Robust Adaptive Boundary Control of a Vibrating String with Time-Varying Constraints
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- 英文论文题名：Robust Adaptive Boundary Control of a Vibrating String with Time-Varying Constraints
- 论文作者：Zhe Jing ; Xiuyu He ; Wei He ; Wei You ; Changyin Sun
- 英文论文作者：Zhe Jing ; Xiuyu He ; Wei He ; Wei You ; Changyin Sun ; School of Automation and Electrical Engineering ; University of Science and Technology Beijing ; Shanghai Institute of Satellite Engineering ; School of Automation ; Southeast University
- 年：2017
- 作者机构：School of Automation and Electrical Engineering,University of Science and Technology Beijing;Shanghai Institute of Satellite Engineering;School of Automation,Southeast University;
- 英文论文关键词：Boundary control ; Vibration control ; Time-varying output constraints ; Flexible structures
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O231
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：5
- 文件大小：645k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, we present the vibration control design for a string with the boundary time-varying output constraints.To prevent the constraint violations, a novel barrier Lyapunov function is proposed for the control design and stability analysis.The dynamics of the string is a distributed parameter system described by a partial differential equations(PDE) and two ordinary differential equations(ODEs). Firstly, model-based barrier control is employed to suppress the vibration of a nonlinear string under the boundary time-varying output constraints. Subsequently, adaptive control is designed to handle the system parametric uncertainties. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed design.
In this paper, we present the vibration control design for a string with the boundary time-varying output constraints.To prevent the constraint violations, a novel barrier Lyapunov function is proposed for the control design and stability analysis.The dynamics of the string is a distributed parameter system described by a partial differential equations(PDE) and two ordinary differential equations(ODEs). Firstly, model-based barrier control is employed to suppress the vibration of a nonlinear string under the boundary time-varying output constraints. Subsequently, adaptive control is designed to handle the system parametric uncertainties. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed design.
In this paper, we present the vibration control design for a string with the boundary time-varying output constraints.To prevent the constraint violations, a novel barrier Lyapunov function is proposed for the control design and stability analysis.The dynamics of the string is a distributed parameter system described by a partial differential equations(PDE) and two ordinary differential equations(ODEs). Firstly, model-based barrier control is employed to suppress the vibration of a nonlinear string under the boundary time-varying output constraints. Subsequently, adaptive control is designed to handle the system parametric uncertainties. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed design.
引文
[1]O.M.A.Per lvar Barth Berntsen and B.J.Leira,“Ensuring mooring line integrity by dynamic positioning:Controller design and experimental tests,”Automatica,vol.45,pp.1285-1290,2009.
[2]R.K.Mitra,A.K.Banik,and S.Chatterjee,“State feedback control of surge oscillations of two-point mooring system,”Journal of sound and vibration,vol.386,pp.1-20,2017.
[3]J.-Y.Choi,K.-S.Hong,and K.-J.Yang,“Exponential stabilization of an axially moving tensioned strip by passive damping and boundary control,”Journal of Vibration and Control,vol.10,no.5,pp.661-682,2004.
[4]K.-J.Yang,K.-S.Hong,and F.Matsuno,“Boundary control of an axially moving steel strip under a spatiotemporally varying tension,”JSME International Journal Series,vol.C 47,no.2,pp.665-674,2004.
[5]Y.Li,D.Aron,and C.D.Rahn,“Adaptive vibration isolation for axially moving strings:theory and experiment,”Automatica,vol.38,no.3,pp.379-390,2002.
[6]N.Wang,H.-N.Wu,and L.Guo,“Coupling-observer-based nonlinear control for flexible air-breathing hypersonic vehicles,”Nonlinear Dynamics,vol.78,no.3,pp.2141-2159,2014.
[7]B.Bhikkaji,S.R.Moheimani,and I.R.Petersen,“A negative imaginary approach to modeling and control of a collocated structure,”IEEE/ASME Transactions on Mechatronics,vol.17,no.4,pp.717-727,2012.
[8]S.Ge,T.Lee,and G.Zhu,“Non-model-based position control of a planar multi-link flexible robot,”Mechanical Systems and Signal Processing,vol.11,no.5,pp.707-724,1997.
[9]S.S.Ge,T.H.Lee,and G.Zhu,“A nonlinear feedback controller for a single-link flexible manipulator based on a finite element model,”Journal of Robotic Systems,vol.14,no.3,pp.165-178,1997.
[10]A.Armaou and P.Christofides,“Wave suppression by nonlinear finite-dimensional control,”Chemical Engineering Science,vol.55,no.14,pp.2627-2640,2000.
[11]L.Meirovitch and H.Baruh,“On the problem of observation spillover in self adjoint distributed parameter systems,”Journal of Optimization Theory and Applications,vol.39,no.2,pp.269-291,1983.
[12]B.-Z.Guo and W.Guo,“The strong stabilization of a one-dimensional wave equation by non-collocated dynamic boundary feedback control,”Automatica,vol.45,no.3,pp.790-797,2009.
