机械控制理论基础知识培训教材.docx

Fundamentals of Mechanical Control Theory机械控制理论基础（Bilingual Course 双语教学）School of Mechanical Engineering机械工程学院Teaching Material: Linear Control System Analysis and Design Fourth Edition教材：线性控制系统分析与设计 第4版References 参考书目1. 杨叔子，机械工程控制基础，第四版，武汉，华中理工大学出版社 2. 绪方盛彦, 现代控制工程, 科学出版社，1978 3. 李友善, 自动控制原理(上册) , 国防工业出版社 4. 张伯鹏, 控制工程基础, 机械工业出版社 5. 阳含和, 机械控制工程(上册) , 机械工业出版社 6. 姚伯威, 控制工程基础, 电子科技大学出版社 7. 薛定宇, 控制系统计算机辅助设计MATLAB语言及应用, 清华大学出版社 Learning requirement 学习要求1. All exercises and experiment reports must be done in English, and all questions must be answered in English. 所有的作业和实验报告必须用英文完成，所有的问题必须用英文回答。2. must be present (must not be absent) 上课不能缺席3. taking notes：Dont merely copy the blackboard, trying to write down what you consider is important. 作笔记：不能仅仅抄黑板，而是要记下你认为重要的东西。4. preview 预习5. review 复习6. do exercises and experiments independently 独立完成作业和实验7. summarizing, concluding 总结，概括8. Dont read the book word by word, the emphases should be put on the understanding the concepts, terminologies as well as their logic relations. 不要一个单词一个单词地读书，应该将重点放在概念、术语以及它们之间的逻辑关系的理解上9. Daring to put forward questions. 勇于提出问题10. If you have any question, please contact me. 如果你有什么问题，请联系我Final examination result 考试成绩评定1. Daily behaves: 30%. Including: present, exercises, experiments.平时成绩占30%，包括：到课率，作业，实验2. Final examination: 70%. 考试成绩占70%Well, we will get to business（言归正传）, well begin the first chapter.CHAPTER 1 INTRODUCTION 第一章 绪论1.1 INTRODUCTION 引言1.2 INTRODUCTION TO CONTROL SYSTEMS 控制系统引言1.3 DEFINITIONS 定义1.4 HISTORICAL BACKGROUND 历史背景1.5 DIGITAL CONTROL DEVELOPMENT 数字控制的发展1.6 MATHEMATICAL BACKGROUND 数学背景（基础）1.7 GENERAL NATURE OF THE ENGINEERING CONTROL PROBLEM 工程控制问题的一般特点1.8 COMPUTER LITERACY 计算机文化1.9 OUTLINE OF TEXT 全文概括1.1 Introduction 引言With the rapidly development of the modern science and technologies, man created many miracles. One of them is the invention of automatic control equipments. Today, we cant live on without the help of these auto-machines. 随着现代科技的迅速发展，人类创造了很多奇迹。其中之一就是自动控制设备。今天，如果没有这些自动机器的帮助，我们几乎无法生存。Automatic control systems permeate (渗透) life in all advanced societies today.现在，自动控制系统技术已经渗透到所有的高级社会生活。produce goods required by an increasing world population制造满足日益增长的人口需求的商品travel to the moon and explore outer space到月球旅行和探索外层空间space vehicles, the space shuttle, space stations飞船、航天飞机、空间站 reconfigurable flight control systems 重组的飞行控制系统1.2 Introduction to control systems 控制系统引言There are many equipments with control systems in our daily lives, such as: 我们的日常生活中有很多带控制系统的设备，例如： Refrigerators冰箱Robots机器人air-conditioner空调auto-washers 全自动洗衣机elevators电梯pilotless aircraft无人驾驶飞机men 人类Example: toaster 例子：烤箱input: timer 输入：时间output: degree of darkness and crispness 输出：面包的黑度和松脆程度The output quantity has no influence on the input quantity, there is no feedback in this system. 输出量对输入量没有影响，系统中不存在反馈。马达速度电枢电压磁场电流激磁电压源电枢电压源电压选择器直流马达期望的面包黑度设定Example: DC shunt motor 例子：直流并励马达input: armature voltage 输入：电枢电压output: speed of the shaft 输出：轴的转速DC: Direct Current 直流AC: Alternating Current 交流open-loop control systems: Systems in which the output quantity has no effect upon the input quantity开环控制系统：输出量不影响输入量的系统functional block diagram: 功能框图输出输入参考动态单元参考选择器输入指令command input: desired darkness of the toast or the desired speed of the motor 指令输入：（面包的）期望黑度或者电动机的期望转速reference-selector block: selection of the value of time on the toaster timer or the value of voltage applied to the motor armature 参考选择器框：烤箱上定时器的时间值或电枢两端外加电压值的选择reference input: output of the reference-selector block 参考输入：参考选择器框的输出dynamic unit: the unit which the reference input is applied to 动态单元：参考输入应用的单元desired output: output of the dynamic unit 期望输出：动态单元的输出closed-loop control systems: Systems in which the output has a direct effect upon the input quantity闭环控制系统：输出影响到输入的系统。