PMLSM悬浮平台的二阶滑模控制研究
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摘要
基于教育部博士学科点专项科研基金为背景,以永磁直线同步电机(PMLSM)悬浮平台高精度定位系统为研究对象。针对PMLSM悬浮平台系统的特点,现有的控制方法不能完全满足其对于高精度和强鲁棒性的双重要求,因此本课题结合二阶滑模直接动态解耦控制和离散二阶滑模位置控制的控制策略,对水平方向和竖直方向之间存在的高非线性强耦合,以及参数变化和负载扰动等不确定性因素影响PMLSM悬浮平台系统的定位精度问题进行研究。主要研究内容包括如下几个部分:
在对PMLSM悬浮平台系统模型分析研究的基础上,针对水平推力和法向力之间存在非线性耦合,加之负载扰动和参数变化等不确定性因素降低了系统的伺服性能等问题。为了保证PMLSM悬浮平台动子的定位精度,针对上述问题分别独立设计水平轴和竖直轴的二阶滑模(2-SMC)控制器对PMLSM悬浮平台实行直接动态解耦控制。控制律使用螺旋算法,二阶滑模算法可以把开关函数的不连续控制作用在滑模变量的高阶微分上,因此可以削弱抖振。仿真结果表明该控制策略能够实现对水平方向和竖直方向的动态解耦,使系统对参数变化和负载扰动具有很强的鲁棒性,从而提高了定位精度。
为了使PMLSM悬浮平台系统在实际工程中具有很好的实用性,对其进行离散化,并且针对离散系统,采用预设收敛律算法设计了离散二阶滑模位置控制器。仿真结果表明,离散二阶滑模控制策略仍然能够使PMLSM悬浮平台具有很高的定位精度,并且对于突加负载和参数变化等不确定扰动依然有很好的鲁棒性,此外也大大减小了抖振。
The project supported by Specialized Research Foundation of Ministry of Education Doctoral Program as background, and suspended platform driven by permanent magnet linear synchronous motor (PMLSM) with a unilateral core as the research object. respectively using the discrete second order sliding mode control and the control strategy with discrete second order sliding mode position control, to study the precise positioning of the PMLSM suspended platform which has many uncertainty such as variables has nonlinear coupling, Levitation stiffness is low and has parameters change, end effect and the load disturbance. The thesis mainly includes the following components:
Based on the analysis of PMLSM Floating platform system model, against the problems that the servo performance is affected by the nonlinear coupling between vertical thrust and normal force, load disturbance and parameters uncertainty. In order to ensure the mover positioning strictly of the PMLSM levitation platform, the second-order sliding (2-SMC) controllers of the horizontal axis and vertical axis are designed to directly decoupling control. Control law is achieved by twisting algorithm. The discontinuous control effects on the high order differential of variables, in theory, can reduce buffeting. Simulation results show that the control strategy can decouple between horizontal direction and vertical direction, enhance the robustness performance of the system against parameter variations and load disturbances and improve the positioning precision.
Discretion on the system, in order to make the controller have good usability in the actual project, and the discrete second order sliding mode position controller is designed using default convergence law algorithm for discrete system. Simulation results show that the discrete second order sliding mode control is still able to make the PMLSM levitation platform have high positioning accuracy, and strong robustness for uncertainties such as load disturbance and parameters change, and weakening the chattering at the same time.
