基于非奇异终端滑模的物料提升机位置控制
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摘要
为解决一类物料提升机在惯性参数不确定情况下的精确位置控制问题,基于非奇异终端滑控制方法设计了物料提升机的控制器,并将其用于单斗-链式旋臂物料提升机。仿真试验结果表明,和现有隐式李雅普诺夫函数连续反馈位置控制器相比,所提出的控制器将系统位移响应最大超调量从144%减少为10.6%,调节时间从2.84减少为1.95 s;角位移响应的最大超调量从62.8%减少到0,调节时间从2.3减少为2.0 s,有效改善了物料提升机工作过程中的控制品质。该研究为物料提升机的控制器设计提供了参考。
When implementing different tasks,the servo systems of elevator must adapt to various working loads with different weight or inertia,which may lead to the remarkable variation of system inertial parameters.Due to uncertain inertial parameters,the traditional proportional-integral-differential(PID)control algorithm has poor robustness and cannot achieve high-accuracy position control.A novel nonlinear control scheme is needed to deal with the problem of uncertain inertial parameters.To realize position control with high accuracy and stability for the elevator with uncertain inertial parameters,a control method based on global non-singular terminal sliding mode was proposed for a single-bucket-chain elevator.By adding a nonlinear term to the conventional linear sliding mode surface,the terminal sliding mode could make the system state converge to the sliding surface in finite time.The global non-singular terminal sliding mode technique was used for elevator system to achieve robust stability and guarantee transient response,and the boundary layer control was adopted to avoid chattering introduced by control switching.The stability of the closed-loop system was guaranteed based on the Lyapunov theory.Firstly,the dynamic model of the single-bucket-chain elevator was set up based on the Lagrange method.Secondly,a controller based on global non-singular terminal sliding mode was designed for a single-bucket-chain elevator.Finally,to illustrate the proposed controller with the global non-singular terminal sliding mode had better performances than the continuous feedback controller based on implicit Lyapunov function,numerical simulations had been carried out on the basis of MATLAB/Simulink simulation platform.The position response,speed response and the control input response of hoist part and rotation part were analyzed respectively.The position response results showed that the maximum overshoot by global non-singular terminal sliding mode method was 10.6% while it was 144% by the implicit Lyapunov function continuous feedback controller(ILFCFC).The control settling time was decreased from 2.84 to 1.95 s.The angle position response results showed that the global non-singular terminal sliding mode method had no overshoot while it was 62.8% by the ILFCFC.The control settling time was decreased from 2.3 to 2.0 s.The speed response results showed that the speed maximums by global non-singular terminal sliding mode method were 0.91 m/s and 1.05 rad/s while they were 3.69 m/s and 4.98 rad/s by the ILFCFC.The control input response results showed that the maximum by global non-singular terminal sliding mode method were 633.4 N and 399.6 N·m respectively for hoist part and rotation part while they were 1440 N and 1289 N·m by the ILFCFC.Through the comparison with the continuous feedback controller based on implicit Lyapunov function,the position response was faster,the position maximum overshoot was smaller,and the speed response and the control input response varied more smoothly and rapidly for global non-singular terminal sliding mode method.The control system had better dynamic and static performance.The correctness and effectiveness of control method with non-singular terminal sliding mode was verified by computer simulation in this paper.The control method with global non-singular terminal sliding mode can improve control quality and has great robustness to uncertain inertial parameters,which will lay a foundation for further study of the elevator control.