functional block diagram of a single-input single-output (SISO):指令输入参考选择器参考输入激励信号前向元件反馈信号反馈元件系统动态部分输出单输入单输出系统的功能框图：characteristic: the output is fed back and is compared with the input 特性：输出是反馈并与输入比较comparison unit: performs comparison between the reference input and the feedback signal and results in an actuating signal 比较单元：执行参考输入与反馈信号之间的比较，并产生一个激励信号Example: home heating control system 家用取暖控制系统期望室内温度设定热空气排出口实际室内温度继电器恒温器炉子A bimetallic coil in the thermostat is affected by both the actual room temperature (output) and the reference-selector setting. 恒温器中的双金属片既受到实际室温（输出），又受到参考选择器设定的室温双重影响。Another example: Refer to Ch. material P1-14 其它的例子：见材料1141.3 Definitions 定义From the preceding discussion the following definitions are evolved, based in part on the standards of the IEEE, and are used in this text. 根据前面的讨论，引伸出了下列使用在本文中的定义，部分是基于IEEE标准1。IEEE: Institute for Electrical and Electronic Engineers 电气和电子工程师学会美System. A combination of components that act together to perform a function not possible with any of the individual parts. 系统 许多部件的组合，这些部件组合起来能完成一定的功能，而其中任何单独的部件不能完成此功能。Command input. The motivating input signal to the system, which is independent of the output of the system and exercises complete control over it (if the system is completely controllable). 指令输入 加到系统的激励输入信号，该信号与系统的输出无关，并且在整个过程中对系统进行全面控制(假设系统是完全可控的)。Reference selector(reference input element). The unit that establishes the value of the reference input. The reference selector is calibrated in terms of the desired value of the system output. 参考选择器(参考输入环节) 建立参考输入值的单元。根据系统输出的期望值对参考选择器进行设定。Reference input. The reference signal produced by the reference selector, i.e., the command expressed in a form directly usable by the system. It is the actual signal input to the control system. 参考输入 参考选择器产生的参考信号，即以系统能直接使用形式表示的指令，它是控制系统的实际输入信号。Disturbance input. A disturbance input signal to the system that has an unwanted effect on the system output. 干扰输入 系统的干扰输入信号对系统的输出产生一个不需要的影响。Forward element (system dynamics). The unit that reacts to an actuating signal to produce a desired output. This unit does the work of controlling the output and thus may be a power amplifier. 前向环节(系统动态环节) 它在激励信号作用下产生期望输出。该环节起控制输出的作用，因此它可能是一个功率放大器。Output (controlled variable). The quantity that must be maintained at a prescribed value, i.e., it must follow the command input without responding to disturbance inputs. 输出(被控变量) 这个量必须维持在所规定的值上，即跟随指令输入。Open-loop control system. A system in which the output has no effect upon the input signal. 开环控制系统 输出不影响输入的系统。Feedback element. The unit that provides the means for feeding back the output quantity, or a function of the output, in order to compare it with the reference input. 反馈环节 该环节将输出量或输出的函数反馈到输入端，使之与参考输入进行比较。Actuating signal. The signal that is the difference between the reference input and the feedback signal. It is the input to the control unit that causes the output to have the desired value. 激励信号 它是参考输入和反馈信号两者之差的信号。它激励控制环节，使输出达到期望值。Closed-loop control system . A system in which the output has an effect upon the input quantity in such a manner as to maintain the desired output value. 