网络控制系统的分析与综合
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摘要
随着计算机技术、网络技术的迅猛发展以及控制系统规模的日益扩大,21世纪的控制系统将以网络为主要特征。网络控制系统(Networked Control Systems,简称NCSs)是控制、计算机、通信、网络等多种技术交叉融合的产物,它可以应用于几乎任何带有控制器的分布设备需要进行数据交换的场合,体现了控制系统向网络化、集成化、分布化、节点智能化的发展趋势,NCSs是当前控制系统发展的新阶段。由于具有成本低、连接线数少、易于扩展维护、高效、高可靠性和信息资源共享等诸多优点,使得NCSs已在工业自动化、智能交通、机器人、航空航天、国防等领域获得了广泛的应用。但是,NCSs中由于网络的引入,不可避免地带来了许多问题:如网络传输时滞、数据丢包、多包传输、时钟异步等等。这些问题的存在,不但会降低控制系统的性能,甚至导致系统的不稳定,从而使得对NCSs的分析和设计变得十分复杂。因此,对NCSs的分析与综合是当前控制理论研究的重要内容,也已成为国内外学者研究的热点问题之一。
本文从控制理论及算法的角度出发,围绕NCSs中的一些基本问题,利用Lyapunov稳定性理论、时滞系统理论、随机系统理论及线性矩阵不等式(LMIs)方法、奇异系统方法、自由权矩阵方法等的一些现有结果对NCSs的建模、稳定性和控制进行了相关研究,在对NCSs的分析与综合过程中给出了这些基本问题的研究结果。
首先,本文介绍了NCSs的产生背景、发展历程、基本概念特点等,详细阐述了其基本内容。从控制和网络通信两个角度较全面地对国内外NCSs主要研究内容、典型研究方法进行了概括总结,指出了存在的问题及本文待研究的内容。
由于控制网络是NCSs中的重要组成部分,而时滞问题是NCSs中的核心问题之一,因此本文系统阐述了控制网络的基本概念和基本内容,重点讨论和分析了以太网(Ethernet)、控制网(ControlNet)和CAN总线三种典型控制网络的特点和性能。同时还对NCSs中的时滞问题进行详细的分析,讨论了时滞的组成、定义及其对NCSs的影响等。这些定性的分析和讨论对于研究NCSs的建模、稳定性分析与控制具有重要的指导意义和参考价值。
针对现有的研究结果大多局限于单回路NCSs的建模与分析,分别建立了多时滞NCSs和一类不确定多时滞MIMO的NCSs的各种模型,基于Lyapunov稳定性理论和LMIs方法研究了多时滞NCSs的时滞相关稳定性和镇定性问题,给出了基于广义Lyapunov矩阵方程(不等式)和LMIs形式的较小保守性的稳定和镇定判据,并设计了无记忆状态反馈控制器。
针对一类MIMO的NCSs模型,在考虑常时滞、时变时滞和系统不确定性等情形下,分别利用时滞系统理论、LMIs方法、奇异系统方法以及引入自由权矩阵等方法分析了这类不确定多时滞NCSs的鲁棒稳定性问题,给出了基于LMIs形式的与时滞相关/无关、与时滞导数相关/无关的稳定判据。同时还给出了相应的标称系统的稳定结论。与其它文献结论相比,这些结论保守性较小且更具有广泛性和一般性。数字实例和仿真表明了这些方法的有效性。
考虑到系统的不确定性及外界干扰,建立了具有丢包和时滞的NCSs模型,将其等效为一个不确定马尔可夫切换时滞系统。针对此模型,构造出一种新型的Lyapunov-Krasovskii泛函,利用Lyapunov稳定性理论、随机时滞系统理论并结合LMIs技巧和自由权矩阵等方法,研究了该系统与时滞相关的鲁棒稳定性、镇定性及具有一定干扰抑制水平的Η∞控制器设计等问题。给出了一系列基于LMIs的较小保守性的鲁棒随机稳定和镇定条件,这些结论与现有文献相比保守性更小且更具有广泛性,同时还给出了相应最大允许时滞边界(MADB)的求解算法。实例仿真说明了方法的有效性。
针对NCSs可能存在的随机扰动,研究了具有时变时滞和不确定性的线性、非线性随机扰动NCSs的鲁棒稳定性和均方指数稳定性问题。通过运用Lyapunov稳定性理论、随机时滞系统理论并结合LMIs技巧和自由权矩阵等方法,得到了一系列基于LMIs的保守性较小的鲁棒随机稳定、均方指数稳定的判据,这些结果对于确定型系统同样适用。同时给出了相应的实例仿真表明了该方法的有效性和优越性。
设计了一个NCSs的实验仿真平台。实现了对给定系统在实际网络上的仿真实验,从而为NCSs的分析和设计提供了较好的仿真环境。但是,该平台目前只是一个初步的仿真平台,在以后的工作中有待进一步完善。
最后,对全文研究工作做了总结,并对今后进一步开展的研究工作进行了展望。
With the rapid development of computer technology and network technology, together with the increasing scale of control system, the main feature of control system in 21st is involved with network. Networked control systems (NCSs) come into being by combination control technology with computer technology, communication technology and network technology, etc., wich can be applied in almost any distributed devices with controller requring data exchange. The appearance of NCSs manifest the developed trend of control systems, i.e. neworked, integrated, distributed and nodes intelligentized. NCSs are the new stage of current development of control systems. The enormous advantages of NCSs, including lower cost, reduced weight and power, simpler installation and maintenance, ease of system diagnosis, and increased system flexibility, etc., which have made NCSs increasingly popular in many real-time distributed control applications such as industrial automation, intelligent vehicle systems, mobile robotics, advance aircraft and spacecraft and national defence, etc.. However, the insertion of the network in the feedback control loop brings many new issues inevitably such as network-induced delay, data packet dropouts, multiple-packet transmission, clock synchronization, etc.. These issues can degrade the performance of control systems and can even destabilize the system, which make the analysis and design of NCSs complex. Therefore, analysis and synthesis of NCSs have become one of the most important issues in control theories study, and also have received considerable attention and interest by researchers in recent years.
