摘要
永磁同步直线电机可利用电磁推力直接驱动运动机构生成直线运动,相对传统“旋转电机+滚珠丝杠”的间接驱动方式,具有高速度、高精度和大推力的优点,在高性能制造装备、精密测量仪器等领域具有广阔的应用前景。本文针对永磁同步直线电机复杂机电耦合系统分析及控制方法展开研究,建立了机电耦合系统模型,提出了永磁直线同步电机的高效电磁场计算及精确仿真方法,提出了非正弦反电动势永磁同步直线电机矢量控制新方法,开发了控制系统并进行了实验验证。
本文首先由电磁场麦克斯韦方程出发,阐述了永磁同步直线电机机电耦合系统的基本理论及分析方法,利用机电耦合系统的能量分析方法,推导了永磁同步直线电机推力方程,建立了机电耦合系统模型,为永磁同步直线电机的电磁场计算、机电耦合系统仿真以及控制系统设计与分析提供了理论基础。
针对永磁同步直线电机二维恒定磁场计算,阐述了二维恒定磁场边值问题及其有限元计算方法,并对永磁同步直线电机端部效应力、齿槽效应力分别进行了计算。介绍了保角变换及数值许-可变换,建立了考虑永磁体形状的永磁同步直线电机的离散线电流等效模型,分析了线电流磁场的边值问题在保角变换下的不变性,推导了基于保角变换的永磁同步直线电机复杂有槽气隙的磁场求解公式,并利用磁场计算结果分析了永磁体形状对永磁同步直线电机性能的影响。
分析了永磁同步直线电机理想仿真模型,针对控制系统精确动态仿真,推导了相变量模型的状态方程,考虑电机非理想结构对永磁磁链、电感、齿槽力的影响,提出了一种基于电磁场数值计算结果的永磁同步直线电机相变量仿真建模方法,利用Simulink/SimpowerSystems建立了基于电感、齿槽力、永磁磁链样条插值函数的永磁同步直线电机S-function仿真模型,并实验验证了模型的有效性。
传统矢量控制基于正弦反电动势假设,考虑非正弦反电动势的影响,推导了表示为电流矢量及永磁磁链导数矢量点积形式的推力方程,得出了任意波形反电动势表面式永磁同步电机的矢量控制原理。考虑永磁磁链谐波的影响,引入d′q′白轴坐标系,提出了一种id=0的非正弦反电动势永磁同步电机矢量控制新方法。同时,针对齿槽力等周期性扰动,采取了齿槽力前馈补偿、重复控制补偿的PI速度控制器等措施。
最后,采用DSP+FPGA+IPM硬件体系结构,设计、实现了永磁同步直线电机控制系统,并针对本文所提出的永磁同步直线电机机电耦合系统分析与控制方法进行了实验验证。
Comparing with the traditional indirect drive system--"rotary motor + ball screw", permanent magnet synchronous linear motors (PMSLMs) can produce linear motion directly. With the advantages of high speed, high precision and high thrust, PMSLMs have wide application foreground in many fields such as high-performance manufacturing equipment, precision measuring instruments and so on. The dissertation focuses on the analysis and control of PMSLMs. In which, the electromechanical coupling model of PMSLMs is established; an efficient calculation method of magnetic field, and an accurate simulation method are proposed for PMSLMs; a new vector control method is put forward for the non-sinusoidal back-electromotive-force (back-EMF) PMSLMs. The software and hardware of control system are designed and implemented, at the same time the proposed methods are validated by experiments.
Firstly, based on the Maxwell equations of electromagnetic field, the basic theory and analysis methods of PMSLMs are described. With the energy analysis method of electromechanical coupling system, the force equation is derivated, and then the electromechanical coupling model of PMSLMs is established. Thus, a theoretical basis is provided for the magnetic field calculation, mechatronic system simulation, and control system design and analysis.
