析了系统的稳定性，导致了现在被称为劳斯-赫尔维茨定理的结果。 1877{ cite book − − − | author = Routh, E.J. − − 作者: 劳斯 e.j。 − − − | year = 1877 − − 1877年 − − | title = A Treatise on the Stability of a Given State of Motion, Particularly Steady Motion: Particularly Steady Motion − − − | 题目: 论述给定运动状态的稳定性，特别是稳定运动: 特别是稳定运动 − − | url = https://archive.org/details/atreatiseonstab00routgoog − − − Https://archive.org/details/atreatiseonstab00routgoog − − − | publisher = Macmillan and co. − − 出版商麦克米伦出版公司。 − − | isbn = − − − | isbn − − }}</ref><ref name=Hurwitz1964>{{cite journal − − − 1964{ cite journal − − − | author = Hurwitz, A. − − 作者: Hurwitz，a。 − − | year = 1964 − − − 1964年 − − | title = On The Conditions Under Which An Equation Has Only Roots With Negative Real Parts − − − 关于方程只有带负实部根的条件 − − − | journal = Selected Papers on Mathematical Trends in Control Theory − − 控制理论中的数学趋势论文选 − − }}</ref> − − {} / ref+ − − − − − − A notable application of dynamic control was in the area of manned flight. The [[Wright brothers]] made their first successful test flights on December 17, 1903 and were distinguished by their ability to control their flights for substantial periods (more so than the ability to produce lift from an airfoil, which was known). Continuous, reliable control of the airplane was necessary for flights lasting longer than a few seconds. − − A notable application of dynamic control was in the area of manned flight. The Wright brothers made their first successful test flights on December 17, 1903 and were distinguished by their ability to control their flights for substantial periods (more so than the ability to produce lift from an airfoil, which was known). Continuous, reliable control of the airplane was necessary for flights lasting longer than a few seconds. − − − − − − − − By [[World War II]], control theory was becoming an important area of research. [[Irmgard Flügge-Lotz]] developed the theory of discontinuous automatic control systems, and applied the [[bang–bang control|bang-bang principle]] to the development of [[autopilot|automatic flight control equipment]] for aircraft.<ref>{{cite journal|last1=Flugge-Lotz|first1=Irmgard|last2=Titus|first2=Harold A.|title=Optimum and Quasi-Optimum Control of Third and Fourth-Order Systems|journal=Stanford University Technical Report|date=October 1962|issue=134|pages=8–12|url=http://www.dtic.mil/dtic/tr/fulltext/u2/621137.pdf}}</ref><ref>{{cite book|last1=Hallion|first1=Richard P.|editor1-last=Sicherman|editor1-first=Barbara|editor2-last=Green|editor2-first=Carol Hurd|editor3-last=Kantrov|editor3-first=Ilene|editor4-last=Walker|editor4-first=Harriette|title=Notable American Women: The Modern Period: A Biographical Dictionary|url=https://archive.org/details/notableamericanw00sich|url-access=registration|date=1980|publisher=Belknap Press of Harvard University Press|location=Cambridge, Mass.|isbn=9781849722704|pages=[https://archive.org/details/notableamericanw00sich/page/241 241–242]}}</ref> Other areas of application for discontinuous controls included [[fire-control system]]s, [[guidance system]]s and [[electronics]]. − − By World War II, control theory was becoming an important area of research. Irmgard Flügge-Lotz developed the theory of discontinuous automatic control systems, and applied the bang-bang principle to the development of automatic flight control equipment for aircraft. Other areas of application for discontinuous controls included fire-control systems, guidance systems and electronics. − − 到了第二次世界大战，控制理论成为一个重要的研究领域。Irmgard fl gge-lotz 发展了非连续自动控制系统理论，并将 bang-bang 原理应用于飞机自动飞行控制装置的开发。不连续控制的其他应用领域包括火控系统、制导系统和电子学。 − − − − − − Sometimes, mechanical methods are used to improve the stability of systems. For example, [[Stabilizer (ship)|ship stabilizers]] are fins mounted beneath the waterline and emerging laterally. In contemporary vessels, they may be gyroscopically controlled active fins, which have the capacity to change their angle of attack to counteract roll caused by wind or waves acting on the ship. − − Sometimes, mechanical methods are used to improve the stability of systems. For example, ship stabilizers are fins mounted beneath the waterline and emerging laterally. In contemporary vessels, they may be gyroscopically controlled active fins, which have the capacity to change their angle of attack to counteract roll caused by wind or waves acting on the ship. − − 有时采用机械方法来提高系统的稳定性。