不确定时滞跳变系统的鲁棒无源控制研究
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摘要
随着科学技术的飞速发展,传统的控制理论和控制方法越来越显示出局限性,特别是高技术领域,如机器人、飞行器、大型柔性结构等,对控制系统的精确度也提出了更高的要求,这种工程实践的迫切需要是促进鲁棒控制理论迅速发展的主要因素之一。
在工业过程控制系统中,当物质和能量沿着特定的传输介质传输时,就会出现滞后,时滞是物质和能量运动过程中固有的特性,时滞现象是极其普遍的,如核反应堆、通信系统、传送系统、化工过程系统等都是典型的时滞系统。时滞的存在使得系统的分析和综合变得更加复杂和困难,同时,时滞的存在也往往是系统不稳定、振荡或系统性能变差的根源之一。因此,研究带时间延迟不确定跳变系统的鲁棒控制更具有重要的理论意义和实际指导价值。
无源性概念产生于电路理论,其后形成系统的无源性理论,并在控制理论研究以及工程系统设计中起着很重要的作用。由于无源性和稳定性有着紧密的联系,常用来分析系统的稳定性,并广泛应用于系统镇定问题的研究中。另外,耗散性理论在系统稳定性研究中也起着重要作用,其本质含义是存在一个非负的能量函数(即存储函数),使得系统的能量损耗总小于能量的供给率。而无源性则是耗散性的一个重要方面,它将输入输出的乘积作为能量的供给率,体现了系统在有界输入条件下能量的衰减特性。事实上,基于Lyapunov(李亚普诺夫)函数的稳定性理论也可以从无源性的角度加以解释。可以说,无源性是稳定性的一种更高层次的抽象。因此,研究系统的鲁棒无源控制具有重要的理论意义和实际指导价值。
本文主要从无源领域入手,利用Lyapunov-Krasovskii函数,根据线性矩阵不等式理论,研究了几种不同不确定跳变系统的鲁棒无源性、鲁棒严格无源性问题以及不同跳变系统的鲁棒无源滤波器的设计问题,所得的结果以线性矩阵不等式给出,并利用Matlab线性矩阵不等式工具箱进行系统仿真,用数值例子说明所得结果的可行性和有效性。经过理论分析、计算机仿真研究,表明本文所给出的鲁棒无源稳定性判据对不同跳变系统进行控制是可行的、有效的。
With the rapid development of science and technology, the traditional methods of control theory shows more and more limitations, Especially in high-tech fields, such as robots, aircraft, large flexible structures and so on, also put forward higher requirements for the accuracy of the control system. One of the main factors of the rapid development of robust control theory is the urgent need of this engineering practice.
In the industrial process control system, when the matter and energy along a particular transmission medium transmission, there will be delay, time delay is characteristics inherent in the process of matter and energy campaign. Time-delay phenomenon is extremely common, such as nuclear reactors, communications systems, transmission systems, chemical process systems are typically time-delay systems. The existence of time-delay makes the system analysis and synthesis become more complex and difficult, while the existence of time-delay is often one of the causes of system instability, system oscillation, or deterioration of system performance. Therefore, it has more important theoretical significance and practical guiding value to study the robust control for uncertain Markov jump systems with time-delay.
From actual conditions, the concept of passiveness appears in circuit theory, then it becomes passive theory of system, and plays a very important role in the research of control theory and engineering system design. As the closely linked of passivity and stability, we use the link to analyze the stability of the system now, while the link is also widely used in the study of system stabilization. In addition, the theory of dissipative stability also plays an important role in the system stability. Its very nature means that there is a non-negative energy function (ie the storage function), such that the system's energy loss is always smaller than the energy supply rate. Passive is an important aspect of dissipative, which makes the product of input-output energy suppy rate as the energy supply rate, this manifests the attenuation characteristic of energy about the system under bounded input conditions.
In our papers, base on the Lyapunov-Krasovskii functional method in LMI technique, we study several uncertain markovian jump systems with time-delays, including the robust passive stability, robust strictly passive stability, the controller design and the filter design. Finally, give the results in the form of linear matrix inequalities (LMIs), and then simulate system using Matlab LMI toolbox. Numerical examples illustrate the feasibility and effectiveness of the developed technique. Through theoretical analysis and computer simulation, we can get that those are effective and available that the robust passive stability criteria of uncertain markovian jump system which are investigated in this article.
