控制理論基礎 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background of control theory(控制理論基礎) 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. 按照美國大百科全書的解釋，所謂系統(tǒng)就是反映“一個各種物體的集合，根據(jù)其性質或人的愿望而結合起來以至形成一個集中、復雜的整體”。數(shù)學中的系統(tǒng)理論就是對這種由若干“物體”構成的集合當其受到某些條件和輸入作用的行為和阻斷進行研究的一門學問。系統(tǒng)理論的抽象性質源于這樣一個事實：系統(tǒng)理論更關心物體組成部件的數(shù)學性質而不是其物理形式。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.控制理論通常與實際應用有關。一般認為，控制系統(tǒng)是任意一個這樣的系統(tǒng)：其目的是為了以某種期望的方式來調(diào)節(jié)或控制諸如能量、信息、資金等等牧師量的流動。從更一般的意義上講，控制系統(tǒng)就是一個按照一定方式由很多元件或功能單元構成的結合體，其目的是為了獲得期望的結果。本書中，假定控制理論包括所有與控制系統(tǒng)設計和分析問題有關的內(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是對開環(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)的目標以及所有可獲取的先驗知識而選定的。輸入變量決不會受到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作用在開環(huán)系統(tǒng)上，或者如果其行為不能完全掌握的話，則該系統(tǒng)的輸出就不會完全如預期般動作。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.另一類常見的控制系統(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)輸出行為有關的信息所校正。一個反饋系統(tǒng)經(jīng)常能更好的應付不期望的振動作用以及系統(tǒng)動態(tài)性能的不確定性。然而，閉環(huán)控制并不一定總是優(yōu)于開環(huán)控制。當輸出的測量誤差足夠大或不期望的振動無關緊要時，閉環(huán)控制的性能就會比開環(huán)控制的差。2 introduction to modern control theory現(xiàn)代控制理論導論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.研究重點朝向最優(yōu)控制和最優(yōu)系統(tǒng)設計的轉移。(c) the continuing developments in digital computer technology.數(shù)字計算機技術的不斷發(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。對二將熟知方法在其他知識領域中應用的廣泛認同。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，更為真實的模型往往具有非線性和時變參數(shù)。以前往往忽略的一些系統(tǒng)問題例如關聯(lián)問題以及通過環(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)展先進的社會中，朝著更加宏偉目標的發(fā)展趨勢是很明顯的。這也就意味著要處理具有大量相互關聯(lián)部件的復雜系統(tǒng)。對二更加精確和更加有效的需求已經(jīng)改變了對控制系統(tǒng)性能要求的重點。以百分超調(diào)量、調(diào)節(jié)時間、帶寬等來表示的經(jīng)典技術指標已經(jīng)在很多場合讓位二最優(yōu)性準則，例如最小能耗、最低成本和最短時間操作等。依據(jù)這些準則的最優(yōu)化合得想要避免處理討厭的非線性一中變得更為困難。即使基本受近期系統(tǒng)是線性和時不變的，最優(yōu)控制理論也經(jīng)常規(guī)定要采用非線性、時變的控制規(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.計算機技術的不斷發(fā)展，已經(jīng)對控制領域產(chǎn)生了三個方面的主要影響。影響之一與超大規(guī)模的巨型機有關?，F(xiàn)在能夠進行建模、分析和控制研究的問題的規(guī)模和困難級別都已經(jīng)大大超過了本書第一版時的情況。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.計算機技術的第二個影響與微型機在數(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。經(jīng)典控制理論中圖解方法占主導地位，這是因為當時圖解是解決某些問題的唯一方法?，F(xiàn)在每一個控制工程設計人員都很容易獲得功能強大的計算機軟件包，用于進行系統(tǒng)的分析和設計工作。老的圖解方法并沒有消亡，不過已經(jīng)能夠自動進行工作了。它們之所以仍然存在的原因是其所有的直觀性和指導性。然而，一些完全不同的技術經(jīng)常對計算機更加適合。盡管計算機可用于執(zhí)行經(jīng)典的變換反變換運算，然而用計算機對微分方程直接進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.第三方面計算機的影響來自于如今計算機就像在控制系統(tǒng)中其他常規(guī)元件應用得一樣普及。計算機在成本、規(guī)模和可靠性方面的優(yōu)勢使其能夠理普遍地應用于很多系統(tǒng)中。這就意味著離散時間和數(shù)字式的控制系統(tǒng)現(xiàn)在應該受到遠勝于以往的重視。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于上述的發(fā)展趨勢。這是因為時間域技術及其數(shù)學表達語言（例如矩陣、線性向量空間等）在計算機上應用是非常理想的。計算機的發(fā)展也是狀態(tài)變量方法之所以會產(chǎn)生的一個主要原因。