面向高速加工的NURBS曲线插补及直线电机鲁棒控制技术研究
|
摘要
数控技术是现代制造业中的关键技术，集微电子、计算机、信息处理、自动检测、自动控制等高新技术于一体，具有高精度和高效率等特点，对制造业实现柔性自动化、集成化、智能化起着举足轻重的作用。数控加工向高速方向发展要求数控系统具有优良的数据通讯模式、先进的插补和伺服控制算法、快速的译码及刀补计算模块等，其中插补和伺服控制是数控加工中的核心功能模块，其性能好坏将直接影响加工精度和加工效率，研究适合高速加工特点的插补和控制算法，对于提高高速加工数控系统的性能具有十分重要的意义。本文在分析国内外数控技术发展现状和趋势的基础上，对高速数控加工中的NURBS曲线直接插补技术及直线电机鲁棒控制技术进行了深入研究，主要包括以下内容：
1.考虑进给速度和插补精度的关系，并结合柔性加减速机制，提出一种加速度和加加速度约束的平滑自适应NURBS(Non-uniform RationalB-spline)曲线插补算法。算法采用2阶Taylor展开式进行下一插补点的迭代计算，根据插补精度要求自适应调整进给速度，并在调整过程中采用加速度与加加速度约束的S型加减速曲线对进给速度重新规划，得到平滑的速度过渡曲线。算法保证了稳定而高速的进给速度，合理的误差范围和平滑无冲击的进给过程，有利于提高加工效率和加工质量。
2.进给速度和进给加速度是数控加工的重要加工参数，设置不当则会影响加工效率或对机床使用寿命产生影响。本文从机床加减速能力和插补精度方面考虑，分析高速加工中进给运动应满足的约束条件。将进给运动分解到各运动轴，根据机床进给轴的力学(电机驱动力／力矩、进给系统所受的惯性力及切削力)模型，推导了多轴联动加工时进给速度、加速度与各进给轴驱动能力以及加工路径几何特性之间的约束关系，使得加工过程中机床各运动轴的加减速始终处于其加工能力范围内。
3.对基于“最差状态点”进行加工的方法加以改进，提出满足插补精度和机床加减速双重约束的分段恒定速度自适应插补算法。算法根据加工路径的曲线信息、机床加工能力及加工要求确定“最差状态点”，并结合自适应插补思想，采用分段高速加工，根据进给约束模型得到不同恒定速度加工段及速度过渡段，并将这些信息存储在一个五元的自适应Lookup链表中，插补过程中通过查找该链表确定进给参数。与“最差状态点”加工方法相比，该算法能够在保证加工精度并满足机床加减速能力的前提下，充分利用机床的加工能力，缩短加工时间，提高加工效率。
4．直线电机是高速加工数控设备的发展趋势之一。由于直线电机的零传动特性，系统参数(动子质量、粘滞摩擦系数等)变化及外部干扰都将直接影响伺服系统的性能。本文针对直线电机伺服控制的特点，将二自由度控制思想与H_∞控制算法相结合，提出了一种“MMC(模型匹配控制)+H_∞+MFC(模型跟踪控制)”的复合控制器结构，对输入和输出分别设计控制器，一方面保证系统对指令的准确跟踪能力，另一方面保证系统对这些不确定性干扰因素的鲁棒性。
在上述研究的基础上，以实验室现有的直线电机和工控机为平台构建两轴联动原型系统，对提出的NURBS曲线插补算法及直线电机控制算法进行了实验测试。结果表明，本文设计的插补算法能够保证高速进给，满足插补精度要求，并且电机运行过程平稳无冲击，轮廓精度高。另外，电机控制算法的阶跃响应实验表明，该控制器对系统参数变化具有较强的鲁棒性，验证了该算法的可行性和优良的控制性能。
Computer numerical control (CNC) is a key technology in modern machining industry. It integrates the technology of micro-electronics, computer, signal processing, automatic measurement, automatic control and etc. With the advantages of high precision and high efficiency, CNC machining plays an important role for machining industry. High speed CNC machining requests for excellent data communication mechanism, advanced interpolation and servo control strategy, fast decoding and cutter offset algorithm, and etc. Among these functions, interpolation and servo control are two core modules of CNC machining, which have great impacts on machining precision and efficiency. Research on interpolation and servo control technology for high speed CNC machining is very important to enhance the performance of high speed machining. In this thesis, high speed CNC machining oriented NURBS interpolation technology and linear motor robust control technology are investigated, which include:
1 A smooth adaptive NURBS (Non-Uniform Rational B-Spline) interpolation algorithm with limited acceleration and jerk constraints is proposed, considering the relationship between feedrate and interpolation error, and flexible acceleration/deceleartion mechanism. The 2nd order Taylor expansion is employed for next point parametric iteration. The feedrate is adaptively changed according to the demand of interpolation precision. In the adaptive area, an acceleration/deceleration and jerk limited S curve is used to replan the feedrate, to get smooth feedrate profile. With this interpolator, steady and fast feedrate, confined interpolation error, and a smooth and shock-free machining process is obtained, which enhances the machining efficiency and quality.
