机床用磁悬浮系统悬浮高度的鲁棒控制研究
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摘要
磁悬浮进给系统具有无污染、无机械接触、无摩擦、无润滑、定位精度高、进给速度及加速度高等优良特性,因此提出在龙门移动式数控机床中采用磁悬浮技术以消除移动横梁与导轨间的摩擦,即将移动横梁悬浮在静止导轨上方,使其不与导轨接触,彻底消除摩擦,实现精加工。
本文首先在查阅大量国内外参考文献的基础上介绍了龙门移动式数控机床悬浮横梁的进给结构,阐述了移动横梁的悬浮原理,建立了磁悬浮进给系统的单铁悬浮非线性数学模型;在此基础上,对磁悬浮非线性系统采用输出反馈适应性反演控制策略并进行控制系统仿真。其次,运用反馈线性化方法对系统的非线性模型进行线性化处理,分别得到线性电压控制模型和电流控制模型。在线性化模型的基础上,设计了滑模变结构控制器,仿真结果表明该控制方案具有强鲁棒性,快速性的优点也存在着抖振的不足;为消除滑模控制在切换面上存在的抖振,设计了滑模——神经网络的双自由度控制算法,即采用滑模控制原理设计系统的输入控制,再用神经网络来设计输出反馈控制,仿真结果表明神经网络的自学习和处理能力可以削弱滑模控制中的抖振现象。最后针对系统在运行过程中系统可能受到参数摄动、未建模动态以及刀具切削部件引起的系统质量变化等扰动,设计了适应性滑模-H~∞控制,利用适应性控制理论估测滑模控制中不确定的参数值以降低抖振,利用适应性滑模控制器结合鲁棒控制H~∞理论来抑制干扰,以增加系统的鲁棒性。仿真结果表明,此控制器能有效地估测变化的系统参数、具有小稳态误差和高鲁棒性,可以使系统达到精确定位的目的。
Electromagnetic levitation system has many good quality characteristics such as no pollution, no mechanical contact, no friction, no lubrication, high precision positioning and high feed speed and acceleration. Therefore electromagnetic levitation technology is adopted in gantry NC machine tool to eliminate the friction between the crossbeam and guide, namely the crossbeam is levitated upon the guide without contact in order to achieve finishing-cut.
First, on the basis of reading many foreign and domestic references, it summarizes the structure and the principle of operation of the gantry NC machine tool moving crossbeam to analyze the levitation theory. The mathematic model is built. The output feedback adaptive backstepping control is applied in the electromagnetic levitation nonlinear system based on this. Second, the nonlinear model is linearized by using feedback linearization method and linear voltage control and current control model are obtained respectively. On the basis of the model, sliding mode controller is designed, the simulation result shows it has advantage of strong robustness and rapidity but there is chattering as well. In order to eliminate the chattering of sliding mode surface, two-degree-freedom control with sliding mode and neural network is proposed. Namely the input controller is designed based on sliding mode control method and the output feedback controller is realized by a neural network. The simulation result shows the chattering can be effectively weakened by self-learning and treatment capacity of the neural network. Lastly, focus on the disturbance of parameter perturbation, unmodeled dynamics and system quality changed by cutting, the adaptive sliding- H~∞control is designed. The adaptive control is adopted to estimate uncertain parameter to improve chattering. In order to weaken the disturbance, adaptive sliding mode controller with H~∞method is applied to strengthen the system robustness. The simulation results are illustrated that the controller can achieve the accurate orientation with effectively estimate system parameter, little steady state error and strong robustness.
