专业英语电气工程P2U3教学.ppt

自动化专业英语教程,教学课件,July 28, 2007,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,A 根轨迹 1.课文内容简介：主要介绍自动控制原理中根轨迹的定义、幅角与幅值判据、绘制根轨迹的规则、根轨迹法用于系统设计和补偿等内容。 2.温习自动控制原理中有关根轨迹的内容。 3. 生词与短语 factored adj. 可分解的 depict v. 描述 conjugate adj. 共轭的 vector n. 矢量 argument n. 辐角，相位 counterclockwise adj. 逆时针的 odd multiple 奇数倍 even multiple 偶数倍,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,plot v. 绘图 n. 曲线图 sketch v., n. （绘）草图，素描 facilitate v. 使容易，促进 coincide v. 一致 asymptote n. 渐进线 integer n. 整数 intersect v. 相交 real axis 实轴 symmetrical adj. 对称的 breakaway point 分离点 arrival point 汇合点 departure angle 出射角 arrival angle 入射角 thereof adv. 将它（们） imaginary axis 虚轴 passive adj. 被动的，无源的,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,active adj. 主动的，有源的 network n. 网络，电路 phase-lead n. 相位超前 phase-lag n. 相位滞后 4. 难句翻译 1 as any single parameter, such as a gain or time constant, is varied from zero to infinity. 当任意单一参数，如增益或时间常数，从零变到无穷时。 2 These effects increase in strength with decreasing distance. 随着到原点距离的减小，它们的作用强度会增加。 此处distance指零（极）点到原点的距离。 3 Ignoring for the weaker effect of the added pole, which is often placed at 10 times the distance to the origin, the zero 忽略常被置于10倍于零点到原点距离处的附加极点的微弱作用，零点,The Root Locus,Introduction,The three basic performance criteria for a control system are stability, acceptable steady-state accuracy, and an acceptable transient response. With the system transfer function known, the Routh-Hurwitz criterion will tell us whether or not a system is stable. If it is stable, the steady-state accuracy can be determined for various types of inputs. To determine the nature of the transient response, we need to know the location in the s plane of the roots of the characteristic equation. Unfortunately, the characteristic equation is normally unfactored and of high order.,The root locus technique is a graphical method of determining the location of the roots of the characteristic equation as any single parameter, such as a gain or time constant, is varied from zero to infinity.1 The root locus, therefore, provides information not only as to the absolute stability of a system but also as to its degree of stability, which is another way of describing the nature of the transient response. If the system is unstable or has an unacceptable transient response, the root locus indicates possible ways to improve the response and is a convenient method of depicting qualitatively the effects of any such changes.,The Angle and Magnitude Criteria,Without transport lag the transfer function of a system can be reduced to a ratio of polynomials such that,The root locus technique is developed by expressing the characteristic function D(s) as the sum of the integer unity and a new ratio of polynomials in s. The characteristic equation will be written as,where K is the parameter of interest, -z1, -z2 . are the (open-loop) zeros and p1, -p2, are the (open-loop) poles. K is independent of s and must not appear in the polynomials Z(s) and P(s). The form of KZ (s) and P(s) is important; these poles and zeros may be real or complex conjugates. Note in Eq. (2-3A-2) that the coefficient of s is always set equal to unity for root locus operations.,A zero is a value of s that makes Z(s) equal to zero and is given the symbol o. Do not automatically assume that this zero is also a closed-loop zero that makes N(s) equal to zero in the system (closed-loop) transfer function; it may be, but is not necessarily so. A pole is a value of s that makes P(s) equal to zero and is given the symbol x. The sn term represents n poles, all equal to zero and located at the origin of the s plane. A root of the characteristic equation has previously been defined as a value of s that makes D(s) equal to zero.,Since s is a complex variable and the poles and zeros may be complex, KZ(s)/P(s) is a complex function and may, therefore, be handled as vector having a magnitude and an associated angle or argument. Each of the factors on the right side of Eq.(2-3A-2)can also be treated as vector with an individual magnitude and associated angle, as shown in Fig.2-3A-1. Notice that the angle is measured from the horizontal and is positive in the counterclockwise direction. If we express each factor in polar form, then,If we now collect the magnitudes together and multiply the exponentials together, we can write Returning to the characteristic equation of Eq. (2-3A-3) and solving for KZ(s)/P(s) yields,k=0,1,2,Since -1 can be reprsented by a vector of unity magnitude and an angle that is an odd multiple of 180o. According to Eq.(2-3A-3) and Eq.(2-3A-4),we can find two criteria that make the characteristic function D(s) equal to zero , i.e, there are two criteria which can find system (close-loop) poles as K is increased from 0 to .,Magnitude critertion:,Rules for Root Locus Plotting,Applying angle and magnitude criterion, the root loci can obviously be plotted by a computer, however, well introduce rapid sketching techniques. The following guides are provided to facilitate the plotting of root loci: 1. For K=0 the close-loop poles coincide with the open-loop poles, 2. For K close-loop poles approach the open-loop zero. 3. There are as many as locus branches as there are open-loop poles. A branch starts, for K=0, at each open-loop pole. As K is increased, the closed-loop pole positions trace out loci, which end, for K, at the open-loop zeros.,4. If there are fewer open-loop zeros than poles (ji), those branches for which there are no open-loop zeros left to go to tend to infinity along asymptotes. The number of asymptotes is (i-j). 