高精度永磁直线伺服系统的研究
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摘要
在现代加工工业领域,诸如激光切割、高速磨床、精密车床、加工中心等很多场合都需要高速度高精度的直线运动,而传统的方法只能借助于旋转电动机和滚轴丝杆等中间环节来获得直线运动,这就不可避免地存在惯性大、摩擦大、有反向间隙等缺点。近年来,随着直线电机技术的进步,越来越多的场合开始直接应用它来获得直线运动。由于采用直接驱动(Direct Drive)技术,直线电机具有动态响应快,控制精度高,可以超高速运行等优点,而这恰恰满足了高速精密加工技术的要求。为了探索和拓展直线电机在精密加工领域的应用,本文用系统集成的方法设计了一套永磁直线伺服系统,并通过Matlab仿真技术研究其实现高性能、高精度运行的控制算法。
首先,本文根据永磁同步直线电动机在d-q坐标系下的状态空间模型,采用磁场定向原理和i_d=0的控制策略,对电机模型进行了解耦和线性化处理,得到了它的频域模型。基于这个模型,我们分别采用H_∞闭环增益成形方法和前馈控制技术,设计了一个速度环的鲁棒PID控制器和一个速度前馈控制环节。仿真结果证明,鲁棒PID控制器不仅具有良好的抗外扰能力,同时对系统的内部参数如动子质量、电枢电阻、主磁极磁链等参数的摄动也具有很强的鲁棒性;而引入前馈环节后,还可以进一步提高系统的响应速度和控制精度。此外,论文还分析了一种伪微分前馈控制方法,它也是一种带前馈的PI控制方法,但由于引入了一个伪造的速度微分反馈项,使它在动态性能和噪声抑制方面都有不少提高。同时,这种控制方法的设计不依赖于对象的模型,比较适合于工程应用。
为了实现直线伺服系统的高精度定位控制。本文首先研究由位移指令得到速度指令的速度规划方案,然后根据速度控制的研究基础,设计了一套具有速度和加速度双前馈的P/PI型位置、速度双环控制系统,由前馈通道提供主控指令,而主通道控制器进行误差控制。仿真结果显示,系统具有极高的响应速度和控制品质,其稳态定位误差趋于0,动态定位误差可以控制在微米级。该系统有五个控制参数,本文采用遗传算法对控制参数进行了优化选择,遗传算法的适应度函数综合考虑了系统的控制性能和鲁棒性能,从仿真结果观察,优化参数取得了满意的控制效果。此外,本文还研究了基于伪微分前馈控制方法的位置控制,但其性能与双前馈P/PI方法相去甚远。
论文从设备的选型、安装和初步调试,到控制算法的选择和优化,完成了整个永磁直线伺服系统的初期设计任务,为永磁直线伺服系统的开发和应用奠定了基础。
In modern machining industry, laser-cutting, high-speed milling and scanning machines require fast and accurate linear motions. But traditional drives need to use rotational motors and lead screw or toothed belts to obtain linear motions, which leads to some mechanical problems such as backlash, large frictional, inertial loads and structural flexibilities. With the development of linear motors, recently, they are becoming increasingly popular in such applications. Due to the direct-drive technology, linear motor exhibits the property of high accuracy, high speed and excellent dynamic responsivity, which just satisfies the requirement of high speed machining (HSM). In order to explore the linear motor applications in machining tools, here, we designed a linear servo system via selecting a permanent magnet synchronous linear motor (PMSLM) and a linear encoder. Our aim is to develop some algorithms to realize high accuracy and high performance control for this linear servo system.
First, we applied field-oriented principle and the strategy of i_d = 0 to the state space model of PMSLM in d-q coordinates, and obtained a decoupling model and an approximate linearization model in frequency domain of the motor and driver system. Based on these models, we designed a robust PID controller of speed-loop by means of H_∞closed-loop gain shaping techniques. Moreover, a speed feed-forward block could be obtained easily from the frequency domain model of PMSLM and its driver. The robust PID controller exhibits good robustness against external disturbances and internal parameter perturbation by simulation results. When the feed-forward block is added, the responsive speed and control accuracy of the system will be improved more. Moreover, a pseudo derivative feed-forward (PDFF) method is analyzed in this thesis. As a type of PI control with feed-forward, PDFF can be designed independently from the plant model which is very suitable for engineering applications. Due to the pseudo derivative item of speed feedback, the dynamic performance and noise control of PDFF is improved greatly.
