多Euler-Lagrange系统抑制抖振分布式有限时间包含控制
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摘要
为了抑制多Euler-Lagrange系统分布式包含控制时控制输出的抖振现象,且实现系统的有限时间收敛,对多EulerLagrange系统的抑制抖振分布式有限时间包含控制方法进行了研究.在系统存在模型不确定性与外界干扰的情形下,采用有限时间滑模控制方法,结合系统的模型特点,提出了分布式有限时间包含控制算法.首先,通过定义包含控制误差变量和选取合适的高阶有限时间滑模变量,设计了一种分布式有限时间包含控制律.为了实现控制器输出的抑制抖振特性,将符号函数项包含在控制律的导数中,经过积分后,可以得到连续的控制输出.针对系统存在的模型不确定性和外界干扰,设计了自适应估计律对其上界进行估计和补偿.基于图论和矩阵理论,利用Lyapunov方法证明了系统能够在有限时间内稳定,且模型不确定性和外界干扰的估计是有效的.最后,选取多机械臂系统作为模型进行了仿真验证.结果表明,所提控制算法对滑模控制中因不连续的切换项产生的抖振现象有很好的抑制作用,且系统可以在有限时间内实现收敛.
This study is carried out to investigate the distributed chattering reduction finite-time containment control for multiple Euler-Lagrange systems with systems model uncertainties and external disturbances. Firstly,by defining containment control error variables and choosing an appropriate high-order finite-time sliding variable,a distributed finite-time containment control algorithm was designed. To reduce chattering,the sign function term was included in the derivative of the control law and the continuous control output was obtained by definite integral.Besides,adaptive estimation laws were proposed to approximate the upper bound of the model uncertainties and external disturbances. Based on the graph theory and matrix theory,it is demonstrated that the systems are stable in finite time and the estimation to model uncertainties and external disturbances is effective by Lyapunov method.Finally,simulation results show the effectiveness of the control law.
This study is carried out to investigate the distributed chattering reduction finite-time containment control for multiple Euler-Lagrange systems with systems model uncertainties and external disturbances. Firstly,by defining containment control error variables and choosing an appropriate high-order finite-time sliding variable,a distributed finite-time containment control algorithm was designed. To reduce chattering,the sign function term was included in the derivative of the control law and the continuous control output was obtained by definite integral.Besides,adaptive estimation laws were proposed to approximate the upper bound of the model uncertainties and external disturbances. Based on the graph theory and matrix theory,it is demonstrated that the systems are stable in finite time and the estimation to model uncertainties and external disturbances is effective by Lyapunov method.Finally,simulation results show the effectiveness of the control law.
引文
[1]CAO Lu,CHEN Xiaoqian. Input-output linearization minimum slidingmode error feedback control for spacecraft formation with large perturbations[J]. Proceedings of Institution of Mechanical Engineering,Part G:Journal of Aerospace Engineering. 2015,229(2):352. DOI:10. 1177/0954410014533674
[2]SUN Yanchao,MA Guangfu,LIU Mengmeng,et al. Distributed finite-time configuration containment control for satellite formation[J]. Proceedings of the Institution of Mechanical Engineers Part G:Journal of Aerospace Engineering,2017,231(9):1609. DOI:10.1177/0954410 016656877
[3]BULLO F,FRAZZOLI E,PAVONE M,et al. Dynamics vehicle routing for robotic systems[J]. Proceedings of the IEEE,2011,99(9):1482. DOI:10. 1109/JPROC. 2011. 2158181
[4]SUN Yanchao,MA Guangfu,LIU Mengmeng,et al. Distributed finite-time coordinated control for multi-robot systems[J].Transactions of the Institute of Measurement and Control,2018,40(9):2912. DOI:10. 1177/0142331217711493
[5]DONG Weijie. On consensus algorithms of multiple uncertain mechanical systems with a reference trajectory[J]. Automatica,2011,47(9):2023. DOI:10. 1016/j. automatica. 2011. 05. 025
[6]HONG Yiguang,HU Jiangping,GAO Linxin. Tracking control for multi-agent consensus with an active leader and variable topology[J]. Automatica, 2006, 42(7):1177. DOI:10. 1016/j. automatica. 2006. 02. 013.
