Chapter 1
FOUNDATION OF MODERN CONTROL THEORY
Introduction to Control Systems
第一章 现代控制理论的基础 控制系统简介

In this chapter, the development history of control systems is first reviewed. Then the basic difference between conventional control theory and modern control theory is represented, and some basic terminologies are defined. Subsequently, the design of control system is briefly explained that encompasses conventional control approach and modern control approach. The iterative nature of design allows us to seek satisfied performance specifications by means of educated trial-and-error repetition. Finally, the future evolution of control systems is introduced.
本章首先回顾了控制系统的发展历史。然后表示传统控制理论和现代控制理论之间的基本区别，并定义了一些基本术语。随后，简要解释了控制系统的设计，包括传统的控制方法和现代的控制方法。设计的迭代性质使我们能够通过有根据的试错重复来寻求满意的性能规格。最后，介绍了控制系统的未来发展。

$>$$>$>> Be able to recount a brief history of control systems and their role in society.
$>$$>$>> 能够简要讲述控制系统的历史及其在社会中的作用。
$>$$>$>> Understand the basic difference between modern control theory and conventional control theory.
$>$$>$>> 了解现代控制理论和传统控制理论之间的基本区别。
$>$$>$>> Be capable of discussing the future of controls in the context of their evolutionary pathways.
$>$$>$>> 能够在其进化途径的背景下讨论控制的未来。

Automatic control has played a vital role in the advance of engineering and science. In addition to its extreme importance in space-vehicle systems, missile-guidance systems, robotic systems, and the like, automatic control has become an important and integral part of modern manufacturing and industrial processes. For example, automatic control is essential in the numerical control of machine tools in the manufacturing industries, in the design of autopilot systems in the aerospace industries, and in the design of cars and trucks in the automobile industries. It is also essential in such industrial operations as controlling pressure, temperature, humidity, viscosity, and flow in the process industries.
自动控制在工程和科学的进步中发挥了至关重要的作用。除了在航天器系统、导弹制导系统、机器人系统等中极为重要之外，自动控制还已成为现代制造和工业流程中不可或缺的重要组成部分。例如，自动控制在制造业的机床数控、航空航天工业的自动驾驶系统设计以及汽车行业的汽车和卡车设计中是必不可少的。它在控制过程工业中的压力、温度、湿度、粘度和流量等工业作中也是必不可少的。

Since advances in the theory and practice of automatic control provide the means for attaining optimal performance of dynamic systems, improving productivity, relieving the drudgery of many routine repetitive manual operations, and more, most engineers and scientists must now have a good understanding of this field.
由于自动控制理论和实践的进步为实现动态系统的最佳性能、提高生产力、减轻许多常规重复手动作的苦差事等提供了手段，因此大多数工程师和科学家现在必须对这个领域有很好的了解。

An interesting history of early work on feedback control has been written by O. Mayr (1970), who traces the control of mechanisms to antiquity. Two of the earliest examples are the control of flow rate to regulate a water clock and the control of liquid level in a wine vessel, which is thereby kept full regardless of how many cups are dipped from it. The control of fluid-flow rate is reduced to the control of fluid level, since a small orifice will
O. Mayr （1970） 写了一段关于反馈控制的早期工作的有趣历史，他将机制的控制追溯到古代。最早的两个例子是控制流速以调节水钟和控制酒瓶中的液位，因此无论从中浸入多少杯子，酒杯都会保持满。流体流速的控制简化为液位的控制，因为小孔口将
produce constant flow if the pressure is constant，which is the case if the level of the liquid above the orifice is constant．The mechanism of the liquid－level control invented in antiquity and still used today（for example，in the water tank of the ordinary flush toilet）is the float valve．As the liquid level falls，so does the float，allowing the flow into the tank to increase；as the level rises，the flow is reduced and，if necessary，cut off．Fig．1． 1 shows how a float valve operates．Notice here that sensor and actuator are not separate devices but， instead，are contained in the carefully shaped float－and－supply－tube combination．
如果压力恒定，则产生恒定的流量，如果孔口上方的液位恒定，则会产生恒定的流量。古代发明并至今仍在使用的液位控制机制（例如，在普通冲水马桶的水箱中）是浮子，valve.As 液位下降，浮子也是如此，允许进入水箱的流量增加;随着液位的升高，流量减少，必要时会切断。图 1.1 显示浮球阀的工作原理请注意，传感器和执行器不是单独的设备，而是包含在精心设计的浮球和供气管组合中。