To solve the 2D constant magnetic field of PMSLMs, the 2D constant magnetic field boundary value problem and finite element method are described. And the forces caused by the endding effect and the slotting effect of PMSLMs are calculated respectively. Then, the conformal mapping (CM) and the numerical Schwarz-Christoffel (S-C) mapping are described. The punctual curren equivalent model of PM is established considering the PM's shape, the invariance of punctual current magnetic field boundary value problem under the conformal mapping is analyzed. The solution of complex slotting air gap magnetic field of PMSLMs using conformal mapping is derived, and the effects of PM shape on PMSLMs are analyzed.
Precise dynamic simulaition of PMSLMs can't be carried out using the ideal model. Considering the effects of non-ideal structure on the PM flux linkage, inductances, cogging force, a phase variable model based on the numerical calculation of magnetic field is proposed for PMSLMs. The state equations of phase variable model are derived. The S-function simulation model of PMSLMs is established based on the spline interpolation of inductances, cogging force, and PM flux linkage using Simulink/SimpowerSystems, and the model is verified with experiments.
A general vector control principle of surface-mounted permanent magnet motors with arbitrary back-EMF waveform is presented. The principle is derived from the force equation in the dot product form of the current vector and the permanent magnet flux linkage derivative vector. Based on a new d'q' reference frame considering the effects of PM flux linkage harmonic, a new vector control method is proposed for the non-sinusoidal back-EMF PMSLMs. According to periodic disturbances, the cogging force feedforward compensation and PI speed controller with repetitive control compensation are used.
The control system is designed and implemented based on DSP+FPGA+IPM hardware architecture. And the validity of proposed analysis and control methods are verified by experiments.
引文
[1]T. Jahns, W. Soong. Pulsating torque minimization techniques for permanent magnet AC motor drives-A review. IEEE Trans. Ind. Electron.,1996,43(2):321-330.
[2]P. V. Braembussche, J. Swevers, H. V. Brussel, et al. Accurate tracking control of linear synchronous motor machine tool axes. Mechatronics,1996,6(5):507-21.
[3]K. K. Tan, T. H. Lee, H. F. Dou, et al. Precision Motion Control Design and Implementation, ser. Advances in Industrial Control Series. New York:Springer-Verlag, 2001.
[4]J. F. Gieras, Z. J. Piech. Linear Synchronous Motors:Transportation and Automation Systems. Boca Raton, FL:CRC Press,2000.
[5]叶云岳.直线电机原理与应用.北京：机械工业出版社,2000.
[6]Hellinger, R., Mnich, P.. Linear Motor-Powered Transportation:History, Present Status, and Future Outlook. Proceedings of the IEEE,2009,97(11):1892-1900.
[7]Kou Baoquan, Li Liyi, Zhang Chengming. Analysis and Optimization of Thrust Characteristics of Tubular Linear Electromagnetic Launcher for Space-Use. IEEE Transactions on Magnetics,2009,45(1):250-255.
[8]Z. Q. Zhu, X. P. Xia, D. Howe, et al. Reduction of cogging force on slotless linear permanent magnet force. IEE Proc.—Electr. Power Appl.,1997,144(4):277-282.
[9]K. C. Lim, J. K. Woo, G. H. Kang, et al. Detent force minimization techniques in permanent magnet linear synchronous motors. IEEE Trans. Magn.,2002,38(2): 1157-1160.
[10]Z. Q. Zhu, D. Howe. Influence of design parameters on cogging torque in permanent magnet machines. IEEE Trans. Energy Convers.,2000,15(4):407-412.
[11]G. Otten, J. A. de Vries, J. van Amerongen, et al. Linear motor motion control using a learning forward controller. IEEE/ASME Trans. Mechatronics,1997,2(3):179-187.
[12]K. K. Tan, S. N. Huang, T. H. Lee. Robust adaptive numerical compensation for friction and force ripple in permanent-magnet linear motors. IEEE Trans. Magn.,2002,38(1): 221-228.
[13]Y. W. Zhu, D. H. Koo, and Y. H. Cho. Detent force minimization of permanent magnet linear synchronous motor by means of two different methods. IEEE Trans. Magn.,2008, 44(11):4345-4348.
[14]S. I. Kim, J. P. Hong, Y. K. Kim, et al. Optimal design of slotless-type PMLSM considering multiple responses by response surface methodology. IEEE Trans. Magn., 2006,42(4):1219-1222.