5. The directions of the asymptotes are found from the angle condition. The vectors from all m open-loop zeros and n open-loop poles to s have the same angle noted . Hence the asymptote angles must satisfy,(K=any integer). The angles are uniformly distributed.,6. All asymptotes intersect the real axis at a single point, at a distance o to the origin:,7. Loci are symmetrical about the real axis since complex open-loop poles and zeros occur in conjugate pairs. 8. Sections of the real axis to the left of an odd total number of open-loop pole and zeros on this axis form part of the loci, because any trial point on such sections satisfies the angle condition. 9. If the part of the real axis between two o.l. poles (o.l. zeros) belongs to the loci, there must be a point of breakaway from, or arrival at, the real axis. If no other poles and zeros are close by, the breakaway point will be halfway. In Fig. 2-3A-2d, adding the pole p3 pushes the breakaway point away; a zero at the position of p3 would similarly attract the breakaway point.,10. The angle of departure of loci from complex o.l. poles (or of arrival at complex o.l. zeros) is a final significant feature. Apply the angle condition to a trial point very close to p1 in Fig. 2-3A-3. Then the vector angles from other poles and zeros are the same as those to p1. The angle from p1 to this point must satisfy the follows :,Departure angle:,similarly, the arrival angle:,Root Loci for System Design and Compensation,Root loci are used for design to the extent of choosing the gain to obtain a specified damping ratio or time constant. A P (Proportion) control design does not change the shape of the loci. But if dynamic compensation is needed, a series compensator will add poles and zeros to the open-loop pole-zero pattern, in order to change the shape of the loci in a desirable direction.,As indicated in Fig. 2-3A-4, adding a pole pushes the loci away from that pole, and adding a zero pulls the loci toward that zero. These effects increase in strength with decreasing distance. A zero can improve relative stability because it can pull the loci, or parts thereof, away from the imaginary axis, deeper into the left-half plane.,In analog control system, passive and active electrical networks are usually applied to realize these very important forms of compensation. Including a gain, the transfer functions can be written as follows:,For a phase-lead case, zp. Fig.2-3A-5 shows the pole-zero patterns. Phase-lead compensation is an approximation to PD (Proportion-Differential) control, and is often preferable to reduce the effect of signal noise and then to improve stability. Phase-lag compensation is commonly used, like PI (Proportion-integral) control, to improve accuracy. However, phase lead may also improve accuracy, and phase lag may improve stability.,Cases of phase-lead and phase-lag compensation:,In the system of Fig. 2-3A-6a, the P control is to be replaced by