闭环控制系统 输出对输入有影响的系统，这种影响使输出维持期望值。The fundamental difference between the open- and closed-loop systems is the feedback action. 开环与闭环系统两者之间的主要区别是反馈作用Servomechanism (often abbreviated as servo). The term is often used to refer to a mechanical system in which the steady-state error is zero for a constant input signal. Sometimes, by generalization, it is used to refer to any feedback control system. 伺服机构 指的是在常值输入信号下稳态误差为零的机械系统。有时这一术语也可用于任何反馈控制系统。Regulator. This term is used to refer to systems in which there is a constant steady-state output for a constant signal. The name is derived from the early speed and voltage controls, called speed and voltage regulators. 调节器 指的是在常值输入信号下有常值稳态输出的系统。这名称是从早期的速度和电压控制系统引伸(也称速度和电压调节器)得来的。1.4 Historical background 历史背景汽车前进的实际方向（输出）汽车前进的规定方向（输入）A pictorial demonstration of an automobile as a feedback control system驾驶汽车作为反馈控制系统的图示配重Heroes device for opening temple doors. 打开庙门的古老装置James Watts flyball governor飞球调速器, 即蒸汽机离心调速器离心调速器的应用离心调速器的工作原理很简单，假定机器在平衡状态远行时突然加上负载，此时机器速度下降，调速器飞球的高度下降，通过杠杆的作用使蒸汽阀门(它在这里是执行器) 打开以使更多的蒸汽进入机器从而使速度大体上能复原。为了使阀门维持在这个新的开启状态，飞球张开的角度自然和原先(未加负载时)不同，这意味着在有负载时的速度实际不会完全和原先的速度相等，亦即负数的变动产生了转速误差。如果该误差在允许范围内，则上述控制已满足要求，若要求转速不因加上负载而变化，可以设法改变阀门的阀杆长度。后来的发明者设计了自动更新调整机构实现了转速恒定。load disturbance M rotated speed n centrifugal framework expansion sliding cover of comparing framework valve (through the level of the transition framework) steam quantity Q n (Ch1-9)负载扰动下降，则（轴）转速上升，离心力上升，炮弹击中飞机的实际位置提前角雷达天线雷达和计算机线路开火角功率放大器防空火炮反馈激励信号驱动马达Antiaircraft radar-tracking control system 防空雷达跟踪控制系统1868: J C Maxwell, On speed regulating machine, Proceeding of the Royal Society of Landon, Vol. 16 1868年，麦克斯韦尔，速度调节器（飞球控制器），英国皇家学会学报1884: E J Routh, Stability criterion of linear system 1884年，劳斯，线性系统的稳定性判据1923: Heaviside, arithmetic operators method 1923年：海维赛德，拉氏逆变换定理(海维赛德展开式)1930s: H Nyquist, Nyquist Stability criterion 19世纪30年代，奈奎斯特稳定性判据H W Bode, negative feedback amplifiers 波德，负反馈放大器1945: publication of servomechanism 伺服机构的出版1948: publication of Theory of controls 控制理论的出版1950: W R Evans, Root-Locus method 伊文斯根轨迹理论conventional control theory: developed through the late 1950s. Which is effectively applied to many control-design problems, especially to SISO systems. 经典控制理论：是20世纪50年代末以前出现的，已经有效地应用于许多控制设计问题中，特别是对于单输入单输出信号系统。modern control theory: developed for the design of more complicated systems and for multiple-input multiple-output (MIMO) systems 现代控制理论：为了设计更复杂的系统和多输入多输出系统而发展起来的控制理论。The development of control concepts in the engineering field has been extended to the realm of human and biomedical engineering. 控制概念已经从工程界延伸到人类和生物医学工程领域。1.5 Digital control development 数字控制的发展aerospace vehicles: 宇航飞行器control surfaces: 操纵面 stability augmentation system: 增稳系统, SAS control stick: 驾驶杆 airborne digital processors: 机载数字处理器 1.6 Mathematical Background 数学背景differential equations: a classical means, used in the solution of control systems in the early studies. The approach is tedious and does not readily indicate what changes should be made to improve system performance. 微分方程：一种经典方法，在早期研究中用于控制系统的求解。很烦琐，而且不能直接看出为了改善系统的性能应采取什么措施。Laplace transform: transforms differential equations to algebraic equations in order to simplify the above method. 拉普拉斯变换：将微分方程变换为代数方程，以便简化求解。Nyquists method: deals with the application of steady-state frequency-response techniques to feedback amplifier design, extended by Black, Bode, Hall, Harris, etc. 