控制系统的介绍英文翻译

Introduction to Control System

1. 1 HISTORICAL PERSPECTIVE

The desire to control the forces of nature has been with man since early civilizations. Although many examples of control systems existed in early times, it was not until the mid-eighteenth century that several steam engine, and perhaps the most noteworthy invention was the speed control flyball governor invented by James Watt.

The period biginnign about twenty-five years before World War Two saw rapid advances in electronics and especially in circuit theory, aided by the now classical work of Nyquist in the area of stability theory, The requirements of sophisticated weapon systems, submarines, aircraft and the like gave new impetus to the work in control systems before and after the war The advent of the analog computer coupled with advances in electronics saw the beginning of the establishment of control systems as a science. By The mid-fifties, the progress in digital computers had given the engineers a new tool that greatly enhanced their capability to study large and complex systems. The availability of computers also opened the era of data-logging, computer control, and the state space of modern method of analysis.

The sputnik began the space race and large governmental expenditures in the space as well as military effort. During this time. circuits became miniaturized and large sophisticated systems could be put together very compactly thereby allowing a computational and control advantage coupled with systems of small physical dimensions. We were now capable of designing and flying minicomputers and landing men on the moon. The post sputnik age saw much effort in system optimization and adaptive systems.

Finally, the refinement of the chip and related computer development has created an explosion in computational capability and computer-controlled devices. This has led to many innovative methods in manufacturing methods. such as computer-aided design and manufacturing, and the possibility of unprecedented increases in

industrial productivity via the use of computer-controlled machinery, manipulators and robotics.

Today control systems is a science with the art still playing an important role. Much mathematical sophistication has been achieved with considerable interest in optimal control system. The modern approach, having been established as a science, is being applied not only to the traditional control systems, but to newer problems like urban analysis, econometrics, transportation, biomedical problems, energy analysis, and a host of similar problems that affect modern man.

1.2 BIASIC CONCEPTS

Control system analysis is concerned with the study of the behavior of dynamic systems. The analysis relies upon the fundamentals of system theory where the governing differential equations assume a cause-effect relationship. A physical system may be represented as shown in Fig. where the excitation or input is x(t) and the response or output is y(t) . A simple control system is shown in Fig. Here the output is compared to the input signal, and the difference of these two signals becomes the excitation to the physical system, and we speak of the control system , such as described in Fig . involves the obtaining of y(t) given the input and output are specified and we wish to design the system characteristics, then this is known as synthesis.

1.3 SYSTEMS DESCRIPTION

Because control systems occur so frequently in our lives, their study is quite important. Generally, a control system is composed of several subsystems connected in such a way as to yield the proper cause-effect relationship. Since the various subsystems can be electrical, mechanical, pneumatic, biological, etc., the complete description of the entire system requires the understanding of fundamental relationships in many different disciplines. Fortunately, the similarity in the dynamic behavior of different physical systems makes this task easier and more interesting.

As an example of a control system consider the simplified version of the attitude control of a spacecraft illustrated in Fig.1-4. We wish the satellite to have some specific attitude relative to an inertial coordinate

system. The actual attitude is measured by an attitude sensor on board the satellite. If the desired and actual attitudes are not the same, then the comparator sends a signal to the valves which open and cause gas jet firings. These jet firings give the necessary corrective signal to the satellite dynamics thereby it under control .A control system represented this way is said to be represented by block diagrams. Such a representation is helpful in the partitioning of a large system into subsystems and thereby allowing the study of one subsystem at a time. If we have many inputs and outputs that are monitored and controlled, the block diagram appears as illustrated in Fig.1-5. Systems where several variables are monitored and controlled are called multivariable systems. Examples of multivariable systems are found in chemical processing, guidance and control of vehicles, the national economy, urban problems. The number of control systems that surround us is indeed very large. The essential feature of all these systems is in general the same . They all have input ,control ,output, and disturbance variables. They all describe a controller and a plant . They all have some type of a comparator. Finally, in all cases we want to drive the control system to follow a set preconceived commands.

1.4 DESIGN, MODELING ,AND ANALYSIS

Prior to the building of a piece of hardware, a system must be designed, modeled, and analyzed. Actually the analysis is an important and essential feature of the design process. In general, when we design a control system we do so conceptually. Then we generate a mathematical model which is analyzed. The results of this analysis are compared to the performance specifications that are design a control system we do so conceptually. Then we generate a mathematical model which is analysis are compared to the performance specifications that are desired of the proposed system. The accuracy of the results depends upon the quality of the original model of the proposed design. We shall show , in Chapter7, how it is analyzed and then modified so that its performance satisfies the system specifications. The objective then may be considered to be the prediction , prior to construction, of the dynamic behavior that a physical system exhibits, i.e. its natural motion when disturbed from an

equilibrium position and its response when excited by external stimuli. Specifically we are concerned with the speed of response or transient response , and the stability we mean that the output remains within certain reasonable limiting values .The relative weight given to any special requirement is dependent upon the specific application . [2] For example, the air conditioning of the interior of a building may be maintained to +/-1°C and satisfy the occupants. However, the temperature control in certain cryogenic systems requires that the temperature be controlled to within a fraction of a degree. The requirements of speed , accuracy, and stability are quit often contradictory and some compromises must be made . For example, increasing the accuracy generally makes for poor transient response. If the damping is decreased, the system oscillations increase and it may take a long time to reach some steady state value.