例如，船舶稳定器是安装在吃水线以下和横向出现的鳍。在现代船舶中，它们可能是陀螺控制的活动鳍，这种鳍有能力改变攻角，以抵消作用在船上的风浪造成的横摇。 − − − − − − The [[Space Race]] also depended on accurate spacecraft control, and control theory has also seen an increasing use in fields such as economics and artificial intelligence. Here, one might say that the goal is to find an [[internal model (motor control)|internal model]] that obeys the [[Good regulator|good regulator theorem]]. So, for example, in economics, the more accurately a (stock or commodities) trading model represents the actions of the market, the more easily it can control that market (and extract "useful work" (profits) from it). In AI, an example might be a chatbot modelling the discourse state of humans: the more accurately it can model the human state (e.g. on a telephone voice-support hotline), the better it can manipulate the human (e.g. into performing the corrective actions to resolve the problem that caused the phone call to the help-line). These last two examples take the narrow historical interpretation of control theory as a set of differential equations modeling and regulating kinetic motion, and broaden it into a vast generalization of a [[controller (control theory)|regulator]] interacting with a [[plant (control theory)|plant]]. − − The Space Race also depended on accurate spacecraft control, and control theory has also seen an increasing use in fields such as economics and artificial intelligence. Here, one might say that the goal is to find an internal model that obeys the good regulator theorem. So, for example, in economics, the more accurately a (stock or commodities) trading model represents the actions of the market, the more easily it can control that market (and extract "useful work" (profits) from it). In AI, an example might be a chatbot modelling the discourse state of humans: the more accurately it can model the human state (e.g. on a telephone voice-support hotline), the better it can manipulate the human (e.g. into performing the corrective actions to resolve the problem that caused the phone call to the help-line). These last two examples take the narrow historical interpretation of control theory as a set of differential equations modeling and regulating kinetic motion, and broaden it into a vast generalization of a regulator interacting with a plant. − − 太空竞赛也依赖于精确的航天器控制，控制理论在经济学和人工智能等领域的应用也越来越多。在这里，有人可能会说，目标是找到一个内部模型，遵守良好的调节器定理。因此，举例来说，在经济学中，一个(股票或商品)交易模型越准确地代表了市场的行为，它就越容易控制市场(并从中提取“有用的工作”(利润))。在人工智能中，一个例子可能是一个聊天机器人模拟人类的话语状态: 它模拟人类状态越精确(例如:。在电话语音支持热线) ，它可以更好地操纵人类(例如:。进行纠正措施，以解决问题，造成电话呼叫的帮助热线)。最后两个例子将控制理论狭隘的历史解释视为一组微分方程建模和调节动力学运动，并将其扩展为调节器与植物相互作用的广义推广。 − + + +
→历史
[[File:220px-Boulton_and_Watt_centrifugal_governor-MJ.jpg|thumb|right|1788年的Boulton＆Watt发动机中的离心调速器]]
[[File:220px-Boulton_and_Watt_centrifugal_governor-MJ.jpg|thumb|right|1788年的Boulton＆Watt发动机中的离心调速器]]
虽然各种类型的控制系统可以追溯到古代，一个更加正式的领域分析开始于离心式调速器的动力学分析，由物理学家詹姆斯·克拉克·麦克斯韦 James Clerk Maxwell 在1868年进行，名为“统治者”<ref name="Maxwell1867">{{cite journal|author=Maxwell, J.C.|year=1868|title=On Governors|journal=Proceedings of the Royal Society of London|volume=16|pages=270–283|doi=10.1098/rspl.1867.0055|jstor=112510|doi-access=free}}<!--| accessdate = 2008-04-14--></ref>。离心式调速器已经被用来调节风车的速度。麦克斯韦描述并分析了自激振荡现象，其中系统的滞后可能导致系统的过度补偿和不稳定行为。这引起了人们对这个话题的浓厚兴趣，在这期间，Maxwell 的同学，Edward John Routh，抽象出了 Maxwell 关于线性系统的一般类别的结果。
<ref name=Routh1975>{{cite book
| author = Routh, E.J.
| author = Routh, E.J.
|author2=Fuller, A.T.
|author2=Fuller, A.T.
| year = 1975
| year = 1975
| title = Stability of motion
| title = Stability of motion
| publisher = Taylor & Francis
| publisher = Taylor & Francis
| isbn =
| isbn =
}}</ref>
独立地，阿道夫·赫维兹 Adolf Hurwitz 在1877年使用微分方程对系统稳定性进行了分析，得出了现在所说的 Routh–Hurwitz 定理。
<ref name=Routh1877>{{cite book
}}</ref> Independently, [[Adolf Hurwitz]] analyzed system stability using differential equations in 1877, resulting in what is now known as the [[Routh–Hurwitz theorem]].<ref name=Routh1877>{{cite book
| author = Routh, E.J.
