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1、自动化专业英语教程教学课件July 28, 2007Email : http: / 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
2、 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
3、 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 effe
4、cts 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 per
5、formance 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 determi
6、ned 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. Root Locus根轨迹performance criteria性能标准unfac
7、tored不能因式分解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 st
8、ability 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 depic
9、ting qualitatively the effects of any such changes. graphical method绘图绘图 方法any single parameter任意单值单值 参数degree of stability稳稳定裕量nature特性qualitatively定性地The Angle and Magnitude Criteria Without transport lag the transfer function of a system can be reduced to a ratio of polynomials such that W(s)= =
10、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 D(s)=1+K =1+K =0 polynomi als多项式where K is the parameter of interest, -z1, -z2 . are the (open-loop
11、) 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 f
12、or root locus operations. unity1A 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 p
13、ole 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 compl
14、ex 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 ass
15、ociated 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 complex function复变变函数in polar form以极坐标标形式argument幅角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