In order to realize the high accurate position control, firstly, we made a speed plan through which a speed curve can be obtained from a displacement order. According to speed loop control, we design a P/PI position and speed control system with speed and acceleration double feed-forward path. The feed-forward paths provide the main control signals, speed order signal to the input terminal of speed loop and acceleration signal to the input terminal of current loop, and the main path controls the error of position and speed. Simulation results show that the double closed-loop system has strong robustness and excellent control performance with the dynamic error less than 10μm and static error near to zero. There are five major control parameters in this system, here, these parameters are optimized with genetic algorithm and the satisfied results are achieved. Furthermore, the method of PDFF is investigated, but its accuracy is less than that of above method.
This thesis has completed the main design work of the linear servo system from the selections and installations of equipments to the design of control algorithms and the optimization of their parameters. After these work, we will continue to apply these algorithm to the experiment system and realize the design target of system.
首先,本文根据永磁同步直线电动机在d-q坐标系下的状态空间模型,采用磁场定向原理和i_d=0的控制策略,对电机模型进行了解耦和线性化处理,得到了它的频域模型。基于这个模型,我们分别采用H_∞闭环增益成形方法和前馈控制技术,设计了一个速度环的鲁棒PID控制器和一个速度前馈控制环节。仿真结果证明,鲁棒PID控制器不仅具有良好的抗外扰能力,同时对系统的内部参数如动子质量、电枢电阻、主磁极磁链等参数的摄动也具有很强的鲁棒性;而引入前馈环节后,还可以进一步提高系统的响应速度和控制精度。此外,论文还分析了一种伪微分前馈控制方法,它也是一种带前馈的PI控制方法,但由于引入了一个伪造的速度微分反馈项,使它在动态性能和噪声抑制方面都有不少提高。同时,这种控制方法的设计不依赖于对象的模型,比较适合于工程应用。
为了实现直线伺服系统的高精度定位控制。本文首先研究由位移指令得到速度指令的速度规划方案,然后根据速度控制的研究基础,设计了一套具有速度和加速度双前馈的P/PI型位置、速度双环控制系统,由前馈通道提供主控指令,而主通道控制器进行误差控制。仿真结果显示,系统具有极高的响应速度和控制品质,其稳态定位误差趋于0,动态定位误差可以控制在微米级。该系统有五个控制参数,本文采用遗传算法对控制参数进行了优化选择,遗传算法的适应度函数综合考虑了系统的控制性能和鲁棒性能,从仿真结果观察,优化参数取得了满意的控制效果。此外,本文还研究了基于伪微分前馈控制方法的位置控制,但其性能与双前馈P/PI方法相去甚远。
论文从设备的选型、安装和初步调试,到控制算法的选择和优化,完成了整个永磁直线伺服系统的初期设计任务,为永磁直线伺服系统的开发和应用奠定了基础。
In modern machining industry, laser-cutting, high-speed milling and scanning machines require fast and accurate linear motions. But traditional drives need to use rotational motors and lead screw or toothed belts to obtain linear motions, which leads to some mechanical problems such as backlash, large frictional, inertial loads and structural flexibilities. With the development of linear motors, recently, they are becoming increasingly popular in such applications. Due to the direct-drive technology, linear motor exhibits the property of high accuracy, high speed and excellent dynamic responsivity, which just satisfies the requirement of high speed machining (HSM). In order to explore the linear motor applications in machining tools, here, we designed a linear servo system via selecting a permanent magnet synchronous linear motor (PMSLM) and a linear encoder. Our aim is to develop some algorithms to realize high accuracy and high performance control for this linear servo system.
