具有多步丢包的网络化控制系统的分析与控制
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摘要
随着计算机网络的广泛使用和网络技术的不断发展,控制系统与网络通信系统的集成已成为控制网络技术的一个热点,网络化控制系统便在这种背景下应运而生。在传统的控制系统中引入网络作为信号传输媒介,使系统的性能有了很大的改善,但同时也不可避免的带来数据包丢失、网络延迟等问题。这些问题的存在,不仅会降低系统的控制性能,甚至还可能会引起系统的不稳定。因此,在网络化控制系统领域开展研究工作具有积极和重要的意义。
本文的主要进行了具有多步丢包网络化控制系统的控制策略问题的研究。首先,研究了网络化控制系统的基本问题和建模问题。在单数据包传输情况下,建立了具有多步丢包的网络化控制系统的随机模型。基于该随机模型,研究了网络化控制系统的镇定问题。在状态完全可测的情况下,推导出闭环系统状态反馈均方渐进稳定的充分条件,并给出了状态反馈控制器的设计方法。
其次,在系统状态不完全可测的情况下,给出了基于观测器输出反馈稳定的充分条件,并给出了观测器及控制器的设计方法。在存在扰动的情况下,研究了网络化控制系统的H∞控制问题,设计了H∞控制器使系统满足给定的H∞性能指标。上述设计的控制器均以线性矩阵不等式的形式给出,可以通过Matlab的LMIs工具箱直接求解,因此提高了设计的效率。
最后,我们介绍了倒立摆系统,研究了存在多步丢包的情况下,系统的状态反馈镇定问题。在控制器设计的过程中也给出了数值仿真算例,仿真的结果表明了控制算法的有效性。
With the widely use of computer network and the continuous development ofnetwork technology, some considerable interest has been directed to the integratedcontrol systems and network communication systems, and networked control systems(NCS) appear. The insertion of network in the control systems can improve the per-formance of the systems, but inevitably brings the problems such as network-induceddelay, data packet dropouts. The performance of control systems can be degradedand even be destabilized because of the presence of these problems. Therefore, it ispositive and significant to carry out research work in the field of networked controlsystems.
The main research work of this thesis is the strategy of the networked control sys-tems with packet dropouts. Firstly, the basic problems and modeling of the networkedcontrol systems are presented. The stochastic model of networked control systemswith single packet transmission is developed. Some problems of control are studiedbased on this model. The sufficient condition of mean-square asymptotic stability isderived for closed-loop networked control systems when the states of the systems areavailable, and the method of designing the state-feedback controller is presented.
Secondly, the sufficient condition of output-feedback based on the observer fornetworked control systems and the method of designing the controller and observer areobtained when not all the states are available. we also study the problem of H∞controlfor networked control systems when there exists noise and design the H∞controllersuch that the closed-loop system is mean-square asymptotic stability with the givenH∞performance index. The controllers mentioned above are given in the terms ofLMIs which can be solved by LMI Toolbox of the Matlab software, which improvesthe efficiency of the design of the controllers.
Finally, the inverted pendulum system with multiple packet dropouts is presentedand the state feedback controller of the system is obtained according to the idea men-tioned above. Some simulation examples are given in the process of controllers de-sign, whose simulation results indicate the effectiveness of the control algorithm.
本文的主要进行了具有多步丢包网络化控制系统的控制策略问题的研究。首先,研究了网络化控制系统的基本问题和建模问题。在单数据包传输情况下,建立了具有多步丢包的网络化控制系统的随机模型。基于该随机模型,研究了网络化控制系统的镇定问题。在状态完全可测的情况下,推导出闭环系统状态反馈均方渐进稳定的充分条件,并给出了状态反馈控制器的设计方法。
其次,在系统状态不完全可测的情况下,给出了基于观测器输出反馈稳定的充分条件,并给出了观测器及控制器的设计方法。在存在扰动的情况下,研究了网络化控制系统的H∞控制问题,设计了H∞控制器使系统满足给定的H∞性能指标。上述设计的控制器均以线性矩阵不等式的形式给出,可以通过Matlab的LMIs工具箱直接求解,因此提高了设计的效率。
最后,我们介绍了倒立摆系统,研究了存在多步丢包的情况下,系统的状态反馈镇定问题。在控制器设计的过程中也给出了数值仿真算例,仿真的结果表明了控制算法的有效性。
With the widely use of computer network and the continuous development ofnetwork technology, some considerable interest has been directed to the integratedcontrol systems and network communication systems, and networked control systems(NCS) appear. The insertion of network in the control systems can improve the per-formance of the systems, but inevitably brings the problems such as network-induceddelay, data packet dropouts. The performance of control systems can be degradedand even be destabilized because of the presence of these problems. Therefore, it ispositive and significant to carry out research work in the field of networked controlsystems.
