【文章內(nèi)容簡介】 In general, a control problem can be divided into the following steps: 一般而言，一個控制問題可以分成如下步驟：1. A set of performance specifications is established. 建立一組性能指標。2. The performance specifications establish the control problem. 由于性能指標的原因而導致控制問題的存在。3. A set of differential equations that describe the physical system is formulated. 列出一組描述物理系統(tǒng)的微分方程式。4. The differential equations are solved by using conventional control theory aided by available or specially written puter programs. 借助于現(xiàn)成的或?qū)ｉT寫出的計算機程序，使用經(jīng)典控制理論的方法分析解決不同的問題 Computer literacy 計算機文化（普及）FREQR: used for frequency domain analysis 頻率域分析方法PARTL: used for partialfraction expansion of transfer functions and for obtaining a time response 傳遞函數(shù)的部分分式展開和獲得時間響應(yīng)ROOTL: used for obtaining rootlocus data and plots 用于獲得根軌跡數(shù)據(jù)和圖形MATLAB: MATrix LABoratory, which can be use for the analysis and design of control systems and for the simulink simulation 矩陣實驗室，用于控制系統(tǒng)分析與設(shè)計及仿真模擬。 Outline of text 全文概述The text is divided into three parts: 本文分為以下三個部分：PART1: Chap 2~4, provides the mathematical foundation for modeling physical systems and obtaining time solutions using classical or Laplace transform methods. 第1部分：2~4章，討論物理系統(tǒng)建模的數(shù)學基礎(chǔ)，使用經(jīng)典的或拉氏變換方法獲得時域解。PART2 : Chap5~15, represents material that is usually covered in control theory and control system design. 第2部分：5~15章，介紹有關(guān)控制系統(tǒng)理論與設(shè)計的一般方法。PART3: Chap16~18, consists of advanced undergraduate or graduate topics. 第3部分：16~18，本科畢業(yè)生或研究生提高用Appendix A: Table of Laplace transform pairs 附錄A：拉氏變換對表。Appendix B: Interactive CAD programs附錄B：CAD程序We’ll learn the following chapters: chap1~6, 8 我們將學習以下章節(jié)：chap1~6, 8Chap 2 Writing System Equation 系統(tǒng)方程的建立 Introduction (Complementary: The principle of superposition about linear system) 引言（補充：線性系統(tǒng)的疊加原理） Electric circuits and ponents 電路及其元件 Transfer function and block diagram傳遞函數(shù)和方框圖 Mechanical translation systems直線運動機械系統(tǒng) Analogous circuits模擬電路 Summary 總結(jié) Introduction引言In order to research and analysis a system, it is necessary not only to know qualitatively the working principles and it’s 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 (Ch21). So an accurate mathematical model that describes a system pletely must be determined in order to analyze a dynamic system.為了研究和分析一個系統(tǒng)，不僅要定性地了解其工作法則和特性，而且更重要的是定量地描述系統(tǒng)的動態(tài)特性，以揭示系統(tǒng)的結(jié)構(gòu)、參數(shù)以及動態(tài)特性及其它們之間的關(guān)系。所以在分析動態(tài)系統(tǒng)之前，一定要確定完全能描述該系統(tǒng)的精確的數(shù)學模型。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. 在時域內(nèi)描述控制系統(tǒng)動態(tài)特性的是微分方程。我們可以根據(jù)激勵（外力，輸入）和初始條件解微分方程的方法獲得系統(tǒng)的輸出響應(yīng)。linear differential equations with constant coefficients (linear constantcoefficient differential equations or linear timeinvariant, LTI): the relationship between the system input and output is independent of time. 常系數(shù)線性微分方程（常系數(shù)線性或線性時不變微分方程）：系統(tǒng)輸入與輸出之間的關(guān)系與時間無關(guān)。This chapter presents methods for writing the differential and state equations for a variety of electrical, mechanical, thermal, and hydraulic systems. 這一章介紹對于各種電的、機械的、熱的和液壓的系統(tǒng)如何建立微分方程和狀態(tài)方程的方法。The basic physical laws are given for each system, and the associated parameters are defined. 對于每個系統(tǒng)給出基本的物理定理，規(guī)定有關(guān)的參數(shù)。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. 其結(jié)果就是一個微分方程或一組微分方程來描述該系統(tǒng)。這里所得出的方程僅限于線性系統(tǒng)或在它們整個工作范圍內(nèi)可以由線性方程描述的系統(tǒng)。block diagram: represents the flow of information and the functions performed by each ponent in the system. 方框圖：描述系統(tǒng)中的信息流向和每個元件所起的作用。 ? Each function is represented by a block系統(tǒng)的每一部份功能均由一個方框表示 ? Each block is labeled with the name of the ponent 每一個方框上都注明了一個元件的名字 ? The blocks are appropriately interconnected by line segments with arrows (Arrows are used to show the direction of the flow of information.) 方框用帶箭頭的線段相連（箭頭表示信息流動的方向）The use of a block diagram provides a simple means by which the functional relationship of the various ponents can be shown and reveals the operation of the system more readily than does observation of the physical system itself. 方框圖的應(yīng)用提供了一個簡單的方法，通過這個方法可以說明各個部分功能之間的關(guān)系，用它來說明系統(tǒng)的工作情況比考察物理系統(tǒng)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. 從簡單的函數(shù)方框圖中可以清楚地看出，顯然不同的物理系統(tǒng)可以用同樣的方法進行分析。In general, variables that are functions of time are represented by lowercase letters. 通常，時間變量用小寫字母表示。To simplify the writing of differential equations, the D operator notation is used. The symbols D and 1/D are defined by: 為了簡化微分方程的書寫，使用算子符號D。符號D和1/D分別定義如下： （） （）where Y0 represents the value of the integral at time t=0, that is, the initial value of the integral. 式中表示在時刻的積分值，即積分的初始值。The principle of superposition about linear system 線性疊加系統(tǒng)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: 假設(shè)微分方程描述的系統(tǒng)輸入x(t)和輸出y(t)之間的動態(tài)關(guān)系如下： anDny(t)+an1Dn1y(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 timeinvariant, the corresponding system is called linear timeinvariant system. 如果ai (i = 0,1,2,...,n) 和 bj (j = 0,1,2,...,m)是常數(shù)，也就是說，他們與輸入x(t)和輸出y(t)的變化無關(guān)，該方程就稱為線性時不變方程，相應(yīng)的系統(tǒng)稱為線性時不變系統(tǒng)。anDny(t)+an1Dn1y(t)+...+a1Dy(t)+a0y(t)=bmDmx(t)+...+b1Dx(t)+b0x(t) (2) If ai and bj is the function of time t, the equation is called linear timevariant, the corresponding system is called linear timevariant system. 如