控制理論基礎(chǔ) 畢業(yè)論文外文翻譯.doc

第6章 英文資料翻譯6.1控制理論基礎(chǔ)background of control theory(控制理論基礎(chǔ)) 1 system and control theoryaccording to the encyclopedia americana, a system is “an aggregation or assemblage of things so combined by nature or man as to form an integral and complex whole” .mathematical systems theory is the study, of the interruptions and behavior of such an assemblage of “things” when subjected to certain conditions or inputs. the abstract nature of systems theory is due to the fact that it is concerned with mathematical properties rather than the physical form of the constituent parts. 按照美國(guó)大百科全書(shū)的解釋?zhuān)^系統(tǒng)就是反映“一個(gè)各種物體的集合，根據(jù)其性質(zhì)或人的愿望而結(jié)合起來(lái)以至形成一個(gè)集中、復(fù)雜的整體”。數(shù)學(xué)中的系統(tǒng)理論就是對(duì)這種由若干“物體”構(gòu)成的集合當(dāng)其受到某些條件和輸入作用的行為和阻斷進(jìn)行研究的一門(mén)學(xué)問(wèn)。系統(tǒng)理論的抽象性質(zhì)源于這樣一個(gè)事實(shí)：系統(tǒng)理論更關(guān)心物體組成部件的數(shù)學(xué)性質(zhì)而不是其物理形式。control theory is more often concerned with physical application. a control systems is considered to be any system which exists for the purpose of regulating or controlling the flow of energy, information, money, or other quantities in some desired fashion. in more general terms, a control system is an interconnection of many components or functional units in such a way as to produce a desired result, in this book, control theory is assumed to encompass all questions related to design and analysis of control systems.控制理論通常與實(shí)際應(yīng)用有關(guān)。一般認(rèn)為，控制系統(tǒng)是任意一個(gè)這樣的系統(tǒng)：其目的是為了以某種期望的方式來(lái)調(diào)節(jié)或控制諸如能量、信息、資金等等牧師量的流動(dòng)。從更一般的意義上講，控制系統(tǒng)就是一個(gè)按照一定方式由很多元件或功能單元構(gòu)成的結(jié)合體，其目的是為了獲得期望的結(jié)果。本書(shū)中，假定控制理論包括所有與控制系統(tǒng)設(shè)計(jì)和分析問(wèn)題有關(guān)的內(nèi)容。fig.37.1 is a general representation of an open-loop control system. the input or control u(t) is selected based on the goals for the system and all available a priori knowledge about the system. the input is in no way influenced by the output of the system, represented by y(t).if unexpected disturbances act upon an open-loop system, or if its behavior is not completely understood, then the output will not behave precisely as expected.圖37。1是對(duì)開(kāi)環(huán)控制系統(tǒng)的一般性表示。輸入變量或控制作用u（t）是根據(jù)本系統(tǒng)的目標(biāo)以及所有可獲取的先驗(yàn)知識(shí)而選定的。輸入變量決不會(huì)受到y(tǒng)（t）所表示的系統(tǒng)輸出變量的影響。如果有不期望的振動(dòng)作用在開(kāi)環(huán)系統(tǒng)上，或者如果其行為不能完全掌握的話(huà)，則該系統(tǒng)的輸出就不會(huì)完全如預(yù)期般動(dòng)作。another general class of control systems is the closed-loop or feedback control system, as illustrated in fig.37.2.in the closed-loop system, the control u(t) is modified in some way by information about the behavior of the system output. a feedback system is often better able to cope with unexpected disturbances and uncertainties about the systems dynamic behavior. however, it need not be true that closed-loop control is always superior to open-loop control. when the measured output has errors which are sufficiently large, and when unexpected disturbances are relatively unimportant, closed-loop control can have a performance which is inferior to open-loop control.另一類(lèi)常見(jiàn)的控制系統(tǒng)是閉環(huán)或反饋控制系統(tǒng)，如圖37。2所示。閉環(huán)控制系統(tǒng)中，控制作用u（t）被以某種方式由與系統(tǒng)輸出行為有關(guān)的信息所校正。一個(gè)反饋系統(tǒng)經(jīng)常能更好的應(yīng)付不期望的振動(dòng)作用以及系統(tǒng)動(dòng)態(tài)性能的不確定性。