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1、第6章 英文资料翻译6.1控制理论基础Background of Control Theory(控制理论基础) 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 int
2、erruptions 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. 按照美国大百科全书的解释，所谓系统就是反映“一个各种物体的集合
3、，根据其性质或人的愿望而结合起来以至形成一个集中、复杂的整体”。数学中的系统理论就是对这种由若干“物体”构成的集合当其受到某些条件和输入作用的行为和阻断进行研究的一门学问。系统理论的抽象性质源于这样一个事实：系统理论更关心物体组成部件的数学性质而不是其物理形式。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 controll
4、ing 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 questio
5、ns related to design and analysis of control systems.控制理论通常与实际应用有关。一般认为，控制系统是任意一个这样的系统：其目的是为了以某种期望的方式来调节或控制诸如能量、信息、资金等等牧师量的流动。从更一般的意义上讲，控制系统就是一个按照一定方式由很多元件或功能单元构成的结合体，其目的是为了获得期望的结果。本书中，假定控制理论包括所有与控制系统设计和分析问题有关的内容。Fig.37.1 is a general representation of an open-loop control system. The input or contr
6、ol 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, th
7、en the output will not behave precisely as expected.图37。1是对开环控制系统的一般性表示。输入变量或控制作用U（T）是根据本系统的目标以及所有可获取的先验知识而选定的。输入变量决不会受到Y（T）所表示的系统输出变量的影响。如果有不期望的振动作用在开环系统上，或者如果其行为不能完全掌握的话，则该系统的输出就不会完全如预期般动作。Another general class of control systems is the closed-loop or feedback control system, as illustrated in Fig
8、.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
9、-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.另一类常见的控制系统是闭环或反馈控制系统，如图37。2所示。闭环控制系统
10、中，控制作用U（T）被以某种方式由与系统输出行为有关的信息所校正。一个反馈系统经常能更好的应付不期望的振动作用以及系统动态性能的不确定性。然而，闭环控制并不一定总是优于开环控制。当输出的测量误差足够大或不期望的振动无关紧要时，闭环控制的性能就会比开环控制的差。2 Introduction to Modern Control Theory现代控制理论导论Several factors provided the stimulus for the development of modern control theory(a) The necessity of dealing with more re
11、alistic models of systems.处理更加真实的系统模型的必要性。(b) The shift in emphasis towards optimal control and optimal system design.研究重点朝向最优控制和最优系统设计的转移。(c) The continuing developments in digital computer technology.数字计算机技术的不断发展。(d) The shortcomings of previous approaches.原有方法的短缺。(e) A recognition of the applicab
12、ility of well0known methods in other fields of knowledge。对二将熟知方法在其他知识领域中应用的广泛认同。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
13、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.模型中必须包含众多的变量。其次，更为真实的模型往往具有非线性和时变参数。以前往往忽略的一些系统问题例如关联问题以及通过环境形成的反馈等，现在却需要考虑。With an advancing tec
14、hnological 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
15、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 dictat
16、es that nonlinear time-varying control laws be used, even if the basic system is linear and time-invariant.在不断发展先进的社会中，朝着更加宏伟目标的发展趋势是很明显的。这也就意味着要处理具有大量相互关联部件的复杂系统。对二更加精确和更加有效的需求已经改变了对控制系统性能要求的重点。以百分超调量、调节时间、带宽等来表示的经典技术指标已经在很多场合让位二最优性准则，例如最小能耗、最低成本和最短时间操作等。依据这些准则的最优化合得想要避免处理讨厌的非线性一中变得更为困难。即使基本受近期系统是线
17、性和时不变的，最优控制理论也经常规定要采用非线性、时变的控制规律。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
18、they were when the first of this book was written.计算机技术的不断发展，已经对控制领域产生了三个方面的主要影响。影响之一与超大规模的巨型机有关。现在能够进行建模、分析和控制研究的问题的规模和困难级别都已经大大超过了本书第一版时的情况。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 co
19、ntrol 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
20、 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 diff
21、erential equations directly.计算机技术的第二个影响与微型机在数量上的激增以及其在家庭、工作声所随处可用的便利性紧密相关。经典控制理论中图解方法占主导地位，这是因为当时图解是解决某些问题的唯一方法。现在每一个控制工程设计人员都很容易获得功能强大的计算机软件包，用于进行系统的分析和设计工作。老的图解方法并没有消亡，不过已经能够自动进行工作了。它们之所以仍然存在的原因是其所有的直观性和指导性。然而，一些完全不同的技术经常对计算机更加适合。尽管计算机可用于执行经典的变换反变换运算，然而用计算机对微分方程直接进行积分则往往更加有效。The third major impact
22、 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 th
23、e past.第三方面计算机的影响来自于如今计算机就像在控制系统中其他常规元件应用得一样普及。计算机在成本、规模和可靠性方面的优势使其能够理普遍地应用于很多系统中。这就意味着离散时间和数字式的控制系统现在应该受到远胜于以往的重视。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 wi
24、th a computer. Computers are a major reason for the existence of state variable methods.现代控制理论特别适应于上述的发展趋势。这是因为时间域技术及其数学表达语言（例如矩阵、线性向量空间等）在计算机上应用是非常理想的。计算机的发展也是状态变量方法之所以会产生的一个主要原因。Most classical control techniques were developed of linear constant coefficient systems with one input and one output(pe
