时延非线性网络控制系统的鲁棒控制研究
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摘要
在网络控制系统中,网络通讯将成为控制系统的一个重要环节。由于网络传输中存在传输时延,并且这些时延通常具有不确定性和时变性,另外还存在传输数据时序的错乱和丢失等现象,这些都使得系统不再具有定常性和确定性。上述两个方面对控制理论的研究提出了新的挑战和发展机遇。本文系统的分析了网络控制系统的特性,网络的随机时延特性,考虑了这些特性以及外界干扰对系统控制性能的影响,提出了H∞鲁棒控制器的设计方法,解决了网络诱导时延现象和外界干扰给控制系统带来的稳定性和鲁棒性问题。
首先考虑连续系统中时延问题。将非线性被控对象建模为T_S模糊系统,然后将时变问题分为定时延和可变时延,对于两种情况给出了系统分析,并设计了使得系统α次优稳定的控制器。
然后针对非线性T_S模糊闭环网络控制系统短时延和长时延离散化模型,把回路时延的不确定性转化为被控对象系统方程系数矩阵的不确定性,同时考虑外界干扰,利用所提出的基于LMI的次优稳定性鲁棒控制器设计方法,设计出一个状态反馈控制器,该控制器可以使得闭环网络控制系统达到L2增益小于等于γ鲁棒稳定性。
最后通过针对倒立摆T_S模糊模型,利用Matlab中TrueTime工具箱对所设计的系统的通讯平台并进行了仿真,证明了鲁棒控制器设计方法的有效性。
In Networked Control Systems(NCS), Network communication is becoming more and more important in control system. Because of the delays and the uncertainty of the delays, package drop and disorder of data, the control systems are no longer invariable or deterministic. The problems mentioned above arise new challenges and opportunities. This article analyzes the characters of NCS systematically and analyzes the impact which the characters and disturbance bring to the control system. Subsequently, the design of H∞Robust controller was given. This method solved the stability problems and Robust problems which induced from Network delays and disturbance.
Firstly, we focused on the delays problem of continuous system. This problem can be defined as invariable delays and variable delays. Analysis of system is given under both situations, and also the controller which enable systems asymptotic stable.
Secondly, the T_S fuzzy discrete NCS with both short and long delays is studied, respectively. The uncertainty of the delay is converted into the uncertainty of the system matrix. Then the controller is designed base on Linear Matrix inequality (LMI). And the controller could enable the loop system L2 gain smaller thanγrobust stable.
In the end, the T_S fuzzy system of inverted pendulum based on Truetime toolbox of Matlab is set. It is proved that the method in the method is valid.
首先考虑连续系统中时延问题。将非线性被控对象建模为T_S模糊系统,然后将时变问题分为定时延和可变时延,对于两种情况给出了系统分析,并设计了使得系统α次优稳定的控制器。
然后针对非线性T_S模糊闭环网络控制系统短时延和长时延离散化模型,把回路时延的不确定性转化为被控对象系统方程系数矩阵的不确定性,同时考虑外界干扰,利用所提出的基于LMI的次优稳定性鲁棒控制器设计方法,设计出一个状态反馈控制器,该控制器可以使得闭环网络控制系统达到L2增益小于等于γ鲁棒稳定性。
最后通过针对倒立摆T_S模糊模型,利用Matlab中TrueTime工具箱对所设计的系统的通讯平台并进行了仿真,证明了鲁棒控制器设计方法的有效性。
In Networked Control Systems(NCS), Network communication is becoming more and more important in control system. Because of the delays and the uncertainty of the delays, package drop and disorder of data, the control systems are no longer invariable or deterministic. The problems mentioned above arise new challenges and opportunities. This article analyzes the characters of NCS systematically and analyzes the impact which the characters and disturbance bring to the control system. Subsequently, the design of H∞Robust controller was given. This method solved the stability problems and Robust problems which induced from Network delays and disturbance.