Fig．1．1 Early historical control of liquid level and flow
图 1.1 早期历史液位和流量控制
A more recent invention described by Mayr（1970）is a system，designed by Cornelis Drebbel in about 1620 ，to control the temperature of a furnace used to heat all incubator shown in Fig．1．2．The furnace consists of a box to contain the fire，with a flue at the top fitted with a damper．Inside the firebox is the double walled incubator box，the hollow walls of which are filled with water to transfer the heat evenly to the incubator．The temperature sensor is a glass vessel filled with alcohol and mercury and placed in the water jacket around the incubator box．As the fire heats the box and water，the alcohol expands
Mayr（1970）描述的一项较新的发明是 Cornelis Drebbel 在 1620 年左右设计的一种系统，用于控制用于加热所有培养箱的炉子的温度，如图 1.2 所示，炉子由一个装有火的盒子组成，顶部有一个装有阻尼器的烟道，火箱内部是双壁培养箱，其空心壁充满水，将热量均匀地传递到温度传感器是一个装满酒精和水银的玻璃容器，放置在培养箱周围的水套中，box.As 火加热盒子和水，酒精膨胀

Fig．1．2 Drebbel＇s incubator for hatching chicken eggs（Adapted from Mayr，1970）
图 1.2 用于孵化鸡蛋的 Drebbel 孵化器（改编自 Mayr，1970）
and the riser floats up, lowering the damper on the flue. If the box is too cold, the alcohol contracts, the damper is open, and the fire burns hotter. The desired temperature is set by the length of the riser, which sets the opening of the damper for a given expansion of the alcohol.
立管向上浮动，降低烟道上的阻尼器。如果盒子太冷，酒精会收缩，阻尼器会打开，火会燃烧得更热。所需的温度由冒口的长度设置，该冒口为酒精的给定膨胀设置阻尼器的开口。

A famous problem in the chronicles of control systems was the search for a means to control the rotation speed of a shaft. Much early work (Fuller, 1976) seems to have been motivated by the desire to automatically control the speed of the grinding stone in a winddriven flour mill. Of various methods attempted, the one with the most promise used a conical pendulum, or fly-ball governor, to measure the speed of the mill. The sails of the driving windmill were rolled up or let out with ropes and pulleys, much like a window shade, to maintain fixed speed. However, it was adaptation of these principles to the steam engine in the laboratories of James Watt around 1788 that made the fly-ball governor famous. Fig. 1.3 shows a close-up of a fly-ball governor and a sketch of its components.
控制系统编年史中一个著名的问题是寻找一种控制轴转速的方法。许多早期工作（Fuller， 1976）似乎是出于在风力驱动面粉厂中自动控制磨石速度的愿望。在尝试过的各种方法中，最有希望的方法使用锥形摆或飞球调速器来测量磨机的速度。驱动风车的帆用绳索和滑轮卷起或放出，很像窗帘，以保持固定速度。然而，正是这些原理在 1788 年左右詹姆斯·瓦特 （James Watt） 实验室的蒸汽机中进行了改编，才使飞球调速器闻名遐迩。图 1.3 显示了飞球调速器的特写及其组件的草图。

Fig. 1. 3 Operating parts of fly-ball governor
图 1.3 飞球调速器的作部件
The action of the fly-ball governor (also called a centrifugal governor) is simple to describe. Suppose the engine is operating in equilibrium. Two weighted balls spinning around a central shaft can be seen to describe a cone of a given angle with the shaft. When a load is suddenly applied to the engine, its speed will slow, and the balls of the governor will drop to a smaller cone. Thus, the ball angle is used to sense the output speed. This action, through the levers, will open the main valve to the steam chest (which is the actuator) and admit more steam to the engine, restoring most of the lost speed. To hold the steam valve at a new position it is necessary for the fly-balls to rotate at a different angle,implying that the speed under load is not exactly the same as before. We saw this effect earlier with cruise control, where feedback control gave a very small error. To recover the exact same speed in the system, it would require resetting the desired speed setting by changing the length of the rod from the lever to the valve. Subsequent inventors
飞球调速器（也称为离心调速器）的动作很容易描述。假设发动机在平衡状态下运行。可以看到两个绕中心轴旋转的加重球描述了与轴成给定角度的圆锥体。当突然向发动机施加负载时，它的速度会减慢，调速器的球会下降到一个更小的锥体上。因此，球角用于感应输出速度。这个动作，通过杠杆，将打开蒸汽箱（即执行器）的主阀，并将更多的蒸汽引入发动机，恢复大部分损失的速度。为了将蒸汽阀保持在新位置，飞球必须以不同的角度旋转，这意味着负载下的速度与以前不完全相同。我们之前在巡航控制中看到了这种效果，其中反馈控制给出了一个非常小的误差。要在系统中恢复完全相同的速度，需要通过改变从杆到阀门的杆的长度来重置所需的速度设置。后来的发明者