It is important to remember that all real control systems are nonlinear; however , many can be approximated within a useful though limited range as linear systems. Generally, this is an acceptable first approximation. A very important benefit to be derived by assuming linearity is that the superposition theorem applies. If we obtain the response due to two different inputs, then the response due to the combined input is equal to the sum of the individual response due to the combined input is equal to the individual responses. Another benefit is that operational mathematics can be used in the analysis of linear systems. The operational method allows us to transform ordinary differential equations which are much simpler to handle.

Traditionally, control system were represented by higher-order linear differential equations and the techniques of operational mathematics were employed to study these equations. Such an approach is referred to as the classical method and is particularly useful for analyzing systems characterized by a single input and a single output. As systems began to become more complex , it became increasingly necessary to use a digital Computer . The work on a computer can be advantageously carried out if the system under consideration is represented by a set of first-order differential equations and the analysis is carried out via matrix theory.

This is in essence what is referred to as the state space or state variable approach . This method , although applicable to single input-output systems , finds important applications in the multivariable system . Another very attractive benefit is that it enables the control system engineer to study variables inside a system.

Regardless of the approach used in the design and analysis of a control system , we must at least following steps:

(1) Postulate a control system and the system specifications to be

satisfied.

(2) Generate a functional block diagram and obtain a mathematical

representation of the system .

(3) Analyze the system using any of the analytical or graphical

methods applicable to the problem.

(4) Check the performance (speed , accuracy, stability, or other

eriterion) to see if the problem.

(5) Finally, optimize the system parameters so that (1) is satisfied.

控制系统的介绍

1. 历史回顾

早在人类历史文明出现之初，人们就产生了控制自然力的愿望。尽管历史上出现过许多控制系统的实例，但是直到18世纪中叶才出现一些蒸汽驱动的控制装置。这就是所谓的蒸汽机时代，其中最著名的发明要数瓦特的飞球调速器。

20世纪初，关于控制系统的大部分研究工作都和发电，化工等行业有关，而且关于飞机自动驾驶仪的设想也是在这一时期初形成的 。

从二战前的25年开始，电子学特别是电路理论发展迅速。这也得益于奈魁斯特关于稳定性理论方面的研究工作，这一理论到现在也还是经典性上午。战前和战后对尖端试器系统，潜艇。飞行器等方面的需求是对控制系统研究工作强有力的刺激因素。模拟计算机的出现加上电子学的进展奠定了控制系统作为一门科学的基础。到了50年代中期，数字计算机的发展为工程师们提供了一个新的工具，这就大大地加强了他们从事大型和复杂系统的研究能力。计算机的使用开辟了数据采集，计算机控制，状态空间法等现代分析方法的新纪元。

苏联发射的人造地球卫星开始了空间技术上的竞争以及政府在空间技术和军事项目上的大量投资。这期间电路实现了小型化，又大又复杂的系统可以紧凑地放在一起，因此使得计算和控制上的强大优势和物理尺寸小的系统可以相互匹配。现在我们已经可以设计飞行用的小型计算机，使人类降落在月球上。人造地球卫星时代的后期，在系统最优化和自适应系统方面也做了不少努力。

最后，芯片集成度的提高及相关的计算机的开发引起了计算机能力和计算机器件的大爆炸。其结果是出现了许多新的制造方法，如计算机辅助设计和计算机辅助制造，而且计算机控制的机器，机械手和机器人带来了生产率空前提高。

今天，虽然生产工艺仍然起着重要作用，但控制系统已成为一门科学。由于对研究最优控制的浓厚兴趣引起了数学上的发展。已经作为一门学科建立起来的现代控制论，不仅用于传统的控制系统，而且也用来解决许多新的

问题，如城市发展分析，计量经济学，交通，生物医学，能源分析及其他许多类似的，对现代人类有影响的问题。

2. 基本概念

控制系统分析要做的是研究动态系统的性能，这种分析的依据是系统理论中的基本原理，其中描述系统的微分方程都遵循因果关系。其中激励或输入为x （t ），响应或输出为y （t ）。一个简单的控制系统输出信号和输入信号相比较，两者之差成为物理系统的激励，我们称该系统具有反馈。这样一个系统，它的分析包括给定输入时求取y （t ），我们希望设计系统的特性。另一方面，如果给定输入和输出，我们希望设计系统特性，这就是所谓综合。 3. 系统描述

