一种基于控制参数化方法的柔性关节机械臂的最优PID参数整定方法
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摘要
提出了一种基于控制参数化方法的柔性关节机械臂的最优PID参数整定方法.首先,将柔性机械臂的性能指标建模为连续状态不等式约束.然后,将柔性关节机械臂的最优PID参数整定问题转化为含连续状态不等式约束的最优参数选择问题.应用约束转录法结合局部平滑法来处理连续状态不等式约束,从而将含连续状态不等式约束的最优参数选择问题转化为一个标准的可以优化软件包求解的非线性规划问题.最后,通过数值仿真验证了本文提出的方法的有效性.
A control parameterization-based optimal PID tuning scheme for flexible joint manipulator is developed in this paper. The performance specifications of the control system are modeled as continuous state inequality constraints. Then, the optimal PID tuning problem can be formulated as an optimal parameter selection problem subject to continuous inequality constraints. These continuous inequality constraints are tackled by the constraint transcription method with a local smoothing technique. In such a way, the transformed problem becomes a standard nonlinear program, which can be solved via standard optimization software packages. The effectiveness of the proposed method is illustrated by some numerical examples.
A control parameterization-based optimal PID tuning scheme for flexible joint manipulator is developed in this paper. The performance specifications of the control system are modeled as continuous state inequality constraints. Then, the optimal PID tuning problem can be formulated as an optimal parameter selection problem subject to continuous inequality constraints. These continuous inequality constraints are tackled by the constraint transcription method with a local smoothing technique. In such a way, the transformed problem becomes a standard nonlinear program, which can be solved via standard optimization software packages. The effectiveness of the proposed method is illustrated by some numerical examples.
引文
[1] ZAKI A S, MIR H, ELMARAGHY W H. Design, testing and simulation of a flexible robot for the study of dynamics and control[J]. Robotics and Automation. 1998,13(1):24-29.
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[3] KBOYER F, KHALIL W. An efficient calculation of flexible manipulator inverse dynamics[J]. Robotics Research, 1998,17(3):282-293.
[4] SICILIANO B. Closed-loop inverse Kinematics algorithm for constrained flexible manipulators under gravity[J].Robotic Systems, 1999, 16(3):353-362.
[5] ZHU Y,QIU J, TANI J. Simultaneous optimization of atwo-link flexible robot arm[J]. Robotic Systems, 2001,18(1):17-27.
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[8]刘广靖,刘卫午,刘敏.柔性机槭臂末端位置的变结型构模型参考自适应控制[J].机器人,1998, 20(4):292-296.LIU G J, LIU W W, LIU M. Variable structure model reference adaptive control for the end position of acer arm of flexible machine[J]. Robot 1998,20(4):292-296.
[9] SICILIANO B, BOOK W J. A singular perturbation approach to control of lightweight flexible manipulators[J]. Int J Robotics Research, 1988, 7(4):79-90.
[10] TALEBI H A, PATEL R V, ASMER H. Neural network based dynamic modeling of flexiblelink manipulators with application to the SSRMS[J]. Robotic Systems, 2000,17(7):385-401.
[11] AZDIZADEH A, KHORASANI K, PATEL R V. Uncertainty compasentation for a Flexiblelink manipulator using nonlinear h-infinity control[J]. Int J Control.1998, 69(6):753-771.
[12] MOALLEM M,KHORASANI K,PATEL V. Optimum structure design for improving the dynamics of flexiblelink manipulators[J]. Robotics and Automation, 1998,13(4):125-131.
[13] YIM W, SINGH S N. Trajectory control of flexible manipulator using rigid micro-manipulator system[J]. Robotics and Automation. 1997, 12(3):93-99.
[14] LIU K, KUJATH M R. Trajectory optimization for a two-link flexible manipulator[J]. Robotics and Automation, 1996, 11(2):56-71.
[15] FIGUEIREDO J, COSTA J M G. Elastic-link manipulators:modelling, simulation and experiments[J]. Robotics and Automation, 1996,11(1):13-21.
[16] XI F, FENTON R G. Continuous path planning for flexible link manipulators using the algebra of rotations[J].Robotics and Automation,1997,12(4):117-123.
