Trajectory Optimization of a Flexible Manipulator using Backstepping in the form of Partial Differential Equations
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- 英文论文题名：Trajectory Optimization of a Flexible Manipulator using Backstepping in the form of Partial Differential Equations
- 论文作者：Fangfei Cao ; Jinkun Liu
- 英文论文作者：Fangfei Cao ; Jinkun Liu ; School of Automation Science and Electrical Engineering ; Beihang University
- 年：2017
- 作者机构：School of Automation Science and Electrical Engineering,Beihang University;
- 英文论文关键词：Flexible manipulator ; PDE model ; Singular perturbation ; Trajectory optimization ; Backstepping control
- 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：TP241
- 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：6
- 文件大小：321k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, optimal trajectory control of a flexible manipulator is studied on the basis of partial differential equation(PDE) model. The PDE model of the flexible manipulator is established by Hamilton principle. Using singular perturbation theory, the original PDE model is divided into two decomposed subsystems. Differential evolution(DE) algorithm and cubic spline interpolating function method are applied to generate the optimal trajectory, which will minimize the deformation of flexible manipulator. Then, a backstepping boundary control scheme is proposed to regulate the joint along the optimal trajectory and suppress vibration simultaneously. In simulation, the optimum algorithm and backstepping controller are verified by MATLAB.
In this paper, optimal trajectory control of a flexible manipulator is studied on the basis of partial differential equation(PDE) model. The PDE model of the flexible manipulator is established by Hamilton principle. Using singular perturbation theory, the original PDE model is divided into two decomposed subsystems. Differential evolution(DE) algorithm and cubic spline interpolating function method are applied to generate the optimal trajectory, which will minimize the deformation of flexible manipulator. Then, a backstepping boundary control scheme is proposed to regulate the joint along the optimal trajectory and suppress vibration simultaneously. In simulation, the optimum algorithm and backstepping controller are verified by MATLAB.
In this paper, optimal trajectory control of a flexible manipulator is studied on the basis of partial differential equation(PDE) model. The PDE model of the flexible manipulator is established by Hamilton principle. Using singular perturbation theory, the original PDE model is divided into two decomposed subsystems. Differential evolution(DE) algorithm and cubic spline interpolating function method are applied to generate the optimal trajectory, which will minimize the deformation of flexible manipulator. Then, a backstepping boundary control scheme is proposed to regulate the joint along the optimal trajectory and suppress vibration simultaneously. In simulation, the optimum algorithm and backstepping controller are verified by MATLAB.
引文
[1]T.Wang,H.Gao,and J.Qiu,A Combined Fault-Tolerant and Predictive Control for Network-Based Industrial Processes,IEEE Transactions on Industrial Electronics,63(4):2529–2536,2016.
[2]T.Wang,H.Gao,and J.Qiu,A Combined Adaptive Neural Network and Nonlinear Model Predictive Control for Multirate Networked Industrial Process Control,IEEE Transactions on Neural Networks and Learning Systems,27(2):416–425,2016.
[3]T.Wang,J.Qiu,S.Yin,Y.Zhang,H.Gao,J.Fan and T.Chai,Performance-Based Adaptive Fuzzy Tracking Control for Networked Industrial Processes,IEEE Transactions on Cybernetics,46(8):1760–1770,2016.
[4]W.He,C.Sun,and S.S.Ge,Top tension control of a flexible marine riser by using integral-barrier Lyapunov function,IEEE/ASME Transactions on Mechatronics,20(2):497–505,2015.
[5]W.He,and S.S.Ge,Vibration control of a flexible beam with output constraint,IEEE Transactions on Industrial Electronics,62(8):5023–5030,2015.
[6]Z.Zhao,Y.Liu,W.He,and F.Luo,Adaptive boundary control of an axially moving belt system with high acceleration/deceleration,IET Control Theory&Applications,10(11):1299–1306,2016.
[7]Z.Liu,J.Liu,and W.He,Adaptive boundary control of a flexible manipulator with input saturation,International Journal of Control,89(6):1191–1202,2016.
[8]Y.Wei,M.Wang,and J.Qiu,New approach to delaydependent H-infinity filtering for discrete-time Markovian jump systems with time-varying delay and incomplete transition descriptions,IET Control Theory&Applications,7(5):684–696,2013.
[9]Y.Wei,J.Qiu,and J.Karimi,Filtering design for twodimensional Markovian jump systems with state-delays and deficient mode information,Information Sciences,269:316–331,2014.
[10]X.Zhang,W.Xu,S.Nair,and V.Chellaboina,PDE modeling and control of a flexible two-link manipulator,IEEE Transactions on Control Systems Technology,13(2):301–312,2005.
[11]H.Yang,and J.Liu,Distributed piezoelectric vibration control for a flexible-link manipulator based on an observer in the form of partial differential equations,Journal of Sound and Vibration,363:77–96,2016.
[12]M.Kalyoncu,Mathematical modelling and dynamic response of a multi-straight-line path tracing flexible robot manipulator with rotating-prismatic joint,Applied Mathematical Modelling,32(6):1087–1098,2008.