在对PMLSM悬浮平台系统模型分析研究的基础上,针对水平推力和法向力之间存在非线性耦合,加之负载扰动和参数变化等不确定性因素降低了系统的伺服性能等问题。为了保证PMLSM悬浮平台动子的定位精度,针对上述问题分别独立设计水平轴和竖直轴的二阶滑模(2-SMC)控制器对PMLSM悬浮平台实行直接动态解耦控制。控制律使用螺旋算法,二阶滑模算法可以把开关函数的不连续控制作用在滑模变量的高阶微分上,因此可以削弱抖振。仿真结果表明该控制策略能够实现对水平方向和竖直方向的动态解耦,使系统对参数变化和负载扰动具有很强的鲁棒性,从而提高了定位精度。
为了使PMLSM悬浮平台系统在实际工程中具有很好的实用性,对其进行离散化,并且针对离散系统,采用预设收敛律算法设计了离散二阶滑模位置控制器。仿真结果表明,离散二阶滑模控制策略仍然能够使PMLSM悬浮平台具有很高的定位精度,并且对于突加负载和参数变化等不确定扰动依然有很好的鲁棒性,此外也大大减小了抖振。
The project supported by Specialized Research Foundation of Ministry of Education Doctoral Program as background, and suspended platform driven by permanent magnet linear synchronous motor (PMLSM) with a unilateral core as the research object. respectively using the discrete second order sliding mode control and the control strategy with discrete second order sliding mode position control, to study the precise positioning of the PMLSM suspended platform which has many uncertainty such as variables has nonlinear coupling, Levitation stiffness is low and has parameters change, end effect and the load disturbance. The thesis mainly includes the following components:
Based on the analysis of PMLSM Floating platform system model, against the problems that the servo performance is affected by the nonlinear coupling between vertical thrust and normal force, load disturbance and parameters uncertainty. In order to ensure the mover positioning strictly of the PMLSM levitation platform, the second-order sliding (2-SMC) controllers of the horizontal axis and vertical axis are designed to directly decoupling control. Control law is achieved by twisting algorithm. The discontinuous control effects on the high order differential of variables, in theory, can reduce buffeting. Simulation results show that the control strategy can decouple between horizontal direction and vertical direction, enhance the robustness performance of the system against parameter variations and load disturbances and improve the positioning precision.
Discretion on the system, in order to make the controller have good usability in the actual project, and the discrete second order sliding mode position controller is designed using default convergence law algorithm for discrete system. Simulation results show that the discrete second order sliding mode control is still able to make the PMLSM levitation platform have high positioning accuracy, and strong robustness for uncertainties such as load disturbance and parameters change, and weakening the chattering at the same time.
引文
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[25] A. Molenaar, E. H. Zaaijer, H. F. van Beek. A novel low dissipation long stroke planar magnetic suspension and propulsion stage. Sixth International Symposium on Magnetic Bearings, Boston, MA, USA, 1998,(8):650–659.
[26] W-J Kim, D.L. Trumper. Active multivariable optimal control of a planar magnetic levitator. In Proceedings of the 1997 IEEE International Conference on Control Applications, 1997(8): 97-102.
[27] Christopher Nielsen, Cameron Fulford, Manfredi Maggiore. Path following using transverse feedback linearization: application to a maglev positioning system. Automatica, 2010, 46(3): 585-590.
[28] R.B.Owen, M. Maggiore. Implementation and model veri?cation of a magnetic levitation system. IEEE American Control. 2005, 2(7): 1142-1147.
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[31] X. Shan, S.K. Kuo, J. Zhang etc. Ultra precision motion control of a multiple degree of freedom magnetic suspension stage. IEEE/ASME Transactions on Mechatronics, 2002, 7(1): 67–78.
[32] K. S. Jung, Y. S. Baek. Study on a novel contact-free planar system using direct drive DC coils and permanent magnets. IEEE/ASME Transactions on Mechatronics, 2002(2):25–43.
[33] K. Yoshida, A. Fulford, H. Takami. Pass-through-section experiment in mass-reduced-mode of controlled-repulsive PMLSM maglev vehicle by new DTC method. Proceedings of the 2002 Power Conversion Conference, 2002(9): 867-872.
[34]马平,陈振环,李劼科．零传动机床的高速直线进给单元的伺服动刚度研究．中国机械工程，2004,15(7):575-581.
[35] C. C. Wang, M. Y. Chen, L. C. Adaptive sliding mode controller design of a maglev guiding system for application in precision positioning. Proceedings of the 2000 American Control Conference, 2000, 3:1612-1616.
[36] Rafael Becerril Arreolause. Output feedback nonlinear control for a linear motor in suspension mode. Automatic, 2004, 40: 2153-2160.
[37]张柏霖,谢影明,肖曙红.超高速切削的原理与应用.中国机械工程,1995,6(1):14-17.
[38] G. W. McLean. Review of recent progress in linear motors. IEEE Proceedings Pt.Bt.1988, 135: 380-416.
[39] K. C. Lim, J. P. Hong, G. T. Kim. The novel technique considering slot effect by equivalent magnetizing current. IEEE Transactions on Magnetics, 1999, 35(5): 3691-3693.
[40]周赣,黄学良,柏瑞等.磁悬浮平面电机的解耦控制策略.中国电机工程学报, 2009,29(12): 81-86.
[41]孙宜标基于滑动模态的永磁直线同步电动机鲁棒速度控制:(博士学位论文).沈阳:沈阳工业大学:2007.
