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1、自动化专业英语教程,教学课件,July 28,2007,P2U6A Controllability,Observability,and Stability 第二部分第六单元课文A 可控性，可观性和稳定性,A 可控性，可观性和稳定性1.课文内容简介：主要介绍现代控制理论中可控性，可观性的概念、广义上连续系统稳定性的概念和定义、用李亚普诺夫第一方法和李亚普诺夫第二方法确定非线性自激系统的稳定性等内容。2.温习现代控制理论中可控性，可观性、李亚普诺夫第一、第二方法等内容。3.生词与短语,P2U6A Controllability,Observability,and Stability 第二部分第六单
2、元课文A 可控性，可观性和稳定性,state-controllable adj.状态可控（制）的observable adj.可观测的dual adj.双的，对偶的，孪生的fundamental n.基本原理multivariable adj.多变量的guarantee v.,n.保证，担保generalize v.一般化，普及trajectory n.轨迹Liapunov 李亚普诺夫vortices n.vortex 的复数，旋转体（面）converge v.集中，汇聚，收敛asymptotically stable 渐近稳定bound v.限制locally stable 局域稳定glob
3、ally stable 全局稳定,P2U6A Controllability,Observability,and Stability 第二部分第六单元课文A 可控性，可观性和稳定性,reveal v.显现，揭示comprise v.包含violently adv.激烈地straight-forward adj.直截了当的，简单的eigenvalue n.特征根autonomous adj.自治的，自激的decouple v.解耦，退耦portrait n.描述conjunction n.结合identify v.确认，识别，辨识Jacobian matrix 雅戈比矩阵positive def
4、inite 正定incidentally adv.偶然地,P2U6A Controllability,Observability,and Stability 第二部分第六单元课文A 可控性，可观性和稳定性,4.难句翻译1 Since complete state controllability does not necessarily mean complete control of the output,and vice versa,complete output controllability is separately defined in the same manner.因为状态完全能
5、控性不一定意味着输出的完全可控，而且反之亦然，所以输出完全能控性以类似的方式单独定义。2 Only local asymptotic stability with respect to the established equilibrium state can be guaranteed for linear analyses.只有相对于（系统）建立的平衡状态的局域渐近稳定才能保证线性分析（可以应用）。,Controllability and Observability,A plant(or system)is said to be completely state-controllable
6、if it is possible to find an unconstrained control vector u(t)that will transfer any initial state x(t0)to any other state x(t)in a finite time interval.Since complete state controllability does not necessarily mean complete control of the output,and vice versa,complete output controllability is sep
7、arately defined in the same manner.1 A plant is said to be completely observable if the state x(t)can be determined from a knowledge of the output c(t)over a finite time interval.,The dual concepts of controllability and observability are fundamental to the control of multivariable plants,particular
8、ly with regard to optimal control.Complete controllability ensures the existence of an unconstrained control vector and thus the existence of a possible controller.However,it does not tell how to design the controller,nor does it guarantee either a realistic control vector or a practical controller.
9、Complete observability ensures a knowledge of the state or internal behavior of the plant from a knowledge of the output.It does not,however,guarantee that the output variables are physically measurable.,The significance of these two concepts can be illustrated by consideration of a generalized nth-
10、order plant,which will have n state variables and thus n transient(dynamic)modes.The number of control variables will be designated by m,and the number of output variables by p.In a practical control system we expect m and p to be less than n and would like them both to be small in number.If the pla
11、nt is not completely controllable,there will be modes(state variables)that can not be controlled in any way by one or more of the control variables;these modes are decoupled from the control vector.If the plant is not completely observable,there will be modes whose behavior cannot be determined;thes
12、e modes are decoupled from the output vector.,A plant can be divided into four subsystems,as shown in Fig.2-6A-1.Since only the first subsystem A,which is both controllable and observable,has an input-output relationship,it is the only subsystem that can be represented by a transfer function or a tr
