现代控制工程(第五版) - Katsuhiko Ogata

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"现代控制工程，第五版，作者Katsuhiko Ogata，由Prentice Hall出版。本书涵盖了现代控制工程领域的核心概念和技术，适用于高等教育和专业工程实践。" 现代控制工程是自动化、电子工程和系统科学等领域的重要学科，它研究如何设计、分析和优化动态系统的性能。Katsuhiko Ogata的《现代控制工程》第五版是一部广泛使用的教材，旨在提供全面而深入的理论基础和实用方法。该书内容可能包括以下几个关键知识点： 1. **控制系统的基本概念**：书中会介绍控制系统的定义、分类（如开环与闭环系统、连续时间与离散时间系统）以及系统建模的基础知识。 2. **线性代数与矩阵理论**：控制工程中的许多分析和设计工具都基于线性代数，如状态空间模型、特征值分析等。 3. **传递函数和频率响应**：这是分析控制系统动态特性的重要工具，可以帮助理解系统的稳定性和响应速度。 4. **控制系统的稳定性**：包括劳斯-赫尔维茨稳定性判据、根轨迹法和奈奎斯特稳定性判据，这些都是评估系统是否稳定的关键方法。 5. **控制器设计**：包括PID控制器、状态反馈控制、最优控制等，这些设计方法能够改善系统的性能指标，如响应速度、超调量、稳态误差等。 6. **现代控制理论**：可能涉及李雅普诺夫稳定性理论、状态观测器设计、卡尔曼滤波器等高级主题，这些都是现代控制工程的重要组成部分。 7. **MATLAB在控制工程中的应用**：MATLAB是控制工程师常用的工具，用于建模、仿真和控制器设计。书中可能会包含如何使用MATLAB进行控制系统的分析和设计。 8. **数字控制与采样系统**：随着数字技术的发展，数字控制变得越来越重要。这部分可能涉及Z变换、离散时间系统的稳定性分析和数字控制器设计。 9. **非线性控制系统**：虽然本书主要关注线性系统，但可能会对非线性系统的基本概念和分析方法进行简要介绍。 10. **实际系统案例**：为了帮助读者将理论应用于实践，书中通常会包含各种工程应用实例，如航空航天、机械、电力系统等。通过深入学习《现代控制工程》，读者可以掌握控制工程的核心原理，并具备解决复杂控制系统问题的能力。这本书对于学生和专业工程师来说，是一本不可或缺的参考书。

Section 1–2 / Examples of Control Systems 5

Thermometer

Heater

Interface

Controller

InterfaceAmplifier

A/D

converter

Programmed

input

Electric

furnace

Relay

Figure 1–2

Temperature control

system.

to a digital temperature by an A/D converter. The digital temperature is fed to a con-

troller through an interface. This digital temperature is compared with the programmed

input temperature, and if there is any discrepancy (error), the controller sends out a sig-

nal to the heater, through an interface, amplifier, and relay, to bring the furnace tem-

perature to a desired value.

Business Systems. A business system may consist of many groups. Each task

assigned to a group will represent a dynamic element of the system. Feedback methods

of reporting the accomplishments of each group must be established in such a system for

proper operation. The cross-coupling between functional groups must be made a mini-

mum in order to reduce undesirable delay times in the system. The smaller this cross-

coupling, the smoother the flow of work signals and materials will be.

A business system is a closed-loop system.A good design will reduce the manageri-

al control required. Note that disturbances in this system are the lack of personnel or ma-

terials, interruption of communication, human errors, and the like.

The establishment of a well-founded estimating system based on statistics is manda-

tory to proper management. It is a well-known fact that the performance of such a system

can be improved by the use of lead time, or anticipation.

To apply control theory to improve the performance of such a system, we must rep-

resent the dynamic characteristic of the component groups of the system by a relative-

ly simple set of equations.

Although it is certainly a difficult problem to derive mathematical representations

of the component groups, the application of optimization techniques to business sys-

tems significantly improves the performance of the business system.

Consider, as an example, an engineering organizational system that is composed of

major groups such as management, research and development, preliminary design, ex-

periments, product design and drafting, fabrication and assembling, and tesing. These

groups are interconnected to make up the whole operation.

Such a system may be analyzed by reducing it to the most elementary set of com-

ponents necessary that can provide the analytical detail required and by representing the

dynamic characteristics of each component by a set of simple equations. (The dynamic

performance of such a system may be determined from the relation between progres-

sive accomplishment and time.)

6 Chapter 1 / Introduction to Control Systems

Required

product

Management

Research

and

development

Preliminary

design

Experiments

Product

design and

drafting

Fabrication

and

assembling

Testing

Product

Figure 1–3

Block diagram of an engineering organizational system.