[7]QIN Jiahu,ZHENG Weixin,GAO Huijun. Consensus of multiple second-order vehicles with a time-varying reference signal under directed topology[J]. Automatica,2011,47(9):1983. DOI:10.1016/j. automatica. 2011. 05. 014
[8]REN Wei. Distributed leaderless consensus algorithms for networked Euler-Lagrange systems[J]. International Journal of Control,2009,82(11):2137. DOI:10. 1080/00207170902948027
[9]梅杰,张海博,马广富.有向图中网络Euler-Lagrange系统的自适应协调跟踪[J].自动化学报,2011,37(5):596. DOI:10.3724/SP. J. 1004. 2011. 00596MEI Jie, ZHANG Haibo, MA Guangfu. Adaptive coordinated tracking for networked Euler-Lagrange systems under a directed graph[J]. Acta Automatica Sinica,2011,37(5):596. DOI:10. 3724/SP. J. 1004. 2011. 00596
[10]JI M,FERRARI-TRECATE G,EGERSTEDT M,et al. Containment control in mobile networks[J]. IEEE Transactions on Automatic Control,2008,53(5):1972. DOI:10. 1109/TAC. 2008. 930098
[11]孙延超,李传江,姚俊羽,等.无需相对速度信息的多EulerLagrange系统自适应神经网络包含控制[J].控制与决策,2016,31(4):693. DOI:10. 13195/j. kzyjc. 2015. 0198SUN Yanchao,LI Chuanjiang,YAO Junyu,et al. Adaptive neuralnetwork containment control of multiple Euler-Lagrange systems without using relative velocity information[J]. Control and Decision,2016,31(4):693. DOI:10. 13195/j. kzyjc. 2015.0198
[12]MONDAL S,MAHANTA C. Adaptive second order terminal sliding mode controller for robotic manipulators[J]. Journal of the Franklin Institute,2014,351(4):2356. DOI:10. 1016/j. jfranklin. 2013.08. 027
[13]GALICKI M. Finite-time control of robotic manipulators[J].Automatica,2015,51:49. DOI:10. 1016/j. automatica. 2014.10. 089
[14]MEI Jie,REN Wei,MA Guangfu. Distributed coordinated tracking with a dynamic leader for multiple Euler-Lagrange systems[J].IEEE Transactions on Automatic Control,2011,56(6):1415.DOI:10. 1109/TAC. 2011. 2109437
[15] ROCKAFELLAR R T. Convex analysis[M]. New Jersey:Princeton University Press,1972
[16]MEI Jie,REN Wei,MA Guangfu. Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph[J]. Automatica,2012,48(4):653. DOI:10.1016/j. automatica. 2012. 01. 020
[17]BHAT S P,BERNSTEIN D S. Finite-time stability of continuous autonomous systems[J]. SIAM Journal on Control and Optimization, 2000, 38(3):751. DOI:10. 1137/S0363012997321358
[18]HONG Yiguang. Finite-time stabilization and stabilizability of a class of controllable systems[J]. System&Control Letters,2002,46(4):231. DOI:10. 1016/S0167-6911(02)00119-6
[19]KHOO Suiyang,XIE Lihua,MAN Zhihong. Robust finite-time consensus tracking algorithm for multirobot systems[J]. IEEE/ASME Transactions on Mechatronics,2009,14(2):219. DOI:10. 1109/TMECH. 2009. 2014057
[20]SPONG M W, HUTCHINSON S, VIDYASAGAR M. Robot modeling and control[M].[S. l.]:John Wiley&Sons,Inc.,2006
[2]SUN Yanchao,MA Guangfu,LIU Mengmeng,et al. Distributed finite-time configuration containment control for satellite formation[J]. Proceedings of the Institution of Mechanical Engineers Part G:Journal of Aerospace Engineering,2017,231(9):1609. DOI:10.1177/0954410 016656877
[3]BULLO F,FRAZZOLI E,PAVONE M,et al. Dynamics vehicle routing for robotic systems[J]. Proceedings of the IEEE,2011,99(9):1482. DOI:10. 1109/JPROC. 2011. 2158181
[4]SUN Yanchao,MA Guangfu,LIU Mengmeng,et al. Distributed finite-time coordinated control for multi-robot systems[J].Transactions of the Institute of Measurement and Control,2018,40(9):2912. DOI:10. 1177/0142331217711493
[5]DONG Weijie. On consensus algorithms of multiple uncertain mechanical systems with a reference trajectory[J]. Automatica,2011,47(9):2023. DOI:10. 1016/j. automatica. 2011. 05. 025
[6]HONG Yiguang,HU Jiangping,GAO Linxin. Tracking control for multi-agent consensus with an active leader and variable topology[J]. Automatica, 2006, 42(7):1177. DOI:10. 1016/j. automatica. 2006. 02. 013.