13、ansfer function matrix.Conversely,a transfer function or matrix representation of this plant reveals nothing about the dynamic behavior of subsystems B and D and provides no control over the behavior of subsystems C and D.For example,if the modes comprising subsystem B reacted violently to any of th
14、e control variables,the output variables would give no indication of such behavior.Undesirable transients in subsystem C would affect the output,but nothing could be done to modify them.This plant can be made completely controllable by appropriately adding control variables.The task of making the pl
15、ant completely observable,however,is more difficult and will not be discussed further.,Stability,Leaving the concepts of controllability and observability,we need to reexamine the concepts and definitions of stability with regard to continuous-variable systems in general.The stability of stationary
16、linear systems is relatively straight-forward in that it is a property of the system characteristics only,being independent of the initial state and of the magnitude and type of inputs.There is one finite equilibrium(singular)state,and we call the system stable if it returns to that state if disturb
17、ed.Stability is determined by the location of the eigenvalues(roots of the characteristic equation),and there are various techniques for locating the eigenvalues.,For nonstationary linear system and particularly for nonlinear system,stability is no longer dependent only upon the system properties bu
18、t is also dependent upon the initial state and the type and magnitude of any input.Furthermore,there may well be more than one equilibrium state.To discuss stability for these systems,additional definitions and criteria are necessary.We shall limit ourselves to autonomous systems since stability the
19、ory for arbitrary inputs is still undeveloped.,A system is said to be stable if trajectories leaving an initial state return to and remain within a specified region surrounding an equilibrium state.This general definition of stability is often referred to as stability in the sense of Liapunov and pe
20、rmits limit cycles and vortices.If the trajectories of a system that is stable in the sense of Liapunov eventually converge to the equilibrium state,the system is said to be asymptotically stable.If the system is stable only for initial states within a bounded region of state space,it is said to be
21、locally stable or stable in the small.If it is stable for all initial states within the entire state space,it is said to be globally stable or stable in the large.,We should like our control systems to have asymptotic stability,preferably global;if not global,then the region of asymptotic stability
22、should be large enough to include any anticipated disturbances.The stability of classical control theory is asymptotic.It may appear at first glance to be global,but in reality it is local since no system is truly linear.Only local asymptotic stability with respect to the established equilibrium sta
23、te can be guaranteed for linear analyses.,There are three basic methods for determining the stability of nonlinear autonomous systems.One method is to approximate the actual system by a second-order system,plot many trajectories in the phase plane,and examine the resulting phase portrait for regions
24、 of stability and instability.The describing function method can be used in conjunction with the phase plane to search for and identify limit cycles.Another method is known as the first,or indirect,method of Liapunov.It consists of linearizing the nonlinear vector equations about each equilibrium st
25、ate by means of the Jacobian matrix and then examining the corresponding eigenvalues for local stability only.The two methods just mentioned are sometimes lumped together as Liapunovs first method.,The third technique is the second,or direct,method of Liapunov,so called because it does not require s