[15]N. M. Kimoulakis, A. G. Kladas, J. A. Tegopoulos. Cogging Force Minimization in a Coupled Permanent Magnet Linear Generator for Sea Wave Energy Extraction Applications. IEEE Trans. Magn.,2009,45(3):1246-1249.
[16]S. Mohammad, S.M. Islam, S. Tomy, et al. Design considerations of sinusoidally excited permanent-magnet machines for low-torque-ripple applications. IEEE Trans. Ind. App.,2005,41(4):955-962.
[17]P. S. Shin, S. H. Woo, Y. Zhang, et al. An Application of Latin Hypercube Sampling Strategy for Cogging Torque Reduction of Large-Scale Permanent Magnet Motor. IEEE Trans. Magn.,2008,44(11):4421-4424.
[18]N. R. Tavana, A. Shoulaie. Analysis and Design of Magnetic Pole Shape in Linear Permanent-Magnet Machine. IEEE Trans. Magn.,2010,46(4):1000-1006.
[19]唐任远.现代永磁电机理论及设计.北京：机械工业出版社,1997.
[20]B. Sheikh-Ghalavand, S. Vaez-Zadeh, A. Hassanpour Isfahani. An Improved Magnetic Equivalent Circuit Model for Iron-Core Linear Permanent-Magnet Synchronous Motors. IEEE Transactions on Magnetics,2010,46(1):112-120.
[21]汤蕴缪.电机内的电磁场.北京：科学出版社,1998.
[22]M. Amrhein, P.T. Krein.3-D Magnetic Equivalent Circuit Framework for Modeling Electromechanical Devices. IEEE Transactions on Energy Conversion,2009,24(2): 397-405.
[23]Yaow-Ming Chen, Shu-Yuan Fan, Wei-Shin Lu. Performance Analysis of Linear Permanent-Magnet Motors with Finite-Element Analysis. IEEE Transactions on Magnetics,2008,44(3):377-385.
[24]N. Boules. Prediction of no-load flux density distribution in permanent magnet machines. IEEE Trans. Ind. Appl.,1985, IA-21(3):633-643.
[25]Z. Q. Zhu, D. Howe, E. Bolte, et al. Instantaneous magnetic field distribution in brushless permanent magnet dc motors. Part I:Open-circuit field. IEEE Trans. Magn., 1993,29(1):124-135.
[26]Z. Q. Zhu and D. Howe. Instantaneous magnetic field distribution in brushless permanent magnet dc motors. Part Ⅱ:Armature-reaction field. IEEE Trans. Magn.,1993, 29(1):136-142.
[27]Z. Q. Zhu and D. Howe. Instantaneous magnetic field distribution in brushless permanent magnet dc motors. Part III:Effect of stator slotting. IEEE Trans. Magn.,1993, 29(1):143-151.
[28]Z. Q. Zhu, D. Howe. Instantaneous magnetic field distribution in permanent magnet brushless dc motors. Part IV:Magnetic field on load. IEEE Trans. Magn.,1993,29(1): 152-158.
[29]D. Zarko, D. Ban, and T. A. Lipo, "Analytical calculation of magnetic field distribution in the slotted air gap of a surface permanent-magnet motor using complex relative air-gap permeance," IEEE Trans. Magn., vol.42, no.7, pp.1828-1837, Jul.2006.
[30]D. Zarko, D. Ban, T. A. Lipo. Analytical solution for cogging torque in surface permanent-magnet motors using conformal mapping. IEEE Trans. Magn.,2008,44(1): 52-65.
[31]M. Markovic, M. Jufer, Y. Perriard. Reducing the cogging torque in brushless DC motors by using conformal mappings. IEEE Trans. Magn.,2004,40(2):451-455.
[32]M. Markovic, M. Jufer, Y. Perriard. Determination of tooth cogging force in a hard-disk brushless DC motor. IEEE Trans. Magn.,2005,41(12):4421-4426.
[33]T. C. O'Connell, P. T. Krein. A Schwarz-Christoffel-based analytical method for electric machine field analysis. IEEE Trans. Energy Conver.,2009,24(3):565-577.