| author = Routh, E.J.
| year = 1877
| year = 1877
| title = A Treatise on the Stability of a Given State of Motion, Particularly Steady Motion: Particularly Steady Motion
| title = A Treatise on the Stability of a Given State of Motion, Particularly Steady Motion: Particularly Steady Motion
| url = https://archive.org/details/atreatiseonstab00routgoog
| url = https://archive.org/details/atreatiseonstab00routgoog
| publisher = Macmillan and co.
| publisher = Macmillan and co.
| isbn =
| isbn =
}}</ref><ref name=Hurwitz1964>{{cite journal
}}</ref><ref name=Hurwitz1964>{{cite journal
| author = Hurwitz, A.
| author = Hurwitz, A.
| year = 1964
| year = 1964
| title = On The Conditions Under Which An Equation Has Only Roots With Negative Real Parts
| title = On The Conditions Under Which An Equation Has Only Roots With Negative Real Parts
| journal = Selected Papers on Mathematical Trends in Control Theory
| journal = Selected Papers on Mathematical Trends in Control Theory
}}</ref>
}}</ref>
动态控制的一个显著应用是在载人飞行领域。1903年12月17日，莱特兄弟进行了首次成功的试飞，他们的杰出之处在于能够在相当长的时间内控制飞行(比已知的用机翼产生升力的能力还要强)。持续、可靠地控制飞机对于长时间的飞行是非常重要的。
动态控制的一个显著应用是在载人飞行领域。1903年12月17日，莱特兄弟进行了首次成功的试飞，他们的杰出之处在于能够在相当长的时间内控制飞行(比已知的用机翼产生升力的能力还要强)。持续、可靠地控制飞机对于持续时间超过几秒钟的飞行是必要的。
到了第二次世界大战，控制理论成为一个重要的研究领域。IrmgardFlügge-Lotz 发展了非连续自动控制系统理论，并将 bang-bang 原理应用于飞机自动飞行控制装置的开发<ref>{{cite journal|last1=Flugge-Lotz|first1=Irmgard|last2=Titus|first2=Harold A.|title=Optimum and Quasi-Optimum Control of Third and Fourth-Order Systems|journal=Stanford University Technical Report|date=October 1962|issue=134|pages=8–12|url=http://www.dtic.mil/dtic/tr/fulltext/u2/621137.pdf}}</ref><ref>{{cite book|last1=Hallion|first1=Richard P.|editor1-last=Sicherman|editor1-first=Barbara|editor2-last=Green|editor2-first=Carol Hurd|editor3-last=Kantrov|editor3-first=Ilene|editor4-last=Walker|editor4-first=Harriette|title=Notable American Women: The Modern Period: A Biographical Dictionary|url=https://archive.org/details/notableamericanw00sich|url-access=registration|date=1980|publisher=Belknap Press of Harvard University Press|location=Cambridge, Mass.|isbn=9781849722704|pages=[https://archive.org/details/notableamericanw00sich/page/241 241–242]}}</ref>。不连续控制的其他应用领域包括火控系统、制导系统和电子学。
也可以使用机械方法来提高系统的稳定性。例如，船舶稳定器是安装在吃水线下方并横向出现的鳍片就是一种典型的机械控制应用。在现代船舶中，陀螺仪控制的活动鳍片具有改变其迎角的能力，以抵消风或波浪作用在船上引起的侧倾。
二战后，各国开始了太空竞赛，太空竞赛非常依赖于精确的航天器控制。当代，控制理论在经济学和人工智能等领域的应用也越来越多。在这里，有人可能会说，控制得目标是找到一个遵循良好控制器定理的内部模型。因此，举例来说，在经济学中，一个(股票或商品)交易模型越准确地代表了市场的行为，它就越容易控制市场(并从中提取“有用的工作”(利润))。在人工智能中，一个例子可能是一个聊天机器人模拟人类的话语状态: 它模拟人类状态越精确(例如:在电话语音支持热线) ，它可以更好地帮助人类(例如:进行纠正措施，解决问题，防止电话呼叫造成的通话堵塞)。这俩个例子通常是将控制理论的历史解释视为一组微分方程建模和动力学建模，并将其扩展为控制器与平台相互作用的广义推广。
==Open-loop and closed-loop (feedback) control==
==Open-loop and closed-loop (feedback) control==