In the dissertation, some essential issues of NCSs are dicussed from the point of view on control theory and arithmetic. Modelling, stability analysis and control problems of NCSs are investigated based on some existing results of Lyapunov stability theory, time-delay system theory, stochastic system theory combined with linear matrix inequalities (LMIs) techniques, descriptor system approach and free weighting matrices approach. Some new results are given in the process of analysis and synthesis on NCSs.
Firstly, the background, history, basic concepts and features of NCSs are introduced, and some essential issues of NCSs are presented in detail. From points of view on control and network communication, the main research contents and methods of NCSs at home and abroad are summarized comprehensively, and also the existing issues and contents to be studied are given.
Since control network is one of the crucial parts of NCSs and network-induced delay is the essential issues in NCSs, consequently, the basic concepts and contents of control network are introduced. Much emphasis is put on the discussion and analysis for the characteristics and performance of three typical control networks, i.e., Ethernet, ControlNet and CAN Bus. At the same time, the time-delay issues, for example, the components, definition of delay and its impact on NCSs are analyzed detaily. These qualitative analysis and discussion have much important guidance and reference values in studying of modeling, stability analysis and control for NCSs.
In view of previous results on modeling and analysis for NCSs are almost limited to single feedback control loop, a class of multiple time-delays NCSs and multi-input and multi-output (MIMO) NCSs continuous time models are proposed. Delay-dependent stability and stabilization of the NCSs with multiple time-delays are dealed with by utilizing the Lyapunov stability theory combinied with LMIs techniques. Some new less conservative stability and stabilization criteria in terms of generalized Lyapunov matrix equation (inequality) and LMIs are derived. Stabilizing controller via state feedback is formulated by solving a set of LMIs.
Considering a class of MIMO NCSs with constant delays, time-varing delays and structured uncertainties, robust stability is investigated for the uncertain NCSs with multiple time-delays based on Lyapunov stability theory approach, LMIs techniques, descriptor system approach, and free weighting matrices approach, respectively. Some new delay-dependent / delay-independent stability criteria, delay-derivative-dependent / delay-derivative-free stability conditions in terms of LMIs are given, and the results of corresponding norminal systems are also presented. These propsed reuslts are much less conservative and are more general than the existing ones. Numerical examples and simulations are provided to illustrate the effectiveness of the proposed methods.
For the NCSs with data packet dropouts and network-induced delay simultaneously, a model with structured uncertainties and exoteric disturbance is constructed, which is equivalent to an uncertain Markovian switching delayed system. By constructing a new Lyapunov-Krasovskii functional, delay-dependent robust stability, robust stabilization andΗ∞control with a prescribed disturbance attenuation level of the NCSs are investigated by combining Lyapunov stability theory, stochastic delayed system theory with LMIs techniques, descriptor system approach and free weighting matrices approach. A series of robustly stochastically stable and stabilizable criteria in terms of LMIs are obtained, which are much less conservative and more general than the existing ones. Also, the algorithms to get the maximum allowable delay bound (MADB) are given. Numerical examples and simulations show that the methods are effective.
For the NCSs with potential stochastic perturbations, the problems of robust stability and exponential stability in the mean square for a class of uncertain linear and nonlinear stochastic systems with time-varying delay are investigated. Based on Lyapunov stability theory, stochastic delayed system theroy combined with LMIs techniques and some free weighting matrices approach, some less conservative robustly stochastically stable and exponentially stable in the mean square criteria in terms of LMIs are derived, which also hold for their corresponding deterministic systems with time-varying delay. Numerical examples and simulations are given to show that the proposed methods are more effective and are an improvement over previous ones.