本文首先在查阅大量国内外参考文献的基础上介绍了龙门移动式数控机床悬浮横梁的进给结构,阐述了移动横梁的悬浮原理,建立了磁悬浮进给系统的单铁悬浮非线性数学模型;在此基础上,对磁悬浮非线性系统采用输出反馈适应性反演控制策略并进行控制系统仿真。其次,运用反馈线性化方法对系统的非线性模型进行线性化处理,分别得到线性电压控制模型和电流控制模型。在线性化模型的基础上,设计了滑模变结构控制器,仿真结果表明该控制方案具有强鲁棒性,快速性的优点也存在着抖振的不足;为消除滑模控制在切换面上存在的抖振,设计了滑模——神经网络的双自由度控制算法,即采用滑模控制原理设计系统的输入控制,再用神经网络来设计输出反馈控制,仿真结果表明神经网络的自学习和处理能力可以削弱滑模控制中的抖振现象。最后针对系统在运行过程中系统可能受到参数摄动、未建模动态以及刀具切削部件引起的系统质量变化等扰动,设计了适应性滑模-H~∞控制,利用适应性控制理论估测滑模控制中不确定的参数值以降低抖振,利用适应性滑模控制器结合鲁棒控制H~∞理论来抑制干扰,以增加系统的鲁棒性。仿真结果表明,此控制器能有效地估测变化的系统参数、具有小稳态误差和高鲁棒性,可以使系统达到精确定位的目的。
Electromagnetic levitation system has many good quality characteristics such as no pollution, no mechanical contact, no friction, no lubrication, high precision positioning and high feed speed and acceleration. Therefore electromagnetic levitation technology is adopted in gantry NC machine tool to eliminate the friction between the crossbeam and guide, namely the crossbeam is levitated upon the guide without contact in order to achieve finishing-cut.
First, on the basis of reading many foreign and domestic references, it summarizes the structure and the principle of operation of the gantry NC machine tool moving crossbeam to analyze the levitation theory. The mathematic model is built. The output feedback adaptive backstepping control is applied in the electromagnetic levitation nonlinear system based on this. Second, the nonlinear model is linearized by using feedback linearization method and linear voltage control and current control model are obtained respectively. On the basis of the model, sliding mode controller is designed, the simulation result shows it has advantage of strong robustness and rapidity but there is chattering as well. In order to eliminate the chattering of sliding mode surface, two-degree-freedom control with sliding mode and neural network is proposed. Namely the input controller is designed based on sliding mode control method and the output feedback controller is realized by a neural network. The simulation result shows the chattering can be effectively weakened by self-learning and treatment capacity of the neural network. Lastly, focus on the disturbance of parameter perturbation, unmodeled dynamics and system quality changed by cutting, the adaptive sliding- H~∞control is designed. The adaptive control is adopted to estimate uncertain parameter to improve chattering. In order to weaken the disturbance, adaptive sliding mode controller with H~∞method is applied to strengthen the system robustness. The simulation results are illustrated that the controller can achieve the accurate orientation with effectively estimate system parameter, little steady state error and strong robustness.
引文
[1]李剑锋.常导高速磁浮列车搭接结构的悬浮控制技术研究:(硕士学位论文).长沙:国防科学技术大学,2005.
[2]杨霞,李强,郭庆鼎等.基于数控机床进给用磁悬浮直线电机摩擦的消除.控制与检测,2005,(7):41-45.
[3]Oui-Serg Kim,Sang-Ho Lee and Dong-Chul Han.Position performance and straightness error compensation of the magnetic levitation stage supported by the linear magnetic bearing.IEEE Trans.on Industrial Electronics,2003,50(2):374-378.
[4]Kee-Bong Choi,Young Geun Cho,Tadahiko Shinshi.Stabilization of one degree-of-freedom control type levitation table with permanent magnet repulsive forces.Mechatronics,2003,13(6):587-603.
[5]刘恒坤,常文森,佘龙华.磁悬浮系统的非线性控制.控制理论与应用,2005,24(11):1-3.
[6]Zi-Jiang Yang,Kouichi Miyazaki,Shunshoku Kanae.Robust position control of a magnetic levitation system via dynamic surface control technique.IEEE Trans.Ind.Electron,2004,51(1):26-34.
[7]龙晓林,蒋静坪.非线性控制及其先进控制策略.武汉理工大学学报,2004,26(4):8-13.
[8]徐绍辉.电磁永磁混合悬浮系统悬浮控制研究:(博士学位论文).北京:中国科学院电工研究所,2005.
[9]徐湘元.自适应控制理论与应用.北京:电子工业出版,2007.