First, we applied field-oriented principle and the strategy of i_d = 0 to the state space model of PMSLM in d-q coordinates, and obtained a decoupling model and an approximate linearization model in frequency domain of the motor and driver system. Based on these models, we designed a robust PID controller of speed-loop by means of H_∞closed-loop gain shaping techniques. Moreover, a speed feed-forward block could be obtained easily from the frequency domain model of PMSLM and its driver. The robust PID controller exhibits good robustness against external disturbances and internal parameter perturbation by simulation results. When the feed-forward block is added, the responsive speed and control accuracy of the system will be improved more. Moreover, a pseudo derivative feed-forward (PDFF) method is analyzed in this thesis. As a type of PI control with feed-forward, PDFF can be designed independently from the plant model which is very suitable for engineering applications. Due to the pseudo derivative item of speed feedback, the dynamic performance and noise control of PDFF is improved greatly.
In order to realize the high accurate position control, firstly, we made a speed plan through which a speed curve can be obtained from a displacement order. According to speed loop control, we design a P/PI position and speed control system with speed and acceleration double feed-forward path. The feed-forward paths provide the main control signals, speed order signal to the input terminal of speed loop and acceleration signal to the input terminal of current loop, and the main path controls the error of position and speed. Simulation results show that the double closed-loop system has strong robustness and excellent control performance with the dynamic error less than 10μm and static error near to zero. There are five major control parameters in this system, here, these parameters are optimized with genetic algorithm and the satisfied results are achieved. Furthermore, the method of PDFF is investigated, but its accuracy is less than that of above method.
This thesis has completed the main design work of the linear servo system from the selections and installations of equipments to the design of control algorithms and the optimization of their parameters. After these work, we will continue to apply these algorithm to the experiment system and realize the design target of system.
引文
[1]叶云岳.直线电机的原理与应用.北京:机械工业出版社,2000.
[2]郭庆鼎等.直线交流伺服系统的精密控制技术.2000年1月第1版.北京:机械工业出版社,2000
[3]叶云岳,杨天夫.直线电机在制造技术装备中的应用综述.产品与技术,2002年12月,pp33-37
[4]王伟进,直线电机的发展与应用概述.微电机,2004年第1期,44-46
[5]宋书中,胡业发,周祖德.直线电机的发展及应用概况.控制工程,2006年5月,pp200-201
[6]魏志强,王先逵,杨志刚 高速加工机床及其关键技术 制造技术与机床,1998(1):5-7
[7]刘泉,张建民,王先逵.直线电机在机床工业中的最新应用及技术分析,机床与液压,2004年No.6,PP1-3
[8]几种高进给速度机床 制造技术与机床,2002(9)
[9]张伯霖,潘珊珊,于兆勤等 直线电机及其在超高速机床上的应用 中国机械工程,1997(4):85-88
[10]刘金凌,王先逵,冯之敬 高频响直流直线电机 微特电机,1993(4):17-18
[11]陶永华,新型PID控制及其应用,北京:机械工业出版社,2002
[12]叶云岳,陆凯元.直线电机的PID控制与模糊控制.电工技术学报.2001,16(3):11-15
[13]杨霞,任敏.专家控制的PID交流伺服系统的研究.燕山大学学报.2002,26(2):176-178