The main research work of this thesis is the strategy of the networked control sys-tems with packet dropouts. Firstly, the basic problems and modeling of the networkedcontrol systems are presented. The stochastic model of networked control systemswith single packet transmission is developed. Some problems of control are studiedbased on this model. The sufficient condition of mean-square asymptotic stability isderived for closed-loop networked control systems when the states of the systems areavailable, and the method of designing the state-feedback controller is presented.
Secondly, the sufficient condition of output-feedback based on the observer fornetworked control systems and the method of designing the controller and observer areobtained when not all the states are available. we also study the problem of H∞controlfor networked control systems when there exists noise and design the H∞controllersuch that the closed-loop system is mean-square asymptotic stability with the givenH∞performance index. The controllers mentioned above are given in the terms ofLMIs which can be solved by LMI Toolbox of the Matlab software, which improvesthe efficiency of the design of the controllers.
Finally, the inverted pendulum system with multiple packet dropouts is presentedand the state feedback controller of the system is obtained according to the idea men-tioned above. Some simulation examples are given in the process of controllers de-sign, whose simulation results indicate the effectiveness of the control algorithm.
引文
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10 M. Sahebsara, T. W. Chen, S. L. Shah. Optimal H∞Filtering in Networked Con-trol Systems with Multiple Packet Dropouts. Systems and Control Letters. 2008,57(9):696–702
11 M. Sahebsara, T. W. Chen, S. L. Shah. Optimal H2 Filtering in Networked Con-trol Systems with Multiple Packet Dropouts. IEEE Transactions on AutomaticControl. 2007, 52(8):1508–1513
12 P. Antsaklis, J. Baillieul. Guest Editorial Special Issue on Networked ControlSystems. IEEE Transactions on Automatic Control. 2004, 49(9):1421–1423
13 F. L. Lian, J. Moyne, D. Tilbury. Analysis and Modeling of Networked ControlSystems: Mimo Case with Multiple Time Delays. Proceedings of AmericanControl Conference. Arlington, America, 2001:4306–4312
14 L. A. Montestruque, P. Antsaklis. Stability of Model-based Networked ControlSystems with Time-varying Transmission Times. IEEE Transactions on Auto-matic Control. 2004, 49(9):1562–1572
15 M. Branicky, S. Phillips, W. Zhang. Stability of Networked Control Systems:Explicit Analysis of Delay. Proceedings of the American Control Conference.2000, 4:2352–2357
16陈征.基于切换模型的丢包网络控制系统的鲁棒控制技术研究.南京理工大学Ph.D. thesis. 2003
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23 J. Wu, F. Q. Deng. Finite Horizon Optimal Control of Networked Control Sys-tems with Markov Delays. Proceedings of the 6th World Congress on IntelligentControl and Automation. Dalian, China, 2006:4513–4517
24 J. Wu, F. Deng. Finite Horizon Optimal Control of Networked Control Systemswith Markov Delays. Proceeding of the Sixth World Congress on IntelligentControl and Automation. 2006, 1:4513–4517
25 F. L. Lian. Performance Evaluation of Control Networks: Ethernet, Controlnet,and Devicenet. IEEE Control Systems Magazine. 2001, 21(1):57–65
26 Q. Ling, M. Lemmon. Optimal Dropout Compensation in Networked ControlSystems. 42nd IEEE Conference on Decision and Control, 2003. Proceedings.2003, 1:670–675
27朱其新.网络控制系统的建模、分析与控制.南京航空航天大学Ph.D.thesis. 2003
28 M. Yu, L. Wang, T. Chu, et al. Stabilization of Networked Control Systems withData Packet Dropout and Network Delays via Switching System Approach. 43rdIEEE Conference on Decision and Control. 2004, 4:362–367
29 P. Zhivoglyadov, R. Middleton. Networked Control Design for Linear Systems.Automatica. 2003, 39(4):743–750