2. Feedrate and feed acceleration are important machining parameters. If not well designed, it will either reduce machining efficiency, or have bad impact on machine tools' life span. In this thesis, from machine tool's acc/dec capability and interpolation precision point of view, constrains of feed motion for high speed machining is investigated. The feed motion is projected into each feed axis, and based on its mechanical model(motor driving torque/force, Inertial force and cutting force), the constraint relationship between feedrate, feed acceleration, and feed drive capabilities and toolpath geometric characteristics is derived. With this constraint model, the acceleration and deceleration of each axis can be limited within its capability.
3. An adaptive interpolation algorithm with segmented constant feedrate satisfying both constraints of interpolation error and machine tool's acceleration/deceleration capabilities is proposed as an improvement against the traditional "worse condition machining" method. It identifies "worse condition points" along the path according to the curve information, machine tool's capability and machining requirement. Integrated with adaptive interpolation, segmented high speed machining is adopted. Different constant speed segments and speed transition segments are obtained according to the feed motion constraint model, and the corresponding feed information are stored in a penta-element lookup chain table. By referring to the lookup table, the interpolator can automatically determine the feed motion. Compared with "worst case machining", it can take more potentials of machine tools and reduce machining time, under the precondition of satisfying interpolation accuracy and machine tool's acc/dec capabilities, and thus, enhance the machining efficiency.
4. As a typical high speed feed drive, linear motor has become a trend in high speed machine tools. Due to its direct drive characteristics, system parameters perturbation (load mass, vicious coefficient and etc) and load disturbance will have a direct impact on its servo performances. In this thesis, a novel controller "MMC(model match control) +H_∞+MFC(Model following control)", integrating 2 degree-of-freedom (2DOF) control philosophy and H_∞method is proposed. It designs controllers for input and output respectively, which ensures precise tracking capability, and strong robustness to uncertain disturbances.
Based on the above research work, a 2-axis linkage prototype system, consisting an XY cross linear motor table and an industrial PC platform, is set up to test the algorithms investigated in the thesis. Interpolator experiments show that the interpolator algorithm proposed in this thesis ensures a high speed feedrate and meets the demand of interpolation precision. What's more, the whole running process is smooth and shock free with high contour precision. Besides, the step response experiment of the proposed PMLSM controller shows strong robustness to system parameter changes, verifies its feasibility and good performances.