[17] YAZDIZADEH A, KHORASANI K. PAFEL R V. Identification of a two-link flexible manipulators using adaptive time delay neural networks[J]. IEEE Trans Systems,Man, and Cybernetics-Part B:Cybernetics,2000,30(1):165-172.
[18] KATIC D,VUKOBRATIC M. Adaptive no-nlearning and learning connectionist control of manipulation robots with flexible links[J]. Robotics and Automation,1997,12(4):135-145.
[19] TEO K L, GOH C J, WONG K H. A Unified Computational Approach for Optimal Control Problems[M]. New York:John Wiley&Sons Inc, 1991.
[20] JENNINGS L,TEO K L,FISGER M, et al. Optimal Control Software, Theory and User Manual[J]. Department of Mathematics, The University of Western Australia, Australia, 1997.
[21] YANG F,TEO K L,LOXTON R,REHBOCK V,YU C J,et al. An efficient user-friendly visual program for solving optimal control problems[J]. Journal of Industrial and Management Optimization, 2016, 12(2):781-810.
[22]杨捷,邵锐,李冰,等.基于迭代学习的柔性关节机械臂鲁棒输出跟踪[J].哈尔滨工程大学学报.2018,39(2):1-8.YANG J, SHAO R, LI B, et al. Iterative learning observer based robust output feedback tracking control for flexible manipulator[J]. Journal of Harbin Engineering University, 2018, 39(2):1-8.
[23]刘金琨.变结构控制和仿真[M].北京:清华大学出版社出版,2005.
[24]潘博,孙京,于登云.柔性关节空间机械臂建模、控制与仿真[J].系统仿真学报,2010,22(8):1826-1831.PAN B, SUN J, YU D Y, Modeling, control and simu-lation of space manipulators with flexible joints[J].Journal of System Simulation, 2010, 22(8):1826-1831.
[25] WU C Z, TEO K L. Global impulsive optimal control computation[J]. Journal of Industrial and Management Optimization, 2006, 2(6):435-450.
[26] JENNINGS L S, TEO K L. A computational algorithm for functional inequality constrained optimization problems[J]. Automatica J IFAC, 1990, 26:371-375.
[27] TEO K L, JENNINGS L S, LEE H W J, et al. The control parameterization enhancing transform for constrained optimal control Problem, 1999, 314-335.
[28] LI B,YU C J,LOXTON R,TEO K L. Optimal discrete-valued control computation[J]. Journal of Global Optimization, 2013, 56(2):503-518.
[29]刘福才,高静,方李.不同重力环境下的柔性关节空间机械臂自适应鲁棒控制.先进制造与自动化技术[J].2015,25(1):61-69.LIU F C, GAO J, FANG L. Adaptive robust control of flexible joint space manipulators in different gravity environments[J]. 2015, 25(1):61-69.
[2] DAMAREN C J. Modal properties and control system design for two-link flexible manipulators[J]. Robotics research, 1998, 17(6):669-678.
[3] KBOYER F, KHALIL W. An efficient calculation of flexible manipulator inverse dynamics[J]. Robotics Research, 1998,17(3):282-293.
[4] SICILIANO B. Closed-loop inverse Kinematics algorithm for constrained flexible manipulators under gravity[J].Robotic Systems, 1999, 16(3):353-362.
[5] ZHU Y,QIU J, TANI J. Simultaneous optimization of atwo-link flexible robot arm[J]. Robotic Systems, 2001,18(1):17-27.
[6] NATHAN P J, SINGH S N. Sliding mode control and elastic mode stabilization of a robotic arm with flexible links[J]. ASME J Dynamic Systems, Measurement.and Control, 1991, 113:669-676.
[7] GE S S, LEE TH, ZHU G. Variable structure control of a distributed parameter flexible beam[J]. Robotic Systems, 2001, 18(1):17-27.
[8]刘广靖,刘卫午,刘敏.柔性机槭臂末端位置的变结型构模型参考自适应控制[J].机器人,1998, 20(4):292-296.LIU G J, LIU W W, LIU M. Variable structure model reference adaptive control for the end position of acer arm of flexible machine[J]. Robot 1998,20(4):292-296.