An experiment simulation platform for NCSs is developed. Some simulation experiments for the given systems on real network are realized on the platform, thus a comparatively better simulation environment for design and analysis of NCSs is provided. However, the plotform is just an elementary simulation software, much work leaves to be done to make it more perfect in subsequent research.
Finally, a summary has been done for all discussion in the dissertation. The research works in further study are presented.
本文从控制理论及算法的角度出发,围绕NCSs中的一些基本问题,利用Lyapunov稳定性理论、时滞系统理论、随机系统理论及线性矩阵不等式(LMIs)方法、奇异系统方法、自由权矩阵方法等的一些现有结果对NCSs的建模、稳定性和控制进行了相关研究,在对NCSs的分析与综合过程中给出了这些基本问题的研究结果。
首先,本文介绍了NCSs的产生背景、发展历程、基本概念特点等,详细阐述了其基本内容。从控制和网络通信两个角度较全面地对国内外NCSs主要研究内容、典型研究方法进行了概括总结,指出了存在的问题及本文待研究的内容。
由于控制网络是NCSs中的重要组成部分,而时滞问题是NCSs中的核心问题之一,因此本文系统阐述了控制网络的基本概念和基本内容,重点讨论和分析了以太网(Ethernet)、控制网(ControlNet)和CAN总线三种典型控制网络的特点和性能。同时还对NCSs中的时滞问题进行详细的分析,讨论了时滞的组成、定义及其对NCSs的影响等。这些定性的分析和讨论对于研究NCSs的建模、稳定性分析与控制具有重要的指导意义和参考价值。
针对现有的研究结果大多局限于单回路NCSs的建模与分析,分别建立了多时滞NCSs和一类不确定多时滞MIMO的NCSs的各种模型,基于Lyapunov稳定性理论和LMIs方法研究了多时滞NCSs的时滞相关稳定性和镇定性问题,给出了基于广义Lyapunov矩阵方程(不等式)和LMIs形式的较小保守性的稳定和镇定判据,并设计了无记忆状态反馈控制器。
针对一类MIMO的NCSs模型,在考虑常时滞、时变时滞和系统不确定性等情形下,分别利用时滞系统理论、LMIs方法、奇异系统方法以及引入自由权矩阵等方法分析了这类不确定多时滞NCSs的鲁棒稳定性问题,给出了基于LMIs形式的与时滞相关/无关、与时滞导数相关/无关的稳定判据。同时还给出了相应的标称系统的稳定结论。与其它文献结论相比,这些结论保守性较小且更具有广泛性和一般性。数字实例和仿真表明了这些方法的有效性。
考虑到系统的不确定性及外界干扰,建立了具有丢包和时滞的NCSs模型,将其等效为一个不确定马尔可夫切换时滞系统。针对此模型,构造出一种新型的Lyapunov-Krasovskii泛函,利用Lyapunov稳定性理论、随机时滞系统理论并结合LMIs技巧和自由权矩阵等方法,研究了该系统与时滞相关的鲁棒稳定性、镇定性及具有一定干扰抑制水平的Η∞控制器设计等问题。给出了一系列基于LMIs的较小保守性的鲁棒随机稳定和镇定条件,这些结论与现有文献相比保守性更小且更具有广泛性,同时还给出了相应最大允许时滞边界(MADB)的求解算法。实例仿真说明了方法的有效性。
针对NCSs可能存在的随机扰动,研究了具有时变时滞和不确定性的线性、非线性随机扰动NCSs的鲁棒稳定性和均方指数稳定性问题。通过运用Lyapunov稳定性理论、随机时滞系统理论并结合LMIs技巧和自由权矩阵等方法,得到了一系列基于LMIs的保守性较小的鲁棒随机稳定、均方指数稳定的判据,这些结果对于确定型系统同样适用。同时给出了相应的实例仿真表明了该方法的有效性和优越性。
设计了一个NCSs的实验仿真平台。实现了对给定系统在实际网络上的仿真实验,从而为NCSs的分析和设计提供了较好的仿真环境。但是,该平台目前只是一个初步的仿真平台,在以后的工作中有待进一步完善。
最后,对全文研究工作做了总结,并对今后进一步开展的研究工作进行了展望。
With the rapid development of computer technology and network technology, together with the increasing scale of control system, the main feature of control system in 21st is involved with network. Networked control systems (NCSs) come into being by combination control technology with computer technology, communication technology and network technology, etc., wich can be applied in almost any distributed devices with controller requring data exchange. The appearance of NCSs manifest the developed trend of control systems, i.e. neworked, integrated, distributed and nodes intelligentized. NCSs are the new stage of current development of control systems. The enormous advantages of NCSs, including lower cost, reduced weight and power, simpler installation and maintenance, ease of system diagnosis, and increased system flexibility, etc., which have made NCSs increasingly popular in many real-time distributed control applications such as industrial automation, intelligent vehicle systems, mobile robotics, advance aircraft and spacecraft and national defence, etc.. However, the insertion of the network in the feedback control loop brings many new issues inevitably such as network-induced delay, data packet dropouts, multiple-packet transmission, clock synchronization, etc.. These issues can degrade the performance of control systems and can even destabilize the system, which make the analysis and design of NCSs complex. Therefore, analysis and synthesis of NCSs have become one of the most important issues in control theories study, and also have received considerable attention and interest by researchers in recent years.