[34]D. C. J. Krop, E. A. Lomonova, A. J. A. Vandenput. Application of Schwarz-Christoffel mapping to permanent-magnet linear motor analysis. IEEE Trans. Magn.,2008,44(3): 352-359.
[35]B. L. J. Gysen, E. A. Lomonova, J. J. H. Paulides, et al. Analytical and numerical techniques for solving laplace and poisson equations in a tubular permanent magnet actuator:Part Ⅱ. Schwarz-Christoffel mapping. IEEE Trans. Magn.,2008,44(7): 1761-1767.
[36]Z. J. Liu, J. T. Li. Analytical solution of air-gap field in permanentmagnet motors taking into account the effect of pole transition over slots. IEEE Trans. Magn.,2007,43(10): 3872-3883.
[37]Z. J. Liu, J. T. Li. Accurate prediction of magnetic field and magnetic forces in permanent magnet motors using an analytical solution. IEEE Trans. Energy Convers., 2008,23(3):717-726.
[38]Z. Q. Zhu, L. J. Wu, Z. P. Xia. An accurate subdomain model for magnetic field computation in slotted surface-mounted permanent magnet machines. IEEE Trans. Magn.,2010,46(4):1100-1115.
[39]P. Pillay, R. Krishnan. Modeling, simulation, and analysis of permanent-magnet motor drives (Ⅰ):the permanent-magnet synchronous motor drives. IEEE Transactions on Industry Applications,1989,25(2):265-273.
[40]P. Pillay, R. Krishnan. Modeling, simulation, and analysis of permanent-magnet motor drives(Ⅱ):the brushless DC motor drive. IEEE Transactions on Industry Applications, 1989,25(2):274-279.
[41]王兴华,励庆孚,王曙鸿.永磁无刷直流电机负载磁场及其电磁转矩的计算.中国电机工程学报,2003,23(4)：140-144.
[42]R. Leidhold, P. Mutschler. A Linear Synchronous-Motor Model for Evaluation of Sensorless Methods.2006 IEEE International Symposium on Industrial Electronics, 2006:2467-2472.
[43]刘瑞芳,严登俊,胡敏强.永磁无刷直流电机场路耦合运动时步有限元分析.中国电机工程学报,2007,27(12)：59-64.
[44]鲁军勇,张全红.永磁直线直流无刷电机动态性能有限元分析.微特电机,2007,(1)：10-12.
[45]N. M. Abe, J. R. Cardoso. Coupling electric circuit and 2D-FEM model with Dommel's approach for transient analysis. IEEE Trans. Magn.,1998,34:3487-3490.
[46]N. A. Demerdash, J. F. Bangura, A. A. Arkadan. A time-stepping coupled finite element-state space model for induction motor drives-Part 1:Model formulation and machine parameter computation. IEEE Trans. Energy Conversion,1999,14:1465-1471.
[47]J. Vaananen. Circuit theoretical approach to couple two-dimensional finite element models with external circuit equations. IEEE Trans. Magn.,1996,32:400-410.
[48]P. Zhou, W. N. Fu, D. Lin. Numerical modeling of magnetic devices. IEEE Transactions on Magnetics,2004,40(4):1803-1809.
[49]P. Zhou, D. Lin, W. N. Fu, et al. A general cosimulation approach for coupled field-circuit problems. IEEE Transactions on Magnetics,2006,42(4):1051-1054.
[50]M. A. Alhamadi, N. A. Demerdash. Modeling and experimental verification of the performance of a skew mounted permanent magnet brushless DC motor drive with parameters computed from 3D-FE magnetic field solutions. IEEE Transactions on Energy Conversion,1994,9(1):26-35.
[51]F. Soares, P. J. Costa Branco. Simulation of a 6/4 switched reluctance motor based on Matlab/Simulink environment. IEEE Transactions on Aerospace and Electronic Systems, 2001,37(3):989-1009.
[52]O. A. Mohammed, S. Liu, Z. Liu. A phase variable model of brushless dc motors based on finite element analysis and its coupling with external circuits. IEEE Transactions on Magnetics,2005,41(5):1576-1579.