在工业过程控制系统中,当物质和能量沿着特定的传输介质传输时,就会出现滞后,时滞是物质和能量运动过程中固有的特性,时滞现象是极其普遍的,如核反应堆、通信系统、传送系统、化工过程系统等都是典型的时滞系统。时滞的存在使得系统的分析和综合变得更加复杂和困难,同时,时滞的存在也往往是系统不稳定、振荡或系统性能变差的根源之一。因此,研究带时间延迟不确定跳变系统的鲁棒控制更具有重要的理论意义和实际指导价值。
无源性概念产生于电路理论,其后形成系统的无源性理论,并在控制理论研究以及工程系统设计中起着很重要的作用。由于无源性和稳定性有着紧密的联系,常用来分析系统的稳定性,并广泛应用于系统镇定问题的研究中。另外,耗散性理论在系统稳定性研究中也起着重要作用,其本质含义是存在一个非负的能量函数(即存储函数),使得系统的能量损耗总小于能量的供给率。而无源性则是耗散性的一个重要方面,它将输入输出的乘积作为能量的供给率,体现了系统在有界输入条件下能量的衰减特性。事实上,基于Lyapunov(李亚普诺夫)函数的稳定性理论也可以从无源性的角度加以解释。可以说,无源性是稳定性的一种更高层次的抽象。因此,研究系统的鲁棒无源控制具有重要的理论意义和实际指导价值。
本文主要从无源领域入手,利用Lyapunov-Krasovskii函数,根据线性矩阵不等式理论,研究了几种不同不确定跳变系统的鲁棒无源性、鲁棒严格无源性问题以及不同跳变系统的鲁棒无源滤波器的设计问题,所得的结果以线性矩阵不等式给出,并利用Matlab线性矩阵不等式工具箱进行系统仿真,用数值例子说明所得结果的可行性和有效性。经过理论分析、计算机仿真研究,表明本文所给出的鲁棒无源稳定性判据对不同跳变系统进行控制是可行的、有效的。
With the rapid development of science and technology, the traditional methods of control theory shows more and more limitations, Especially in high-tech fields, such as robots, aircraft, large flexible structures and so on, also put forward higher requirements for the accuracy of the control system. One of the main factors of the rapid development of robust control theory is the urgent need of this engineering practice.
In the industrial process control system, when the matter and energy along a particular transmission medium transmission, there will be delay, time delay is characteristics inherent in the process of matter and energy campaign. Time-delay phenomenon is extremely common, such as nuclear reactors, communications systems, transmission systems, chemical process systems are typically time-delay systems. The existence of time-delay makes the system analysis and synthesis become more complex and difficult, while the existence of time-delay is often one of the causes of system instability, system oscillation, or deterioration of system performance. Therefore, it has more important theoretical significance and practical guiding value to study the robust control for uncertain Markov jump systems with time-delay.
From actual conditions, the concept of passiveness appears in circuit theory, then it becomes passive theory of system, and plays a very important role in the research of control theory and engineering system design. As the closely linked of passivity and stability, we use the link to analyze the stability of the system now, while the link is also widely used in the study of system stabilization. In addition, the theory of dissipative stability also plays an important role in the system stability. Its very nature means that there is a non-negative energy function (ie the storage function), such that the system's energy loss is always smaller than the energy supply rate. Passive is an important aspect of dissipative, which makes the product of input-output energy suppy rate as the energy supply rate, this manifests the attenuation characteristic of energy about the system under bounded input conditions.
In our papers, base on the Lyapunov-Krasovskii functional method in LMI technique, we study several uncertain markovian jump systems with time-delays, including the robust passive stability, robust strictly passive stability, the controller design and the filter design. Finally, give the results in the form of linear matrix inequalities (LMIs), and then simulate system using Matlab LMI toolbox. Numerical examples illustrate the feasibility and effectiveness of the developed technique. Through theoretical analysis and computer simulation, we can get that those are effective and available that the robust passive stability criteria of uncertain markovian jump system which are investigated in this article.
引文
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[2]J. C. WILLEMS. Dissipative Dynamical Systems-part II:Linear Systems with Quadratic Supply rates. Arch. Rational Mech,1972,45 (5):352-393
[3]R. SEPULCHRE, M. JANKOVUC, P. V. KOKOTOVIC. Constructive Nonlinear Control. London:Sprnger Variag,1997
[4]Z. H. GUAN, H. ZHANG, S. H. YANG. Robust Passive Control for Internet Based Switching Systems with Time-Delay. Chaos Solitons and Fractals,2008,36 (2):479-486
[5]B. T. CUI, M. G. HUA. Robust Passive Control for Uncertain Discrete-Time Systems with Time-Varying Delays. Chaos Solitons and Fractals,2006,29 (2):331-341
[6]G. F. LI. H. Y. LI, C. W. YANG. Delay-Dependent Robust Passivity Control for Uncertain Time-Delay Systems. Journal of Systems Engineering and Electronics,2007,18 (4):879-884
[7]C. B. FENG, K. J. ZHANG, S. M. FEI. Passivity-Based Design of Robust Control Systems.Acta Automatica Sinica,2009,10:287-297
[8]Q. ZHONG, J. WU, J. M. YANG. Application of Passivity-Based Control in Active Power Filters. Control Theory and Applications,2003,20 (5):713-718
[9]S. V. ARJAN. L2 Gain and Passivity Techniques in Nonlinear Control. London:Sprnger-Variag, 2000
[10]C. LI, B. T. CUI. Delay-Dependent Passive Control of Linear Systems with Nonlinear Perturbation. Journal of Systems Eengineering and Electronics,2008,19(2):346-350
[I1]W. Z. SU, L. H. XIE. Robust Control of Nonlinear Feedback Passive Systems. Systems and Control Letters,1996,28(2):85-93
[12]张侃健,冯纯伯.一类非线性系统的自适应无源化控制.控制与决策,2008,23(4)：890-898
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