[14]J.S.Ko,et al,"Robust digital position control of brushless DC motor with adaptive load torque observer",IEE Proc.-Electr.Power Appl.,Vol.141,No.2,pp.63-70,Mar.,1994
[15]Faa-Jeng Lin,et al.,"A Robust PM Synchronous Motor Drive with Adaptive Uncertainty Observer",IEEE Trans.on Energy Conv.,Vol.14, No.4, December 1999, pp.989-995
[16] K.K.D. Young (editor). Variable Structure Control for Robotics and Aerospace Applications. Elsevier Science Publishers B.V.,1993
[17] Vadim Utkin, Jurgen Guldner, Jingxin Shi. Sliding Mode control in Electromechanical Systems. Taylor & Francis, 1999
[18] K S Low, et al., "A High Performance Linear Motor Drive for Integrated Circuit's Leads Inspection System", IECON'98, Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society, 1998, Vol.3, pp.1321-1325
[19] Cheung N C, Chen Y R, Wu J. H_∞ control of permanent magnet linear motor in transportation systems. Proceedings of the 5th international conference on electrical machines and systems, ICEMS' 2001, Shenyang, China: August 18-20, 2001, 2: 706-709
[20] Chen Y R, Cheung N C, Wu J. H_∞ robust control of permanent magnet linear synchronous motor in high-performance motion system with large parametric uncertainty. The 33rd IEEE power electronics specialists conference, PESC' 2002, Queensland, Australia, June 23-27, 2002, in press
[21] Sanchez-Pena R S, Sznaier M. Robust systems theory and applications. John Wiley & Sons, 1998
[22] Kim J-S, Kim Y-S, Shin J-H, Kim H-J. H_∞, speed control of an induction motor with the two-mass resonant system by LMI. Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society, IECON' 98, 1998, 3: 1439-1444
[23] Hsien T-L, Sun Y-Y, Tsai M-C. H_∞ control for a sensorless permanent-magnet synchronous drive. IEE Proc.-Electr. Power Appl., 1997, 144(3): 173-181
[24] Zhou Kemin. Essentials of Robust Control. New Jersey: Prentic-Hall, Inc.,1998
[25] 申铁龙.H_∞控制理论及应用.北京:清华大学出版社. 1996
[26]Attaianese C,Perfetto A,Tomasso G.Robust position control of DC drive by means of controllers.IEE Proc.-Electr.Power Appl.,1999,146(4):391-396
[27]K.K.Tan,S.N.Huang,H.F.Dou,et al,"Adaptive robust motion control for precise trajectory tracking applications",ISA Transactions 40(2001):57-71
[28]刘金凌,王先逵,吴丹等.直线电机伺服系统的模糊推理自校正PID 控制.清华大学学报(自然科学版).1998,3 8(2):44-46
[29]孙宜标,郭庆鼎,孙艳娜.基于模糊自学习的交流直线伺服系统滑模变结构控制.电工技术学报.2001,16(1):52-56
[30]周箴,赵金,万淑芸等.模糊单神经元混合控制在交流传动系统中的应用.电气传动.1998,(1):21-23
[31]张志远,万沛霖,涂巧玲.应用模糊神经网络完成模糊控制器的设计和仿真.重庆工学院学报.2000,14(2):94-99
[32]张向文,杨海柱,王福忠等.基于神经网络的PMLSM建模.焦作工学院(自然科学版).2002,21(2):136-139
[33]M.S.Ahmed.Neural net based MRAC for a class of nonlinear plants.IEEE Neural Networks.13(2000):111-124
[34]韦巍.智能控制技术的研究现状和展望.机电工程.2000,17(6):1-4
[35]张秀玲.神经网络自适应控制的研究进展及展望.工业仪表与自动化装置.2002,(1):10-14
[36]张广明,张琦.永磁交流伺服系统神经网络模型参考自适应控制.解放军理工大学学报.2000,1(12):66-69
[37]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,(1):19-23
[38]郭庆鼎,迟林春,王成元.基于神经网络给定补偿的永磁同步直线交流伺服H_∞控制.控制与决策.2000,15(1):75-78
[39]C.L.Lin,N.C.Shieh,and P.C.Tung.Robust Wavelet Neuro Control for Linear Brushless Motors.IEEE Trans.on Aerospace and Electronic Systems,2002,38(3):918-932
[40]顾毅.智能控制发展综述.信息技术.2000,(6):39-40.