由于我们生活中经常碰到控制系统，因此对它们的研究相当重要。一般说来，一个控制系统是由几个子系统组合而成的，这些子系统互相联接在一起，从而产生一定的因果关系。各种各样的子系统可能是电气的，机械的，气动的，生物的等等，因此为了完整地描述整个系统，需要了解很多不同学科中的基本关系。所幸的是，不同物理系统的动态性能具有相似性，这就使得这一任务变得比较容易也比较有意思了。

作为控制系统的一个实例，考虑简化的空间飞行器的姿态角控制。我们希望卫星相对某个惯性坐标系具有指定的姿态角，实际的状态角由卫星上的一个姿态角传感器测量。如果期待的姿态角和实际的姿态角不一致，则比较器送出一个信号给阀门，阀门打开使燃气喷出并点火。这些喷射出的火焰为卫星的动态提供必要的纠正信号，从而使卫星处于被控制之中。用这种方法有利于把一个大系统分解成若干个子系统，所以我们一次可以只研究一个子系统。

如果有多个输入和输出需要监控，则方框图就像所示的样子，多个变量要监控的系统称为多变量系统。在化工过程，运载器的导引和控制，国民经济，城市住增长模式，邮政服务以及很多其他的社会和城市问题中都有多变量系统的例子。

我们周围控制系统的数量是很多，这些系统的基本特征总的说来是一样的。它们都有输入，控制，输出和干扰对象；它们都可以描述成一个控制器加上一个被控对象；它们都有某种类型的比较器。最后，在所有情况下，我们都希望控制系统服从一组事先规定的指令。

1．4 设计，建模及分析

一个系统在硬件制造以前必须经过设计，建模和分析。实际上，分析是

设计过程中重要而关键的一部分。一般来说，当我们开始设计一个控制系统时，所做的只是初步构思，然后产生一个用于分析数学模型。分析的结果与将来系统应该具有的性能指标进行比较，结论的精确度取决于用于设计的原始模型的质量。后面第7章里，我们将阐述怎样分析一个初步设计，然后修改，从而使其性能满足系统的指标。在建造系统以前，还要考虑的一件事是预测一个物理系统会呈现的动态性能，即系统受干扰后偏离平衡状态的自由运动以及受外部刺激后产生的响应。我们特别关心响应的速度即瞬态响应，响应的精度即稳态响应以及稳定性等等。所谓稳定性是指输出始终保持在某一合理的范围内。每一项专门要求所占的权重取决于具体应用情况。例如，某一建筑物内使用的空调只要维持+/—0。1度就可以令使用者满意；但某种低温系统中的温度控制则要求把温度控制在几分之一度之内。对速度，精度及稳定性的要求常常是互相矛盾的，必须做出某些折中。例如，提高精度常常使瞬态响应变差。如果减小阻尼则会加剧系统振荡，这就使系统需要较长时间才会达到某个稳态值。 别忘了，所有实际系统中都有非线性，但是许多系统在有限而适用的范围内都可以近似为一个线性系统，这是很重要的。一般说来，这是一个初步的可以接受的近似。在推导中有了这种假设最大的好处是可以应用叠加原理。如果我们得到两个不同输入引起的响应，则两个输入合成的响应就等于它们单独响应之和。另一个好处是在线性系统分析中可以应用算子法。算子法可以使我们把原始微分方程化为代数方程，这样处理起来就简单多了。

控制系统通常用高阶线性微分方程来描述，用算子法来研究这些方程。这种方法称为经典方法，用它来分析单输入单输出系统特别有效。当系统变的越来越复杂时，使用数字计算机就显得非常必要了。如果被研究的系统用一组一阶微分方程组来描述，并用矩阵理论来分析，则在计算机上就很容易完成这一任务。这实际上是所谓的状态或状态变量法。这种方法虽然也能用于单输入单输出系统，更重要的是用于多变量系统。这种方法的另一个诱人之处是它使控制系统工程师可以研究系统内部的变量。

不管在控制系统的设计和分析中用什么方法，我们至少要遵循下列步骤：

（1） 以一个控制系统为出发点，阐明该系统要满足的指标。

（2） 产生一个方块图，获取该系统的一种数学描述。

（3） 用解析法或图解法中任何一种可行的方法分析该系统。

（4） 检查其性能（速度、精度、稳定性，及其他准则）是否满足指标。 最后，优化系统参数，满足（1）的要求。