[10]闫茂德.非线性控制理论与应用.西安:西安电子科技大学出版社,2007.
[11]蔡自兴.智能控制原理与应用.北京:清华大学出版社,2007.
[12]王丽梅,石佳.龙门移动式数控机床横梁磁悬浮控制系统研究.制造技术与机床,2008(2):79-82.
[13]王军闯.NC机床磁悬浮进给机构研究:(硕士学位论文).大连:大连交通大学,2006.
[14]Jan Van Goethem,Gerhard Henneberger,Dynamic simulation of the novel XLEV magnetically levitated control vehicle.Ninth International Symposium on Magnetic Bearings,2004:104-109.
[15]Ren X M,Rad A B,Chan P T.Identification and control of continuous-time nonlinear systems via dynamic neural networks.IEEE Transactions on Industrial Electronics,2003,50(6):478-486.
[16]石佳.机床进给磁悬浮系统的非线性控制方法研究:(硕士学位论文).沈阳:沈阳工业大学,2008.
[17]D.Cho,Y.Kato,D.Spilman.Sliding mode and classical controllers in magnetic levitation system.IEEE Control System Magazine,1993,13(1):42-48.
[18]孙增圻.智能控制理论与技术.北京:清华大学出版社,2000.
[19]Huang S N,Tan K K,Lee T H.Further results on adaptive control for a class of nonlinear systems using neural networks.IEEE,Transactions on Neural Networks,2003,14(5):719-722.
[20]闫茂德,张怀梅.磁悬浮机床主轴的非线性输出反馈自适应控制.机床与液压,2005,(6):116-118.
[21]Pin-Cheng Chen,Chun-Fei Hsu,Tsu-Tian Lee and Chi-Hsu Wang.Fuzzy-identification-based adaptive backstepping control using a self-organizing fuzzy system[J].A Fusion of Foundations,Methodologies and Applications,2009,13(7):308-312.
[22]王芹.基于滑模及K-滤波器的鲁棒自适应控制研究:(硕士学位论文).扬州:扬州大学,2008.
[23]张春明,林飞,宋文超.异步电机鲁棒控制器及其Backstepping设计.控制与决策,2004,19(3):267-272.
[24]解学军,白延宁,张嗣瀛.磁悬浮系统的基于RBF网络的自适应反推控制.控制与决策,2005,20(7):760-763.
[25]刘德生.基于反馈线性化的EMS型磁悬浮列车非线性悬浮控制器设计.国防科技大学学报,2005,27(2):96-101.
[26]王丽梅,石佳.基于反馈线性化的龙门数控机床磁悬浮系统滑模鲁棒控制.机床与液压,2008,36(5):254-256.
[27]孙宜标,郭庆鼎.基于滑模观测器的直线伺服系统反馈线性化速度跟踪控制.控制理论与应用,2004,21(3):391-397.
[28]柯海森.不确定非线性系统的控制研究:(博士学位论文).杭州:浙江大学,2006.
[29]曹学余,汤炳新.磁悬浮球系统的变结构控制.自动化技术与应用,2005,24(4):4-6.
[30]Xu J X,Lee T H,Pan Y J.On the sliding mode control for DC servo mechanisms in the presence of unmodeled dynamics.Mechatronics,2003,(13):755-770.
[31]张铭钧.智能控制技术.哈尔滨::哈尔滨工程大学出版社,2006.
[32]Chao-Lin Kuo,Tzuu-Hseng S.LI,Nai Ren Guo.Design of a Novel Fuzzy Sliding-Mode Control for Magnetic Ball Levitation System.Journal of Intelligent and Robotic Systems.2005,3(9):295-316.
[33]白圣建,黄新生.变结构控制的抖振问题研究.计算机仿真,2006,23(2):155-158.
[34]罗婷婷,刘金棍.基于滑模变结构控制的RBF神经元网络.计算机仿真,2004,21(6):58-61.
[35]王贞艳.一类非线性离散时间系统的变结构控制.系统仿真学报,2005,7(4):2483-2489.