[7]QIN Jiahu,ZHENG Weixin,GAO Huijun. Consensus of multiple second-order vehicles with a time-varying reference signal under directed topology[J]. Automatica,2011,47(9):1983. DOI:10.1016/j. automatica. 2011. 05. 014
[8]REN Wei. Distributed leaderless consensus algorithms for networked Euler-Lagrange systems[J]. International Journal of Control,2009,82(11):2137. DOI:10. 1080/00207170902948027
[9]梅杰,张海博,马广富.有向图中网络Euler-Lagrange系统的自适应协调跟踪[J].自动化学报,2011,37(5):596. DOI:10.3724/SP. J. 1004. 2011. 00596MEI Jie, ZHANG Haibo, MA Guangfu. Adaptive coordinated tracking for networked Euler-Lagrange systems under a directed graph[J]. Acta Automatica Sinica,2011,37(5):596. DOI:10. 3724/SP. J. 1004. 2011. 00596
[10]JI M,FERRARI-TRECATE G,EGERSTEDT M,et al. Containment control in mobile networks[J]. IEEE Transactions on Automatic Control,2008,53(5):1972. DOI:10. 1109/TAC. 2008. 930098
[11]孙延超,李传江,姚俊羽,等.无需相对速度信息的多EulerLagrange系统自适应神经网络包含控制[J].控制与决策,2016,31(4):693. DOI:10. 13195/j. kzyjc. 2015. 0198SUN Yanchao,LI Chuanjiang,YAO Junyu,et al. Adaptive neuralnetwork containment control of multiple Euler-Lagrange systems without using relative velocity information[J]. Control and Decision,2016,31(4):693. DOI:10. 13195/j. kzyjc. 2015.0198
[12]MONDAL S,MAHANTA C. Adaptive second order terminal sliding mode controller for robotic manipulators[J]. Journal of the Franklin Institute,2014,351(4):2356. DOI:10. 1016/j. jfranklin. 2013.08. 027
[13]GALICKI M. Finite-time control of robotic manipulators[J].Automatica,2015,51:49. DOI:10. 1016/j. automatica. 2014.10. 089
[14]MEI Jie,REN Wei,MA Guangfu. Distributed coordinated tracking with a dynamic leader for multiple Euler-Lagrange systems[J].IEEE Transactions on Automatic Control,2011,56(6):1415.DOI:10. 1109/TAC. 2011. 2109437
[15] ROCKAFELLAR R T. Convex analysis[M]. New Jersey:Princeton University Press,1972
[16]MEI Jie,REN Wei,MA Guangfu. Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph[J]. Automatica,2012,48(4):653. DOI:10.1016/j. automatica. 2012. 01. 020
[17]BHAT S P,BERNSTEIN D S. Finite-time stability of continuous autonomous systems[J]. SIAM Journal on Control and Optimization, 2000, 38(3):751. DOI:10. 1137/S0363012997321358
[18]HONG Yiguang. Finite-time stabilization and stabilizability of a class of controllable systems[J]. System&Control Letters,2002,46(4):231. DOI:10. 1016/S0167-6911(02)00119-6
[19]KHOO Suiyang,XIE Lihua,MAN Zhihong. Robust finite-time consensus tracking algorithm for multirobot systems[J]. IEEE/ASME Transactions on Mechatronics,2009,14(2):219. DOI:10. 1109/TMECH. 2009. 2014057
[20]SPONG M W, HUTCHINSON S, VIDYASAGAR M. Robot modeling and control[M].[S. l.]:John Wiley&Sons,Inc.,2006
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