[41]Cruise R J,et al.Reduction of Cogging Forces in Linear Synchronous Motors.IEEE Africon,1999,Vol.2,pp.623-626
[42]Aston T R.25 Years of Linear Motoring.The 6th International Conference on Electrical Machines and Drives,1993,pp.353-358
[43]http://www.trilogysystems.com,Trilogy Linear Motors & Megabyte On-Site Service Company,1999
[44]M.F.Mahman,et al,"Position estimation in solenoid actuators",IEEE Trans.on Industry Applications,Vol.32,No.3,pp.552-559,May/Jun.,1996
[45]M.F.Mahman,et al,"Converting a switching solenoid to a proportional actuator",T.IEE Japan,Vol.116-D,No.5,pp.531-537,1996
[46]N.C.Cheung,et al,"Modelling and control of a high speed,long travel,dual voice coil actuator",IEEE International Conference on Power Electronics and Drives,IPEDS' 97,Vol.1,pp.270-274,May,1997
[47]Cheung N C.A nonlinear,short stroke proportional solenoid.Ph.D.thesis.The University of New South Wales,Australia,1995
[48]P.Pillay and R.Krishnan.Modeling,simulation,and analysis of permanent-magnet motor drives,Part Ⅰ:The permanent-magnet synchronous motor drive.IEEE Trans.Ind.Appl.,Vol.25,No.2,Mar./Apr.1989,pp.265-273
[49]浙江大学电机系电机教研组,《新技术译丛》编译组.直线感应电动机(译文集).北京:科学出版社,1978
[50]王成元等.矢量控制交流伺服驱动电动机.北京:机械工业出版社,1995
[51]姜可薰.电机瞬变过程(修订本).北京:机械工业出版社,1991
[52]高景德,王祥珩,李发海.交流电机及其系统的分析.北京:清华大学出版社,1993
[53]陈渊睿.永磁直线电机的鲁棒滤波与控制.华南理工大学工学博士学位论文.2002年
[54]George Ellis.Control System Design Guide(Third Edition).Publishing House of Electronics Industry,2006.pp189-191
[55]刘希喆,吴捷.永磁同步直线电机速度环自抗扰控制器的设计.电工技术学报,2004,4:pp4-7
[56]刘希喆.永磁直线电机的自抗扰与频域鲁棒控制.华南理工大学工学博士学位论文.2004年
[57]薛定宇.反馈控制系统分析与设计.北京:清华大学出版社,2000
[58]周克敏,J.C.Doyle,K.Glover.鲁棒与最优控制.国防工业出版社,2002,7
[59]王德进.H2和H_∞优化控制理论.哈尔滨工业大学出版社,2000,10
[60]赵文峰.控制系统设计与仿真.西安电子科技大学出版社,2002,3
[61]张尚才.控制工程基础.浙江大学出版社,1991年
[62]薛定宇,陈阳泉.基于MATLAB/Simulink的系统仿真技术与应用.清华大学出版社,2002年.
[63]http://www.mathworks.com/matlabcentral
[64]http://www.kollmorgen.com/
[65]刘金琨.先进PID控制及其MATLAB仿真.2003年1月第1版.电子工业出版社.2003:130-155
[66]雷春林.永磁直线电机的自抗扰控制.华南理工大学工学硕士学位论文.2004年
[67]郑力新,周凯汀,王永初.PID进化设计法.仪器仪表学报.2001,8,22(4):340-343
[68]周凯汀,郑力新.遗传算法在PID自适应控制中的应用.自动化仪表.2002,10,23(10):13-16
[2]郭庆鼎等.直线交流伺服系统的精密控制技术.2000年1月第1版.北京:机械工业出版社,2000
[3]叶云岳,杨天夫.直线电机在制造技术装备中的应用综述.产品与技术,2002年12月,pp33-37
[4]王伟进,直线电机的发展与应用概述.微电机,2004年第1期,44-46
[5]宋书中,胡业发,周祖德.直线电机的发展及应用概况.控制工程,2006年5月,pp200-201
[6]魏志强,王先逵,杨志刚 高速加工机床及其关键技术 制造技术与机床,1998(1):5-7
[7]刘泉,张建民,王先逵.直线电机在机床工业中的最新应用及技术分析,机床与液压,2004年No.6,PP1-3
[8]几种高进给速度机床 制造技术与机床,2002(9)
[9]张伯霖,潘珊珊,于兆勤等 直线电机及其在超高速机床上的应用 中国机械工程,1997(4):85-88
[10]刘金凌,王先逵,冯之敬 高频响直流直线电机 微特电机,1993(4):17-18
[11]陶永华,新型PID控制及其应用,北京:机械工业出版社,2002
[12]叶云岳,陆凯元.直线电机的PID控制与模糊控制.电工技术学报.2001,16(3):11-15
[13]杨霞,任敏.专家控制的PID交流伺服系统的研究.燕山大学学报.2002,26(2):176-178
[14]J.S.Ko,et al,"Robust digital position control of brushless DC motor with adaptive load torque observer",IEE Proc.-Electr.Power Appl.,Vol.141,No.2,pp.63-70,Mar.,1994