[36]汤洁,李训铭.单自由度磁悬浮系统的状态反馈控制.计算机测量与控制,2005,13(9):472-490.
[37]胡继康.磁悬浮轴承的神经网络辨识与非线性控制:(硕士学位论文).兰州:兰州大学,2005.
[38]孙宜标,郭庆鼎.基于RBF神经网络补偿的直线伺服系统滑模鲁棒跟踪控制.控制理论与应用,2004,21(9):252-256.
[39]Chin-Pao Hung.Integral Variable Structure Control of Nonlinear System Using a CMAC Neural Network Learning Approach.IEEE Transactions on Systems,2004,34(1):702-709.
[40]李鸿儒,顾树生.基于神经网络的PMSM自适应滑模控制.控制理论与应用,2005,22(3):461-464.
[41]谢莉莉.基于神经网络的磁悬浮球的模型辨识与变结构控制研究:(硕士学位论文).南京:南京航空航天大学,2007.
[42]孙宜标,郭庆鼎.交流永磁直线伺服系统的神经网络——滑模双自由度控制,电气传动,2002,23(1):19-23.
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[45]J.-J.E.斯洛廷,李卫平.非线性控制应用.北京:国防工业出版社,1992.
[46]Jinunshian Phuah,Jianming Lu.Chattering free sliding mode control in magnetic levitation system.IEEJ Trans.EIS,2005,125(4):600-605.
[47]Wai R J,Lin C M,Hsu C F.Adaptive fuzzy sliding mode control for electrical servo drive.Fuzzy Sets and Systems,2004,(14)3:295-310.
[48]吴刚,张育林,刘昆.两轴型混合磁悬浮轴承变结构控制与仿真研究.系统仿真学报,2006,18(1):251-253.
[49]童克文,张兴.滑模变结构控制及应用.电气应用,2007,26(3):6-10.
[50]穆效江,陈阳舟.滑模变结构控制理论研究综述.控制工程,2007,7(14):1-5.
[51]李琳.滑模变结构控制系统抖振抑制方法研究:(硕士学位论文).大连:大连理工大学,2006.
[2]杨霞,李强,郭庆鼎等.基于数控机床进给用磁悬浮直线电机摩擦的消除.控制与检测,2005,(7):41-45.
[3]Oui-Serg Kim,Sang-Ho Lee and Dong-Chul Han.Position performance and straightness error compensation of the magnetic levitation stage supported by the linear magnetic bearing.IEEE Trans.on Industrial Electronics,2003,50(2):374-378.
[4]Kee-Bong Choi,Young Geun Cho,Tadahiko Shinshi.Stabilization of one degree-of-freedom control type levitation table with permanent magnet repulsive forces.Mechatronics,2003,13(6):587-603.
[5]刘恒坤,常文森,佘龙华.磁悬浮系统的非线性控制.控制理论与应用,2005,24(11):1-3.
[6]Zi-Jiang Yang,Kouichi Miyazaki,Shunshoku Kanae.Robust position control of a magnetic levitation system via dynamic surface control technique.IEEE Trans.Ind.Electron,2004,51(1):26-34.
[7]龙晓林,蒋静坪.非线性控制及其先进控制策略.武汉理工大学学报,2004,26(4):8-13.
[8]徐绍辉.电磁永磁混合悬浮系统悬浮控制研究:(博士学位论文).北京:中国科学院电工研究所,2005.
[9]徐湘元.自适应控制理论与应用.北京:电子工业出版,2007.
[10]闫茂德.非线性控制理论与应用.西安:西安电子科技大学出版社,2007.
[11]蔡自兴.智能控制原理与应用.北京:清华大学出版社,2007.
[12]王丽梅,石佳.龙门移动式数控机床横梁磁悬浮控制系统研究.制造技术与机床,2008(2):79-82.
[13]王军闯.NC机床磁悬浮进给机构研究:(硕士学位论文).大连:大连交通大学,2006.
[14]Jan Van Goethem,Gerhard Henneberger,Dynamic simulation of the novel XLEV magnetically levitated control vehicle.Ninth International Symposium on Magnetic Bearings,2004:104-109.