30 H. Chan, U. Ozguner. Optimal Control of Systems Over a Communication Net-work with Queuesvia a Jump System Approach. Proceedings of the 4th IEEEConference on Control Applications. 1995:1148–1153
31 W. A. Zhang, L. Yu. Output Feedback Stabilization of Networked Control Sys-tems with Packet Dropouts. IEEE Transactions on Automatic Control. 2007,52(9):1705–1710
32 M. Yu, L. Wang, T. Chu. Stability Analysis of Networked Systems with PacketDropout and Transmission Delays: Discrete-time Case. Asian Journal of Control.2005, 7(4):433–439
33 Y. Mei, L. Wang, G. Xie, et al. Stabilization of Networked Control Systems withData Packet Dropout via Switched System Approach. 2004 IEEE InternationalSymposium on Computer Aided Control Systems Desig. 2006:362–367
34 M. S. Branicky. Multiple Lyapunov Functions and Other Analysis Tools forSwitchedand Hybrid Systems. IEEE Transactions on Automatic Control. 1998,43(4):475–482
35刘振安,葛愿.基于数据包丢失的网络控制系统的稳定性分析.工业控制计算机. 2005, 18(6):11–12
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39 O. Costa. Stability Results for Discrete-time Linear Systems with MarkovianJumping Parameters. Journal of mathematical analysis and applications. 1993,179(1):154–178
40 X. Zhang, Y. Zheng, G. Lu. Stochastic Stability of Networked Control Systemswith Network-induced Delay and Data Dropout. Journal of Control Theory andApplications. 2008, 6(4):405–409
41 P. Seiler, R. Sengupta, H. Inc, et al. An H∞Approach to Networked Control.IEEE Transactions on Automatic Control. 2005, 50(3):356–364
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2 A. Mota, P. Fonseca, J. A. Fonseca. Systems Modelling and Identification inCan Based Distributed Control Systems. Proceedings of the IFAC DistributedComputer Control Systems. 2000
3 R. Krtolica, U¨. O¨zgu¨ner, H. Chan, et al. Stability of Linear Feedback Systemswith Random Communication Delays. International Journal of Control. 1994,59(4):925–953
4 W. Zhang, S. B. Michael, M. P. Stepen. Stiblity of Networked Control Systems.IEEE Control Systems Magazine. 2001, 21(2):84–99
5 L. G. Bushnell. Networks and Control. IEEE Control Systems Magazine. 2001,21(1):22–23
6 L. Wei, D. Y. Xue, S. Z. E. Some Basic Issues in Networked Control Systems.Conference on Industrial Electronics and Applications. 2007:2098–2102
7 J. Wu, F. Q. Deng, J. G. Gao. Modeling and Stability of Long Random DelayNetworked Control Systems. Proceedings of the 4th International Conference onMachine Learning and Cybernetics. Guangzhou, China, 2005:947–952
8 G. Walsh, H. Ye. Scheduling of Networked Control Systems. IEEE ControlSystems Magazine. 2001, 21(1):57–65
9 G. C. Walsh, H. Ye, L. Bushnell. Stability Analysis of Networked Control Sys-tems. IEEE Transactions on Control Systems Technology. 2002, 10(3):438–446
10 M. Sahebsara, T. W. Chen, S. L. Shah. Optimal H∞Filtering in Networked Con-trol Systems with Multiple Packet Dropouts. Systems and Control Letters. 2008,57(9):696–702
11 M. Sahebsara, T. W. Chen, S. L. Shah. Optimal H2 Filtering in Networked Con-trol Systems with Multiple Packet Dropouts. IEEE Transactions on AutomaticControl. 2007, 52(8):1508–1513
12 P. Antsaklis, J. Baillieul. Guest Editorial Special Issue on Networked ControlSystems. IEEE Transactions on Automatic Control. 2004, 49(9):1421–1423
13 F. L. Lian, J. Moyne, D. Tilbury. Analysis and Modeling of Networked ControlSystems: Mimo Case with Multiple Time Delays. Proceedings of AmericanControl Conference. Arlington, America, 2001:4306–4312
14 L. A. Montestruque, P. Antsaklis. Stability of Model-based Networked ControlSystems with Time-varying Transmission Times. IEEE Transactions on Auto-matic Control. 2004, 49(9):1562–1572
15 M. Branicky, S. Phillips, W. Zhang. Stability of Networked Control Systems:Explicit Analysis of Delay. Proceedings of the American Control Conference.2000, 4:2352–2357
16陈征.基于切换模型的丢包网络控制系统的鲁棒控制技术研究.南京理工大学Ph.D. thesis. 2003