A functional block diagram may be drawn by using blocks to represent the func-

tional activities and interconnecting signal lines to represent the information or

product output of the system operation. Figure 1–3 is a possible block diagram for

this system.

Robust Control System. The first step in the design of a control system is to

obtain a mathematical model of the plant or control object. In reality, any model of a

plant we want to control will include an error in the modeling process.That is, the actual

plant differs from the model to be used in the design of the control system.

To ensure the controller designed based on a model will work satisfactorily when

this controller is used with the actual plant, one reasonable approach is to assume

from the start that there is an uncertainty or error between the actual plant and its

mathematical model and include such uncertainty or error in the design process of the

control system. The control system designed based on this approach is called a robust

control system.

Suppose that the actual plant we want to control is (s) and the mathematical model

of the actual plant is G(s), that is,

(s)=actual plant model that has uncertainty ¢(s)

G(s)=nominal plant model to be used for designing the control system

(s) and G(s) may be related by a multiplicative factor such as

or an additive factor

or in other forms.

Since the exact description of the uncertainty or error ¢(s) is unknown, we use an

estimate of ¢(s) and use this estimate, W(s), in the design of the controller. W(s) is a

scalar transfer function such that

where is the maximum value of for and is called the H

infinity norm of W(s).

0  v  q冟W(jv)冟冟冟W(s)冟冟

冟冟¢(s)冟冟

6 冟冟W(s)冟冟

= max

0 v q

冟W(jv)冟

苲

(s) = G(s) +¢(s)

苲

(s) = G(s)[1 + ¢(s)]

苲

Section 1–3 / Closed-Loop Control versus Open-Loop Control 7

Using the small gain theorem, the design procedure here boils down to the deter-

mination of the controller K(s) such that the inequality

is satisfied, where G(s) is the transfer function of the model used in the design process,

K(s) is the transfer function of the controller, and W(s) is the chosen transfer function

to approximate ¢(s). In most practical cases, we must satisfy more than one such

inequality that involves G(s), K(s), and W(s)’s. For example, to guarantee robust sta-

bility and robust performance we may require two inequalities, such as

for robust stability

for robust performance

be satisfied. (These inequalities are derived in Section 10–9.) There are many different

such inequalities that need to be satisfied in many different robust control systems.

(Robust stability means that the controller K(s) guarantees internal stability of all

systems that belong to a group of systems that include the system with the actual plant.

Robust performance means the specified performance is satisfied in all systems that be-

long to the group.) In this book all the plants of control systems we discuss are assumed

to be known precisely, except the plants we discuss in Section 10–9 where an introduc-

tory aspect of robust control theory is presented.

1–3 CLOSED-LOOP CONTROL VERSUS OPEN-LOOP CONTROL

Feedback Control Systems. A system that maintains a prescribed relationship

between the output and the reference input by comparing them and using the difference

as a means of control is called a feedback control system. An example would be a room-

temperature control system. By measuring the actual room temperature and comparing

it with the reference temperature (desired temperature), the thermostat turns the heat-

ing or cooling equipment on or off in such a way as to ensure that the room tempera-

ture remains at a comfortable level regardless of outside conditions.

Feedback control systems are not limited to engineering but can be found in various

nonengineering fields as well. The human body, for instance, is a highly advanced feed-

back control system. Both body temperature and blood pressure are kept constant by

means of physiological feedback. In fact, feedback performs a vital function: It makes

the human body relatively insensitive to external disturbances, thus enabling it to func-

tion properly in a changing environment.

(s)

1 + K(s)G(s)

6 1

(s)K(s)G(s)

1 + K(s)G(s)

6 1

W(s)

1 + K(s)G(s)

6 1

8 Chapter 1 / Introduction to Control Systems

Closed-Loop Control Systems. Feedback control systems are often referred to

as closed-loop control systems. In practice, the terms feedback control and closed-loop

control are used interchangeably. In a closed-loop control system the actuating error

signal, which is the difference between the input signal and the feedback signal (which

may be the output signal itself or a function of the output signal and its derivatives

and/or integrals), is fed to the controller so as to reduce the error and bring the output

of the system to a desired value. The term closed-loop control always implies the use of

feedback control action in order to reduce system error.

Open-Loop Control Systems. Those systems in which the output has no effect

on the control action are called open-loop control systems. In other words, in an open-

loop control system the output is neither measured nor fed back for comparison with the

input. One practical example is a washing machine. Soaking, washing, and rinsing in the

washer operate on a time basis. The machine does not measure the output signal, that

is, the cleanliness of the clothes.

In any open-loop control system the output is not compared with the reference input.

