专业英语电气工程P2U6教学课件.ppt

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 Stabili

2、ty 第二部分第六单元课文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

3、bound v. 限制 locally stable 局域稳定 globally 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.

4、结合 identify v. 确认，识别，辨识 Jacobian matrix 雅戈比矩阵 positive definite 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 outpu

5、t controllability is separately defined in the same manner. 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。 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 Observa

6、bility,A plant (or system) is said to be completely state-controllable 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

7、control of the output, and vice versa, complete output controllability is separately 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

8、 observability are fundamental to the control of multivariable plants, particularly 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 controlle

9、r, nor does it guarantee either a realistic control vector or a practical controller. 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 sig

10、nificance of these two concepts can be illustrated by consideration of a generalized nth-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 syste

11、m we expect m and p to be less than n and would like them both to be small in number. If the plant 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. I

12、f the plant is not completely observable, there will be modes whose behavior cannot be determined; these 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

13、an input-output relationship, it is the only subsystem that can be represented by a transfer function or a transfer 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 th

14、e behavior of subsystems C and D. For example, if the modes comprising subsystem B reacted violently to any of the 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 the

15、m. This plant can be made completely controllable by appropriately adding control variables. The task of making the plant 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

16、 concepts and definitions of stability with regard to continuous-variable systems in general. The stability of stationary 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

17、 inputs. There is one finite equilibrium (singular) state, and we call the system stable if it returns to that state if disturbed. Stability is determined by the location of the eigenvalues (roots of the characteristic equation), and there are various techniques for locating the eigenvalues.,For non

18、stationary linear system and particularly for nonlinear system, stability is no longer dependent only upon the system properties but 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 thes