phase lead, intended to “pull“ the locus branches for P control, shown as dashed curves, back to the left by means of the added zero. Ignoring for the weaker effect of the added pole, which is often placed at 10 times the distance to the origin,3 the zero is chosen to satisfy the need for compensation.,In the case of phase-lag compensation, similarly, a pole-zero pair is employed. However, it is added close to the origin, much closer than pictured in Fig. 2-3A-6b to enable the shape of the loci near the origin to be indicated. As suggested by the vectors to a point on the dashed locus, for such a pair the net contribution to the vector angles at the point is small. Therefore, the main branches often change only little. The picture near the origin is of the type shown in Fig. 2-3A-4c. Although the main branches of system are changed little, the interest gain factor z/p contains in the loop gain function, which can be increased to improve the steady-errors.,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,5. 参考译文 A 根轨迹 简介 控制系统三个基本的性能指标是稳定性、满意的稳态精度和满意的暂态响应。如果已知系统的传递函数，劳斯-胡尔维茨判据会告诉我们系统是否稳定。如果系统稳定，可以确定各种类型输入时系统的稳态精度。为了确定暂态响应的特性，我们需要知道特征方程的根在s 平面上的位置。遗憾的是，特征方程通常不能分解成因式并且是高阶的。 根轨迹技术是一种当任意单一参数，如增益或时间常数，从零变到无穷时确定特征方程的根的位置的一种绘图方法。因此，根轨迹不仅提供系统绝对稳定性而且提供稳定裕量的信息，稳定裕量是描述暂态响应特性的另一种方法。如果系统是不稳定的或暂态响应不令人满意，根轨迹给出可能改进响应的方法并很方便地定性描述这些改进的效果。,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,幅角与幅值判据 没有传输延迟，系统的传递函数可以简化成两个多项式之比如下 根轨迹技术是将特征方程D(s)表示为1和一个新的s的多项式之和。特征方程可以写作 公式中K 是我们关注的参数，-z1， -z2， 是开环零点，-p1， -p2， .是开环极点。K 与s 无关，一定不能出现在多项式Z(s),(2-3A-1),(2-3A-2),P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,和P(s)中。KZ(s)/P(s)这个形式是重要的，这些极点和零点可能是实数或共轭复根。注意在公式(2-3A-2)中，s的系数总是定为1以用于根轨迹运算。 零点是使Z(s)等于零的值，用符号 表示。不要自动认为这个零点也是使系统（闭环）传递函数N(s)也等于零的闭环零点；它可能是，但不一定非是。极点是使P(s)等于零的值，用符号 表示。sn 项代表n 重极点，n 个极点都等于零且位于s 平面的原点。特征方程的根以前已经定义为使D(s)等于零的值。 由于s 是复变量，亟待和零点可能是复数，KZ(s)/P(s) 是复变函数，因此可用一个有幅值和与其相关的角度或叫幅角的矢量来表示。在公式(2-3A-2)右边的每一个分解因子可被看作,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,具有独自幅值和幅角的矢量，如图2-3A-1所示。注意幅角是以水平方向为基准、逆时针方向为正来计量的。 如果我们用极坐标表示每一个因子，得到,图 2-3A-1 根轨迹的幅角和幅值,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,如果我们合并幅值项并将指数项相乘，得到 注意特征方程公式(2-3A-3)，求解KZ(s)/P(s)得 而-1可表示成幅值为1，幅角为奇数倍180的矢量。根据公式(2-3A-3)和(2-3A-4)，我们看到有两个参数使特征方程D(s)等于零，即当K从0增加到无穷大时，有两个参数可以确定系统（闭环）极点。,(2-3A-3),(2-3A-4),P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,幅值判据： 幅角判据：,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,绘制根轨迹的规则 应用幅角和幅值判据，显然根轨迹可由计算机绘出，但是，我们要介绍根轨迹草图的快速绘制方法。以下规则有助于根轨迹的绘制。 1. 当K=0时，闭环极点等于开环极点。 2. 当K时，闭环极点趋近开环零点。 3. 根轨迹的分支数等于开环极点数。当K=0时，分支起始于每一个开环极点。随着K值的增加，闭环极点位置绘出根轨迹，当K时，根轨迹终止于开环零点。 4. 如果开环零点少于开环极点（ji），那些无零点趋近的根轨迹分支沿着渐近线趋于无穷大。渐近线的条数为（i-j）。 5. 可从幅角判据中得到渐近线的方向。从所有m个开环零点和n个开环极点到s的矢量具有相同的角度。因此渐近线的角度,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,必须满足 （k=任意整数）。渐近线的角度是均匀分布的。 6. 每一条渐近线与实轴有一个交点，与原点的距离为0 7. 