Firstly, we focused on the delays problem of continuous system. This problem can be defined as invariable delays and variable delays. Analysis of system is given under both situations, and also the controller which enable systems asymptotic stable.
Secondly, the T_S fuzzy discrete NCS with both short and long delays is studied, respectively. The uncertainty of the delay is converted into the uncertainty of the system matrix. Then the controller is designed base on Linear Matrix inequality (LMI). And the controller could enable the loop system L2 gain smaller thanγrobust stable.
In the end, the T_S fuzzy system of inverted pendulum based on Truetime toolbox of Matlab is set. It is proved that the method in the method is valid.
引文
[1] G.C. Walsh, H. Ye, L. Bushnell. Stability analysis of networked control systems, IEEE Trans. Control Syst. Technol, 2002, 10 (3): 438–446.
[2] GC. Walsh, H. Ye, and L. Bushnell. Stability analysis of networked contro l4 systems, Proceedings of American Control Conference, San Diego, CA, USA,1999, Vo1.4:2876-2880
[3] Liou L. W., and Ray A., An integrated communication and control systems: Part III-nonidentical sensor and controller sampling, Journal of Dynamic Systems, Measurement and Control, 1990, 112(4):357-364
[4] R. Luck and A. Ray. An observer-based compensator for distributed delays. Automatica, 1990, Vol.26:903-908
[5]于之训,陈辉堂,王月娟.基于Markov时延特性的闭环网络控制系统研究.控制力量与应用.2002 19(2):263-267
[6]朱其新.网络控制系统的建模、分析与控制[D],南京:南京航空航天大学博士论文,2003.
[7] Matías García-Rivera, Antonio Barreiro. Analysis of networked control systems with drops and variable delays. Automatica 2007 43:2054–2059
[8] Qiu Zhanzhi, Zhang Qingling1, Zhao Zhiwu. Stability of singular networked control systems with control constraint. Journal of Systems Engineering and Electronics2007 18(2):290-296
[9] Nilsson J. Bernhardsson B. Wittenmark B.Stochastic analysis and control of real-time systems with random time delays, Automatica, 1998, 34(1): 57-64
[10]Y Halevi A.Ray. Integrated communication and control systems: Part I- Analysis, Journal of Dynamic Systems, Measurement and Control, 1988, 110(4):367-373
[11]J. Nilsson, Real-time control systems with delays, Ph.D. dissertation, Dept.Automation Control, Lund Institute of Technology, Lund, Sweden, 1998
[12] Mei Yu Long,Wang Tianguang,Chu Fei Hao. An LMI Approach to Networked Control Systems with Data Packet Dropout and Transmission Delays
[13] Hassibi A, Boyd S P, How J P. Control of asynchronous dynamical systems withrate constraints on events. Proceedings of the 38th IEEE Conference on Decision and Control. Piscataway, NJ, USA: IEEE, 1999. 1345-1351.
[14] A. Rabello and A. Bhaya. Stability of asynchronous dynamical systems withrate constraints and applications. Control Theory Appl. 2003 150(5):546
[15]樊卫华.网络控制系统的建模与控制.南京:南京理工大学博士论文
[16] Chen Peng, Yu-Chu Tian. Networked H∞control of linear systems with state quantization. Information Sciences 2007 (177):5763–5774
[17] Roger Brockett .Stabilization of motor networks. Proceeding of the 34thConference on Decision &Control. 1995,1484-1488.
[18] D.Hristu. Stabilization of LTI systems with communication constraints. Proc. Amer. Contr. Conf. Chicago, IL, 2000,2342-2346.
[19] M. S. Branic S.M.Philips W. Zhang, Stability of networked control systems: Explicit analysis of delay, Proceedings of American Control Conference, Chicago, IL, 2000, V61.4: 2352-2357
[20] A.Ray.Distributed Data Communication Networks for Real-time Process Control,Chemical Engineering Communications, 1988, 65, 139-154
[21] Zhang W., Stability analysis of networked control systems. PhD dissertation, Case Western Reserve University,2001
[22] Ling Hou,Anthony N.Michel. Asymptotic stability of systems with saturation constraints. IEEE Transactions On Automatic Control, August 1998.