25、rhaps 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
26、 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
27、 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.大多数经典控制技术都是带有一个输入、一个输出（也许可有数个输入和输出）的线性、常系数系统而发展起来的。经典技术的表述语言是拉普拉斯或Z变换以及传递函数。一旦出现非线性和时变性，经典技术最根本的基础就不复存在了。诸如相平面方法、
28、描述函数法和其他有关方法这样一些很成功的技术能够得以发展的原因就是为了弥补这一短处。然而经典控制理论最大的成功也是局限于低阶系统中。现代控制理论的状态变量法提供了一种统一、高效的方法来描述具有任意阶次、线性或非线性、时变或常系数的各种系统。它也为计算机处理提供了一种理想的表示方法，并引起了许多方面最优化理论的进展。Modern control theory is a recent development in the field of control. Therefore, the name is justified at least as a descriptive title. Howev
29、er, 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
30、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 g
31、enerality of the results, and the economy of thought that linear algebra provides. 现代控制理论是在控制领域中的新发展。因此，可以说它是名副其实。然而，现代控制理论的基础却应该在其他一些发展成熟的领域中寻找。以状态变量形式来表示一个系统的方法完全等价于在哈密尔顿力学中采用通用坐标和通用动量的方法。这种方法的优越性在经典物理学中多年来已经众所周知。当处理各种联立方程时采用矩阵的好处在应用数学领域中也已久为人知。线性代数对现代控制理论的发展更是功不可没。其原因在于线性代数所提供的简洁的表达、通用的结果以及高效的思路。
32、 6.2 反馈系统.Feedback Control（反馈控制）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.
33、 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.这里所研究的这一类控制问题，在工程
34、上具有相当重要的意义。我们所讨论的系统有几个输入，其中某些输入称为控制量，因为这些量是可以人为地控制的，而另一些输入称为外部扰动，它们是很难预知的。例如在工业用加热炉中，可以认为燃料流量、环境温度以及炉内材料装填量都是输入量，其中燃料流量是容易测量和容易控制的，但后面两项通常是不能预知的扰动。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 exter
35、nal 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 t
36、he system state.在这些情况下，控制问题的一个方面在于确定如何处理控制量以便抵消外部扰动对系统状态的影响。解决这个问题的一种可能的方法是不断地测量扰动量，根据该测量值和已知的系统方程式，定出应有的控制输入量（用时间函数表示），以便对系统状态进行合适的控制。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
37、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 rep
38、resenting these two basic strategies of control are shown in Fig.1.另一种不同的方法是组成反馈系统，即不是直接测量扰动量，然后从模型或系统方程组去计算扰动对系统的影响。而是将系统状态的直接的连续的测量值与表示其“希望值”信号相比较，由此产生一个误差信号，再利用误差信号产生系统的输入，而该输入又使误差尽可能的接近于零。这两种基本控制系统结构如图1所示。By some abuse of terminology, the former approach has come to be known as open-loop control
39、, 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 be
40、fore corrective inputs can be computed and applied.由于术语上的某些习惯，前一种方法已被称为开环控制，而后者被称为闭环控制。初看起来这两种方法可能在本质上是等效的。确实，人们可能这样推测：开环控制的方式更好些，因为在扰动引起系统状态发生不希望的变化之前，校正输入早已算好并已加到系统中去了。However, this advantage is more than outweighed by the disadvantages of open-loop control and the inherent advantages of feedback
41、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 f
42、ar 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，这一优点比不上开环控制的缺点和反馈系统的固有优点。首先，在许多
43、情况下，实现上面所提到的开环控制需要一台非常完善的（因而很费钱的）计算装置，以便用它算出抵消预估扰动影响所需的输入量。其次，反馈系统对其数学模型的精度并不很敏感。换句话说，一个合理设计的反馈系统，即使系统内部的特性有相当大的变化，系统仍能满意地工作。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,
44、 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
45、 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 mutu
46、ally 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.反馈方法的另一个主要优点是用一个“反馈回路”来包围原来特性不满意的系统，在许多情况下，人们可能由此而组成一个性能较满意的系
47、统。例如，研究一个垂直飞行的火箭。火箭实质上是一个倒置的摆，由发动机喷出的气流平衡，它本身是不稳定的（只要火箭的中心线与垂直方向有一点偏离，就会使火箭倾倒）。可是，依靠在万向架上转动火箭的发动机，从而合理地改变排气气流的方向，就能保持火箭稳定的垂直飞行。实现改变气流方向的唯一满意的方法就是采用反馈；不断地测出火箭在两个相互垂直平面中运动的角度，使控制器适当地调整火箭发动机的方向。实际上，采用开环控制方法是不可能使原来不稳定的系统变得稳定的。The mathematical tools required for the analysis and design of feedback system
48、s differ according to the structural complexity of the systems to be controlled and according to the objectives the feedback control is meant to achieve.按照控制系统的结构复杂程序和控制对象的不同，分析和设计反馈系统所需要的数学工具是不同的。In the simplest situation, one controls a single plant state variable, called the output, by means of a
49、djustments 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.在最简单的情况下，可以用调节一个对象输入量来控制一个对象状态变量（称为输出）。这时要设计一个包围系统的反馈回路，保证输出以某种能被接受的精度响应特定的时间函数或特定的轨迹，此时都要求瞬态响应不要太“激