根轨迹对称于实轴，因为复数开环极点和零点都是共轭对。 8.实轴上某个区间右侧实轴上的开环零极点数之和为奇数时，这个区间形成根轨迹，因为这个区间上的任一点满足幅角判据。 9.如果实轴上两个开环极点（或两个开环零点）之间有根轨迹，那么实轴上一定存在分离点（或汇合点）。如果附近没有其它的极点和零点，分离（或汇合）点一定位于两个极点（或,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,两个零点）的中间。在图2-3A-2d中，添加极点p3将会推远分离点，类似地，在p3的位置添加一个零点将会吸近分离点。,图 2-3A-2 根轨迹图,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,10. 复数开环极点的出射角（或复数开环零点的入射角）是根轨迹最后一个重要的特征。对图2-3A-3上紧挨着p1的根轨迹上的点应用幅角判据。则有从其它零、极点到这一点的矢量角与它们到p1点的矢量角相同。从p1到这点的角度一定满足如下公式： 出射角： 类似地，入射角：,图 2-3A-3 根轨迹的出射角,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,使用根轨迹法作系统设计与补偿 根轨迹被用于确定增益以获得预想的阻尼比或时间常数。比例控制设计不改变根轨迹的形状。但如果需要动态补偿，一个串联的补偿器会添加极点和零点到开环极、零点图形中去，以按照预想的方向改变根轨迹的图形。 像图2-3A-4所示的那样，添加一个极点会将根轨迹推离这个极点，添加一个零点会将根轨迹吸近这个零点。随着到原点,图 2-3A-4 添加极点或零点的效果,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,距离的减小，它们的作用强度会增加。添加零点可以改善相对稳定性，因为它可以吸引根轨迹、或根轨迹的一部分离开虚轴进入左半平面，较远地离开虚轴。 在模拟控制系统中，通常用无源和有源电路来实现这些非常重要的补偿。包含补偿增益，传递函数具有如下形式： 相位超前时，zp。图 2-3A-5给出了极-零点图形。相位超前补偿近似于PD （比例-微分）控制，经常用,图 2-3A-5 相位超前和相位滞后举例,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,于降低信号噪声，因此而改善稳定性。相位滞后是一种常用的补偿，例如PI （比例-积分）控制，用来改善精度。但是，相位超前可能也改善精度，相位滞后也改善稳定性。 相位超前和相位滞后补偿举例： 在图2-3A-6a中，用相位超前代替比例控制，借助于补偿极点的作用，打算“吸引”比例控制的根轨迹分支回到左半平面,图 2-3A-6 相位补偿,P2U3A The Root Locus 第二部分第三单元课文A 根轨迹,上来。忽略常被置于10倍于零点到原点距离处的附加极点的微弱作用，零点被用来满足补偿的需要。 类似地，在相位滞后补偿中也使用一对极-零点。但是，这对极-零点离原点非常近，比图2-3A-6b 所表示的要近得多，画成这样是为了看清楚靠近原点根轨迹的形状。正像到虚线根轨迹上的点的矢量所表示的那样，这样一对极-零点电路对矢量角的影响很小。因此，主要的根轨迹几乎没有什么变化。靠近原点的图形具有图2-3A-4c 的形状。虽然主要的根轨迹几乎没有什么变化，我们感兴趣的增益系数已包含在回路增益函数中，可增加增益系数以改善稳态误差。,补充：英文科技论文的体例,撰写高质量的科技论文是为了参与学术交流，如在国内外英文学术报刊上发表自己的学术论文，或在学术会议上宣读自己的科技论文等，让其他科技工作者贡享你的学术成果。,国际标准化组织(International Organization for Standardization)、美国国家标准化协会(American National Standards Institute)、英国标准(British Standards)都对科技论文的体例做出了规定。,8.1 英文科技论文的体例,长篇科技报告内容包括：,Front 前部 Front cover 封面 Title page 扉页 Letter of transmittal (forwarding letter) 提交报告书 Distribution list 分发范围 Preface or foreword 序或前言 Acknowledgments 致谢 Abstract 摘要 Table of contents 目录 List of illustration 图表目录,8.1 英文科技论文的体例,MAIN TEXT,Introduction 引言 Experimental procedure and results with subheadings 实验过程与结果 Discussion 讨论 Conclusion 结论 Recommendations 建议,8.1 英文科技论文的体例,BACK 后部,List of references 参考文献 Appendices 附录 Tables 表 Graphics 图 List of abbreviations, signs and symbols 缩写、记号和符号表 Index 索引 Back cover 封底,8.1 英文科技论文的体例,封面包括：,The title 标题 Contract or job number 合同或任务号 The author or authors 作者 Date of issue 完成日期 Report number and serial number 报告编号及系列编号 Name of organization responsible for the report 研究单位 A classification notice (confidential, secret, etc.) 密级（机密、保密等）,8.1 英文科技论文的体例,期刊类科技论文，主要内容包括：,Title 标题 Abstract 摘要 Keywords 关键词 Introduction 引言 Materials and methods, equipment and test (experiment )procedure 材料与方法，设备与试验（实验）过程 Results 结果 Discussions (summary) 讨论 Acknowledgements 致谢 References 参考文献,8.1 英文科技论文的体例,作业10： 一、请将英文翻译成中文。 