[23] Huang Jian, Guan Zhihong and Wang Zhongdong. Exponential stability for networked control systems based on model of nonlinear discrete system with time-varying delay. Journal of Chongqing University. 2004, 3(1): 30-33
[24] Goodwin C. Juan Carlos Aguero, Arie Feuer. State Estimation for Systems Having Random Measurement Delays Using Errors in Variables. The 15th Triennial World Congress. Barcelona, Spain, 2002
[25]P.G Otanez, J.R. Moyne, D.M. Tilbury. Using Deadbands to Reduce Communication in Networked Control Systems. Proceedings of the 2002 American Control Conference
[26]俞立.鲁棒控制—线性矩阵不等式处理方法.清华大学出版社,2002
[27]吴忠强.非线性系统的鲁棒控制及应用.机械工业出版社,2005
[28]佟绍成王涛王艳平唐涧涛.模糊控制系统的设计及稳定性分析.科学出版社,2004
[29]胡寿松.自动控制原理.科学出版社,2001
[30]郑大钟.线性系统理论.清华大学出版社,2001
[31]冯伯纯张侃健.非线性系统的鲁棒控制.科学出版社,2004
[32]薛定宇.系统仿真技术与应用.清华大学出版社,2002
[33] Li-Sheng Hua, Tao Baia. Sampled-data control of networked linear control systems. Automatica 2007 43: 903–911
[34]Jose Yepez, Pau Marti, and Josep M. Fuertes, Control Loop Performance Analysis over Networked Control Systems, IEEE 2002 28th Annual Conference of the Industrial Electronics Society, 2002, Vo1.4:.2880-2885
[35]W Zhang, M S Branicky and S M Philips, Stability of Networked Control Systems, IEEE Control Systems Magazine, 2001, 21(1):84-99
[36] K.J.人strom and B. Wittenmark, Computer-Controlled Systems: Theory and Design, 3rd ed, Englewwood Cliffs, NJ: Prentice-Hall, 1997
[37]R. Luck and A. Ray. An observer-based compensator for distributed delays. Automatica, 1990, Vol.26:903-908
[38]Martin Ohlin , Dan Henriksson , Anton Cervin.TRUETIME 1.5—Reference ManualDepartment of Automatic Control Lund University
[2] GC. Walsh, H. Ye, and L. Bushnell. Stability analysis of networked contro l4 systems, Proceedings of American Control Conference, San Diego, CA, USA,1999, Vo1.4:2876-2880
[3] Liou L. W., and Ray A., An integrated communication and control systems: Part III-nonidentical sensor and controller sampling, Journal of Dynamic Systems, Measurement and Control, 1990, 112(4):357-364
[4] R. Luck and A. Ray. An observer-based compensator for distributed delays. Automatica, 1990, Vol.26:903-908
[5]于之训,陈辉堂,王月娟.基于Markov时延特性的闭环网络控制系统研究.控制力量与应用.2002 19(2):263-267
[6]朱其新.网络控制系统的建模、分析与控制[D],南京:南京航空航天大学博士论文,2003.
[7] Matías García-Rivera, Antonio Barreiro. Analysis of networked control systems with drops and variable delays. Automatica 2007 43:2054–2059
[8] Qiu Zhanzhi, Zhang Qingling1, Zhao Zhiwu. Stability of singular networked control systems with control constraint. Journal of Systems Engineering and Electronics2007 18(2):290-296
[9] Nilsson J. Bernhardsson B. Wittenmark B.Stochastic analysis and control of real-time systems with random time delays, Automatica, 1998, 34(1): 57-64
[10]Y Halevi A.Ray. Integrated communication and control systems: Part I- Analysis, Journal of Dynamic Systems, Measurement and Control, 1988, 110(4):367-373
[11]J. Nilsson, Real-time control systems with delays, Ph.D. dissertation, Dept.Automation Control, Lund Institute of Technology, Lund, Sweden, 1998
[12] Mei Yu Long,Wang Tianguang,Chu Fei Hao. An LMI Approach to Networked Control Systems with Data Packet Dropout and Transmission Delays
[13] Hassibi A, Boyd S P, How J P. Control of asynchronous dynamical systems withrate constraints on events. Proceedings of the 38th IEEE Conference on Decision and Control. Piscataway, NJ, USA: IEEE, 1999. 1345-1351.