然而，閉環(huán)控制并不一定總是優(yōu)于開(kāi)環(huán)控制。當(dāng)輸出的測(cè)量誤差足夠大或不期望的振動(dòng)無(wú)關(guān)緊要時(shí)，閉環(huán)控制的性能就會(huì)比開(kāi)環(huán)控制的差。2 introduction to modern control theory現(xiàn)代控制理論導(dǎo)論several factors provided the stimulus for the development of modern control theory(a) the necessity of dealing with more realistic models of systems.處理更加真實(shí)的系統(tǒng)模型的必要性。(b) the shift in emphasis towards optimal control and optimal system design.研究重點(diǎn)朝向最優(yōu)控制和最優(yōu)系統(tǒng)設(shè)計(jì)的轉(zhuǎn)移。(c) the continuing developments in digital computer technology.數(shù)字計(jì)算機(jī)技術(shù)的不斷發(fā)展。(d) the shortcomings of previous approaches.原有方法的短缺。(e) a recognition of the applicability of well0known methods in other fields of knowledge。對(duì)二將熟知方法在其他知識(shí)領(lǐng)域中應(yīng)用的廣泛認(rèn)同。the transition from simple approximate models, which are easy to work with , to more realistic models produces two effects, first, a larger number of variables must be included in the mode second, a more realistic model is more likely to contain nonlinearities and time-varying parameters. previously ignored aspects of the system, such as interactions and feedback through the environment , are more likely to be included.模型中必須包含眾多的變量。其次，更為真實(shí)的模型往往具有非線(xiàn)性和時(shí)變參數(shù)。以前往往忽略的一些系統(tǒng)問(wèn)題例如關(guān)聯(lián)問(wèn)題以及通過(guò)環(huán)境形成的反饋等，現(xiàn)在卻需要考慮。with an advancing technological society, there is a trend towards more ambitious goals. this also means dealing with complex systems with larger number of interaction components. the need for greater accuracy and efficiency has changed the emphasis on control system performance. the classical specifications in terms of percent overshoot, settling time, abandwidth, etc, have in many cases given way to optimal criteria such as minimum energy, minimum cost, and minimum operation. optimization of these criteria makes it even more difficult to avoid dealing with unpleasant nonlinear. optimal control theory often dictates that nonlinear time-varying control laws be used, even if the basic system is linear and time-invariant.在不斷發(fā)展先進(jìn)的社會(huì)中，朝著更加宏偉目標(biāo)的發(fā)展趨勢(shì)是很明顯的。這也就意味著要處理具有大量相互關(guān)聯(lián)部件的復(fù)雜系統(tǒng)。對(duì)二更加精確和更加有效的需求已經(jīng)改變了對(duì)控制系統(tǒng)性能要求的重點(diǎn)。以百分超調(diào)量、調(diào)節(jié)時(shí)間、帶寬等來(lái)表示的經(jīng)典技術(shù)指標(biāo)已經(jīng)在很多場(chǎng)合讓位二最優(yōu)性準(zhǔn)則，例如最小能耗、最低成本和最短時(shí)間操作等。依據(jù)這些準(zhǔn)則的最優(yōu)化合得想要避免處理討厭的非線(xiàn)性一中變得更為困難。即使基本受近期系統(tǒng)是線(xiàn)性和時(shí)不變的，最優(yōu)控制理論也經(jīng)常規(guī)定要采用非線(xiàn)性、時(shí)變的控制規(guī)律。the continuing advances in computer technology have had three principal effects on the controls field. one of these relates to the gigantic supercomputers. the size and class of problems that can now be modeled , analyzed, and controlled are considerably larger than they were when the first of this book was written.計(jì)算機(jī)技術(shù)的不斷發(fā)展，已經(jīng)對(duì)控制領(lǐng)域產(chǎn)生了三個(gè)方面的主要影響。影響之一與超大規(guī)模的巨型機(jī)有關(guān)?，F(xiàn)在能夠進(jìn)行建模、分析和控制研究的問(wèn)題的規(guī)模和困難級(jí)別都已經(jīng)大大超過(guò)了本書(shū)第一版時(shí)的情況。