26、olution of the differential equations.It is applicable to all types of differential equations of any order,provides some answers to global as well as local stability,and is widely used.,In using the second method of Liapunov,the equilibrium state being investigated is translated to the origin of the
27、 state space so that the autonomous system can be represented by the equation with the equilibrium state xeq=0.The asymptotic stability theorem of Liapunov is the essence of this direct method.This theorem states that the system of Eq.(2-6A-1)is asymptotically stable within the closed region R surro
28、unding the origin if there exists a positive definite scalar function V(x)which will vanish with time along all trajectories originating within the region R.If the region R includes all of the state space,the system is globally stable;if not,the system is locally stable within the finite region R.Th
29、e scalar function V(x)is known as a Liapunov function.It must be continuous within the region R,as must its first partial derivatives.,The requirement that it be positive definite means that V(x)must be greater than zero for all nonzero values of the state variables and that V(0)be equal to zero.In
30、order for V(x)to vanish along all trajectories starting within R,dV(x)/dt must be less than zero,that is,be negative definite.If V(x)0,it is negative semidefinite and the system is guaranteed to be stable only in the sense of Liapunov;if V(x)0 along a trajectory,the system is asymptotically stable.F
31、inally,if V(x)is indefinite,nothing has been proved with respect to the stability of the system,and we must try different V(x)functions until the system has been shown to be either stable or unstable.Incidentally,for stable system the size of the region of guaranteed stability can vary with the choi
32、ce of the Liapunov function.,P2U6A Controllability,Observability,and Stability 第二部分第六单元课文A 可控性，可观性和稳定性,5.参考译文A 可控性，可观性和稳定性可控性和可观性 一台装置（或系统）如果能找到一个无约束控制矢量u(t)在有限的时间间隔内将任意初始状态x(t0)转化为任意其它状态x(t)，则这台装置（或系统）是完全可控的。因为状态完全能控性不一定意味着输出的完全可控，而且反之亦然，所以输出完全能控性以类似的方式单独定义。如果可从有限的时间间隔内的输出c(t)的信息中确定状态x(t)，则装置是完全可观的
33、。可控性和可观性的对偶概念是多变量装置控制的基础，特别是最优控制。完全能控性保证无约束控制矢量的存在，因而存在一个可控制器。但是，完全能控性并没有告说明如何设计控制器，也没有保证物理上可实现的控制矢量或控制器的存在。完全可观性保证从输出信息中可确定状态信息或装置的内部特性。然而，完全可观性并不保证输出变量是物理可测的。,P2U6A Controllability,Observability,and Stability 第二部分第六单元课文A 可控性，可观性和稳定性,通过讨论一个有n个状态变量因而有n个暂态响应的广义n阶装置就可解释这两个概念的意义。控制变量数用m 表示，输出变量数用p 表示。在
34、实际系统中我们期望m 和 p 小于n 并且越少越好。如果装置不是完全能控的，将会有暂态响应（状态变量）不能由一个或多个控制变量用任何方式进行控制；这些暂态响应由控制矢量进行衰减。如果装置不是完全可观的，将有不确定的暂态响应；这些暂态响应由输出矢量进行衰减。,P2U6A Controllability,Observability,and Stability 第二部分第六单元课文A 可控性，可观性和稳定性,如图2-6A-1所示，一台装置可分成四个子系统。因为仅有第一个子系统A 是能观能控的，具有输入-输出关系，所以它是唯一一个可用传递函数或传递函数矩阵表示的子系统。相反，这台装置的传递函数或传递函
35、数矩阵并没有反映子系统B 和 D 的动态特性也没有对子系统C 和 D 的特性进行控制。,图 2-6A-1 一台装置的四个子系统,P2U6A Controllability,Observability,and Stability 第二部分第六单元课文A 可控性，可观性和稳定性,例如，如果子系统 B 的暂态响应对任何控制变量反应强烈，从输出变量中得不到这些特性的信息。子系统C 中不受欢迎的暂态响应会影响到输出，但控制变量对此无能为力。通过适当地增加控制变量可使这台装置完全可控。然而，要使这台装置完全可观，工作会更加困难，这里不作进一步讨论。稳定性 离开可控性和可观性的问题，我们需要讨论广义上连续系
36、统稳定性的概念和定义。定结构线性系统的稳定性比较简单，因为稳定性仅取决于系统本身的特性而与系统的初始状态、输入的幅值和类型无关。有一种有限的（唯一的）平衡状态，如果在扰动的作用下，系统能返回到这个平衡状态，我们称这个系统是稳定的。稳定性由特征根的位置确定（特征方程的根），并且有许多种方法确定特征根的位置。,P2U6A Controllability,Observability,and Stability 第二部分第六单元课文A 可控性，可观性和稳定性,对变结构线性系统，特别是对非线性系统，稳定性不仅取决于系统本身的特性，也取决于系统的初始状态、输入的类型和幅值。此外，可能有不止一个平衡状态。要
37、讨论这些系统的稳定性，附加的定义和判据是必需的。我们将仅讨论自激系统，因为对任意输入情况下的稳定性理论尚未建立。如果离开初始状态的轨迹返回并保持在平衡状态周围规定的区域内，则系统是稳定的。这种稳定性的广义定义通常被认为是李亚普诺夫意义下的稳定性，允许极限环和涡旋环的存在。如果在李亚普诺夫意义下稳定系统的轨迹最终收敛于平衡状态，则系统是渐进稳定的。如果系统仅在初始状态有限的状态空间内稳定，则系统是局域稳定的或叫小稳定。如果系统在整个状态空间内对任意初始状态都稳定，则系统是全局稳定的或叫大稳定。我们喜欢我们的控制系统是渐进稳定的，最好是全局稳定的；如果不是全局稳定的，最好渐进稳定的区域能包含任何预