[14] A. Rabello and A. Bhaya. Stability of asynchronous dynamical systems withrate constraints and applications. Control Theory Appl. 2003 150(5):546
[15]樊卫华.网络控制系统的建模与控制.南京:南京理工大学博士论文
[16] Chen Peng, Yu-Chu Tian. Networked H∞control of linear systems with state quantization. Information Sciences 2007 (177):5763–5774
[17] Roger Brockett .Stabilization of motor networks. Proceeding of the 34thConference on Decision &Control. 1995,1484-1488.
[18] D.Hristu. Stabilization of LTI systems with communication constraints. Proc. Amer. Contr. Conf. Chicago, IL, 2000,2342-2346.
[19] M. S. Branic S.M.Philips W. Zhang, Stability of networked control systems: Explicit analysis of delay, Proceedings of American Control Conference, Chicago, IL, 2000, V61.4: 2352-2357
[20] A.Ray.Distributed Data Communication Networks for Real-time Process Control,Chemical Engineering Communications, 1988, 65, 139-154
[21] Zhang W., Stability analysis of networked control systems. PhD dissertation, Case Western Reserve University,2001
[22] Ling Hou,Anthony N.Michel. Asymptotic stability of systems with saturation constraints. IEEE Transactions On Automatic Control, August 1998.
[23] Huang Jian, Guan Zhihong and Wang Zhongdong. Exponential stability for networked control systems based on model of nonlinear discrete system with time-varying delay. Journal of Chongqing University. 2004, 3(1): 30-33
[24] Goodwin C. Juan Carlos Aguero, Arie Feuer. State Estimation for Systems Having Random Measurement Delays Using Errors in Variables. The 15th Triennial World Congress. Barcelona, Spain, 2002
[25]P.G Otanez, J.R. Moyne, D.M. Tilbury. Using Deadbands to Reduce Communication in Networked Control Systems. Proceedings of the 2002 American Control Conference
[26]俞立.鲁棒控制—线性矩阵不等式处理方法.清华大学出版社,2002
[27]吴忠强.非线性系统的鲁棒控制及应用.机械工业出版社,2005
[28]佟绍成王涛王艳平唐涧涛.模糊控制系统的设计及稳定性分析.科学出版社,2004
[29]胡寿松.自动控制原理.科学出版社,2001
[30]郑大钟.线性系统理论.清华大学出版社,2001
[31]冯伯纯张侃健.非线性系统的鲁棒控制.科学出版社,2004
[32]薛定宇.系统仿真技术与应用.清华大学出版社,2002
[33] Li-Sheng Hua, Tao Baia. Sampled-data control of networked linear control systems. Automatica 2007 43: 903–911
[34]Jose Yepez, Pau Marti, and Josep M. Fuertes, Control Loop Performance Analysis over Networked Control Systems, IEEE 2002 28th Annual Conference of the Industrial Electronics Society, 2002, Vo1.4:.2880-2885
[35]W Zhang, M S Branicky and S M Philips, Stability of Networked Control Systems, IEEE Control Systems Magazine, 2001, 21(1):84-99
[36] K.J.人strom and B. Wittenmark, Computer-Controlled Systems: Theory and Design, 3rd ed, Englewwood Cliffs, NJ: Prentice-Hall, 1997
[37]R. Luck and A. Ray. An observer-based compensator for distributed delays. Automatica, 1990, Vol.26:903-908
[38]Martin Ohlin , Dan Henriksson , Anton Cervin.TRUETIME 1.5—Reference ManualDepartment of Automatic Control Lund University