1.考虑进给速度和插补精度的关系，并结合柔性加减速机制，提出一种加速度和加加速度约束的平滑自适应NURBS(Non-uniform RationalB-spline)曲线插补算法。算法采用2阶Taylor展开式进行下一插补点的迭代计算，根据插补精度要求自适应调整进给速度，并在调整过程中采用加速度与加加速度约束的S型加减速曲线对进给速度重新规划，得到平滑的速度过渡曲线。算法保证了稳定而高速的进给速度，合理的误差范围和平滑无冲击的进给过程，有利于提高加工效率和加工质量。
2.进给速度和进给加速度是数控加工的重要加工参数，设置不当则会影响加工效率或对机床使用寿命产生影响。本文从机床加减速能力和插补精度方面考虑，分析高速加工中进给运动应满足的约束条件。将进给运动分解到各运动轴，根据机床进给轴的力学(电机驱动力／力矩、进给系统所受的惯性力及切削力)模型，推导了多轴联动加工时进给速度、加速度与各进给轴驱动能力以及加工路径几何特性之间的约束关系，使得加工过程中机床各运动轴的加减速始终处于其加工能力范围内。
3.对基于“最差状态点”进行加工的方法加以改进，提出满足插补精度和机床加减速双重约束的分段恒定速度自适应插补算法。算法根据加工路径的曲线信息、机床加工能力及加工要求确定“最差状态点”，并结合自适应插补思想，采用分段高速加工，根据进给约束模型得到不同恒定速度加工段及速度过渡段，并将这些信息存储在一个五元的自适应Lookup链表中，插补过程中通过查找该链表确定进给参数。与“最差状态点”加工方法相比，该算法能够在保证加工精度并满足机床加减速能力的前提下，充分利用机床的加工能力，缩短加工时间，提高加工效率。
4．直线电机是高速加工数控设备的发展趋势之一。由于直线电机的零传动特性，系统参数(动子质量、粘滞摩擦系数等)变化及外部干扰都将直接影响伺服系统的性能。本文针对直线电机伺服控制的特点，将二自由度控制思想与H_∞控制算法相结合，提出了一种“MMC(模型匹配控制)+H_∞+MFC(模型跟踪控制)”的复合控制器结构，对输入和输出分别设计控制器，一方面保证系统对指令的准确跟踪能力，另一方面保证系统对这些不确定性干扰因素的鲁棒性。
在上述研究的基础上，以实验室现有的直线电机和工控机为平台构建两轴联动原型系统，对提出的NURBS曲线插补算法及直线电机控制算法进行了实验测试。结果表明，本文设计的插补算法能够保证高速进给，满足插补精度要求，并且电机运行过程平稳无冲击，轮廓精度高。另外，电机控制算法的阶跃响应实验表明，该控制器对系统参数变化具有较强的鲁棒性，验证了该算法的可行性和优良的控制性能。
Computer numerical control (CNC) is a key technology in modern machining industry. It integrates the technology of micro-electronics, computer, signal processing, automatic measurement, automatic control and etc. With the advantages of high precision and high efficiency, CNC machining plays an important role for machining industry. High speed CNC machining requests for excellent data communication mechanism, advanced interpolation and servo control strategy, fast decoding and cutter offset algorithm, and etc. Among these functions, interpolation and servo control are two core modules of CNC machining, which have great impacts on machining precision and efficiency. Research on interpolation and servo control technology for high speed CNC machining is very important to enhance the performance of high speed machining. In this thesis, high speed CNC machining oriented NURBS interpolation technology and linear motor robust control technology are investigated, which include:
1 A smooth adaptive NURBS (Non-Uniform Rational B-Spline) interpolation algorithm with limited acceleration and jerk constraints is proposed, considering the relationship between feedrate and interpolation error, and flexible acceleration/deceleartion mechanism. The 2nd order Taylor expansion is employed for next point parametric iteration. The feedrate is adaptively changed according to the demand of interpolation precision. In the adaptive area, an acceleration/deceleration and jerk limited S curve is used to replan the feedrate, to get smooth feedrate profile. With this interpolator, steady and fast feedrate, confined interpolation error, and a smooth and shock-free machining process is obtained, which enhances the machining efficiency and quality.
2. Feedrate and feed acceleration are important machining parameters. If not well designed, it will either reduce machining efficiency, or have bad impact on machine tools' life span. In this thesis, from machine tool's acc/dec capability and interpolation precision point of view, constrains of feed motion for high speed machining is investigated. The feed motion is projected into each feed axis, and based on its mechanical model(motor driving torque/force, Inertial force and cutting force), the constraint relationship between feedrate, feed acceleration, and feed drive capabilities and toolpath geometric characteristics is derived. With this constraint model, the acceleration and deceleration of each axis can be limited within its capability.
3. An adaptive interpolation algorithm with segmented constant feedrate satisfying both constraints of interpolation error and machine tool's acceleration/deceleration capabilities is proposed as an improvement against the traditional "worse condition machining" method. It identifies "worse condition points" along the path according to the curve information, machine tool's capability and machining requirement. Integrated with adaptive interpolation, segmented high speed machining is adopted. Different constant speed segments and speed transition segments are obtained according to the feed motion constraint model, and the corresponding feed information are stored in a penta-element lookup chain table. By referring to the lookup table, the interpolator can automatically determine the feed motion. Compared with "worst case machining", it can take more potentials of machine tools and reduce machining time, under the precondition of satisfying interpolation accuracy and machine tool's acc/dec capabilities, and thus, enhance the machining efficiency.