When implementing different tasks,the servo systems of elevator must adapt to various working loads with different weight or inertia,which may lead to the remarkable variation of system inertial parameters.Due to uncertain inertial parameters,the traditional proportional-integral-differential(PID)control algorithm has poor robustness and cannot achieve high-accuracy position control.A novel nonlinear control scheme is needed to deal with the problem of uncertain inertial parameters.To realize position control with high accuracy and stability for the elevator with uncertain inertial parameters,a control method based on global non-singular terminal sliding mode was proposed for a single-bucket-chain elevator.By adding a nonlinear term to the conventional linear sliding mode surface,the terminal sliding mode could make the system state converge to the sliding surface in finite time.The global non-singular terminal sliding mode technique was used for elevator system to achieve robust stability and guarantee transient response,and the boundary layer control was adopted to avoid chattering introduced by control switching.The stability of the closed-loop system was guaranteed based on the Lyapunov theory.Firstly,the dynamic model of the single-bucket-chain elevator was set up based on the Lagrange method.Secondly,a controller based on global non-singular terminal sliding mode was designed for a single-bucket-chain elevator.Finally,to illustrate the proposed controller with the global non-singular terminal sliding mode had better performances than the continuous feedback controller based on implicit Lyapunov function,numerical simulations had been carried out on the basis of MATLAB/Simulink simulation platform.The position response,speed response and the control input response of hoist part and rotation part were analyzed respectively.The position response results showed that the maximum overshoot by global non-singular terminal sliding mode method was 10.6% while it was 144% by the implicit Lyapunov function continuous feedback controller(ILFCFC).The control settling time was decreased from 2.84 to 1.95 s.The angle position response results showed that the global non-singular terminal sliding mode method had no overshoot while it was 62.8% by the ILFCFC.The control settling time was decreased from 2.3 to 2.0 s.The speed response results showed that the speed maximums by global non-singular terminal sliding mode method were 0.91 m/s and 1.05 rad/s while they were 3.69 m/s and 4.98 rad/s by the ILFCFC.The control input response results showed that the maximum by global non-singular terminal sliding mode method were 633.4 N and 399.6 N·m respectively for hoist part and rotation part while they were 1440 N and 1289 N·m by the ILFCFC.Through the comparison with the continuous feedback controller based on implicit Lyapunov function,the position response was faster,the position maximum overshoot was smaller,and the speed response and the control input response varied more smoothly and rapidly for global non-singular terminal sliding mode method.The control system had better dynamic and static performance.The correctness and effectiveness of control method with non-singular terminal sliding mode was verified by computer simulation in this paper.The control method with global non-singular terminal sliding mode can improve control quality and has great robustness to uncertain inertial parameters,which will lay a foundation for further study of the elevator control.
引文
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[16]刘浩蓬,龙长江,万鹏,等.植保四轴飞行器的模糊PID控制[J].农业工程学报,2015,31(1):71-77.Liu Haopeng,Long Changjiang,Wan Peng,et al.Fuzzy self-adjusting proportion integration differentiation for eppoquadrocopter[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2015,31(1):71-77.(in Chinese with English abstract)
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[18]杜慧秋.基于模糊自适应不确定性机械臂的轨迹跟踪控制[J].电机与控制学报,2005,9(3):238-243.Du Huiqiu.Tracking control of uncertain robotic manipulator system based on a fuzzy adaptive approach[J].Electric Machines and Control,2005,9(3):238-243.(in Chinese with English abstract)
[19]梁喜凤,杨犇,王永维.番茄收获机械手轨迹跟踪模糊控制仿真与试验[J].农业工程学报,2013,29(17):16-23.Liang Xifeng,Yang Ben,Wang Yongwei.Simulation and test of trajectory tracking control for tomato harvesting manipulator based on fuzzy logic compensation[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2013,29(17):16-23.(in Chinese with English abstract)
[20]刘强,冯培恩.惯性参数大范围变化机械伺服系统鲁棒跟踪控制[J].控制理论与应用,2005,22(6):983-986.Liu Qiang,Feng Penen.Robust tracking control of mechanical servo systems with inertial parameters varying in large range[J].Control Theory&Applications,2005,22(6):983-986.
[21]Van M,Kang H J,Suh Y S,et al.Output feedback tracking control of uncertain robot manipulators via higher-order sliding-mode observer and fuzzy compensator[J].Journal of Mechanical Science and Technology,2013,27(8):2487-2496.
[22]Bartoszewicz A,Patton R J.Sliding mode control[J].International Journal of Adaptive Control and Signal Processing,2007,21(8/9):635-637.