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)典控制技術都是帶有一個輸入、一個輸出（也許可有數(shù)個輸入和輸出）的線性、常系數(shù)系統(tǒng)而發(fā)展起來的。經(jīng)典技術的表述語言是拉普拉斯或z變換以及傳遞函數(shù)。一旦出現(xiàn)非線性和時變性，經(jīng)典技術最根本的基礎就不復存在了。諸如相平面方法、描述函數(shù)法和其他有關方法這樣一些很成功的技術能夠得以發(fā)展的原因就是為了彌補這一短處。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、高效的方法來描述具有任意階次、線性或非線性、時變或常系數(shù)的各種系統(tǒng)。它也為計算機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域中的新發(fā)展。因此，可以說它是名副其實。然而，現(xiàn)代控制理論的基礎卻應該在其他一些發(fā)展成熟的領域中尋找。以狀態(tài)變量形式來表示一個系統(tǒng)的方法完全等價于在哈密爾頓力學中采用通用坐標和通用動量的方法。這種方法的優(yōu)越性在經(jīng)典物理學中多年來已經(jīng)眾所周知。當處理各種聯(lián)立方程時采用矩陣的好處在應用數(shù)學領域中也已久為人知。線性代數(shù)對現(xiàn)代控制理論的發(fā)展更是功不可沒。其原因在于線性代數(shù)所提供的簡潔的表達、通用的結果以及高效的思路。 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控制問題，在工程上具有相當重要的意義。我們所討論的系統(tǒng)有幾個輸入，其中某些輸入稱為控制量，因為這些量是可以人為地控制的，而另一些輸入稱為外部擾動，它們是很難預知的。例如在工業(yè)用加熱爐中，可以認為燃料流量、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量和容易控制的，但后面兩項通常是不能預知的擾動。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，控制問題的一個方面在于確定如何處理控制量以便抵消外部擾動對系統(tǒng)狀態(tài)的影響。解決這個問題的一種可能的方法是不斷地測量擾動量，根據(jù)該測量值和已知的系統(tǒng)方程式，定出應有的控制輸入量（用時間函數(shù)表示），以便對系統(tǒng)狀態(tài)進行合適的控制。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)，即不是直接測量擾動量，然后從模型或系統(tǒng)方程組去計算擾動對系統(tǒng)的影響。而是將系統(tǒng)狀態(tài)的直接的連續(xù)的測量值與表示其“希望值”信號相比較，由此產(chǎn)生一個誤差信號，再利用誤差信號產(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)結構如圖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.由于術語上的某些習慣，前一種方法已被稱為開環(huán)控制，而后者被稱為閉環(huán)控制。初看起來這兩種方法可能在本質上是等效的。確實，人們可能這樣推測：開環(huán)控制的方式更好些，因為在擾動引起系統(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)點比不上開環(huán)控制的缺點和反饋系統(tǒng)的固有優(yōu)點。首先，在許多情況下，實現(xiàn)上面所提到的開環(huán)控制需要一臺非常完善的（因而很費錢的）計算裝置，以便用它算出抵消預估擾動影響所需的輸入量。其次，反饋系統(tǒng)對其數(shù)學模型的精度并不很敏感。換句話說，一個合理設計的反饋系統(tǒng)，即使系統(tǒng)內(nèi)部的特性有相當大的變化，系統(tǒng)仍能滿意地工作。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.反饋方法的另一個主要優(yōu)點是用一個“反饋回路”來包圍原來特性不滿意的系統(tǒng)，在許多情況下，人們可能由此而組成一個性能較滿意的系統(tǒng)。例如，研究一個垂直飛行的火箭?；鸺龑嵸|上是一個倒置的擺，由發(fā)動機噴出的氣流平衡，它本身是不穩(wěn)定的（只要火箭的中心線與垂直方向有一點偏離，就會使火箭傾倒）?？墒牵揽吭谌f向架上轉動火箭的發(fā)動機，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。實現(xiàn)改變氣流方向的唯一滿意的方法就是采用反饋；不斷地測出火箭在兩個相互垂直平面中運動的角度，使控制器適當?shù)卣{(diào)整火箭發(fā)動機的方向。實際上，采用開環(huán)控制方法是不可能使原來不穩(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)的結構復雜程序和控制對象的不同，分析和設計反饋系統(tǒng)所需要的數(shù)學工具是不同的。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.在最簡單的情況下，可以用調(diào)節(jié)一個對象輸入量來控制一個對象狀態(tài)變量（稱為輸出）。這時要設計一個包圍系統(tǒng)的反饋回路，保證輸出以某種能被接受的精度響應特定的時間函數(shù)或特定的軌跡，此時都要求瞬態(tài)響應不要太“激烈”，持續(xù)時間不要太長。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)（或對象）的控制輸入為u ,外部擾動為d ,輸出為y ,它們都是標量。問題就在于要圍繞此對象設計一個反饋系統(tǒng)，它包括：(a)測量裝置，產(chǎn)生輸出量的連續(xù)測量值ym；(b)比較器，在比較器中，從參考輸入yr(或稱給定值、希望輸出)中減去測量值ym，產(chǎn)生誤差信號e；(c)控制器，它由誤差信號e產(chǎn)生適合于控制對象的輸入u 。我們把這種結構稱為單回路反饋系統(tǒng)，這一術語表明了控制的基本特點，即只用一個輸入來控制對象的一個狀態(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