奈魁斯持方法，涉及到稳态频率响应计算法在反馈放大器设计中的应用。root-locus theory: presented by Evans, permits the graphical evaluation of both the time and the frequency response. 根轨迹理论：伊文斯提出，可以对时间和频率响应进行图解计算。Mathematical models: a set of mathematical equations describing a physical system. Once the Mathematical models are set up, the subsequent method of analysis is independent of the nature of the physical system; i.e., it does not matter whether the system is electrical, mechanical, or something else. This technique helps the designer to spot similarities based upon previous experience. 数学模型：用一组数学方程描述一个控制系统，一旦数学模型建立起来，后面的分析就与物理系统的结构特性无关，即不管系统是电的，机械的，或者其它什么系统。这种方法有助于设计人员根据以前的经验找出各系统之间的相似性。No single design method is intended to be used to the exclusion of the others. Depending upon the known factors and the simplicity or complexity of a control-system problem, a designer may use one method exclusively or a combination of methods. With experience in the design of feedback control systems comes the ability to use the advantages of each method. 每种方法的应该都不是绝对的。根据一个控制系统问题的已知因素和复杂程度，设计者可以只使用其中一种方法，或将几种方法结合起来使用。根据每个人在反馈控制设计中的经验，可以最大程度地利用各种方法的优点。1.7 General nature of the engineering control problem 工程控制问题的一般性质In general, a control problem can be divided into the following steps: 一般而言，一个控制问题可以分成如下步骤：1. A set of performance specifications is established. 建立一组性能指标。2. The performance specifications establish the control problem. 由于性能指标的原因而导致控制问题的存在。3. A set of differential equations that describe the physical system is formulated. 列出一组描述物理系统的微分方程式。4. The differential equations are solved by using conventional control theory aided by available or specially written computer programs. 借助于现成的或专门写出的计算机程序，使用经典控制理论的方法分析解决不同的问题1.8 Computer literacy 计算机文化（普及）FREQR: used for frequency domain analysis 频率域分析方法PARTL: used for partial-fraction expansion of transfer functions and for obtaining a time response 传递函数的部分分式展开和获得时间响应ROOTL: used for obtaining root-locus data and plots 用于获得根轨迹数据和图形MATLAB: MATrix LABoratory, which can be use for the analysis and design of control systems and for the simulink simulation 矩阵实验室，用于控制系统分析与设计及仿真模拟。1.9 Outline of text 全文概述The text is divided into three parts: 本文分为以下三个部分：PART1: Chap 24, provides the mathematical foundation for modeling physical systems and obtaining time solutions using classical or Laplace transform methods. 第1部分：24章，讨论物理系统建模的数学基础，使用经典的或拉氏变换方法获得时域解。PART2 : Chap515, represents material that is usually covered in control theory and control system design. 第2部分：515章，介绍有关控制系统理论与设计的一般方法。PART3: Chap1618, consists of advanced undergraduate or graduate topics. 第3部分：1618，本科毕业生或研究生提高用Appendix A: Table of Laplace transform pairs 附录A：拉氏变换对表。Appendix B: Interactive CAD programs附录B：CAD程序Well learn the following chapters: chap16, 89, 11 我们将学习以下章节：chap16, 89, 11Chap 2 Writing System Equation 系统方程的建立2.1 Introduction (Complementary: The principle of superposition about linear system) 引言（补充：线性系统的叠加原理）2.2 Electric circuits and components 电路及其元件2.5 Transfer function and block diagram传递函数和方框图2.6 Mechanical translation systems直线运动机械系统2.7 Analogous circuits模拟电路2.16 Summary 总结2.1 Introduction引言In order to research and analysis a system, it is necessary not only to know qualitatively the working principles and its characteristics, but also more important to quantitatively describe dynamic properties of the system, to reveal the relationship between the structure, parameters as well as dynamic properties of the system (Ch2-1). So an accurate mathematical model that describes a system completely must be determined in order to analyze a dynamic system.