【作者】 汪志鸣；

【导师】 郑毓蕃；

【作者基本信息】 华东师范大学 ， 系统分析与集成， 2003， 博士

【摘要】 工程实践中遇到的动态系统通常是连续时间系统，与此相反，大多数复杂系统的反馈控制却是通过观察采样点上的系统行为来进行控制的，结果所得到的反馈控制系统是个混合系统，它含有连续信号和离散信号，这样的系统称之为采样系统，当今连续受控系统中数字控制器的广泛运用促进了对采样系统的研究，已有的线性采样系统理论显然不能满足处理非线性采样系统的需要，因此近年来非线性采样系统的分析与设计已经成为国际控制论界的持续的研究热点之一。 利用计算机等一类离散控制装置来控制连续时间的受控对象时，都会遇到把连续时间系统化为等价的离散时间系统的问题，通过采样器和保持器来实现离散时间的采样控制，对于非线性连续受控系统，由于连续系统的时间离散化后一般得不到其等价的精确离散化模型表示的有限形式，实际上由其近似离散化模型代替来设计控制器，而近似会引起信号失真，那么基于近似离散化模型上设计的采样控制器，它是否同样对原连续受控系统有效?这是一个理论上需要认真研究的问题，1998年以来，A．Teel，D．Nesic等最先研究这样一类非线性控制系统的镇定问题，他们在采样间隔充分小的条件下，给出了各类以实用稳定方式的可镇定充分条件，通常对于实际控制器而言，其执行机构的工作响应频率是有限制的，控制器的采样周期不可能任意小，而在工业控制实践中，往往给定采样周期，然后进行控制器设计，这是许多采样系统所面临的情况，因此当采样周期固定条件下的这样一类基本问题仍然没有解决，郑毓蕃教授首先研究了采样间隔固定条件下非线性采样系统的镇定问题，他用连续原型的方法研究了指数稳定类型的镇定问题，P Kokotovic在2001年的国际自动化(Automatica[13])杂志上也提出这样的问题，本文在采样周期固定的条件下，研究基于近似离散化模型上设计的镇定采样控制器控制其连续受控系统的各类镇定问题，我们采用精确离散化模型与连续受控系统之间的镇定关系加上研究该精确离散化模型和近似离散化模型之间的镇定关系这样的技术路线，前者处理的方法与线性采样系统的理论有相似之处，因为精确离散化模型的状态在采样点上与连续受控系统的状态一致，而后者可纳入离散系统研究的轨道，唯一的区别是离散化模型是个含参数T的离散系统，利用离散李雅普诺夫函数直接方法，给出了关于参数了一致的指数稳定，渐近稳定以及输入到状态稳定概念并研究它们的各类镇定问题的充分条件，以及讨论相应的设计问题，全文包括以下几个部分： 第一部分：对于基于近似离散化模型上设计控制器的非线性采样系统问题产生的背景，研究现状和发展前景作一个大概的回顾，并且对解决问题所采用的方法给出基本的框架，并提出了保证本文方法有效的2个基本假设。 第二部分：含参数离散时间动力系统的李雅普诺夫函数理论是我们问题研究的数学基础，特别是含参数离散李雅普诺大逆定理的现代处理至关重要，它是相关的扰动分析的理论根基，为了研究的需要，我们用K类函数刻划含参数离散动力系统的各种稳定性，并且得到了相应稳定性的等价定理，同时对含参数离散动力系统的李雅普诺夫函数理论给出较系统的处理，特别给出了离散动力系统用K函数表征的一些技术性引理。 第三部分：在采样周期固定的条件下，研究基于近似离散化模型上设计的关于参数T一致的渐近稳定采样控制器能够以渐近稳定方式一致镇定其连续受控系统的条件。在所设计的控制器下，首先讨论连续受控系统的近似离散化模型和精确离散化模型之间的镇定关系，其次讨论连续受控系统和精确离散化模型之间的镇定关系，最后综合得到基于近似离散化模型上设计的关于参数T一致的控制器能够以渐近稳定方式一致镇定连续受控系统的各种充分条件。 第四部分：在采样周期固定的条件下，研究基于近似离散化模型上设计的关于参数T一致的指数稳定采样控制器能够以指数稳定或者渐近稳定方式一致镇定其连续受控系统的各种条件，处理的思想方法与第三部分大致相同，但该问题要比渐近稳定的结果要好得多. 第五部分二输入到状态稳定(155)是上世纪80年代末在研究控制论问题时才提出的较新的稳定性概念，本文首先给出局部155与存在局部李雅普诺夫155函数之间的等价定理.在此基础上研究基于近似离散化模型上设计的关于参数T一致的局部155反馈控制器能够一致局部155可镇定连续受控系统的问题，特别证明了155可镇定与可镇定是等价的结论.分别讨论了在局部截断误差满足无穷小上界条件和有界条件下的各类局部155可镇定问题. 第六部分:首先研究可容许采样周期的上界T’的存在性及其估计，指出T’实际上是近似离散化闭环系统的一个奇异点.因此可以利用奇异点理沦和方法来估计可容许采样周期的上确界T’的问题.在前面镇定问题理论工作的基础上，我们给出各种设计方法，在解析条件下，提出反馈线性化设计方法处理局部截断误差满足无穷小上界条件的情况.最后给出仿真例子. 第六部分:问题的总结和展望，提出未解决的问题以及研究方向. 在固定采样间隔条件下，基于近似离散化模型上设计一的采样控制器控制其连续?更多还原