[42]孙宜标,杨雪,夏加宽等.基于对角化法的永磁直线同步电机二阶滑模控制.中国电机工程学报,2008,28(12):124-128.
[43]蔡丽华.非线性奇异摄动系统的二阶滑模控制设计及应用研究:(硕士学位论文).天津:天津大学,2002.
[44]史忠科,吴方向,王蓓等.鲁棒控制理论.北京:国防工业出版社,2003.
[45] R. Benayache, S. M. MahmoudL. Chrifi-Alaoui. Controller design using second order sliding mode algorithm with an application to a coupled-tank liquid-level system. IEEE International Conference on Control and Automation,2009(5): 58-563.
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[47]于进勇,顾文锦,赵红超.飞航导弹纵向控制系统的二阶滑模控制设计.系统仿真学报2003,15(7):1319-1321.
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[2]李黎川,丁玉成,卢秉恒.超精密磁悬浮工作台及其解耦控制.机械工程学报,2004, 40(9):84-88.
[3]郭庆鼎,王成元,周美文等.直线交流伺服系统的精密控制技术.北京:机械工业出版社,2000.
[4]李群明,万梁,段吉安等.磁悬浮平台系统的机电耦合动力学模型及稳定性分析.光学精密工程,2007,15(4):535-542.
[5]王成元,夏加宽,杨俊友等.电机现代控制技术.北京:机械工业出版社,2006.
[6]刘德君,郭庆鼎,翁秀华.直线电机驱动的磁悬浮平台推力动态解耦控制.沈阳工业大学学报,2005,27(1):43-47.
[7]郝晓红,梅雪松,张东升等.新型磁悬浮精密定位平台的研究.西安交通大学学报,2005,39(9):937-940.
[8]物鹰飞,周兆英.超精密定位工作平台.微细加工,2002,6(2):41-47.
[9]郭亮,陈本.永精密磁悬浮工作平台的力特性分析.中国电机工程学报,2008,28(27):118-122.
[10] O. Brydon, M .Maggiore, J. Apkarian. A high-precision magnetically levitated positioning stage. IEEE Control Systems Magazine, 2006, 26(3): 82–95.
[11]王义娜.PMLSM悬浮平台的鲁棒控制研究:(硕士学位论文)沈阳:沈阳工业大学,2011.
[12]万梁.磁悬浮运动平台的控制系统研究:(硕士学位论文)长沙:中南大学,2007.
[13] Z. Zhang, C. H. Menq. Six-axis magnetic levitation and motion control. IEEE Transactions on Robotics, 2007, 23(2):196–205.
[14]郭庆鼎,刘德君,赵希梅.基于输入解耦的6DOF磁悬浮平台悬浮高度的H∞控制.电工技术学报,2005,20(11):70-74.
[15] S. Verma, W. Jong Kim,H. Shakir. Multi-axis maglev nanopositioner for precision manufacturing and manipulation applications. IEEE Transactions on Industry Applications, 2005, 41(5): 1159–1167.
[16] W-J Kim, D. L. Tbumper. Linear motor-levitated stage for photolithography. CIRP Annals Manufacturing Technology, 1997, 46(1):447-450.
[17] S. K. Kuo, X. Shan, C. H. Menq. Large travel ultra precision x-y motion control of a magnetic suspension stage. IEEE/ASME Transactions on Mechatronics,2003,8(3):334–341.
[18] S. K. Kuo, C.H. Menq. Modeling control of a six-axis precision motion control stage. IEEE/ASME Transactions on Mechatronics, 2005, 10(1): 50–59.
[19] M.Y. Chen, M.J. Wang, L. C. Fu. Modeling and controller design of a maglev guiding system for application in precision positioning. IEEE/ASME Transactions on Industrial Electronics, 2003, 50(3): 493-506.
[20] Cameron Fulford, Manfredi Maggiore, Jacob Apkarian. Control of a 5DOF Magnetically LevitatedPositioning Stage. IEEE Transactions on Control Systems Technology, 2009, 17 (4): 844–852.
[21] S. Verma, W. jong Kim, J. Gu. Six-axis nanopositioning device with precision magnetic levitation technology. IEEE/ASME Transactions on Mechatronics, 2004, 9(2): 384–391.
[22] J. Gu, W. Jong Kim,S. Verma. Nanoscale motion control with a compact minimum-actuator magnetic levitator.Journal of Dynamic Systems, Measurement, and Control,2005(127): 433–442.