[53]O. A. Mohammed, S. Liu, Z. Liu. Physical modeling of PM synchronous motors for integrated coupling with machine drives. IEEE Transactions on Magnetics,2005,41(5): 1628-1631.
[54]Liu Shuo, O. A. Mohammed, Z.Liu. An Improved FE-Based Phase Variable Model of PM Synchronous Machines Including Dynamic Core Losses. IEEE Transactions on Magnetics,2007,43(4):1801-1804.
[55]D. C. Hanselman. Minimum torque ripple, maximum efficiency excitation of brushless permanent magnet motors. IEEE Trans. Ind. Electron.,1994,41(3):292-300.
[56]P. L. Chapman, S. D. Sudhoff, C. A. Whitcomb. Optimal current control strategies for surface-mounted permanent-magnet synchronous machine drives. IEEE Trans. Electromag. Compat.,1999,14(4):1043-1050.
[57]S. J. Park, H. W. Park, M. H. Lee, et al. A new approach for minimum-torque-ripple maximum-efficiency control of BLDC motor. IEEE Trans. Ind. Electron.,2000,7(1): 109-114.
[58]P. Mattavelli, L. Tubiana, and M. Zigliotto. Torque-ripple reduction in PM synchronous motor drives using repetitive current control. IEEE Trans. Power Electron.,2005,20(6): 1423-1431.
[59]揭贵生,马伟明,耿建明等.无刷直流电机的一种新型转矩与效率优化控制.中国电机工程学报,2006,26(24)：131-136.
[60]F. Aghili. Adaptive reshaping of excitation currents for accurate torque control of brushless motors. IEEE Transactions on Control Systems Technology,2008,16(2): 356-364.
[61]Geun-Ho Lee, Sung-I1 Kim, Jung-Pyo Hong, et al. Torque Ripple Reduction of Interior Permanent Magnet Synchronous Motor Using Harmonic Injected Current. IEEE Transactions on Magnetics,2008,44(6):1582-1585.
[62]D. G. Holmes, T. A. Lipo, B. P. McGrath, et al. Optimized Design of Stationary Frame Three Phase AC Current Regulators. IEEE Transactions on Power Electronics,2009, 24(11):2417-2426.
[63]J. Hung and Z. Ding. Design of current to reduce torque ripple in brushless permanent magnet motors. Proc. Inst. Elect. Eng.,1993,140(4):260-266.
[64]S.-J. Kang, S.-K. Sul. Direct torque control of brushless DC motor with nonideal trapezoidal back EMF. IEEE Trans. Power Electron.,1995,10(6):796-802.
[65]S. K. Chung, H. S. Kim, C. G. Kim, et al. A new instantaneous torque control of PM synchronous motor for high-performance direct-drive applications. IEEE Trans. Power Electron.,1998,13(3):388-400.
[66]B. Grcar, P. Cafuta, G. Stumberger, et al. Control-based reduction of pulsating torque for PMAC machines. IEEE Transactions on Energy Conversion,2002,17(2):169-175.
[67]Y. Liu, Z. Q. Zhu, D. Howe. Direct torque control of brushless DC drives with reduced torque ripple. IEEE Trans. Ind. Appl.,2005,41(2):599-608.
[68]Z. Q. Zhu, Y. Liu, and D. Howe. Minimizing the influence of cogging torque on vibration of PM brushless machines by direct torque control. IEEE Trans. Magn.,2006, 42(10):3512-3514.
[69]高瑾,胡育文,黄文新等.六边形磁链轨迹的无刷直流电机直接自控制.中国电机工程学报,2007,27(15)：64-69.
[70]H. F. Lu, L. Zhang, and W. L. Qu. A new torque control method for torque ripple minimization of BLDC motors with un-ideal back EMF, IEEE Trans. Power Electron., 2008,23(2):950-958.
[71]S. B. Ozturk, H. A. Toliyat. Direct Torque and Indirect Flux Control of Brushless DC Motor. IEEE/ASME Transactions on Mechatronics,2011,16(2):351-360.