1、part2:unit3:B:第1段翻译； 2、part2:unit3:B:第2段翻译；,P2U3B The Frequency Response Methods: Nyquist Diagrams 第二部分第三单元课文B 频率相应方法;奈氏图,B 频率相应方法：奈氏图 1.课文内容简介：主要介绍自动控制原理中使用频率相应方法的必要性和优点、频率传递函数、奈奎斯特稳定判据、增益裕量和相角裕量等内容。 2.温习自动控制原理中讲解频域特性的有关章节。 3. 生词与短语 periodic adj. 周期性的 random adj. 随机的 misinterpretation n. 曲解，误译 develop v. 导出，引入 forcing frequency 强制频率 partial fraction expansion 部分分式展开式 bracket v. 加括号 arbitrary adj. 任意的,P2U3B The Frequency Response Methods: Nyquist Diagrams 第二部分第三单元课文B 频率相应方法;奈氏图,polar plot 极坐标图 tip n. 顶端 versus prep. 对 the theory of residues 余数定理 identity n. 一致性，等式 omit v. 省略 simplicity n. 简单 contour n. 轮廓，外形 enclose v. 围绕 semicircle n. 半圆形 radius n. 半径 undergo v. 经历 net n. 净值；adj. 净值的 revolution n. 旋转 encircle v. 环绕 indentation n. 缺口,P2U3B The Frequency Response Methods: Nyquist Diagrams 第二部分第三单元课文B 频率相应方法;奈氏图,infinitesimal adj. 无限小的 misleading indication 导致错误的读数 4. 难句翻译 1 The wind loading of a tracking radar antenna, for example, results from a mean velocity component that varies with time plus superimposed random gusts. 例如，跟踪雷达天线的风力负载是由一个随时间变化的平均速度成分与叠加的随机阵风组成的。 2 , it is only approximate and is subject to misinterpretation. 只是近似的而且容易判断错误。 3 It is also the negative phase shift (i.e., clockwise rotation) of KZ(s)/P(s) which will make the curve pass through -1. 它也是能使曲线通过-1点的KZ(s)/P(s)的负相位移动（即顺时针旋转）的角度。,P2U3B The Frequency Response Methods: Nyquist Diagrams 第二部分第三单元课文B 频率相应方法;奈氏图,5. 参考译文 B 频率响应：奈奎斯特图 简介 有时在频域而不是在根轨迹的s域开展研究工作是必要或有益的。因为做系统分析时，根轨迹法需要传递函数，但获得某些元件、子系统以致系统的传递函数很困难、甚至是不可能的。在这种情况下，可用实验方法确定在已知频率和幅值的正弦测试波作用下的频率响应。 输入信号的性质也影响系统分析和设计方法的选择。许多命令输入仅仅是让系统从一个稳态转移到另一个稳态。这类输入可用位置、速度和加速度恰当的步骤进行充分的描述，并适合在s域作分析。但是，当各个步骤的时间间隔减少到系统没有时间到达每一步输入的稳态时，用阶跃表示法和s域作分析就力不从心了。如此快速变化的命令输入（或扰动）可能是周期的、随机的、或二者并存。例如，跟踪雷达天线的风力负载,P2U3B The Frequency Response Methods: Nyquist Diagrams 第二部分第三单元课文B 频率相应方法;奈氏图,是由一个随时间变化的平均速度成分与叠加的随机阵风组成的。如果这些输入的频率分布可以计算、检测甚至预测，频率响应可用来确定输入对系统输出的作用。 频率响应是一种稳态响应。虽然可以得到某些关于暂态响应的信息，但这些信息只是近似的而且容易判断错误。 频率传递函数 有必要建立在频域使用的输入-输出关系，即频率传递函数。讨论具有已知传递函数G(s)的线性系统，施加正弦输入 或 公式中r0是幅值，0是输入或强制频率。转换后的输出是,P2U3B The Frequency Response Methods: Nyquist Diagrams 第二部分第三单元课文B 频率相应方法;奈氏图,C(s)的部分分数展开式为 公式中-r1, -r2, 是传递函数特征方程的根。反变换为 公式中头两项代表来自正弦输入的无阻尼振荡，其它项是暂态响应。如果系统是稳定的，暂态响应将随时间衰减到零，留下来的是稳态响应。,P2U3B The Frequency Response Methods: Nyquist Diagrams 第二部分第三单元课文B 频率相应方法;奈氏图,系数C1和C2用海维赛德展开定理求得 将结果代入C1和C2，式(2-3B-1)为,(2-3B-1),(2-3B-2),P2U3B The Frequency Response Methods: Nyquist Diagrams 第二部分第三单元课文B 频率相应方法;奈氏图,因为它们是复变函数 公式中角度是G(j0)的幅角，等于(ImG/ReG)的余切。式(2-3B-2)现可写成 因为括弧内的项等于sin(0t+)，稳态响应可以写成,P2U3B The Frequency Response Methods: Nyquist Diagrams 第二部分第三单元课文B 频率相应方法;奈氏图,从这些公式中我们看到给一个线性稳定系统施加正弦输入会产生一个正弦稳态响应，输入和输出频率相同，但有一个相角位移 并且幅值可能不同。这个稳态正弦响应被称作系统的频率响应。由于相角是与复变函数G(j0)相关的角度而幅值比(c0/r0)是G(j0)的幅值，G(j0)的情况说明了频域下稳态输入-输出关系。 G(j0)称作频率传递函数并可将传递函数G(s)中的s 用j0替代而得到。因此，如果通过实验可以确定G(j0)，将j0换成s即可得到G(s)。 对一个给定的系统，如果输入频率从零到无穷大每单位时间弧度变化时的幅值比和相角已知，则频率响应可以完全确定。,P2U3B The Frequency Response