【Abstract】 Dynamical systems encountered in engineering usually evolve in continuous time. Contrasting this, in feedback control the most majority of complex systems are controlled using sampled observations of system behavior taken at discrete time instants. Thus the resulting controlled systems are hybrid systems, which are called sampled-data systems, involving both continuous-time and discrete-time signals. The investigation of sampled-data systems is motivated primarily due to the widespread use of digitally implemented controller in present-day feedback control of continuous-time systems. Linear sampled-data control theory does not suffice to deal with nonlinear sampled-data systems. Hence analysis and design of nonlinear sampled-data systems has been, in recent years, a subject of growing interest in the international community of control research.When a continuous-time plant is controlled using a digitally implemented controller, it is often faced that a continuous-time plant is transformed into its equivalent discrete-time model. A digital controller is usually designed on the base of approximate discrete-time models of the continuous-time nonlinear systems because it is difficult to obtain the closed form of the exact discrete-time model for nonlinear control systems. Approximation usually makes signal distortion. A natural question is raised that the controllers based on the approximate models are still working for the original continuous-time systems. This is a question that must be seriously investigated. A. Teel, D. Nesic etc. initially studied ISS stabilization of nonlinear sample-data systems of this type in 1998. Practical stabilization of nonlinear sampled-data systems based on discrete-time approximation with sufficiently small sampling periods has been studied in recent years. The sufficient conditions have been given for the practical stabilization of the above case. Often in practice, however, response frequency of implemented devices is limited and a sampling period could not be sufficiently small, and furthermore a sampling period T is usually fixed prior to the design of the controller in engineering. This is a common situation for many nonlinear sampled-data systems. A fundamental design question is therefore left open for the case when the sampling period T is fixed first. Prof. Zheng Yufan was first to investigate the case of a fixed sampling period. He studied exponential stabilization using continuous prototype approach. And the distinguished scientist P. Kokotovic also proposed such kind of question in his paper "Constructive Nonlinear Control: A Historical Perspective", Automatica 37, 2001, 637-662. In this paper, we shall restrict ourselves to the subject of stabilization of nonlinear sample-data systems in the case of T fixed prior to the design of the controller. We study stabilization between the controlled continuous-time plant and its equivalent exact discrete-time model using the feedback controller designed on its approximate discrete-time models and stabilization between the exact discrete-time model and the approximate discrete-time models using the same controller. The approach we use for the former is similar to the one for linear sampled-data systems because the exact discrete-time model just coincides a state of the continuous-time plant at sampling instants. The latter is brought into the framework of pure discrete-time investigation. So a discrete Lyapunov direct method and its modern theory with k class function is applicable to the case of the latter. In this paper, various kinds of stabilization are investigated for the cases of exponential stability, asymptotic stability and their relevant practical stability. Meanwhile, various sufficient conditions are given. Furthermore, Various tools of nonlinear control design are introduced Thepaper is organized as follows:In the part one, we introduce a background and currant research situation of nonlinear sampled-data systems using digital controller designed on the base of the approximation and brief a main ide更多还原