[13]Q.-L.Hu,Z.Wang,and H.Gao,“Sliding mode and shaped input vibration control of flexible systems,”IEEE Transactions on Aerospace and Electronic Systems,vol.44,no.2,pp.503-519,2008.
[14]G.Yan,H.-N.Wu,J.-W.Wang,and G.Lei,“Feedback control design with vibration suppression for flexible air-breathing hypersonic vehicles,”Science China Information Sciences,vol.57,no.3,pp.1-14,2014.
[15]A.El Jai and A.Pritchard,“Sensors and actuators in distributed systems,”International Journal of Control,vol.46,no.4,pp.1139-1153,1987.
[16]B.-Z.Guo and F.-F.Jin,“The active disturbance rejection and sliding mode control approach to the stabilization of the euler-bernoulli beam equation with boundary input disturbance,”Automatica,vol.49,no.9,pp.2911-2918,2013.
[17]D.Halim and S.R.Moheimani,“Spatial resonant control of flexible structures-application to a piezoelectric laminate beam,”IEEE Transactions on Control Systems Technology,vol.9,no.1,pp.37-53,2001.
[18]W.He,S.S.Ge,B.V.E.How,Y.S.Choo,and K.-S.Hong,“Robust adaptive boundary control of a flexible marine riser with vessel dynamics,”Automatica,vol.47,no.4,pp.722-732,2011.
[19]W.He and S.S.Ge,“Robust adaptive boundary control of a vibrating string under unknown time-varying disturbance,”IEEE Transactions on Control Systems Technology,vol.20,no.1,pp.48-58,2012.
[20]Q.C.Nguyen and K.-S.Hong,“Asymptotic stabilization of a nonlinear axially moving string by adaptive boundary control,”Journal of Sound and Vibration,vol.329,no.22,pp.4588-4603,2010.
[21]H.-N.Wu and J.-W.Wang,“Static output feedback control via pde boundary and ode measurements in linear cascaded odebeam systems,”Automatica,vol.50,no.11,pp.2787-2798,2014.
[22]H.-N.Wu,J.-W.Wang,and H.-X.Li,“Design of distributed h∞fuzzy controllers with constraint for nonlinear hyperbolic pde systems,”Automatica,vol.48,no.10,pp.2535-2543,2012.
[23]H.-N.Wu and B.Luo,“Neural network based online simultaneous policy update algorithm for solving the hji equation in nonlinear h∞control,”IEEE Transactions on Neural Networks and Learning Systems,vol.23,no.12,pp.1884-1895,2012.
[24]W.He,S.Zhang,and S.S.Ge,“Adaptive boundary control of a nonlinear flexible string system,”IEEE Transactions on Control Systems Technology,vol.22,no.3,pp.1088-1093,2014.
[25]H.-N.Wu and H.-X.Li,“Finite-dimensional constrained fuzzy control for a class of nonlinear distributed process systems,”IEEE Transactions on Systems,Man,and Cybernetics,Part B(Cybernetics),vol.37,no.5,pp.1422-1430,2007.
[26]B.Ren,S.S.Ge,K.P.Tee,and T.H.Lee,“Adaptive neural control for output feedback nonlinear systems using a barrier lyapunov function,”IEEE Transactions on Neural Networks,vol.21,no.8,pp.1339-1345,2010.
[27]K.P.Tee,S.S.Ge,and E.H.Tay,“Barrier lyapunov functions for the control of output-constrained nonlinear systems,”Automatica,vol.45,no.4,pp.918-927,2009.
[28]G.H.Hardy,J.E.Littlewood,and G.Polya,“Inequalities,”1959.
[29]M.S.De Queiroz,D.M.Dawson,S.P.Nagarkatti,and F.Zhang,Lyapunov-based control of mechanical systems.Springer Science&Business Media,2012.
[30]K.P.Tee,B.Ren,and S.S.Ge,“Control of nonlinear systems with time-varying output constraints,”Automatica,vol.47,no.11,pp.2511-2516,2011.
[2]R.K.Mitra,A.K.Banik,and S.Chatterjee,“State feedback control of surge oscillations of two-point mooring system,”Journal of sound and vibration,vol.386,pp.1-20,2017.
[3]J.-Y.Choi,K.-S.Hong,and K.-J.Yang,“Exponential stabilization of an axially moving tensioned strip by passive damping and boundary control,”Journal of Vibration and Control,vol.10,no.5,pp.661-682,2004.
[4]K.-J.Yang,K.-S.Hong,and F.Matsuno,“Boundary control of an axially moving steel strip under a spatiotemporally varying tension,”JSME International Journal Series,vol.C 47,no.2,pp.665-674,2004.
[5]Y.Li,D.Aron,and C.D.Rahn,“Adaptive vibration isolation for axially moving strings:theory and experiment,”Automatica,vol.38,no.3,pp.379-390,2002.
[6]N.Wang,H.-N.Wu,and L.Guo,“Coupling-observer-based nonlinear control for flexible air-breathing hypersonic vehicles,”Nonlinear Dynamics,vol.78,no.3,pp.2141-2159,2014.
[7]B.Bhikkaji,S.R.Moheimani,and I.R.Petersen,“A negative imaginary approach to modeling and control of a collocated structure,”IEEE/ASME Transactions on Mechatronics,vol.17,no.4,pp.717-727,2012.