[23] F. Auer, H. F. van Beek. Practical application of a magnetic bearing and linear propulsion unit for six degree of freedom positioning. Fourth International Symposium on Magnetic Bearings, Zurich,Switzerland, 1994, 8:183–188.
[24] A. Molenaar, F. Auer, H. F. van Beek. Application of magnetic bearing for contactless ultra high precision positioning. Fifth International Symposium on Magnetic Bearings, Kanazawa, Japan, 1996(8):441–445.
[25] A. Molenaar, E. H. Zaaijer, H. F. van Beek. A novel low dissipation long stroke planar magnetic suspension and propulsion stage. Sixth International Symposium on Magnetic Bearings, Boston, MA, USA, 1998,(8):650–659.
[26] W-J Kim, D.L. Trumper. Active multivariable optimal control of a planar magnetic levitator. In Proceedings of the 1997 IEEE International Conference on Control Applications, 1997(8): 97-102.
[27] Christopher Nielsen, Cameron Fulford, Manfredi Maggiore. Path following using transverse feedback linearization: application to a maglev positioning system. Automatica, 2010, 46(3): 585-590.
[28] R.B.Owen, M. Maggiore. Implementation and model veri?cation of a magnetic levitation system. IEEE American Control. 2005, 2(7): 1142-1147.
[29] Robert Brydon Owen, Manfredi Maggiore, Jacob Apkarian. Nonlinear control design for a high-precision contactless positioning system using magnetic levitation. Proceedings of IEEE Control Applications Conference, 2005, (8): 481-486.
[30] Robert Brydon Owen. Implementation of high precision position system using contactless magnetic levitation: (PhD Dissertation). University of Toronto, 2005.
[31] X. Shan, S.K. Kuo, J. Zhang etc. Ultra precision motion control of a multiple degree of freedom magnetic suspension stage. IEEE/ASME Transactions on Mechatronics, 2002, 7(1): 67–78.
[32] K. S. Jung, Y. S. Baek. Study on a novel contact-free planar system using direct drive DC coils and permanent magnets. IEEE/ASME Transactions on Mechatronics, 2002(2):25–43.
[33] K. Yoshida, A. Fulford, H. Takami. Pass-through-section experiment in mass-reduced-mode of controlled-repulsive PMLSM maglev vehicle by new DTC method. Proceedings of the 2002 Power Conversion Conference, 2002(9): 867-872.
[34]马平,陈振环,李劼科．零传动机床的高速直线进给单元的伺服动刚度研究．中国机械工程，2004,15(7):575-581.
[35] C. C. Wang, M. Y. Chen, L. C. Adaptive sliding mode controller design of a maglev guiding system for application in precision positioning. Proceedings of the 2000 American Control Conference, 2000, 3:1612-1616.
[36] Rafael Becerril Arreolause. Output feedback nonlinear control for a linear motor in suspension mode. Automatic, 2004, 40: 2153-2160.
[37]张柏霖,谢影明,肖曙红.超高速切削的原理与应用.中国机械工程,1995,6(1):14-17.
[38] G. W. McLean. Review of recent progress in linear motors. IEEE Proceedings Pt.Bt.1988, 135: 380-416.
[39] K. C. Lim, J. P. Hong, G. T. Kim. The novel technique considering slot effect by equivalent magnetizing current. IEEE Transactions on Magnetics, 1999, 35(5): 3691-3693.
[40]周赣,黄学良,柏瑞等.磁悬浮平面电机的解耦控制策略.中国电机工程学报, 2009,29(12): 81-86.
[41]孙宜标基于滑动模态的永磁直线同步电动机鲁棒速度控制:(博士学位论文).沈阳:沈阳工业大学:2007.
[42]孙宜标,杨雪,夏加宽等.基于对角化法的永磁直线同步电机二阶滑模控制.中国电机工程学报,2008,28(12):124-128.
[43]蔡丽华.非线性奇异摄动系统的二阶滑模控制设计及应用研究:(硕士学位论文).天津:天津大学,2002.
[44]史忠科,吴方向,王蓓等.鲁棒控制理论.北京:国防工业出版社,2003.
[45] R. Benayache, S. M. MahmoudL. Chrifi-Alaoui. Controller design using second order sliding mode algorithm with an application to a coupled-tank liquid-level system. IEEE International Conference on Control and Automation,2009(5): 58-563.
[46] Doyle, J. C. Stein G. Multivariable feedback design: concepts for a classical/modern synthesis. IEEE Transactions on Automatic Control.1981, 26(1): 4-16.
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