17 A. Ray. Distributed Data Conununieation Networks for Real Time Process Con-trol. Chemical Engineering Communication. 1988, 65(2):139–145
18 Y. Tipsuwan, M. Chow. Control Methodologies in Networked Control Systems.Control Engineering Practice. 2003, 11(10):1099–1111
19 H. J. Gao, X. Y. Meng, T. W. Chen. Stabilization of Networked Control Systemswith a New Delay Characterization. IEEE Transactions on Automatic Control.2008, 53(9):2142–2148
20 H. Shousong, Z. Qixin. Stochastic Optimal Control and Analysis of Stability ofNetworked Control Systems with Long Delay. Automatica. 2003, 39(11):1877–1884
21 M. Garc′?a-Rivera, A. Barreiro. Analysis of Networked Control Systems withDrops and Variable Delays. Automatica. 2007, 43(12):2054–2059
22 W. Kim, K. Ji, A. Ambike. Networked Real-time Control Strategy Dealing withStochastic Time Delays and Packet Losses. Journal of Dynamic Systems, Mea-surement, and Control. 2006, 128:681–685
23 J. Wu, F. Q. Deng. Finite Horizon Optimal Control of Networked Control Sys-tems with Markov Delays. Proceedings of the 6th World Congress on IntelligentControl and Automation. Dalian, China, 2006:4513–4517
24 J. Wu, F. Deng. Finite Horizon Optimal Control of Networked Control Systemswith Markov Delays. Proceeding of the Sixth World Congress on IntelligentControl and Automation. 2006, 1:4513–4517
25 F. L. Lian. Performance Evaluation of Control Networks: Ethernet, Controlnet,and Devicenet. IEEE Control Systems Magazine. 2001, 21(1):57–65
26 Q. Ling, M. Lemmon. Optimal Dropout Compensation in Networked ControlSystems. 42nd IEEE Conference on Decision and Control, 2003. Proceedings.2003, 1:670–675
27朱其新.网络控制系统的建模、分析与控制.南京航空航天大学Ph.D.thesis. 2003
28 M. Yu, L. Wang, T. Chu, et al. Stabilization of Networked Control Systems withData Packet Dropout and Network Delays via Switching System Approach. 43rdIEEE Conference on Decision and Control. 2004, 4:362–367
29 P. Zhivoglyadov, R. Middleton. Networked Control Design for Linear Systems.Automatica. 2003, 39(4):743–750
30 H. Chan, U. Ozguner. Optimal Control of Systems Over a Communication Net-work with Queuesvia a Jump System Approach. Proceedings of the 4th IEEEConference on Control Applications. 1995:1148–1153
31 W. A. Zhang, L. Yu. Output Feedback Stabilization of Networked Control Sys-tems with Packet Dropouts. IEEE Transactions on Automatic Control. 2007,52(9):1705–1710
32 M. Yu, L. Wang, T. Chu. Stability Analysis of Networked Systems with PacketDropout and Transmission Delays: Discrete-time Case. Asian Journal of Control.2005, 7(4):433–439
33 Y. Mei, L. Wang, G. Xie, et al. Stabilization of Networked Control Systems withData Packet Dropout via Switched System Approach. 2004 IEEE InternationalSymposium on Computer Aided Control Systems Desig. 2006:362–367
34 M. S. Branicky. Multiple Lyapunov Functions and Other Analysis Tools forSwitchedand Hybrid Systems. IEEE Transactions on Automatic Control. 1998,43(4):475–482
35刘振安,葛愿.基于数据包丢失的网络控制系统的稳定性分析.工业控制计算机. 2005, 18(6):11–12
36宗群,王鹤.基于观测器的丢包网络控制系统控制器设计.系统工程与电子技术. 2007, 29(002):259–261
37 X. Feng, K. Loparo, Y. Ji, et al. Stochastic Stability Properties of Jump LinearSystems. IEEE Transactions on Automatic Control. 1992, 37(1):38–53
38 M. Yu, L. Wang, T. Chu, et al. Modelling and Control of Networked Systems viaJump System Approach. IET Control Theory Appl. 2008, 2(6):535–541
39 O. Costa. Stability Results for Discrete-time Linear Systems with MarkovianJumping Parameters. Journal of mathematical analysis and applications. 1993,179(1):154–178
40 X. Zhang, Y. Zheng, G. Lu. Stochastic Stability of Networked Control Systemswith Network-induced Delay and Data Dropout. Journal of Control Theory andApplications. 2008, 6(4):405–409
41 P. Seiler, R. Sengupta, H. Inc, et al. An H∞Approach to Networked Control.IEEE Transactions on Automatic Control. 2005, 50(3):356–364
42于之训,蒋平.具有传输延迟的网络控制系统中状态观测器的设计.信息与控制. 2000, 29(002):125–130
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