4. As a typical high speed feed drive, linear motor has become a trend in high speed machine tools. Due to its direct drive characteristics, system parameters perturbation (load mass, vicious coefficient and etc) and load disturbance will have a direct impact on its servo performances. In this thesis, a novel controller "MMC(model match control) +H_∞+MFC(Model following control)", integrating 2 degree-of-freedom (2DOF) control philosophy and H_∞method is proposed. It designs controllers for input and output respectively, which ensures precise tracking capability, and strong robustness to uncertain disturbances.
Based on the above research work, a 2-axis linkage prototype system, consisting an XY cross linear motor table and an industrial PC platform, is set up to test the algorithms investigated in the thesis. Interpolator experiments show that the interpolator algorithm proposed in this thesis ensures a high speed feedrate and meets the demand of interpolation precision. What's more, the whole running process is smooth and shock free with high contour precision. Besides, the step response experiment of the proposed PMLSM controller shows strong robustness to system parameter changes, verifies its feasibility and good performances.
引文
[1]陈德中．我国模具先进制造技术的发展．航空制造技术，3：24-26，2000．
[2]H Schulz and St. Hock. High-speed milling of dies and moulds--cutting conditions andtechnoligy. Annals of the CIRP, 44(1):35-38, 1995.
[3]P Fallbohmer, C A Rodriguez, and T. Ozel. High-speed machining of cast iron and alloy steelsfor die and mold manufacturing. Journal of Materials Processing Technology, 98:104-115,2000.
[4]童红峰，李江雄，吴福中，巫新海．高速加工技术及其在模具制造中的应用．模具制造， 11(6)：34-37，2002．
[5]J．H.绍克．高速切削在模具加工中的应用及发展趋势．航空制造技术，3：37-38，2000．
[6]H Schulz. High-speed machining. Annals of the CIRP, 41(2):637-643, 1992.
[7]J Tlusty. High-speed machining. Annals of the CIRP, 42(2):733-7387, 1993.
[8]S Smith and J Tlusty. Current trends in high-speed machining. Transactions of the ASMEJournal of Engineering for Industry, 119:664-666, 1997.
[9]艾兴．高速切削加工技术．北京：国防工业出版社，2003．
[10]张伯霖．高速切削技术及应用．北京：机械工业出版社，2002．
[11]杨志勇，殷国增．国产数控机床与冶金工业的发展．数控机床市场，，6，2005．
[12]邹兆东，贺艳．数控系统发展趋势．机械研究与应用，19：24-26，2006．
[13]罗然宾．数控技术和装备发展趋势及对策．装备制造技术，1，2006．
[14]周济．数控加工技术．国防工业出版社，2002．
[15]王西彬，解丽静．超高速切削技术及其新进展．中国机械工程，1：190-194，2000．
[16]刘学杰．高速切削及主要相关技术．包头钢铁学院学报，17(1)，1998．
[17]林胜．数控高速切削加工技术(上，下)．航空制造工程，2-3：16-17，14-15，1997．
[18]杨祖孝．用直线电机实现高速机床进给驱动．制造技术与机床，3：14-16，1999．
[19]Yoram Koren. Computer control of manufacturing systems. New York: McGraw-Hill, 1983.
[20]Daniel C H Yang and Tom Kong. Parametric interpolator versus linear interpolator for precisionCNC machining. Computer Aided Design, 26(3):225-234, 1994.
[21]S Bedi, I Ali, and N Quan. Advanced interpolation techniques for NC machines. Transactionsof the ASME Journal of Engineering for Industry, 115:329-336, 1993.
[22]M Shpitalni, Y Koren, and C C Lo. Realtime curve interpolators. Computer Aided Design,26(11):832-838, 1994.
[23]M Y Cheng, M C Tsai, and J C Kuo. Real-time NURBS command generators for CNC servocontrollers. International Journal of Machine Tools and Manufacture, 42:801-813,2002.
[24]Rida T. Farouki, Jairam Manjunathaiah, and Guo-Feng Yuan. G codes for the specification ofpythagorean-hodograph tool paths and associated feedrate functions on open-architecture CNCmachines. InternationalJournal of Machine tools and Manufacturing, 39:123-142, 1999.
[25]Sung Ho Nam and Min Yang Yang. A study on a generalized parametric interpolator withreal-time jerk-limited acceleration. Computer Aided Design, 2004(36):27-36,2004.