the second impact of computer technology has to do with the proliferation and wide availability of microcomputers in homes and in the work place. classical control theory was dominated by graphical methods because at the time that was the only way to solve certain problems. now every control designer has easy access to powerful computer packages for system analysis and design the old graphic methods have not yet disappeared, but have been automated. they survive because of the insight and intuition that they can provide. however, some different techniques are often better suited to a computer. a1though a computer can be used to carry out the classical transform-inverse transform methods, it is usually more efficient for a computer to integrate differential equations directly.計(jì)算機(jī)技術(shù)的第二個(gè)影響與微型機(jī)在數(shù)量上的激增以及其在家庭、工作聲所隨處可用的便利性緊密相關(guān)。經(jīng)典控制理論中圖解方法占主導(dǎo)地位，這是因?yàn)楫?dāng)時(shí)圖解是解決某些問(wèn)題的唯一方法?，F(xiàn)在每一個(gè)控制工程設(shè)計(jì)人員都很容易獲得功能強(qiáng)大的計(jì)算機(jī)軟件包，用于進(jìn)行系統(tǒng)的分析和設(shè)計(jì)工作。老的圖解方法并沒(méi)有消亡，不過(guò)已經(jīng)能夠自動(dòng)進(jìn)行工作了。它們之所以仍然存在的原因是其所有的直觀性和指導(dǎo)性。然而，一些完全不同的技術(shù)經(jīng)常對(duì)計(jì)算機(jī)更加適合。盡管計(jì)算機(jī)可用于執(zhí)行經(jīng)典的變換反變換運(yùn)算，然而用計(jì)算機(jī)對(duì)微分方程直接進(jìn)行積分則往往更加有效。the third major impact of computers is that they are now so commonly used as just another component in the control system. their cost, size and reliability make it possible to use them routinely in many systems. this means that the discrete=tie and digital system control now deserver much more attention than it did in the past.第三方面計(jì)算機(jī)的影響來(lái)自于如今計(jì)算機(jī)就像在控制系統(tǒng)中其他常規(guī)元件應(yīng)用得一樣普及。計(jì)算機(jī)在成本、規(guī)模和可靠性方面的優(yōu)勢(shì)使其能夠理普遍地應(yīng)用于很多系統(tǒng)中。這就意味著離散時(shí)間和數(shù)字式的控制系統(tǒng)現(xiàn)在應(yīng)該受到遠(yuǎn)勝于以往的重視。modern control theory is well suited to the above trends because its time-domain techniques and its mathematical language (matrices, linear vector space, etc.) are ideal when dealing with a computer. computers are a major reason for the existence of state variable methods.現(xiàn)代控制理論特別適應(yīng)于上述的發(fā)展趨勢(shì)。這是因?yàn)闀r(shí)間域技術(shù)及其數(shù)學(xué)表達(dá)語(yǔ)言（例如矩陣、線(xiàn)性向量空間等）在計(jì)算機(jī)上應(yīng)用是非常理想的。計(jì)算機(jī)的發(fā)展也是狀態(tài)變量方法之所以會(huì)產(chǎn)生的一個(gè)主要原因。most classical control techniques were developed of linear constant coefficient systems with one input and one output(perhaps a few inputs and outputs).the language of classical techniques is the laplace or z-transform and transfer functions .when nonlinearities and time variations are present ,the very basic for these classical techniques is removed. some successful techniques such as phase-plane methods, describing functions, and other ad hoc methods, have been developed to alleviate this shortcoming. however, the greatest success has been limited to low-order systems. the state variable approach of modern control theory provides a uniform and powerful method of representing systems of arbitrary order, linear or nonlinear, with time-varying or constant coefficients. it provides an ideal formulation for computer implementation and is responsible for much of the progress in optimization theory.大多數(shù)經(jīng)典控制技術(shù)都是帶有一個(gè)輸入、一個(gè)輸出（也許可有數(shù)個(gè)輸入和輸出）的線(xiàn)性、常系數(shù)系統(tǒng)而發(fā)展起來(lái)的。經(jīng)典技術(shù)的表述語(yǔ)言是拉普拉斯或z變換以及傳遞函數(shù)。一旦出現(xiàn)非線(xiàn)性和時(shí)變性，經(jīng)典技術(shù)最根本的基礎(chǔ)就不復(fù)存在了。