第六次课3学时.docx

1、第六次课第六次课 3 学时学时 第六次课（3学时）UNIT 4 A：The Frequency Response Methods:Bode Plots 背景知识：已知系统的频率特性 A()ej（），将 20lg A()和（）分别画出，并且横轴取对数坐标，则得到 Bode图。Bode图包含了系统的全部动态特性，从稳定性、稳态误差到瞬态响应均在 Bode图中得到反映。由于 Bode 图具有很清晰的物理意义，工程人员也喜欢利用其来分析和设计控制系统。有一点要注意的是，通常都是用开环传递函数的 Bode图来分析闭环系统的特性。New words:against prep 以为背景，以为对照 decib

2、el n.分贝 common logarithm 常对数 Bode plot 伯德图 minimum phase 最小相位 unit n.单位 polar plot 极坐标图 interpret v.解释、口译 slop n.斜率 lag n.(相位)滞后 l ead n.(相位)超前 asymptote n.渐进线 deviation n.偏差 decade n.十倍 abrupt a.陡峭的、突然的 crossover frequency 穿越频率 gain margin 增益裕量 phase margin 相角裕量 product n.乘积 解释（开头五段译文）：The frequenc

3、y transfer function of a system or of its function can be presented either by the single Nyquist diagram(a polar plot)or by plots of the amplitude ratio and the phase angle against the input(forcing)frequency.It is customary to plot the amplitude ratio in decibels and the phase angle in degree again

4、st the common logarithm of the input frequency.In this form,the two plots are known as Bode plots(after H.W.Bode).There are exact Bode plots,which are best prepared with a computer,and straight-line asymptotic plots,which can be quickly and easily sketched or plotted by hand using the techniques to

5、be developed and discussed in this article.系统的频率特性可以用 Nyquist 图（极坐标图）或者用其幅值（比）和相角为因变量，输入信号的频率为自变量绘图。在绘图时通常幅值（比）用分贝表示，相角用度表示，输入信号的频率按常用对数取值。以上这两个图称为伯德图（以 H.W.Bode命名）。可以用计算机绘出精确的伯德图。在本文中将讨论用手工绘制的技巧简单而快速地绘制直线渐进线图。Bode plots of the system transfer function are used to determine the effects of various in

6、puts(including a step)upon the steady-stat response of the system.Since the frequency response is a steady-state response,the system must be stable and its stability must be determined before the system Bode plots can be used.系统传递函数的伯德图可以用于确定各种输入（包括阶跃输入）下系统的稳态响应。因为频率响应为稳态响应，所以系统必须是稳定且其稳定性必须在绘制伯德图之前确

7、定。Bode plots are most commonly used with the frequency function to examine the stability of a system.When the function has no pole or zero inside the right-half s plane,i.e.the function is minimum phase,the Bode plots can be sketched rather rapidly with a knowledge of the four elementary factors tha

8、t appear in the function.These terms are:Frequency-invariant terms K.Zeros and poles at the origin(j)n First order terms or real poles and zeros(j+1)n Second order poles and zeros .伯德图和频率（特性）函数 一起用来确定系统的稳定性。当该函数无零点和极点在 S 平面右半部时，即系统为最小相位系统，可以使用函数的四个快速地绘出伯德图。这四个量分别是：与频率无关的系数 K。在原点的零点和极点个数。一阶项，即实数零点和极点

9、个数。二阶项，即零点和极点。For a product,and.The phase angle is expressed as a sum.The magnitude M will also be expressed as a sum,by using decibels(dB)as units:对于乘积：，这里，而 。相角 表现为和的形式，幅值 M 如果使用分贝为单位也表现为和的形式：In Bode plots,the magnitude M in dB and the phase angle in degrees are plotted against on semilog paper.Th

10、e development has shown the following:Bode magnitude and phase-angle plots of are obtained by summing those of its elementary factors.These plot are much easier to make than polar plots or Nyquist diagrams,and can readily be interpreted in terms of different aspects of system performance.在伯德图中幅值 M 使

11、用分贝，相角 使用度，画在 为横坐标的半对数纸上。以上推导表明：的幅值和相角伯德图可以分别由各个基本因子的伯德图相加而得到。这些伯德图比极坐标图要容易画，且可以方便地解释系统性能。In Bode plot,the phase margin m is the sum of 180and the phase angle at the frequency where (i.e.,0dB).Hence,as shown by the partial plots in Fig.2-4A-2,the phase margin m is the distance of the phase-angle cur

