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1、自动化专业英语教程教学课件July 28, 2007Email : http: / 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,
2、 and Stability 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
3、stable 渐近稳定 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 conj
4、unction n. 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, comple
5、te output 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
6、Observability 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 co
7、mplete 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. Controllability可控性Observability 可
8、观测性state- controllable状态可控unconstrained无约束的The dual concepts of controllability and 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 existe
9、nce 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. Complete observability ensures a knowledge of the state or internal behavior of the plant from a knowledge of the output. It does n
10、ot, however, guarantee that the output variables are physically measurable. dual concepts对偶的概念control of multivariable plants多变量的控制对象possible controller可能的控制器physically measurable物理可测The significance of these two concepts can“ be illustrated by consideration of a generalized nth-order plant, which w
11、ill 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 plant is not com
12、pletely 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; these mode
13、s are decoupled from the output vector. state variables状态变 量designated指定Transient mode暂态 响应decoupled衰减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 su
14、bsystem 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 the behavior of subsystems C and D. For example,
15、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 them. 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. dynamic behavior动态 特性indication指示，信息Undesirable transients不受欢迎的暂态 响应modes暂态 响应Stabi