[15]Ren X M,Rad A B,Chan P T.Identification and control of continuous-time nonlinear systems via dynamic neural networks.IEEE Transactions on Industrial Electronics,2003,50(6):478-486.
[16]石佳.机床进给磁悬浮系统的非线性控制方法研究:(硕士学位论文).沈阳:沈阳工业大学,2008.
[17]D.Cho,Y.Kato,D.Spilman.Sliding mode and classical controllers in magnetic levitation system.IEEE Control System Magazine,1993,13(1):42-48.
[18]孙增圻.智能控制理论与技术.北京:清华大学出版社,2000.
[19]Huang S N,Tan K K,Lee T H.Further results on adaptive control for a class of nonlinear systems using neural networks.IEEE,Transactions on Neural Networks,2003,14(5):719-722.
[20]闫茂德,张怀梅.磁悬浮机床主轴的非线性输出反馈自适应控制.机床与液压,2005,(6):116-118.
[21]Pin-Cheng Chen,Chun-Fei Hsu,Tsu-Tian Lee and Chi-Hsu Wang.Fuzzy-identification-based adaptive backstepping control using a self-organizing fuzzy system[J].A Fusion of Foundations,Methodologies and Applications,2009,13(7):308-312.
[22]王芹.基于滑模及K-滤波器的鲁棒自适应控制研究:(硕士学位论文).扬州:扬州大学,2008.
[23]张春明,林飞,宋文超.异步电机鲁棒控制器及其Backstepping设计.控制与决策,2004,19(3):267-272.
[24]解学军,白延宁,张嗣瀛.磁悬浮系统的基于RBF网络的自适应反推控制.控制与决策,2005,20(7):760-763.
[25]刘德生.基于反馈线性化的EMS型磁悬浮列车非线性悬浮控制器设计.国防科技大学学报,2005,27(2):96-101.
[26]王丽梅,石佳.基于反馈线性化的龙门数控机床磁悬浮系统滑模鲁棒控制.机床与液压,2008,36(5):254-256.
[27]孙宜标,郭庆鼎.基于滑模观测器的直线伺服系统反馈线性化速度跟踪控制.控制理论与应用,2004,21(3):391-397.
[28]柯海森.不确定非线性系统的控制研究:(博士学位论文).杭州:浙江大学,2006.
[29]曹学余,汤炳新.磁悬浮球系统的变结构控制.自动化技术与应用,2005,24(4):4-6.
[30]Xu J X,Lee T H,Pan Y J.On the sliding mode control for DC servo mechanisms in the presence of unmodeled dynamics.Mechatronics,2003,(13):755-770.
[31]张铭钧.智能控制技术.哈尔滨::哈尔滨工程大学出版社,2006.
[32]Chao-Lin Kuo,Tzuu-Hseng S.LI,Nai Ren Guo.Design of a Novel Fuzzy Sliding-Mode Control for Magnetic Ball Levitation System.Journal of Intelligent and Robotic Systems.2005,3(9):295-316.
[33]白圣建,黄新生.变结构控制的抖振问题研究.计算机仿真,2006,23(2):155-158.
[34]罗婷婷,刘金棍.基于滑模变结构控制的RBF神经元网络.计算机仿真,2004,21(6):58-61.
[35]王贞艳.一类非线性离散时间系统的变结构控制.系统仿真学报,2005,7(4):2483-2489.
[36]汤洁,李训铭.单自由度磁悬浮系统的状态反馈控制.计算机测量与控制,2005,13(9):472-490.
[37]胡继康.磁悬浮轴承的神经网络辨识与非线性控制:(硕士学位论文).兰州:兰州大学,2005.
[38]孙宜标,郭庆鼎.基于RBF神经网络补偿的直线伺服系统滑模鲁棒跟踪控制.控制理论与应用,2004,21(9):252-256.
[39]Chin-Pao Hung.Integral Variable Structure Control of Nonlinear System Using a CMAC Neural Network Learning Approach.IEEE Transactions on Systems,2004,34(1):702-709.
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