[13]Z.Mohamed,and M.O.Tokhi,Command shaping techniques for vibration control of a flexible robot manipulator,Mechatronics,14(1):69–90,2004.
[14]W.He,S.Zhang,and S.S.Ge,Adaptive Control of a Flexible Crane System with the Boundary Output Constraint,IEEE Transactions on Industrial Electronics,61(8):4126–4133,2014.
[15]M.Korayem,A.Nikoobin,and V.Azimirad,Trajectory optimization of flexible link manipulators in point-to-point motion,Robotica,27(6):825–840,2009.
[16]B.Pond,and I.Sharf,Experimental Evaluation of Flexible Manipulator Trajectory Optimization,Journal of Guidance Control&Dynamics,24(4):834–843,2001.
[17]P.Kokotovic,Applications of Singular Perturbation Techniques to Control Problems,Siam Review,26(4):501–550,1984.
[18]H.Yousefi,and H.Handroos,and A.Soleymani,Application of differential evolution in system identification of a servohydraulic system with a flexible load,Mechatronics,18(9):513–528,2008.
[19]T.Wang,Y.Zhang,J.Qiu,and H.Gao,Adaptive Fuzzy Backstepping Control for A Class of Nonlinear Systems With Sampled and Delayed Measurements,IEEE Transactions on Fuzzy Systems,23(2):302–312,2015.
[2]T.Wang,H.Gao,and J.Qiu,A Combined Adaptive Neural Network and Nonlinear Model Predictive Control for Multirate Networked Industrial Process Control,IEEE Transactions on Neural Networks and Learning Systems,27(2):416–425,2016.
[3]T.Wang,J.Qiu,S.Yin,Y.Zhang,H.Gao,J.Fan and T.Chai,Performance-Based Adaptive Fuzzy Tracking Control for Networked Industrial Processes,IEEE Transactions on Cybernetics,46(8):1760–1770,2016.
[4]W.He,C.Sun,and S.S.Ge,Top tension control of a flexible marine riser by using integral-barrier Lyapunov function,IEEE/ASME Transactions on Mechatronics,20(2):497–505,2015.
[5]W.He,and S.S.Ge,Vibration control of a flexible beam with output constraint,IEEE Transactions on Industrial Electronics,62(8):5023–5030,2015.
[6]Z.Zhao,Y.Liu,W.He,and F.Luo,Adaptive boundary control of an axially moving belt system with high acceleration/deceleration,IET Control Theory&Applications,10(11):1299–1306,2016.
[7]Z.Liu,J.Liu,and W.He,Adaptive boundary control of a flexible manipulator with input saturation,International Journal of Control,89(6):1191–1202,2016.
[8]Y.Wei,M.Wang,and J.Qiu,New approach to delaydependent H-infinity filtering for discrete-time Markovian jump systems with time-varying delay and incomplete transition descriptions,IET Control Theory&Applications,7(5):684–696,2013.
[9]Y.Wei,J.Qiu,and J.Karimi,Filtering design for twodimensional Markovian jump systems with state-delays and deficient mode information,Information Sciences,269:316–331,2014.
[10]X.Zhang,W.Xu,S.Nair,and V.Chellaboina,PDE modeling and control of a flexible two-link manipulator,IEEE Transactions on Control Systems Technology,13(2):301–312,2005.
[11]H.Yang,and J.Liu,Distributed piezoelectric vibration control for a flexible-link manipulator based on an observer in the form of partial differential equations,Journal of Sound and Vibration,363:77–96,2016.
[12]M.Kalyoncu,Mathematical modelling and dynamic response of a multi-straight-line path tracing flexible robot manipulator with rotating-prismatic joint,Applied Mathematical Modelling,32(6):1087–1098,2008.
[13]Z.Mohamed,and M.O.Tokhi,Command shaping techniques for vibration control of a flexible robot manipulator,Mechatronics,14(1):69–90,2004.
[14]W.He,S.Zhang,and S.S.Ge,Adaptive Control of a Flexible Crane System with the Boundary Output Constraint,IEEE Transactions on Industrial Electronics,61(8):4126–4133,2014.
[15]M.Korayem,A.Nikoobin,and V.Azimirad,Trajectory optimization of flexible link manipulators in point-to-point motion,Robotica,27(6):825–840,2009.
[16]B.Pond,and I.Sharf,Experimental Evaluation of Flexible Manipulator Trajectory Optimization,Journal of Guidance Control&Dynamics,24(4):834–843,2001.
[17]P.Kokotovic,Applications of Singular Perturbation Techniques to Control Problems,Siam Review,26(4):501–550,1984.
[18]H.Yousefi,and H.Handroos,and A.Soleymani,Application of differential evolution in system identification of a servohydraulic system with a flexible load,Mechatronics,18(9):513–528,2008.
[19]T.Wang,Y.Zhang,J.Qiu,and H.Gao,Adaptive Fuzzy Backstepping Control for A Class of Nonlinear Systems With Sampled and Delayed Measurements,IEEE Transactions on Fuzzy Systems,23(2):302–312,2015.