[9] SICILIANO B, BOOK W J. A singular perturbation approach to control of lightweight flexible manipulators[J]. Int J Robotics Research, 1988, 7(4):79-90.
[10] TALEBI H A, PATEL R V, ASMER H. Neural network based dynamic modeling of flexiblelink manipulators with application to the SSRMS[J]. Robotic Systems, 2000,17(7):385-401.
[11] AZDIZADEH A, KHORASANI K, PATEL R V. Uncertainty compasentation for a Flexiblelink manipulator using nonlinear h-infinity control[J]. Int J Control.1998, 69(6):753-771.
[12] MOALLEM M,KHORASANI K,PATEL V. Optimum structure design for improving the dynamics of flexiblelink manipulators[J]. Robotics and Automation, 1998,13(4):125-131.
[13] YIM W, SINGH S N. Trajectory control of flexible manipulator using rigid micro-manipulator system[J]. Robotics and Automation. 1997, 12(3):93-99.
[14] LIU K, KUJATH M R. Trajectory optimization for a two-link flexible manipulator[J]. Robotics and Automation, 1996, 11(2):56-71.
[15] FIGUEIREDO J, COSTA J M G. Elastic-link manipulators:modelling, simulation and experiments[J]. Robotics and Automation, 1996,11(1):13-21.
[16] XI F, FENTON R G. Continuous path planning for flexible link manipulators using the algebra of rotations[J].Robotics and Automation,1997,12(4):117-123.
[17] YAZDIZADEH A, KHORASANI K. PAFEL R V. Identification of a two-link flexible manipulators using adaptive time delay neural networks[J]. IEEE Trans Systems,Man, and Cybernetics-Part B:Cybernetics,2000,30(1):165-172.
[18] KATIC D,VUKOBRATIC M. Adaptive no-nlearning and learning connectionist control of manipulation robots with flexible links[J]. Robotics and Automation,1997,12(4):135-145.
[19] TEO K L, GOH C J, WONG K H. A Unified Computational Approach for Optimal Control Problems[M]. New York:John Wiley&Sons Inc, 1991.
[20] JENNINGS L,TEO K L,FISGER M, et al. Optimal Control Software, Theory and User Manual[J]. Department of Mathematics, The University of Western Australia, Australia, 1997.
[21] YANG F,TEO K L,LOXTON R,REHBOCK V,YU C J,et al. An efficient user-friendly visual program for solving optimal control problems[J]. Journal of Industrial and Management Optimization, 2016, 12(2):781-810.
[22]杨捷,邵锐,李冰,等.基于迭代学习的柔性关节机械臂鲁棒输出跟踪[J].哈尔滨工程大学学报.2018,39(2):1-8.YANG J, SHAO R, LI B, et al. Iterative learning observer based robust output feedback tracking control for flexible manipulator[J]. Journal of Harbin Engineering University, 2018, 39(2):1-8.
[23]刘金琨.变结构控制和仿真[M].北京:清华大学出版社出版,2005.
[24]潘博,孙京,于登云.柔性关节空间机械臂建模、控制与仿真[J].系统仿真学报,2010,22(8):1826-1831.PAN B, SUN J, YU D Y, Modeling, control and simu-lation of space manipulators with flexible joints[J].Journal of System Simulation, 2010, 22(8):1826-1831.
[25] WU C Z, TEO K L. Global impulsive optimal control computation[J]. Journal of Industrial and Management Optimization, 2006, 2(6):435-450.
[26] JENNINGS L S, TEO K L. A computational algorithm for functional inequality constrained optimization problems[J]. Automatica J IFAC, 1990, 26:371-375.
[27] TEO K L, JENNINGS L S, LEE H W J, et al. The control parameterization enhancing transform for constrained optimal control Problem, 1999, 314-335.
[28] LI B,YU C J,LOXTON R,TEO K L. Optimal discrete-valued control computation[J]. Journal of Global Optimization, 2013, 56(2):503-518.
[29]刘福才,高静,方李.不同重力环境下的柔性关节空间机械臂自适应鲁棒控制.先进制造与自动化技术[J].2015,25(1):61-69.LIU F C, GAO J, FANG L. Adaptive robust control of flexible joint space manipulators in different gravity environments[J]. 2015, 25(1):61-69.