[15]Faa-Jeng Lin,et al.,"A Robust PM Synchronous Motor Drive with Adaptive Uncertainty Observer",IEEE Trans.on Energy Conv.,Vol.14, No.4, December 1999, pp.989-995
[16] K.K.D. Young (editor). Variable Structure Control for Robotics and Aerospace Applications. Elsevier Science Publishers B.V.,1993
[17] Vadim Utkin, Jurgen Guldner, Jingxin Shi. Sliding Mode control in Electromechanical Systems. Taylor & Francis, 1999
[18] K S Low, et al., "A High Performance Linear Motor Drive for Integrated Circuit's Leads Inspection System", IECON'98, Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society, 1998, Vol.3, pp.1321-1325
[19] Cheung N C, Chen Y R, Wu J. H_∞ control of permanent magnet linear motor in transportation systems. Proceedings of the 5th international conference on electrical machines and systems, ICEMS' 2001, Shenyang, China: August 18-20, 2001, 2: 706-709
[20] Chen Y R, Cheung N C, Wu J. H_∞ robust control of permanent magnet linear synchronous motor in high-performance motion system with large parametric uncertainty. The 33rd IEEE power electronics specialists conference, PESC' 2002, Queensland, Australia, June 23-27, 2002, in press
[21] Sanchez-Pena R S, Sznaier M. Robust systems theory and applications. John Wiley & Sons, 1998
[22] Kim J-S, Kim Y-S, Shin J-H, Kim H-J. H_∞, speed control of an induction motor with the two-mass resonant system by LMI. Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society, IECON' 98, 1998, 3: 1439-1444
[23] Hsien T-L, Sun Y-Y, Tsai M-C. H_∞ control for a sensorless permanent-magnet synchronous drive. IEE Proc.-Electr. Power Appl., 1997, 144(3): 173-181
[24] Zhou Kemin. Essentials of Robust Control. New Jersey: Prentic-Hall, Inc.,1998
[25] 申铁龙.H_∞控制理论及应用.北京:清华大学出版社. 1996
[26]Attaianese C,Perfetto A,Tomasso G.Robust position control of DC drive by means of controllers.IEE Proc.-Electr.Power Appl.,1999,146(4):391-396
[27]K.K.Tan,S.N.Huang,H.F.Dou,et al,"Adaptive robust motion control for precise trajectory tracking applications",ISA Transactions 40(2001):57-71
[28]刘金凌,王先逵,吴丹等.直线电机伺服系统的模糊推理自校正PID 控制.清华大学学报(自然科学版).1998,3 8(2):44-46
[29]孙宜标,郭庆鼎,孙艳娜.基于模糊自学习的交流直线伺服系统滑模变结构控制.电工技术学报.2001,16(1):52-56
[30]周箴,赵金,万淑芸等.模糊单神经元混合控制在交流传动系统中的应用.电气传动.1998,(1):21-23
[31]张志远,万沛霖,涂巧玲.应用模糊神经网络完成模糊控制器的设计和仿真.重庆工学院学报.2000,14(2):94-99
[32]张向文,杨海柱,王福忠等.基于神经网络的PMLSM建模.焦作工学院(自然科学版).2002,21(2):136-139
[33]M.S.Ahmed.Neural net based MRAC for a class of nonlinear plants.IEEE Neural Networks.13(2000):111-124
[34]韦巍.智能控制技术的研究现状和展望.机电工程.2000,17(6):1-4
[35]张秀玲.神经网络自适应控制的研究进展及展望.工业仪表与自动化装置.2002,(1):10-14
[36]张广明,张琦.永磁交流伺服系统神经网络模型参考自适应控制.解放军理工大学学报.2000,1(12):66-69
[37]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,(1):19-23
[38]郭庆鼎,迟林春,王成元.基于神经网络给定补偿的永磁同步直线交流伺服H_∞控制.控制与决策.2000,15(1):75-78
[39]C.L.Lin,N.C.Shieh,and P.C.Tung.Robust Wavelet Neuro Control for Linear Brushless Motors.IEEE Trans.on Aerospace and Electronic Systems,2002,38(3):918-932
[40]顾毅.智能控制发展综述.信息技术.2000,(6):39-40.