諸如相平面方法、描述函數(shù)法和其他有關(guān)方法這樣一些很成功的技術(shù)能夠得以發(fā)展的原因就是為了彌補(bǔ)這一短處。然而經(jīng)典控制理論最大的成功也是局限于低階系統(tǒng)中?，F(xiàn)代控制理論的狀態(tài)變量法提供了一種統(tǒng)一、高效的方法來(lái)描述具有任意階次、線(xiàn)性或非線(xiàn)性、時(shí)變或常系數(shù)的各種系統(tǒng)。它也為計(jì)算機(jī)處理提供了一種理想的表示方法，并引起了許多方面最優(yōu)化理論的進(jìn)展。modern control theory is a recent development in the field of control. therefore, the name is justified at least as a descriptive title. however, the foundation of modern control theory is to be found in other well-established fields. representing a system in terms of state variables is equivalent to the approach of hamiltonian mechanics, using generalized coordinates and generalized moment. the advantages of this approach have been well known in classical physics for many years. the advantages of using matrices when deal with simultaneous equations of various kinds have long been appreciated in applied mathematics. the field of linear algebra also contributes heavily to modern control theory. this due to the concise notation, the generality of the results, and the economy of thought that linear algebra provides. 現(xiàn)代控制理論是在控制領(lǐng)域中的新發(fā)展。因此，可以說(shuō)它是名副其實(shí)。然而，現(xiàn)代控制理論的基礎(chǔ)卻應(yīng)該在其他一些發(fā)展成熟的領(lǐng)域中尋找。以狀態(tài)變量形式來(lái)表示一個(gè)系統(tǒng)的方法完全等價(jià)于在哈密爾頓力學(xué)中采用通用坐標(biāo)和通用動(dòng)量的方法。這種方法的優(yōu)越性在經(jīng)典物理學(xué)中多年來(lái)已經(jīng)眾所周知。當(dāng)處理各種聯(lián)立方程時(shí)采用矩陣的好處在應(yīng)用數(shù)學(xué)領(lǐng)域中也已久為人知。線(xiàn)性代數(shù)對(duì)現(xiàn)代控制理論的發(fā)展更是功不可沒(méi)。其原因在于線(xiàn)性代數(shù)所提供的簡(jiǎn)潔的表達(dá)、通用的結(jié)果以及高效的思路。 6.2 反饋系統(tǒng).feedback control（反饋控制）the class of control problems to be examined here is one of considerable engineering interest. we shall consider systems with several inputs, some known as controls because they may be manipulated and others called external disturbances, which are quite unpredictable. for example, in an industrial furnace we may consider the fuel flow, the ambient temperature, and the loading of material into the furnace to be inputs. of these, the fuel flow is accessible and can readily be controlled, while the latter two are usually unpredictable disturbances.這里所研究的這一類(lèi)控制問(wèn)題，在工程上具有相當(dāng)重要的意義。我們所討論的系統(tǒng)有幾個(gè)輸入，其中某些輸入稱(chēng)為控制量，因?yàn)檫@些量是可以人為地控制的，而另一些輸入稱(chēng)為外部擾動(dòng)，它們是很難預(yù)知的。例如在工業(yè)用加熱爐中，可以認(rèn)為燃料流量、環(huán)境溫度以及爐內(nèi)材料裝填量都是輸入量，其中燃料流量是容易測(cè)量和容易控制的，但后面兩項(xiàng)通常是不能預(yù)知的擾動(dòng)。in such situations, one aspect of the control problem is to determine how the controls should be manipulated so as to counteract the effects of the external disturbances on the state of the system. one possible approach to the solution of this problem is to use a continuous measurement of the disturbances, and from this and the known system equations to determine what the control inputs should be as functions of time to give appropriate control of the system state.在這些情況下，控制問(wèn)題的一個(gè)方面在于確定如何處理控制量以便抵消外部擾動(dòng)對(duì)系統(tǒng)狀態(tài)的影響。解決這個(gè)問(wèn)題的一種可能的方法是不斷地測(cè)量擾動(dòng)量，根據(jù)該測(cè)量值和已知的系統(tǒng)方程式，定出應(yīng)有的控制輸入量（用時(shí)間函數(shù)表示），以便對(duì)系統(tǒng)狀態(tài)進(jìn)行合適的控制。