[23]Liu Jinkun Sun Fuchun.A novel dynamic terminal sliding mode control of uncertain nonlinear systems[J].Journal of Control Theory and Applications,2007,5(2):189-193
[24]杨庆华,王燕,高峰,等.基于摆线运动的黄瓜采摘机器人终端滑模轨迹跟踪控制[J].农业工程学报,2009,25(5):94-99.Yang Qinghua,Wang Yan,Gao Feng,et a1.Trajectory tracking with terminal sliding mode control of cucumber picking robot manipulator based on cycloidal motion[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2009,25(5):94-99.(in Chinese with English abstract)
[25]夏国清,武慧勇,赵昂,等.船舶航向跟踪系统自适应滤波反步终端滑模控制[J].北京理工大学学报,2015,35(2):180-185.Xia Guoqiang,Wu Huiyong,Zhao Ang,et al.Terminal sliding mode control for ship course tracking problem based on adaptive filtering backstepping[J].Transactions of Beijing Institute of Technology,2015,35(2):180-185.(in Chinese with English abstract)
[26]苗卓广,谢寿生,张波,等.航空发动机自适应全局快速非奇异Terminal滑模控制[J].航空动力学报,2013,28(11):2634-2640.Miao Zhuoguang,Xie Shousheng,Zhang Bo,et al.Adaptive global fast non-singular terminal sliding mode control for aero-engine[J].Journal of Aerospace Power,2013,28(11):2634-2640.(in Chinese with English abstract)
[27]李浩,梁婕,梁海波,等.不确定二阶系统的非奇异快速终端滑模控制[J].航天控制,2014,32(4):8-12.Li Hao,Liang Jie,Liang Haibo,et al.Nonsingular fast terminal sliding mode control for uncertain decond order system[J].Aerospace Control,2014,32(4):8-12.(in Chinese with English abstract)
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[2]王艳敏,冯勇,夏红伟,等.多输入不确定系统的平滑非奇异终端滑模控制[J].控制与决策,2015,30(1):161-165.Wang Yanmin,Feng Yong,Xia Hongwei,et al.Smooth nonsingular terminal sliding mode control of uncertain multi-input systems[J].Control and Decision,2015,30(1):161-165.(in Chinese with English abstract)
[3]郭宇飞,侯保林.基于隐式Lyapunov函数的一类不确定性机械臂位置控制方法[J].南京理工大学学报,2013,37(3):350-355.Guo Yufei,Hou Baolin.Position control method for uncertainty manipulators based on implicit Lyapunov function[J].Journal of Nanjing University of Science and Technology,2013,37(3):350-355.(in Chinese with English abstract)
[4]Khoo S,Zhao S,Man Z.Adaptive fast finite-time multiplesurface sliding control for a class of uncertain non-linear systems[J].International Journal of Modelling Identification&Control,2012,16(4):392-400.
[5]Do M T,Man Zhihong,Zhang Cishen,et al.A new sliding mode-based learning control for uncertain discrete-time systems[J].International Conference on Control Automation Robotics&Vision,2012,13(1):741-746.
[6]Tran X,Kang H.Adaptive hybrid High-Order terminal sliding mode control of MIMO uncertain nonlinear systems and its application to robot manipulators[J].International Journal of Precision Engineering&Manufacturing,2015,16(2):255-266.
[7]Huang Jiangshuai,Wen Changyun,Wang Wei,et al.Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems[J].Automatica,2015,51:292-301.
[8]陈志勇,陈力.具有外部扰动及不确定载荷参数双臂空间机器人的拟增广鲁棒与自适应混合控制[J].工程力学,2010,27(12):27-33.Chen Zhiyong,Chen Li.Robust-adaptive combined control for dual-arm space robot with external disturbances and uncertain parameters[J].Engineering Mechanics,2010,27(12):27-33.(in Chinese with English abstract)
[9]侯润民,刘荣忠,侯远龙,等.自适应模糊小波滑模控制在交流伺服系统中的应用[J].兵工学报,2014,35(6):769-775.Hou Runmin,Liu Rongzhong,Hou Yuanlong,et al.Application of adaptive fuzzy wavelet neural sliding mode control in AC servo system[J].Acta Armamentarii,2014,35(6):769-775.(in Chinese with English abstract)
[10]郭亚军,王晓锋,马大为,等.自适应反演滑模控制在火箭炮交流伺服系统中的应用[J].兵工学报,2011,32(4):493-497.Guo Yajun,Wang Xiaofeng,Ma Dawei,et al.Application of adaptive backstepping sliding mode control in alternative current servo system of rocket gun[J].Acta Armamentarii,2011,32(4):493-497.(in Chinese with English abstract)
[11]洪昭斌,陈力.具有未知参数漂浮基双臂空间机器人惯性空间复合自适应控制[J].中国机械工程,2010,21(1):12-16.Hong Zhaobin,Chen Li.Composite adaptive control in work space of free-floating dual-arm spatial robot system with unknown parameters[J].China Mechanical Engineering,2010,21(1):12-16.(in Chinese with English abstract)
