Background of Control Theory(控制理论基础) 外文翻译

Background of Control Theory

System and Control Theory

According to the Encyclopedia Americana，a system is "an aggregation ox assemblage of things so combined by nature or man as to form an integral and complex whale". 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 faun of the constituent parts.

Control theory is mare often concerned with physical applications. A control system is considered to he any system which exists for the purpose or 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.

Fig. 37. 1 is a general representation of an open loop control system, the ingot or control u(t) is selected hayed 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，them the output will not behave precisely as expected.

Another general class of control systems is the closed-loop or f feedback control system，as illustrated in Fig. 37. 2, to 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 system's dynamic behavior. However，it need not be true that closed-look 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.

Introduction to Modern Control Theory

Several factors provided the stimulus for the development of modern control theory:

(a)The necessity of dealing with more realistic models of systems,

(b)The shift in emphasis towards optimal control and optimal system design.

(c)The continuing developments in digital computer technology.

(d)Tine shortcomings of previous approaches.

(e)A recognition of the applicability of well-known methods ire other fields of

knowledge.

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 model. Second，a mare realistic model is mare likely to captain

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.

With an advancing technological society，there is a trend towards more ambitious goals. This also means dealing with complex systems with a larger number of interacting 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, bandwidth, etc.,have in many cases given way to optimal criteria such as minimum energy，minimum cost，and minimum time operation. Optimization of these criteria makes it even more difficult to avoid dealing with unpleasant nonlinearities. Optimal control theory often dictates that nonlinear time-varying control laws he used, even if the basic system is linear and time-invariant.

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 hook was written.

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. Although a computer can he used to carry out the classical transform-inverse transform methods, it is usually more efficient for a computer to integrate differential equations directly,

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-time and

digital system control nor}r deserves much more attention than it did in the past. Modern control theory LS 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. Most classical control techniques were developed for 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 its optimization theory.

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 end generalized moments. The advantages of this approach have been well-known in classical physics for many years. The advantages of using matrices when deals with simultaneous equations of carious 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.

控制理论基础

系统及控制理论

按照美工大百科全书的解释，所谓系统就是指“一个各种物体的集合，格局其他性质或人的愿望而结合起来以致形成一个集中、复杂的整体”。数学中的系统理论，就是对这种由若干“物体”过程的集合，当其受到某些条件和输入作用的影响后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的一个事实：系统理论更关心物体组成的部件的数学性质而不是其物理形式。

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，资金等等物理量的流动。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，期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理论包括所有系统设计和分析问题有关的内容。

图３７.１是对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得的知识而选定的。输入变量绝不会受到ｙ（ｔ）所表示的系统输出变量的影响。如果有不期望的扰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。

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。

闭环控制系统中，控制作用ｕ（ｔ）被以某种方式由于系统输出行为的信息所校正。一个反馈系统经常能更好的应付不期望的扰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扰动无关紧要时，闭环控制的性能就会比开环控制的差。

现代控制理论讨论

有几个因素激励了现代控制理论的发展：

（ａ）处理更加真实的系统模型的必要性。

（ｂ）研究重点向最优化控制和最优化系统设计的转移。

（ｃ）数字计算机技术的不断发展。

（ｄ）以前的办法的缺陷。

（ｅ）对于将熟知方法在其他知识领域中应用的广泛认同。

这种从简单、易用的近似模型到更加真实模型的转移产生了两个方面的影响：首先，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个时变参数。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反馈等，现在却需要考虑。在不断发展先进技术的社会中朝着更加宏伟目标的发展趋势是很明显的。这就意味着要处理具有大量相互关联部件的复杂系统。对于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、带宽等来表示的精雕技术指标已经在很多场合让位于最优性准则，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似的想要避免处理讨厌的非线性一事变得更为困难。即使基本受控系统式线性和时不变的，

最优化控制理论也经常规定要采用非线性，时变的控制规律。

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的第一版的情况。

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、工作场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，这是因为当时图解式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。他们之所以仍然存在的原因是其多具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。尽管计算机课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。

第三方面计算机的影响来自于如今计算机就想在控制系统中其他常规元件用于的一样普及。计算机在成本、规模和可靠性方面的优势使其能够更普遍的应用于很多系统中。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。

现代控制理论特别适应上述的发展趋势。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。

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、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个短处。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达方法，并引起了许多方面的最优化理论的进展。

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再其他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式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。