[26]Kaan Erkorkmaz and Yusuf Altintas. High speed CNC system design. part i: jerk limitedtrajectory generation and quintic spline interpolation. InternationalJournal of Machine Tools& Manufacture, 41:1323-1345,2001.
[27]叶伯生，杨叔子．任意三维抛物线的一种高速插补方法．华中理工大学学报，24(11)：15- 17，1996．
[28]叶伯生，杨叔子．CNC系统中三次参数样条曲线的插补算法．华中理工大学学报，， 24(9)：9-12，1996．
[29]Qiyi G Zhang and R B Greenway. Development and implementation of a NURBS curve motioninterpolator. Robotics and Computer-Integrated Manufaturing, 14:27-36, 1998.
[30]Rong Shine Lin. Real-time surface interpolator for 3-D parametric surface machining on 3-axis machine tools. International Journal of Machine Tools and manufacturing, 40:1516-1526,2000.
[31]M C Tsai, C W Cheng, and Cheng M Y. A real-time NURBS surface interpolator for precision three-axis CNC machining. International Journal of Machine Tools and Manufacturing,43:1217-1227,2003.
[32]周济，周艳红，周云飞．自由曲面的CNC直接插补加工技术．高技术通讯，11：30-35， 1998．
[33]王水来，周云飞，朱志红．复杂曲面实时插补系统的开发．中国机械工程，9(5)：38-41， 1998．
[34]S S Yeh and P L Hsu. The speed-controlled interpolator for machining parametric curves.Computer Aided Design, 31:347-359, 1999.
[35]Tsai Y F Farouki, R T. Exact taylor series coefficients for variable-feedrate cnc curve interpolators. Computer Aided Design, 33:155-165, 2001.
[36]Mi Ching Tsai and Chung Wei Cheng. A real-time predictor-corrector interpolator for CNC machining. Transactions of the ASME Journal of Manufacturing Science and Engineering, 125:449-460,2003.
[37]Syh Shiuh Yeh and Pau Lo Hsu. Adaptive-feedrate interpolation for parametric curves with a confined chord error. Computer Aided Design, 34:229-237, 2002.
[38]Tsehaw Yong and Ranga Narayanaswami. A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining. Computer Aided Design, 35:1249-1259,??2003．
[39]杜道山．面向模具高速切削加工全软件数控系统若干共性基础问题研究．上海交通大学 博士学位论文，2006．
[40]Rida T. Farouki, Yi Feng Tsai, and Curtis S. Wilson. Physical constraints on feedrates and feedaccelerations along curved tool paths. Computer Aided Geometric Design, 17:337-359,2000.
[41]Yi-Feng Tsai, Rida T. Farouki, and Bryan Feldman. Performance analysis of CNC interpolators for time-dependent feedrates along PH curves. Computer Aided Geometric Design, 18:245-265,2001.
[42]陈金成，徐志明，钟廷修，蒋厚宗．机床沿曲线高速加工时的运动学与动力学特性分 析．机械工程学报，38(1)：31-34，2002．
[43]Zhi Ming Xu, Jin Cheng Chen, and Zheng Jin Feng. Performance evaluation of a real-timeinterpolation algorithm for NURBS curves. International Journal of Advanced ManufacturingTechnology, 20:270-276, 2002.