[41]Cruise R J,et al.Reduction of Cogging Forces in Linear Synchronous Motors.IEEE Africon,1999,Vol.2,pp.623-626
[42]Aston T R.25 Years of Linear Motoring.The 6th International Conference on Electrical Machines and Drives,1993,pp.353-358
[43]http://www.trilogysystems.com,Trilogy Linear Motors & Megabyte On-Site Service Company,1999
[44]M.F.Mahman,et al,"Position estimation in solenoid actuators",IEEE Trans.on Industry Applications,Vol.32,No.3,pp.552-559,May/Jun.,1996
[45]M.F.Mahman,et al,"Converting a switching solenoid to a proportional actuator",T.IEE Japan,Vol.116-D,No.5,pp.531-537,1996
[46]N.C.Cheung,et al,"Modelling and control of a high speed,long travel,dual voice coil actuator",IEEE International Conference on Power Electronics and Drives,IPEDS' 97,Vol.1,pp.270-274,May,1997
[47]Cheung N C.A nonlinear,short stroke proportional solenoid.Ph.D.thesis.The University of New South Wales,Australia,1995
[48]P.Pillay and R.Krishnan.Modeling,simulation,and analysis of permanent-magnet motor drives,Part Ⅰ:The permanent-magnet synchronous motor drive.IEEE Trans.Ind.Appl.,Vol.25,No.2,Mar./Apr.1989,pp.265-273
[49]浙江大学电机系电机教研组,《新技术译丛》编译组.直线感应电动机(译文集).北京:科学出版社,1978
[50]王成元等.矢量控制交流伺服驱动电动机.北京:机械工业出版社,1995
[51]姜可薰.电机瞬变过程(修订本).北京:机械工业出版社,1991
[52]高景德,王祥珩,李发海.交流电机及其系统的分析.北京:清华大学出版社,1993
[53]陈渊睿.永磁直线电机的鲁棒滤波与控制.华南理工大学工学博士学位论文.2002年
[54]George Ellis.Control System Design Guide(Third Edition).Publishing House of Electronics Industry,2006.pp189-191
[55]刘希喆,吴捷.永磁同步直线电机速度环自抗扰控制器的设计.电工技术学报,2004,4:pp4-7
[56]刘希喆.永磁直线电机的自抗扰与频域鲁棒控制.华南理工大学工学博士学位论文.2004年
[57]薛定宇.反馈控制系统分析与设计.北京:清华大学出版社,2000
[58]周克敏,J.C.Doyle,K.Glover.鲁棒与最优控制.国防工业出版社,2002,7
[59]王德进.H2和H_∞优化控制理论.哈尔滨工业大学出版社,2000,10
[60]赵文峰.控制系统设计与仿真.西安电子科技大学出版社,2002,3
[61]张尚才.控制工程基础.浙江大学出版社,1991年
[62]薛定宇,陈阳泉.基于MATLAB/Simulink的系统仿真技术与应用.清华大学出版社,2002年.
[63]http://www.mathworks.com/matlabcentral
[64]http://www.kollmorgen.com/
[65]刘金琨.先进PID控制及其MATLAB仿真.2003年1月第1版.电子工业出版社.2003:130-155
[66]雷春林.永磁直线电机的自抗扰控制.华南理工大学工学硕士学位论文.2004年
[67]郑力新,周凯汀,王永初.PID进化设计法.仪器仪表学报.2001,8,22(4):340-343
[68]周凯汀,郑力新.遗传算法在PID自适应控制中的应用.自动化仪表.2002,10,23(10):13-16