12、ve above-180 at the crossover frequency,where the magnitude plot crosses the 0 dB axis.Similarly,the gain margin equals 1 divided by the magnitude at the frequency where the phase angle is.,the gain margin in dB,is therefore the distance of the magnitude below 0dB at this frequency,as shown in Fig.2

13、-4A-2.在 Bode图中，相角稳定裕量 m 为 180 加上 时的频率处对应的相角值。因此，如图 2-4A-2所示，相角稳定裕量 m 为相角曲线在穿越频率（幅值曲线穿越 0 dB 线处）处与-180 线的距离。同样，增益裕量等于 1除以相角为 时对应频率的幅值。因此，,以 dB来表示，为如图 Fig.2-4A-2.所示的频率处，幅值曲线与 0分贝线的距离。教材中注释 1的翻译：对于超前环节，其 Bode图同样与相应的滞后环节的 Bode图成镜象。B:Nonlinear Control System 背景知识：世界上所有的系统都是非线性系统。只不过是因为，有一部分非线性系统的非线性不是很严重

14、，在一定的条件下可以用线性模型来近似。常见的非线性特性有：跳跃、饱和、死区、继电特性、磁滞回环等。对于非线性系统，最根本的一条就是：迭加原理不成立。相平面法和函数法是 2 种常用的分析非线性系统的方法。New words:operating point 工作点 relay n.继电器 independent variable 自变量 nonlinear time-varying 非线性时变 principle of superposition 迭加原理 phase plane 相平面 describing function 描述函数 limit cycle 极限环 harmonic n.谐波

15、subharmonic 次谐波 jump phenomenon 跳跃现象 tangent a.相切的、接触的 n.切线、正切 nonlinear gain 非线性增益 saturation n.饱和 deadband n.死区 backlash n.齿（轮间）隙 hysteresis n.（磁）滞回线 Coulomb friction 库伦摩擦 isocline n.等倾线 阅读 12分钟（阅读至 84 页倒数第 8 行）翻译示例 In practice,most systems are nonlinear for large enough variations about the opera

16、ting point,and linearization is based on the assumption that these variations are sufficiently small.But this cannot be satisfied,for example,for systems that include relays,which can switch position for very small changes.Startup and shutdown also frequently require the consideration of nonlinear e

17、ffects,because of the size of the transients.实际上，大多数的系统当在工作点周围有较大的变化时，都是非线性的。线性化的是基于这样的假设：变化足够的小。但是这种条件通常得不到满足，例如当系统包含继电器时，即使是很小的变化，也会引起较大的变化。起动和停止时通常也要考虑非线性的影响，因为相对系统的动态特性，系统的非线性是不能忽略的。The principle of superposition does not apply to nonlinear systems.This has serious consequences.In fact,the analy

18、sis and design techniques so far,including the use of transfer function and Laplace transforms,are no longer valid.Worse,there is no general equivalent technique to replace them.Instead,a number of techniques exist,each of limited purpose and limited applicability.We only introduce the well-known ph

19、ase plane and describing function methods.迭加原理不适用于非线性系统。这一点的后果是严重的。事实上，至今为止所讨论的分析和设计技术包括传递函数和拉氏变换已经不适用了。更糟糕的是，并没有一般的方法能够取代它们。有那么几种方法，但是各自存在限定的目的和范围。我们将介绍比较熟知的相平面法和描述函数法。The nature of the response depends on input and initial conditions.For example,a nonlinear system can change from sable to unstable

20、,or vice versa,if the size of step input is doubled.（非线性系统）响应的特性取决于输入或者初始条件。例如，当阶跃输入的的幅度增大一倍时，非线性系统可能会从稳定变得不稳定；反之亦然。Instability shows itself frequently in the form of limit cycles.These are oscillations of fixed amplitude and frequency which can be sustained in the feedback loop even if the system i

21、nput is zero.In linear systems an unstable transient grows theoretically to infinite amplitude,but nonlinear effects limit this growth.（非线性系统）的不稳定性通常表现为极限环的形式。其振荡以固定的幅值和频率在反馈环中维持即使系统的输入为零。对于不稳定的线性系统其瞬态过程的幅值在理论上会趋于无穷大，但是非线性特性会限制其增长。The jump phenomenon is illustrated by the frequency response plot in