[44]陈金成，徐志明，徐正飞，钟廷修，蒋厚宗．基于分段三次样条曲线的高速加工平滑运 动轮廓自适应算法研究．机械工程学报，38(5)：61-65，2002．
[45]刘可照．基于机床动力学特性的NURBS曲线直接插补的研究．华中科技大学硕士学位论 文，2004．
[46]刘可照，彭芳瑜，吴昊，胡建兵．基于机床动力学特性的NURBS曲线直接插补．机床与 液压，11：19-22，2004．
[47]彭芳瑜，何莹，罗忠诚，李宾．NURBS曲线机床动力学特性自适应直接插补．华中科技 大学学报(自然科学版)，33(7)：80-83，2005．
[48]黄翔，曾荣，岳伏军，廖文和．NURBS插补技术在高速加工中的应用研究．南京航空航 天大学学报，34(1)：82-85，2002．
[49]游有鹏，王珉，朱剑英．NURBS曲线高速高精度加工的插补控制．计算机辅助设计与图 形学学报，13(10)：943-947，2001．
[50]杨海成．五次样条在数控加工中的全过程应用技术．西北工业大学博士学位论文．
[51]周凯，谭仲毅．STEP-NC数控系统的NURBS曲面插补方法．制造技术与机床，12，2006．
[52]梁宏斌，王永章，李霞．自动调节进给速度的NURBS插补算法的研究与实现．计算机集 成制造系统，03，2006．
[53]徐志祥，赵国勇，赵福令，周栋梁．一种基于NURBS插补器的多轴交叉耦合控制方法． 机械科学与技术，12，2006．
[54]叶佩青，赵慎良．微小直线段的连续插补控制算法研究．中国机械工程，15(15)：1354- 1356，2004．
[55]王宇晗，肖凌剑，曾水生，吴祖育，钟胜波．小线段高速加工速度衔接数学模型．上海 交通大学学报，38：6，2004．
[56]游有鹏，王珉，朱剑英．参数曲线的自适应插补算法．南京航空航天大学学报， 32(6)：667-671，2000．
[57]Koepfer Chris. Linear motor drives - a fast track for machine tools. In Modern Machine Shop,1994.
[58]郭庆鼎，赵希梅．数控机床直线伺服驱动控制的若干问题与展望．沈阳工业大学学报， 28(3)：273-277，2006．
[59]叶云岳．直线电机原理与应用．北京：机械工业出版社，2000．
[60]张柏霖，夏红梅，黄晓明．数控机床高速化的研究与应用．中国机械工程，12(10)：1132- 1136，2001．
[61]王先逵，陈定积，吴丹．机床进给系统用直线电动机综述．制造技术与机床，8：18-20， 2001．
[62]郜业猛，杨正新，于世江，张翊诚．直线电机在数控机床进给系统中应用现状与趋势． 合肥工业大学学报(自然科学版)，25，2002．
[63]钟扬，叶云岳，赵光宙．直线感应电机的新型PID控制研究综述．微特电机，2：27-30， 2002．
[64]G Pritschow and W Philipp. Direct drives for high-dynamic machine tool axes. Annals of the CIRP, 1990, 39(1): 413-416, 39(1):413-416, 1990.
[65]邓中亮，王先逵．直线电机的智能化PID控制．电气传动，23(2)：25-29，1993．
[66]秦忆，周永鹏，邓中华．现代交流伺服系统.武汉：华中理工大学出版社，1995．
[67]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)，38(2)：44-46，1998．
[68]M Kinouchi and N Iwatusk. Application of fuzzy PI control to improve the position accuracy of a rotate-linear motor driven by two dimension, ultrasonic actuators. Microprocessors and Microsystems, 24:105-112,2000.
[69]Kang J. Chang. Gou-Jen Wang, Chuan-Tzueng Fong. Neural-network-based self-tuning PI controller for precise motion control of PMAC motors. IEEE Transactions on Industrial Electronics, 48(2):408-415,2001.
[70]ID郎道(法)著，康景利译．论自适应控制.北京：北京理工大学出版社，1991．
[71]B Yao, M Al-Majed, and M Tomizuka. High performance robust motion control of machine tools: an adaptive robust control approach and comparative experiments. IEEE/ASME Trans Mechatronics, 2(2):63-76, 1997.
[72]B Yao and M Tomizuka. Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form. Automatica, 33(5):893-900, 1997.
[73]郭庆鼎，王军．基于在线辨识补偿的永磁直线同步电机模型参考自适应神经网络速度控 制．电气传动，4：16-19，2000．
[74]R Marino, S Peresada, and P Valigi. Adaptive input-output linearizing control of induction motors. IEEE Transactions on Automatatic Control, 38:208-221, 1993.
[75]John Y Hung, Weibing Gao, and James C. Hung. Variable structure control: a survey. IEEE Trans. Industrial Electronics, 40(1), 1993.
[76]Vl Utkin. Sliding model control design principles and applications to electric drives. IEEETrans. Ind. Electron, 40:23-36, 1993.
[77]Kawamura Atsuo and Sakamoto Kiyoshi. Chattering reduction of disturbance observer basedsliding mode control. IEEE Trans. Industry Applications, 30(2), 1994.