a different approach is to construct a feedback system, that is, rather than measure the disturbances directly and then compute their effects on the system from the model or system equations, we compare direct and continuous measurements of the accessible system states with signals representing their “desired values” to form an error signal, and use this signal to produce inputs to the system which will drive the error as close to zero as possible. diagrams representing these two basic strategies of control are shown in fig.1.另一種不同的方法是組成反饋系統(tǒng)，即不是直接測(cè)量擾動(dòng)量，然后從模型或系統(tǒng)方程組去計(jì)算擾動(dòng)對(duì)系統(tǒng)的影響。而是將系統(tǒng)狀態(tài)的直接的連續(xù)的測(cè)量值與表示其“希望值”信號(hào)相比較，由此產(chǎn)生一個(gè)誤差信號(hào)，再利用誤差信號(hào)產(chǎn)生系統(tǒng)的輸入，而該輸入又使誤差盡可能的接近于零。這兩種基本控制系統(tǒng)結(jié)構(gòu)如圖1所示。by some abuse of terminology, the former approach has come to be known as open-loop control, and the latter as closed-loop control. at first sight, the two approaches might to be essentially equivalent. indeed, one might surmise that an open-loop control scheme is preferable since it is not necessary to wait until the disturbances have produced an undesirable change in the system state before corrective inputs can be computed and applied.由于術(shù)語(yǔ)上的某些習(xí)慣，前一種方法已被稱(chēng)為開(kāi)環(huán)控制，而后者被稱(chēng)為閉環(huán)控制。初看起來(lái)這兩種方法可能在本質(zhì)上是等效的。確實(shí)，人們可能這樣推測(cè)：開(kāi)環(huán)控制的方式更好些，因?yàn)樵跀_動(dòng)引起系統(tǒng)狀態(tài)發(fā)生不希望的變化之前，校正輸入早已算好并已加到系統(tǒng)中去了。however, this advantage is more than outweighed by the disadvantages of open-loop control and the inherent advantages of feedback systems. first, in many cases the implementation of the open-loop control suggested above would require a very sophisticated (and hence expensive) computing device to determine the inputs required to counteract the predicted disturbance effects. second, a feedback system turns out to be inherently far less sensitive to the accuracy with which a mathematical model of the system has been determined. put another way, a properly designed feedback system will still operate satisfactorily even when the internal properties of the system change by significant amounts.然而，這一優(yōu)點(diǎn)比不上開(kāi)環(huán)控制的缺點(diǎn)和反饋系統(tǒng)的固有優(yōu)點(diǎn)。首先，在許多情況下，實(shí)現(xiàn)上面所提到的開(kāi)環(huán)控制需要一臺(tái)非常完善的（因而很費(fèi)錢(qián)的）計(jì)算裝置，以便用它算出抵消預(yù)估擾動(dòng)影響所需的輸入量。其次，反饋系統(tǒng)對(duì)其數(shù)學(xué)模型的精度并不很敏感。換句話(huà)說(shuō)，一個(gè)合理設(shè)計(jì)的反饋系統(tǒng)，即使系統(tǒng)內(nèi)部的特性有相當(dāng)大的變化，系統(tǒng)仍能滿(mǎn)意地工作。another major advantage of the feedback approach is that by placing a “feedback loop” around a system which initially has quite unsatisfactory behavior. consider, for example, a rocket in vertical flight. this is essentially an inverted pendulum, balancing on the gas jet produced by the engine, and inherently unstable (any deviation of the rocket axis from the vertical will cause the rocket to topple over).it can, however, be kept stable in vertical flight by appropriate changes in the direction of the exhaust jet, which may be achieved by rotating the engine on its gymbal mountings. the only satisfactory way of achieving these variations in jet direction is to use a feedback strategy in which continuous measurements of the angular motions of the rocket in two mutually perpendicular vertical planes cause a controller to make appropriate adjustments to the direction of the rocket engine. stabilization of an inherently unstable system could not be achieved in practice by an open-loop control strategy.