[8]S.Ge,T.Lee,and G.Zhu,“Non-model-based position control of a planar multi-link flexible robot,”Mechanical Systems and Signal Processing,vol.11,no.5,pp.707-724,1997.
[9]S.S.Ge,T.H.Lee,and G.Zhu,“A nonlinear feedback controller for a single-link flexible manipulator based on a finite element model,”Journal of Robotic Systems,vol.14,no.3,pp.165-178,1997.
[10]A.Armaou and P.Christofides,“Wave suppression by nonlinear finite-dimensional control,”Chemical Engineering Science,vol.55,no.14,pp.2627-2640,2000.
[11]L.Meirovitch and H.Baruh,“On the problem of observation spillover in self adjoint distributed parameter systems,”Journal of Optimization Theory and Applications,vol.39,no.2,pp.269-291,1983.
[12]B.-Z.Guo and W.Guo,“The strong stabilization of a one-dimensional wave equation by non-collocated dynamic boundary feedback control,”Automatica,vol.45,no.3,pp.790-797,2009.
[13]Q.-L.Hu,Z.Wang,and H.Gao,“Sliding mode and shaped input vibration control of flexible systems,”IEEE Transactions on Aerospace and Electronic Systems,vol.44,no.2,pp.503-519,2008.
[14]G.Yan,H.-N.Wu,J.-W.Wang,and G.Lei,“Feedback control design with vibration suppression for flexible air-breathing hypersonic vehicles,”Science China Information Sciences,vol.57,no.3,pp.1-14,2014.
[15]A.El Jai and A.Pritchard,“Sensors and actuators in distributed systems,”International Journal of Control,vol.46,no.4,pp.1139-1153,1987.
[16]B.-Z.Guo and F.-F.Jin,“The active disturbance rejection and sliding mode control approach to the stabilization of the euler-bernoulli beam equation with boundary input disturbance,”Automatica,vol.49,no.9,pp.2911-2918,2013.
[17]D.Halim and S.R.Moheimani,“Spatial resonant control of flexible structures-application to a piezoelectric laminate beam,”IEEE Transactions on Control Systems Technology,vol.9,no.1,pp.37-53,2001.
[18]W.He,S.S.Ge,B.V.E.How,Y.S.Choo,and K.-S.Hong,“Robust adaptive boundary control of a flexible marine riser with vessel dynamics,”Automatica,vol.47,no.4,pp.722-732,2011.
[19]W.He and S.S.Ge,“Robust adaptive boundary control of a vibrating string under unknown time-varying disturbance,”IEEE Transactions on Control Systems Technology,vol.20,no.1,pp.48-58,2012.
[20]Q.C.Nguyen and K.-S.Hong,“Asymptotic stabilization of a nonlinear axially moving string by adaptive boundary control,”Journal of Sound and Vibration,vol.329,no.22,pp.4588-4603,2010.
[21]H.-N.Wu and J.-W.Wang,“Static output feedback control via pde boundary and ode measurements in linear cascaded odebeam systems,”Automatica,vol.50,no.11,pp.2787-2798,2014.
[22]H.-N.Wu,J.-W.Wang,and H.-X.Li,“Design of distributed h∞fuzzy controllers with constraint for nonlinear hyperbolic pde systems,”Automatica,vol.48,no.10,pp.2535-2543,2012.
[23]H.-N.Wu and B.Luo,“Neural network based online simultaneous policy update algorithm for solving the hji equation in nonlinear h∞control,”IEEE Transactions on Neural Networks and Learning Systems,vol.23,no.12,pp.1884-1895,2012.
[24]W.He,S.Zhang,and S.S.Ge,“Adaptive boundary control of a nonlinear flexible string system,”IEEE Transactions on Control Systems Technology,vol.22,no.3,pp.1088-1093,2014.
[25]H.-N.Wu and H.-X.Li,“Finite-dimensional constrained fuzzy control for a class of nonlinear distributed process systems,”IEEE Transactions on Systems,Man,and Cybernetics,Part B(Cybernetics),vol.37,no.5,pp.1422-1430,2007.
[26]B.Ren,S.S.Ge,K.P.Tee,and T.H.Lee,“Adaptive neural control for output feedback nonlinear systems using a barrier lyapunov function,”IEEE Transactions on Neural Networks,vol.21,no.8,pp.1339-1345,2010.
[27]K.P.Tee,S.S.Ge,and E.H.Tay,“Barrier lyapunov functions for the control of output-constrained nonlinear systems,”Automatica,vol.45,no.4,pp.918-927,2009.
[28]G.H.Hardy,J.E.Littlewood,and G.Polya,“Inequalities,”1959.
[29]M.S.De Queiroz,D.M.Dawson,S.P.Nagarkatti,and F.Zhang,Lyapunov-based control of mechanical systems.Springer Science&Business Media,2012.
[30]K.P.Tee,B.Ren,and S.S.Ge,“Control of nonlinear systems with time-varying output constraints,”Automatica,vol.47,no.11,pp.2511-2516,2011.
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