[78]赵金，万淑云，孙晓鹏等．交流伺服系统基于滑模变结构理论的控制方案综述．电气传 动，26(1)：2-6，1996．
[79]孙宜标，郭庆鼎，石丽梅．基于推力观测器的直线式交流伺服系统滑模变结构控制．电 工技术学报，13(2)：1-5，1998．
[80]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，16(1)：52-56，2001．
[81]D M Alter and T C Tsao. Control of linear motors for machine tool feed drives: design andimplementation of optimal feedback control. ASME J Dyn Syst. Meas. Control, 118:649-656,1996.
[82]徐月同，傅建中，陈子辰．永磁直线同步电机进给系统H∞控制策略的研究．浙江大学 学报(工学版)，39(6)：789-794，2005．
[83]B J Kang, L S Hung, S K Kuo, S C Lin, and C M Liaw. H∞2DOF control for the motionof a magnetic suspension positioning stage driven by inverter-fed linear motor. Mechatronics,13:677-696,2003.
[84]Wei Te Su and Chang Ming Liaw. Adaptive position control for a LPMSM drive based onadapted inverse model and robust disturbance observer. IEEE transactions on Power Electronics,21(2):505-517,2006.
[85]蓝益鹏，郭庆鼎．永磁直线伺服系统H∞鲁棒控制．沈阳工业大学学报，26(3)：281-283， 2004．
[86]蓝益鹏，郭庆鼎，孙宜标．永磁直线伺服系统的速度H∞控制器优化设计．电工技术学 报，5：76-80，2004．
[87]周悦，郭威，郭庆鼎，郭扬．最优预见补偿控制在PMLSM伺服系统中的应用．沈阳建 筑工程学院学报，16(1)：75-78，2000．
[88]T Fukuda and T Shibata. Theory and application of neural networks for industrial controlsystems. IEEE Trans. Ind. Electon, 39:3-20, 1992.
[89]H C Tseng and Hwang V H. Servo controller tuning with fuzzy logic. IEEE Trans. Contr. Syst.Technol, 1:262-269, 1993.
[90]P.V Goode and M.Y. Chow. Using a neural/fuzzy system to extract heuristic knowledge ofincipient faults in induction motors-part i: Methodology. IEEE Trans. Ind. Electron, 42:121-138, 1995.
[1]Les Piegl and Wayne Tiller. The NURBS Book (2nd Edition). Springer, 1997.
[2]Daniel C H Yang and Tom Kong. Parametric interpolator versus linear interpolator for precisioncnc machining. Computer Aided Design, 26(3):225-234, 1994.
[3]M Y Cheng, M C Tsai, and J C Kuo. Real-time nurbs command generators for cnc servocontrollers. International Journal of Machine Tools and Manufacture, 42:801-813,2002.
[4]施法中．计算机辅助几何设计与非均匀有理B样条．高等教育出版社，2001．
[5]李爱平．现代机床的控制技术．同济大学出版社，1999．
[6]苏步青，华宣积，忻元龙．实用微分几何引论．北京：科学技术出版社，1986．
[7]Dong Il Kim, Jae Wook Jeon, and Sungwun Kim. Software acceleration/deceleration methods for industrial robots and cnc machine tools. Mechatronics, 4(1):37-53, 1994.
[8]Jae Wook Jeon and Young Youl Ha. A generalized approach for the acceleration and deceleration of industrial robots and cnc machine tools. IEEE Transactions On Industrial Electronics, 47(1):133-139,2000.
[9]Jae Wook Jeon. Efficient acceleration and deceleration techqique for short distance movementin industrial robots and cnc machine tools. Electronics Letters, 36(8):766-768, 2000.
[10]G Pritschow. Control techniques of machine tools and industrial robots. Institute of controltechnology for machine tools and manufacturing units, 1997.
[11]F C Wang and P K Wright. Open architecture controller for machine tools.part 2: A real time quintic spline interpolator. Journal of machufacturing science and Engineering, 120(2):425-432, 1998.
[12]陈金成．多轴联动高性能数控加工的运动优化与复杂轨迹实时控制策略研究．PhD thesis， 上海交通大学，2001．
[13]Yi Feng Tsai. Real-time CNC interpolators for precision machining of complex shapes with Pythagorean-hodograph curves. PhD thesis, The University of Michigan, 2000.