In the dissertation, some essential issues of NCSs are dicussed from the point of view on control theory and arithmetic. Modelling, stability analysis and control problems of NCSs are investigated based on some existing results of Lyapunov stability theory, time-delay system theory, stochastic system theory combined with linear matrix inequalities (LMIs) techniques, descriptor system approach and free weighting matrices approach. Some new results are given in the process of analysis and synthesis on NCSs.
Firstly, the background, history, basic concepts and features of NCSs are introduced, and some essential issues of NCSs are presented in detail. From points of view on control and network communication, the main research contents and methods of NCSs at home and abroad are summarized comprehensively, and also the existing issues and contents to be studied are given.
Since control network is one of the crucial parts of NCSs and network-induced delay is the essential issues in NCSs, consequently, the basic concepts and contents of control network are introduced. Much emphasis is put on the discussion and analysis for the characteristics and performance of three typical control networks, i.e., Ethernet, ControlNet and CAN Bus. At the same time, the time-delay issues, for example, the components, definition of delay and its impact on NCSs are analyzed detaily. These qualitative analysis and discussion have much important guidance and reference values in studying of modeling, stability analysis and control for NCSs.
In view of previous results on modeling and analysis for NCSs are almost limited to single feedback control loop, a class of multiple time-delays NCSs and multi-input and multi-output (MIMO) NCSs continuous time models are proposed. Delay-dependent stability and stabilization of the NCSs with multiple time-delays are dealed with by utilizing the Lyapunov stability theory combinied with LMIs techniques. Some new less conservative stability and stabilization criteria in terms of generalized Lyapunov matrix equation (inequality) and LMIs are derived. Stabilizing controller via state feedback is formulated by solving a set of LMIs.
Considering a class of MIMO NCSs with constant delays, time-varing delays and structured uncertainties, robust stability is investigated for the uncertain NCSs with multiple time-delays based on Lyapunov stability theory approach, LMIs techniques, descriptor system approach, and free weighting matrices approach, respectively. Some new delay-dependent / delay-independent stability criteria, delay-derivative-dependent / delay-derivative-free stability conditions in terms of LMIs are given, and the results of corresponding norminal systems are also presented. These propsed reuslts are much less conservative and are more general than the existing ones. Numerical examples and simulations are provided to illustrate the effectiveness of the proposed methods.
For the NCSs with data packet dropouts and network-induced delay simultaneously, a model with structured uncertainties and exoteric disturbance is constructed, which is equivalent to an uncertain Markovian switching delayed system. By constructing a new Lyapunov-Krasovskii functional, delay-dependent robust stability, robust stabilization andΗ∞control with a prescribed disturbance attenuation level of the NCSs are investigated by combining Lyapunov stability theory, stochastic delayed system theory with LMIs techniques, descriptor system approach and free weighting matrices approach. A series of robustly stochastically stable and stabilizable criteria in terms of LMIs are obtained, which are much less conservative and more general than the existing ones. Also, the algorithms to get the maximum allowable delay bound (MADB) are given. Numerical examples and simulations show that the methods are effective.
For the NCSs with potential stochastic perturbations, the problems of robust stability and exponential stability in the mean square for a class of uncertain linear and nonlinear stochastic systems with time-varying delay are investigated. Based on Lyapunov stability theory, stochastic delayed system theroy combined with LMIs techniques and some free weighting matrices approach, some less conservative robustly stochastically stable and exponentially stable in the mean square criteria in terms of LMIs are derived, which also hold for their corresponding deterministic systems with time-varying delay. Numerical examples and simulations are given to show that the proposed methods are more effective and are an improvement over previous ones.
An experiment simulation platform for NCSs is developed. Some simulation experiments for the given systems on real network are realized on the platform, thus a comparatively better simulation environment for design and analysis of NCSs is provided. However, the plotform is just an elementary simulation software, much work leaves to be done to make it more perfect in subsequent research.
Finally, a summary has been done for all discussion in the dissertation. The research works in further study are presented.
引文
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