[72]P. Van den Braembussche, J. Swevers, H. van Brussel. Design and Experimental Validation of Robust Controllers for Machine Tool Drives with Linear Motor. Mechatronics,2001,11:545-562.
[73]L. Xu, B. Yao. Output feedback adaptive robust precision motion control of linear motors. Automatica,2001,37(7):1029-1039.
[74]Hyo-Sung Ahn, YangQuan Chen, Huifang Dou. State-periodic adaptive compensation of cogging and Coulomb friction in permanent-magnet linear motors. IEEE Transactions on Magnetics,2005,41(1):90-98.
[75]W. T. Su, C. M. Liaw. Adaptive positioning control for a LPMSM drive based on adapted inverse model and robust disturbance observer. IEEE Trans. Power Electron., 2006,21(2):505-517.
[76]YangQuan Chen, K. L. Moore, V. Bahl. Learning feedforward control using a Dilated B-spline network:frequency Domain Analysis and design. IEEE Transactions on Neural Networks,2004,15(2):355-366.
[77]Kok Kiong Tan, Huifang Dou, Yangquan Chen, et al. High precision linear motor control via relay-tuning and iterative learning based on zero-phase filtering. IEEE Transactions on Control Systems Technology,2001,9(2):244-253.
[78]Wei-Te Su, Chang-Ming Liaw. Adaptive positioning control for a LPMSM drive based on adapted inverse model and robust disturbance observer. IEEE Transactions on Power Electronics,2006,21(2):505-517.
[79]Y.A.-R.I. Mohamed, E.F. El-Saadany. A Current Control Scheme With an Adaptive Internal Model for Torque Ripple Minimization and Robust Current Regulation in PMSM Drive Systems. IEEE Transactions on Energy Conversion,2008,23(1):92-100.
[80]Faa-Jeng Lin, Li-Tao Teng, Hen Chu. A Robust Recurrent Wavelet Neural Network Controller With Improved Particle Swarm Optimization for Linear Synchronous Motor Drive. IEEE Transactions on Power Electronics,2008,23(6):3067-3078.
[81]L. Bascetta, P. Rocco, G. Magnani. Force Ripple Compensation in Linear Motors Based on Closed-Loop Position-Dependent Identification. IEEE/ASME Transactions on Mechatronics,2010,15(3):349-359.
[82]Si-Lu Chen, Kok Kiong Tan, Sunan Huang, et al. Modeling and Compensation of Ripples and Friction in Permanent-Magnet Linear Motor Using a Hysteretic Relay. IEEE/ASME Transactions on Mechatronics,2010,15(4):586-594.
[83]温熙森,邱静,陶俊勇.机电系统分析动力学及其应用.北京：科学出版社,2003.
[84]L. N. Trefethen. Numerical computation of the Schwarz-Christoffel transformation. SIAM J. Sci. Stat. Comput.,1980,1:82-102.
[85]T. A. Driscoll. Algorithm 756:A MATLAB toolbox for Schwarz-Christoffel mapping. ACM Trans. Math. Softw.,1996,22(2):168-186.
[86]T. A. Driscoll. Schwarz-Christoffel Toolbox User's Guide:Version 2.3. Newark, DE: Dept. Math. Sci., Univ. Delaware,2005.
[87]T. A. Driscoll. Algorithm 843:Improvements to the Schwarz-Christoffel Toolbox for MATLAB. ACM Trans. Math. Softw.,2005,31:239-251.
[88]T. A. Driscoll and L. N. Trefethen, Schwarz-Christoffel Mapping. Cambridge, U.K.: Cambridge Univ. Press,2002.
[89]T. C. O'Connell, P. T. Krein. A preliminary investigation of computer-aided Schwarz-Christoffel transformation for electric machinedesign and analysis. IEEE Workshops Comput. Power Electron (COMPEL'06),2006,166-172.
[90]T. C. O'Connell, P. T. Krein. The Schwarz-Christoffel analytical method applied to electric machine slot shape optimization," in Proc. IEEE Int. Electric Machines and Drives Conf.,2007,1:341-346.