22、Fig.2-4B-1.If the frequency of the input is reduced from high value,the amplitude of the response drops suddenly at the vertical tangent point C to the value at D.跳跃现象如图 Fig.2-4B-1 所示，该图解释了输出幅值与输入频率之间的关系。如果输入的频率从一个比较高的数值减小，响应的幅值会突然垂直的相切点 C 下降到点D。Unit 5 A:Introduction to Modern Control Theory 背景知识：现代

23、控制理论（以状态方程和状态空间为标志）出现在上个世纪 60 年代末，70年代初。开始时主要是应用在航天领域。经典控制理论主要是使用描述系统输入、输出关系的模型（传递函数、频率特性），而现代控制理论则是使用描述系统内部特性的变量（状态变量）。由于采用时域模型，现代控制理论特别适合于使用计算机，而计算机的广泛应用为现代控制理论的发展提供了动力。New Words:advent n.（事件、时期）的出现、到来 stimulus n.刺激 realistic a.实际的、现实的 optimal control 最优控制 applicability n.适用性 bandwidth n.带宽 phase-

24、plane 相平面 describing function 描述函数 alleviate v.减轻、减小 prominently adv.显著地、突出地 numeric solution 数值解 n-dimensional a.n维的 field n.域、数域 State of the Union message(also State of Union address)a yearly address delivered in January by the President of the US to congress,giving the administrations view of th

25、e state of the nation and plans for legislation.(see Oxford English Reference Dictionary).（美国总统）国情咨文 解释：When differential equations are encountered,they are linearized and subjected to whatever constraints are necessary to establish useful input-output relationships.当使用微分方程时，要对其进行线性化并受限于一定的约束条件才能建立有

26、用的输入-输出关系。A recognition of the applicability of well-known methods in other fields of knowledge.认识到其他领域的一些有名的方法的适用性。Optimal control theory often dictates that nonlinear time varying control law be used,even if the basic system is linear and time-invariant.即使系统是线性定常的，最优控制理论通常给出非线性时变控制律。When nonlinear

27、ities and time variation are present,the very basis for classical techniques is removed.Some successful techniques such as phase-plane,describing function,and ad hoc methods,have been developed to alleviate this shortcoming.当系统存在非线性和时变特性时，经典方法赖以存在的基础就不存在了。一些成功的方法，如相平面法、描述函数法以及一些特定的方法可以改进经典控制理论。翻译示例：

28、With an advancing technological society,there is a trend towards more ambitious goals.This also means dealing with complex system with a larger number of interesting components.The need for greater accuracy and efficiency has changed the emphasis on control system performance.The classical specifica

29、tions in terms of percent overshoot,settling time,bandwidth,etc.,have in many cases given way to optimal criteria such as minimum energy,minimum cost,and minimum time operation.Optimization of these criteria makes it even more difficult to avoid dealing with unpleasant nonlinearities.Optimal control

30、 theory often dictates that nonlinear time varying control law be used,even if the basic system is linear and time-invariant.随着社会技术的进步，人们总是选择更高的目标。这就意味着要处理复杂的具有更多相互作用的部件的系统。由于需要更高的精度和效率控制系统的性能指标已经发生变化。经典的指标如超调量、调节时间、带宽等已经让位于最优化指标如最小能量、最小成本已经最小时间等。即使系统是线性定常的，最优控制理论通常给出非线性时变控制律。The concept of state oc

31、cupies a central position in modern control theory.However,it appear in many other technical and non-technical context as well.In thermodynamics the equations of state are prominently used.Binary sequential networks are normally analyzed in term of their state.In everyday life,monthly financial stat

32、ements are commonplace.The President state of the Union meesage is another familiar example.状态的概念在现代控制理论中占据中心位置。然而其也出现在其他技术和非技术领域。在热力学中状态方程的概念被突出地使用。二进制序列网络通常使用状态的术语进行分析。在日常生活中每月的也使用财政（财务）状况。美国总统的国情咨文也是一个熟悉的例子。In all of these examples the concept of state is essentially the same.It is a complete sum

33、mary of the status of the system at a particular point in time.Knowledge of the state at some initial time t0 plus knowledge of the system inputs after t0,allows the determination of the state at a later time t1.As far as the state at t1 is concerned,it makes no difference how the initial state was attained.Thus the state at t0 constitutes a complete history of the system behavior prior to t0,inso