Thus, to each reference input there corresponds a fixed operating condition; as a result,

the accuracy of the system depends on calibration. In the presence of disturbances, an

open-loop control system will not perform the desired task. Open-loop control can be

used, in practice, only if the relationship between the input and output is known and if

there are neither internal nor external disturbances. Clearly, such systems are not feed-

back control systems. Note that any control system that operates on a time basis is open

loop. For instance, traffic control by means of signals operated on a time basis is another

example of open-loop control.

Closed-Loop versus Open-Loop Control Systems. An advantage of the closed-

loop control system is the fact that the use of feedback makes the system response rela-

tively insensitive to external disturbances and internal variations in system parameters.

It is thus possible to use relatively inaccurate and inexpensive components to obtain the

accurate control of a given plant, whereas doing so is impossible in the open-loop case.

From the point of view of stability, the open-loop control system is easier to build be-

cause system stability is not a major problem. On the other hand, stability is a major

problem in the closed-loop control system, which may tend to overcorrect errors and

thereby can cause oscillations of constant or changing amplitude.

It should be emphasized that for systems in which the inputs are known ahead of

time and in which there are no disturbances it is advisable to use open-loop control.

Closed-loop control systems have advantages only when unpredictable disturbances

and/or unpredictable variations in system components are present. Note that the

output power rating partially determines the cost, weight, and size of a control system.

The number of components used in a closed-loop control system is more than that for

a corresponding open-loop control system. Thus, the closed-loop control system is

generally higher in cost and power.To decrease the required power of a system, open-

loop control may be used where applicable. A proper combination of open-loop and

closed-loop controls is usually less expensive and will give satisfactory overall system

performance.

Most analyses and designs of control systems presented in this book are concerned

with closed-loop control systems. Under certain circumstances (such as where no

disturbances exist or the output is hard to measure) open-loop control systems may be

desired. Therefore, it is worthwhile to summarize the advantages and disadvantages of

using open-loop control systems.

The major advantages of open-loop control systems are as follows:

1. Simple construction and ease of maintenance.

2. Less expensive than a corresponding closed-loop system.

3. There is no stability problem.

4. Convenient when output is hard to measure or measuring the output precisely is

economically not feasible. (For example, in the washer system, it would be quite ex-

pensive to provide a device to measure the quality of the washer’s output, clean-

liness of the clothes.)

The major disadvantages of open-loop control systems are as follows:

1. Disturbances and changes in calibration cause errors, and the output may be

different from what is desired.

2. To maintain the required quality in the output, recalibration is necessary from

time to time.

1–4 DESIGN AND COMPENSATION OF CONTROL SYSTEMS

This book discusses basic aspects of the design and compensation of control systems.

Compensation is the modification of the system dynamics to satisfy the given specifi-

cations.The approaches to control system design and compensation used in this book

are the root-locus approach, frequency-response approach, and the state-space ap-

proach. Such control systems design and compensation will be presented in Chapters

6, 7, 9 and 10. The PID-based compensational approach to control systems design is

given in Chapter 8.

In the actual design of a control system, whether to use an electronic, pneumatic, or

hydraulic compensator is a matter that must be decided partially based on the nature of

the controlled plant. For example, if the controlled plant involves flammable fluid, then

we have to choose pneumatic components (both a compensator and an actuator) to

avoid the possibility of sparks. If, however, no fire hazard exists, then electronic com-

pensators are most commonly used. (In fact, we often transform nonelectrical signals into

electrical signals because of the simplicity of transmission, increased accuracy, increased

reliability, ease of compensation, and the like.)

Performance Specifications. Control systems are designed to perform specific

tasks. The requirements imposed on the control system are usually spelled out as per-

formance specifications. The specifications may be given in terms of transient response

requirements (such as the maximum overshoot and settling time in step response) and

of steady-state requirements (such as steady-state error in following ramp input) or may

be given in frequency-response terms. The specifications of a control system must be

given before the design process begins.

For routine design problems, the performance specifications (which relate to accura-

cy, relative stability, and speed of response) may be given in terms of precise numerical

values. In other cases they may be given partially in terms of precise numerical values and

Section 1–4 / Design and Compensation of Control Systems 9

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现代控制工程(第五版) - Katsuhiko Ogata

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如何使用MATLAB软件模拟自动控制系统并验证其稳定性和性能？请结合'Ogata的现代控制工程第五版'中的理论知识。

设计自动控制系统时，如何运用MATLAB软件模拟系统稳定性和性能？结合'Ogata的现代控制工程第五版'中的理论。

在设计一个自动控制系统时，如何通过MATLAB软件来模拟并验证系统的稳定性和性能？请结合'Ogata的现代控制工程第五版'中的理论知识。

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