[12]张福海,付宜利,王树国.惯性参数不确定的自由漂浮空间机器人自适应控制研究[J].航空学报,2012,33(12):2347-2354.Zhang Fuhai,Fu Yili,Wang Shuguo.Adaptive control of free-floating space robot with inertia parameter uncertainties[J].Acta Aeronautica et Astronautica Sinica,2012,33(12):2347-2354.(in Chinese with English abstract)
[13]陈力.参数不确定空间机械臂系统的鲁棒自适应混合控制[J].控制理论与应用,2004,21(4):512-516.Chen Li.Robust and adaptive composite control of space manipulator system with uncertain parameters[J].Control Theory&Applications,2004,21(4):512-516.(in Chinese with English abstract)
[14]梁捷,陈力.柔性空间机械臂末端运动及柔性振动的模糊自适应补偿控制[J].兵工学报,2011,32(1):45-57.Liang Jie,Chen Li.Fuzzy logic adaptive compensation control of end-effect montion and flexible vibration for space-based flexible manipulator[J].Acta Armamentarii,2011,32(1):45-57.(in Chinese with English abstract)
[15]杨泽斌,汪明涛,孙晓东.基于自适应模糊神经网络的无轴承异步电机控制[J].农业工程学报,2014,30(2):78-86.Yan Zebin,Wang Mingtao,Sun Xiaodong.Control system of bearingless induction motors based on adaptive neuro-fuzzy inference system[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2014,30(2):78-86.(in Chinese with English abstract)
[16]刘浩蓬,龙长江,万鹏,等.植保四轴飞行器的模糊PID控制[J].农业工程学报,2015,31(1):71-77.Liu Haopeng,Long Changjiang,Wan Peng,et al.Fuzzy self-adjusting proportion integration differentiation for eppoquadrocopter[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2015,31(1):71-77.(in Chinese with English abstract)
[17]梁捷,陈力.空间机械臂关节运动的自适应模糊补偿控制[J].系统仿真学报,2011,23(3):577-582.Liang Jie,Chen Li.Fuzzy logic adaptive compensation control for space manipulator to track desired trajectory in joint space[J].Journal of System Simulation,2011,23(3):577-582.(in Chinese with English abstract)
[18]杜慧秋.基于模糊自适应不确定性机械臂的轨迹跟踪控制[J].电机与控制学报,2005,9(3):238-243.Du Huiqiu.Tracking control of uncertain robotic manipulator system based on a fuzzy adaptive approach[J].Electric Machines and Control,2005,9(3):238-243.(in Chinese with English abstract)
[19]梁喜凤,杨犇,王永维.番茄收获机械手轨迹跟踪模糊控制仿真与试验[J].农业工程学报,2013,29(17):16-23.Liang Xifeng,Yang Ben,Wang Yongwei.Simulation and test of trajectory tracking control for tomato harvesting manipulator based on fuzzy logic compensation[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2013,29(17):16-23.(in Chinese with English abstract)
[20]刘强,冯培恩.惯性参数大范围变化机械伺服系统鲁棒跟踪控制[J].控制理论与应用,2005,22(6):983-986.Liu Qiang,Feng Penen.Robust tracking control of mechanical servo systems with inertial parameters varying in large range[J].Control Theory&Applications,2005,22(6):983-986.
[21]Van M,Kang H J,Suh Y S,et al.Output feedback tracking control of uncertain robot manipulators via higher-order sliding-mode observer and fuzzy compensator[J].Journal of Mechanical Science and Technology,2013,27(8):2487-2496.
[22]Bartoszewicz A,Patton R J.Sliding mode control[J].International Journal of Adaptive Control and Signal Processing,2007,21(8/9):635-637.
[23]Liu Jinkun Sun Fuchun.A novel dynamic terminal sliding mode control of uncertain nonlinear systems[J].Journal of Control Theory and Applications,2007,5(2):189-193
[24]杨庆华,王燕,高峰,等.基于摆线运动的黄瓜采摘机器人终端滑模轨迹跟踪控制[J].农业工程学报,2009,25(5):94-99.Yang Qinghua,Wang Yan,Gao Feng,et a1.Trajectory tracking with terminal sliding mode control of cucumber picking robot manipulator based on cycloidal motion[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2009,25(5):94-99.(in Chinese with English abstract)
[25]夏国清,武慧勇,赵昂,等.船舶航向跟踪系统自适应滤波反步终端滑模控制[J].北京理工大学学报,2015,35(2):180-185.Xia Guoqiang,Wu Huiyong,Zhao Ang,et al.Terminal sliding mode control for ship course tracking problem based on adaptive filtering backstepping[J].Transactions of Beijing Institute of Technology,2015,35(2):180-185.(in Chinese with English abstract)
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