[91]K. Boughrara, D. Zarko, R. Ibtiouen, et al. Magnetic Field Analysis of Inset and Surface-Mounted Permanent-Magnet Synchronous Motors Using Schwarz-Christoffel Transformation. IEEE Transactions on Magnetics,2009,45(8):3166-3178.
[92]K. Boughrara, R. Ibtiouen, D. Zarko, et al. Magnetic Field Analysis of External Rotor Permanent-Magnet Synchronous Motors Using Conformal Mapping. IEEE Transactions on Magnetics,2010,46(9):3684-3693.
[93]M. Inoue, K. Sato. An approach to a suitable stator length for minimizing the detent force of permanent magnet linear synchronous motors. IEEE Trans. Magn.,2000,36(4): 1890-1893.
[94]O. A. Mohammed, S. Liu, Z. Liu, et al. Finite-element-based nonlinear physical model of iron-core transformers for dynamic simulations. IEEE Transactions on Magnetics, 2006,42(4):1027-1030.
[95]O. A. Mohammed, S. Liu, Z. Liu. Internal Short Circuit Fault Diagnosis for PM Machines Using FE-Based Phase Variable Model and Wavelets Analysis. IEEE Transactions on Magnetics,2007,43(4):1729-1732.
[96]O. A. Mohammed, S. Liu, Z. Liu. FE-based physical phase variable model of PM synchronous machines under stator winding short circuit faults. Science, Measurement & Technology, IET,2007,1(1):12-16.
[97]O. A. Mohammed, S. Liu, Z. Liu. Physics-based phase variable model of machines and transformers from electromagnetic field computations. World Automation Congress, 2008:1-5.
[98]S. Obe Emeka, A. Binder. Direct-phase-variable model of a synchronous reluctance motor including all slot and winding harmonics. Energy Conversion and Management, 2011,52(1):284-291.
[99]N. Mohan, T. M. Undeland, W. P. Robbins. Power electronics:converters, applications, and design. New York:John Wiley &Sons Inc.,1995:669-695.
[100]储剑波,胡育文,黄文新.一种抑制永磁同步电机转速脉动的方法.电工技术学报,2009,24(12)：43-49.
[101]Weizhe Qian, Sanjib K.Panda, Jian-Xin Xu. Torque Ripple Minimization in PM Synchronous Motors Using Iterative Learning Control. IEEE Trans, on Power Electronics,2004,19(2):272-279.
[102]Runzi Cao, Kay-Soon Low. A Repetitive Model Predictive Control Approach for Precision Tracking of a Linear Motion System. IEEE Transactions on Industrial Electronics,2009,56(6):1955-1962.
[103]P.Mattavelli, L. Tubiana, M. Zigliotto. Torque-Ripple Reduction in PM Synchronous Motor Drives Using Repetitive Current Control. IEEE Transactions on Power Electronics,2005,20(6):1423-1431.
[104]孙宜标,闫峰,刘春芳.基于μ理论的永磁直线同步电机鲁棒重复控制.中国电机工程学报,2009,29(30)：52-57.
[105]B. K. Bose现代电力电子学与交流传动.北京：机械工业出版社,2005.
[106]李永东.交流电机数字控制系统.北京：机械工业出版社,2003.
[107]秦忆.现代交流伺服系统.武汉：华中理工大学出版社,1995.
[108]李叶松,黄恒,雷力,等.高性能全数字交流感应电机驱动系统的研究.电力电子技术,2004,38(2)：75-77.
[109]李叶松,宋宝,秦忆.全数字交流永磁同步电机伺服系统设计.电力电子技术,2002,36(3)：26-28.
[110]苏健勇,李铁才.基于多任务模式的高性能通用交流伺服控制器设计.中国电机工程学报,2007,27(18)：55-60.
[111]穆海华,周云飞,温新,等.直线电机齿槽推力波动的标定与补偿方法.电机与控制学报,2009,13(5)：721-727.
[112]H.H. Mu, Y.F. Zhou, X. Wen, et al. Calibration and compensation of cogging force effect in a permanent magnet linear motor. Mechatronics,2009,19(4):577-585.