反饋方法的另一個(gè)主要優(yōu)點(diǎn)是用一個(gè)“反饋回路”來(lái)包圍原來(lái)特性不滿(mǎn)意的系統(tǒng)，在許多情況下，人們可能由此而組成一個(gè)性能較滿(mǎn)意的系統(tǒng)。例如，研究一個(gè)垂直飛行的火箭?；鸺龑?shí)質(zhì)上是一個(gè)倒置的擺，由發(fā)動(dòng)機(jī)噴出的氣流平衡，它本身是不穩(wěn)定的（只要火箭的中心線(xiàn)與垂直方向有一點(diǎn)偏離，就會(huì)使火箭傾倒）?？墒?，依靠在萬(wàn)向架上轉(zhuǎn)動(dòng)火箭的發(fā)動(dòng)機(jī)，從而合理地改變排氣氣流的方向，就能保持火箭穩(wěn)定的垂直飛行。實(shí)現(xiàn)改變氣流方向的唯一滿(mǎn)意的方法就是采用反饋；不斷地測(cè)出火箭在兩個(gè)相互垂直平面中運(yùn)動(dòng)的角度，使控制器適當(dāng)?shù)卣{(diào)整火箭發(fā)動(dòng)機(jī)的方向。實(shí)際上，采用開(kāi)環(huán)控制方法是不可能使原來(lái)不穩(wěn)定的系統(tǒng)變得穩(wěn)定的。the mathematical tools required for the analysis and design of feedback systems differ according to the structural complexity of the systems to be controlled and according to the objectives the feedback control is meant to achieve.按照控制系統(tǒng)的結(jié)構(gòu)復(fù)雜程序和控制對(duì)象的不同，分析和設(shè)計(jì)反饋系統(tǒng)所需要的數(shù)學(xué)工具是不同的。in the simplest situation, one controls a single plant state variable, called the output, by means of adjustments to a single plant input. the problem is to design a feedback loop around the system which will ensure that the output changes in response to certain specified time functions or trajectories with an acceptable degree of accuracy. in either case, the transients which are inevitably excited should not be too “violent” or persist for too long.在最簡(jiǎn)單的情況下，可以用調(diào)節(jié)一個(gè)對(duì)象輸入量來(lái)控制一個(gè)對(duì)象狀態(tài)變量（稱(chēng)為輸出）。這時(shí)要設(shè)計(jì)一個(gè)包圍系統(tǒng)的反饋回路，保證輸出以某種能被接受的精度響應(yīng)特定的時(shí)間函數(shù)或特定的軌跡，此時(shí)都要求瞬態(tài)響應(yīng)不要太“激烈”，持續(xù)時(shí)間不要太長(zhǎng)。in a typical situation, shown in fig.2 we are given a system, or plant, with control input u , external disturbance d ,and output y ,all scalars. the problem is to design a feedback system around the plant consisting of (a) a device which produces a continuous measurement ym of the output; (b) a comparator in which this signal is subtracted from a reference input (or set point, or desired output) yr, representing the desired value of the output, to produce an error signal e; and (c) a controller which uses the error signal e to produce an appropriate input u to the plant. we shall call this configuration a single-loop feedback system, a term which is meant to convey the essential feature that just one of the plant states (the output y) is to be controlled using only one input. the objective of the feedback system is to make the output y(t) follow its desired value yr(t) as closely as possible even in the presence of nonzero disturbances d(t). the ability of a system to do so under steady-state conditions is known as static accuracy.圖2表示了一種典型的情況，系統(tǒng)（或?qū)ο螅┑目刂戚斎霝閡 ,外部擾動(dòng)為d ,輸出為y ,它們都是標(biāo)量。問(wèn)題就在于要圍繞此對(duì)象設(shè)計(jì)一個(gè)反饋系統(tǒng)，它包括：(a)測(cè)量裝置，產(chǎn)生輸出量的連續(xù)測(cè)量值ym；(b)比較器，在比較器中，從參考輸入yr(或稱(chēng)給定值、希望輸出)中減去測(cè)量值ym，產(chǎn)生誤差信號(hào)e；(c)控制器，它由誤差信號(hào)e產(chǎn)生適合于控制對(duì)象的輸入u 。我們把這種結(jié)構(gòu)稱(chēng)為單回路反饋系統(tǒng)，這一術(shù)語(yǔ)表明了控制的基本特點(diǎn)，即只用一個(gè)輸入來(lái)控制對(duì)象的一個(gè)狀態(tài)（輸入y）。反饋系統(tǒng)的目的就在于即使存在非零擾動(dòng)d(t)，輸出量y(t)也將盡可能地接近希望量yr(t)。在穩(wěn)態(tài)條件下，系統(tǒng)這種能力被稱(chēng)為靜態(tài)精度。frequently yr is a constant, in which case we call the feedback system a regulator system. an example is the speed control