为了研究和分析一个系统，不仅要定性地了解其工作法则和特性，而且更重要的是定量地描述系统的动态特性，以揭示系统的结构、参数以及动态特性及其它们之间的关系。所以在分析动态系统之前，一定要确定完全能描述该系统的精确的数学模型。The differential equations of control systems describe the dynamic performances of the systems in time domain. We can get output response of the system by solving differential equations on given forces and initial conditions. 在时域内描述控制系统动态特性的是微分方程。我们可以根据激励（外力，输入）和初始条件解微分方程的方法获得系统的输出响应。linear differential equations with constant coefficients (linear constant-coefficient differential equations or linear time-invariant, LTI): the relationship between the system input and output is independent of time. 常系数线性微分方程（常系数线性或线性时不变微分方程）：系统输入与输出之间的关系与时间无关。This chapter presents methods for writing the differential and state equations for a variety of electrical, mechanical, thermal, and hydraulic systems. 这一章介绍对于各种电的、机械的、热的和液压的系统如何建立微分方程和状态方程的方法。The basic physical laws are given for each system, and the associated parameters are defined. 对于每个系统给出基本的物理定理，规定有关的参数。The result is a differential equation, or a set of differential equations, that describes the system. The equations derived are limited to linear systems or to systems that can be represented by linear equations over their useful operating range. 其结果就是一个微分方程或一组微分方程来描述该系统。这里所得出的方程仅限于线性系统或在它们整个工作范围内可以由线性方程描述的系统。block diagram: represents the flow of information and the functions performed by each component in the system. 方框图：描述系统中的信息流向和每个元件所起的作用。 Each function is represented by a block系统的每一部份功能均由一个方框表示 Each block is labeled with the name of the component 每一个方框上都注明了一个元件的名字 The blocks are appropriately interconnected by line segments with arrows (Arrows are used to show the direction of the flow of information.) 方框用带箭头的线段相连（箭头表示信息流动的方向）The use of a block diagram provides a simple means by which the functional relationship of the various components can be shown and reveals the operation of the system more readily than does observation of the physical system itself. 方框图的应用提供了一个简单的方法，通过这个方法可以说明各个部分功能之间的关系，用它来说明系统的工作情况比考察物理系统本身要容易得多。The simple functional block diagram shows clearly that apparently different physical systems can be analyzed by the same techniques. 从简单的函数方框图中可以清楚地看出，显然不同的物理系统可以用同样的方法进行分析。In general, variables that are functions of time are represented by lowercase letters. 通常，时间变量用小写字母表示。To simplify the writing of differential equations, the D operator notation is used. The symbols D and 1/D are defined by: 为了简化微分方程的书写，使用算子符号D。符号D和1/D分别定义如下： （2.1） （2.2）where Y0 represents the value of the integral at time t=0, that is, the initial value of the integral. 式中表示在时刻的积分值，即积分的初始值。The principle of superposition about linear system 线性叠加系统原理It is assumed that the differential equation describing the dynamic relationship between the input x(t) and the output y(t) is as following: 假设微分方程描述的系统输入x(t)和输出y(t)之间的动态关系如下： anDny(t)+an-1Dn-1y(t)+.+a1Dy(t)+a0y(t)=bmDmx(t)+.+b1Dx(t)+b0x(t)(1) If ai (i = 0,1,2,.,n) and bj (j = 0,1,2,.,m) are all constants, that is, they are not the functions as well as derivatives of y(t) and x(t), the equation is called linear time-invariant, the corresponding system is called linear time-invariant system. 如果ai (i = 0,1,2,.,n) 和 bj (j = 0,1,2,.,m)是常数，也就是说，他们与输入x(t)和输出y(t)的变化无关，该方程就称为线性时不变方程，相应的系统称为线性时不变系统。anDny(t)+an-1Dn-1y(t)+.+a1Dy(t)+a0y(t)=bmDmx(t)+.+b1Dx(t)