38、期的扰动。古典控制理论的稳定性是渐进稳定的。,P2U6A Controllability,Observability,and Stability 第二部分第六单元课文A 可控性，可观性和稳定性,乍看起来是全局稳定的，但实际上是局域稳定的，因为没有任何一个系统是真正线性的。只有相对于（系统）建立的平衡状态的局域渐近稳定才能保证线性分析（可以应用）。有三种基本方法来确定非线性自激系统的稳定性。一种方法是用一个二阶系统来近似实际系统，在相平面上画出许多条轨迹，检查画出的相位图以确定稳定和不稳定区域。描述函数法与相平面结合可用来寻找和确定极限环。另一种方法叫作李亚普诺夫第一或间接方法。这种方法首先用雅
39、可比矩阵线性化每一个平衡状态的非线性矢量方程，然后检查相应的特征根以确定局域稳定性。上面提到的两种方法有时合称为李亚普诺夫第一方法。第三种方法叫作李亚普诺夫第二法或直接方法，之所以这样叫是因为这种方法不需解微分方程。这种方法可用于所有类型、任意阶数的微分方程，提供全局以及局域稳定性的答案，因而得到广泛应用。,P2U6A Controllability,Observability,and Stability 第二部分第六单元课文A 可控性，可观性和稳定性,在应用李亚普诺夫第二方法时，要研究的平衡状态转化为状态空间的原点，因此自激系统可用如下方程：平衡状态为xeq=0。李亚普诺夫渐进稳定定理是这种
40、直接方法的本质。定理说的是：如果存在正定标量函数V(x)沿着区域R 内的所有轨迹随时间衰减为零，则方程(2-6A-1)所表示的系统在闭合区域R 内是渐进稳定的。如果区域R 包含所有的状态空间，系统是全局稳定的；否则，系统在有限的区域R 内是局域稳定的。标量函数V(x)叫作李亚普诺夫函数。李亚普诺夫函数在区域R 内一定是连续的，它的一阶偏导数也一定是连续的。,(2-6A-1),P2U6A Controllability,Observability,and Stability 第二部分第六单元课文A 可控性，可观性和稳定性,李亚普诺夫函数是正定的要求指的是对状态变量的所有非零值V(x)大于零并且V
41、(0)等于零。为了保证沿区域R 内出发的所有轨迹V(x)衰减到零，dV(x)/dt 必须小于零，即，是负定的。如果 0，它是负半定的，系统仅在李亚普诺夫意义上是稳定的；如果沿着轨迹，系统是渐进稳定的。最后，如果 是不定的，则对系统的稳定性不说明任何问题，我们必须试验各种V(x)函数直到证明系统是稳定或不稳定的。另外，稳定系统能保证稳定区域的大小与选择的李亚普诺夫函数有关。,补充：摘要的写作（二）,摘要的句型,introduce(s)propose(s)present(s)describe(s)discuss(es)deal(s)withbear(s)onshow(s),1.This paper
42、(the author(s),8.3 摘要的写作,本文介绍了/提出了/描述了/讨论了/展示了,This paper proposes a technique called ZVS.,introduced proposed presented described discussed studied,2.In this paper,is(are),摘要的句型,8.3 摘要的写作,本文介绍了/提出了/描述了/讨论了/展示了,A technique which is called ZVS is proposed in this paper.,This paper is,concerned(chiefl
43、y)withaimed(mainly)atintended to,+the,studydeterminationelucidation,of,摘要的句型,8.3 摘要的写作,本文主要针对进行研究,This paper is aimed at the study of the parallel operation of inverters.,5.has(have),concludedgainedobtainedyieldedarrived atgeneratedacquired,摘要的句型,8.3 摘要的写作,本文可以得出,We has concluded that the efficiency
44、 of the converter is high from the result of experiment.,These studiesThis research,lead(s)us to,concludesuggestpostulate a conclusiona belief,that,6.,摘要的句型,8.3 摘要的写作,8.3 摘要的写作,This paper describes the objects,contents,significance,and impact of Information Super Highways project being constructed w
45、orldwide.,本文阐述了国际上建设“信息高速公路”的目标、内容、意义及其影响。,Simulation and experiment of temperature control system result show that the control system is effective to deal with unknown nonlinear dynamic system.,温度控制系统的仿真和实验结果表明：该控制系统对于处理未知的非线性动态系统是有效的。,本文提出一种新型零电压开关全桥变换器。通过在变压器原边加入合适的电感实现零电压开关。文中详细分析了该变换器的工作原理和零电压开
46、关条件。给出了1KW样机的实验结果。,8.3 摘要的写作,The experimental results of a 1kW prototype converter are also included in this paper.,A novel ZVS full-bridge converter is proposed in this paper.,This paper proposes a novel ZVS full-bridge converter.,The ZVS for the switches is achieved by adding an proper inductor in
47、 series with the primary winding of the transformer.,The operational principle and the realization of ZVS for switches are analyzed.,本文提出一种新颖的反激逆变器，详细阐述了其工作原理、控制方案和设计方法。该逆变器工作于断续模式，是由两路双向反激直流变换器输入并联输出串联组成的一种单级隔离逆变器。,This paper proposes a novel flyback inverter and detailedly introduces the operation
48、al principal,control scheme and the design method of the circuit.,This inverter works in the discontinuous conduction mode(DCM).,It is a single stage isolated inverter which consists of two bi-directional flyback dc-dc converters in parallel at input and in series at output.,8.3 摘要的写作,本文提出了一种可串联或并联输
49、出的BUCK逆变器，该逆变电路具有高频高效率运行的特点。通过合理的开关逻辑电路，实现了该逆变器串联或并联输出，从而根据需要提供两种不同规格的输出电压，满足不同负载设备的需要。,This inverter can realize series or parallel output through proper switch logic circuit,which can provide two kinds of voltage according to the need of different load device.,A novel buck inverter to realize seri
50、es or parallel output is proposed in this paper.,The proposed inverter has the characteristics of high frequency and efficiency.,8.3 摘要的写作,Abstract：This paper proposes a novel Phase-Shifted Zero-Voltage-Switching Three-Level converter.The operational principle of novel converter is analyzed,the real
