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.
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。
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.
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。
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. 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。
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，nd 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.
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。
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.
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。
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,
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。
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.
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。
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.
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。
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.
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。
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.
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。
If we examine the word control, we find several meanings given in dictionary, e.g. command, direct, govern, and regulate. Thus, a control system may be regarded as a group of physical components arranged to direct the flow of energy to a machine or process in such a manner as to achieve the desired performance.
The word automatic means self-moving or self-acting; thus an automatic control system is a self-acting control system.
如果查询单词控制，我们会在字典中找到一些意思：命令，执行，管理和规范。因此控制系统可以称为是一组物理器件组合在一起执行机械或者程序的能量流动，从而获得给定特性。
自动这个单词的意思是自运动，自动做，因此一个自动控制系统是自动做控制系统。
An important distinction applied to control systems, whether automatic or otherwise, is that between open-loop and closed-loop operation. Automatic control, including this distinction, can perhaps be best introduced by means of a simple example.
不管是自动还是其他种类，控制系统的一个重要区别是开环控制还是闭环控制。自动控制包涵这种区别可以通过一个简单的例子来做最好的介绍。
Assumed that the oven shown in Fig.8.1 is heated by an electric heater controlled by a switch that provides several levels of current to the heating element. The setting of the switch represents the input quantity since it activates the system to produce the output. The temperature of the oven is the output or controlled quantity. Since the current to the heater is the quantity being altered, we can think of it as manipulated quantity.
假设图中所示的炉被电热器加热，加热器由一个给加热元件提供几个档位电流的开关控制。开关的位置代表输入量因为他驱动系统从而产生输出。炉的温度是输出或者被控制量。由于加热器的电流是该变量，我们可以认为他是控制量。
For a given setting of the control switch the oven temperature will reach a value related to the heater current and heat losses through the oven walls. If the temperature is unsatisfactory, this fact by itself can in no way alter the input to the oven control. Thus it can be said that the output quantity has no effect on the input quantity. The control in this case is identified as an open-loop control system. If some condition such as the ambient temperature surrounding the oven should change, the oven temperature will also change. Thus the open-loop control system cannot correct for changes that disturb the controlled quantity.
对于一个给定的开关控制设置，炉的温度会达到一个与加热电流和通过炉壁损失的热量有关的值。如果温度不理想，这种情况下他自己无法改变输入来控制。因此这被称为输出量对输入量没有影响。这种控制被称为开环控制系统。如果一些情况，炉周围的环境温度改变，炉的温度也会改变。因此开环控制系统不能校正由于干扰产生改变的被控量。
A human being can be added to the system for the purpose of maintaining the oven temperature at a desired value. This is shown in Fig.8.2. By observing a thermometer within the over, the person could alter the position of the control switch to more nearly achieve the required temperature. It is important to note that the addition of the human operator has provided a means by which the output is fed back and compared with the desired value. Actual control of the heating element depends on the error or deference between the desired and actual temperatures. Any necessary change is made in the direction of reducing this error. For example, if the temperature were low, the heater current would be increased to provide more heat.
人可以被添加到系统中从而达到维持炉温在期望值的目的。图所示通过观察炉里的温度计人可以改变控制开关的位置从而更接近的获得需要温度。特别强调的是，人的参与提供了一种输出量反馈到输入并与期望值相比较的方法。实际控制加热元件依靠期望温度和实际温度之间的差异。指挥中通过任何必要的改变来减少误差。例如，如果温度降低，加热电流就要增加来提供更多的热量。
Systems in which the output has an effect upon the input are called closed-loop control systems or, more commonly, feedback controls systems. The feedback capture of the system in Fig.8.2 may be seen by tracing the closed-loop. The function of comparing the actual temperature with the desired value is performed in the mind of the operator, and the command is executed by the response of his muscles. Even though close-loop control of the oven is established by the operator, the results may be less then satisfactory. The temperature will cycle above and blew the desired value as the operator adjusts the switch even though the excursions would tend to decrease with operator experience. A change in the level of the power source or in the ambient temperature surrounding the oven would adversely affect the system‘s output. In addition, watching a thermometer and operating a switch would be a dull and time-consuming task. This arrangement could be described as a manual closed-loop control system.
输出对输入有影响的系统称之为闭环控制系统，或者更通俗的称为反馈控制系统。图中，通过跟踪闭环系统可以看到反馈的本质。比较实际温度和期望温度的功能是在操作者的大脑中完成的，命令通过他的肌肉执行。即使炉的闭环控制系统由人建立，结果可能并不理想，操作者调整开关即使偏差会趋于减小随着操作者的经验，温度仍然会在期望值上下浮动。电源电平的改变或是炉周围环境温度的改变，会不利的影响系统的输出，另外观察温度计和控制开关是一种枯燥又费时的任务，这个方案可以称为手动闭环控制系统。
To further improve performance and obtain more precise control, the human may be replaced by a mechanical, electrical, or other form of comparisons and control unit. Fig 8.3 shows, on the automatic basic, that is, without human intervention. The temperature is now measured by a thermocouple, a device that generates an electrical voltage proportional to temperature. This voltage is fed back and compared with a reference voltage that represents the desired temperature. The difference between the two voltages is amplified electronically and controls the current to the heating element. Since the voltage feedback is subtracted from the reference voltage, it is known as a negative-feedback signal.
为了更加提高性能并且获得更加精确地控制，人可以被机械的、电气的或者其他形式比较和控制单元代替。图所示在自动的基础上即没有人的参与，温度由温度计测量，这个设备产生与温度成比例的电压，这个电压反馈到代表期望温度的参考电压并与之比较。这两个电压之差被电气放大，并且控制加热元件的电流由于电压反馈是从参考电压中减去的，它被称为是负反馈信号。
The example has illustrated how automatic closed-loop control is employed to perform a task more rapidly and consistently than can be accomplished by a human being. The use of negative feedback in a closed-loop control system tends to maintain a desired value of a quantity or condition by measuring the existing value, comparing it to the desired value, and using the difference as a means of initiating action to reduce the difference. The negative-feedback concept has become the foundation for automatic-control-system design. 这个例子说明了自动闭环控制可以比人参与完成的控制更快更稳定的完成一个任务。闭环控制系统中负反馈的应用趋向于维持一个量在期望值或是这样一个状态：通过测量实际值并与期望值相比较，然后用差别作为启动动作来减小差别。负反馈概念已经成为自动控制设计的基础。