[14]迟永琳，明良玉，吴祖育，蔡建国．基于windows nt和linux的开放式数控系统．上海交 通大学学报，37(1)：44-46，2003．
[15]S S Yeh and P L Hsu. The speed-controlled interpolator for machining parametric curves. Computer Aided Design, 31:347-359, 1999.
[16]Syh Shiuh Yeh and Pau Lo Hsu. Adaptive-feedrate interpolation for parametric curves with a confined chord error. Computer Aided Design, 34:229-237, 2002.
[17]Tsehaw Yong and Ranga Narayanaswami. A parametric interpolator with confined chord errors, acceleration and deceleration for nc machining. Computer Aided Design, 35:1249-1259, 2003.
[1]苏步青，华宣积，忻元龙．实用微分几何引论．北京：科学技术出版社，1986．
[2]Herbert Schulz and Toshimichi Moriwaki. High-speed machining. Annals of the CIRP,41(2):637-643, 1992.
[3]S Smith and J Tlusty. Current trends in high-speed machining. Transactions of the ASMEJournal of Engineering for Industry, 119:664-666, 1997.
[4]J Tlusty. High-speed machining. Annals of the CIRP, 42(2):733-7387, 1993.
[5]杨楸，唐恒龄，廖伯瑜．机床动力学．机械工业出版社，北京，1983．
[6]M A Elbestawi and R Sagherian. Parameter adaptive control in peripheral milling. Interna-tional Journal of Machine Tools and Manufacture, 27(3):399-414, 1987.
[7]陈金成，徐志明，钟廷修，蒋厚宗．机床沿曲线高速加工时的运动学与动力学特性分 析．机械工程学报，38(1)：31-34，2002．
[8]Zhi Ming Xu, Jin Cheng Chen, and Zheng Jin Feng. Performance evaluation of a real-timeinterpolation algorithm for NURBS curves. International Journal of Advanced ManufacturingTechnology, 20:270-276, 2002.
[9]陈金成，徐志明，徐正飞，钟廷修，蒋厚宗．基于分段三次样条曲线的高速加工平滑运 动轮廓自适应算法研究．机械工程学报，38(5)：61-65，2002．
[10]刘可照．基于机床动力学特性的NURBS曲线直接插补的研究．华中科技大学硕士学位论 文，2004．
[11]刘可照，彭芳瑜，吴昊，胡建兵．基于机床动力学特性的NURBS曲线直接插补．机床与 液压，11：19-22，2004．
[12]彭芳瑜，何莹，罗忠诚，李宾．NURBS曲线机床动力学特性自适应直接插补．华中科技 大学学报(自然科学版)，33(7)：80-83，2005．
[13]陈金成．多轴联动高性能数控加工的运动优化与复杂轨迹实时控制策略研究．上海交通 大学博士学位论文，2001．
[1]吴大榕．电机学(上).北京：电力工业出版社，1981．
[2]吴大榕．电机学(下)．北京：电力工业出版社，1981．
[3]陈坚．交流电机数学模型及调速系统.北京：国防工业出版社，1989．
[4]王成元．矢量控制交流何服驱动电动机．机械工业出版社，1995．
[5]陈文纯．电机瞬变过程.北京：机械工业出版社，1982．
[6]叶云岳．直线电机原理与应用．北京：机械工业出版社，2000．
[7]纳斯尔S A，波尔达Ⅰ(著)，龙遐令等(译)．直线电机．北京：科学出版社，1982．
[8]邓中华秦忆，周永鹏．现代交流何服系统.武汉：华中理工大学出版社，1995．
[9]郝晓弘，靳方义．永磁无刷直流方波电机控制特性及其伺服系统控制策略．电气传动自 动化，21(3)：25-29，1999．
[10]符曦.高磁场永磁式电动机及其驱动系统.北京：机械工业出版社，1997．
[11]唐任远．现代永磁电机理论与设计．北京：机械工业出版社，1997．
[12]郭庆鼎，王成元．直线交流伺服系统的精密控制技术．出版社：机械工业出版社，2000．
[1]郭庆鼎，王成元．直线交流伺服系统的精密控制技术．出版社：机械工业出版社，2000．
[2]申铁龙．H∞控制理论与应用．北京：清华大学出版社社，1996．
[3]B A Francis, J W Helton, and G Zames. On h∞optimal sensitivity theory for SISO feedbacksystems. IEEE Transactions on Automatic Control, 29:9-16, 1984.
[4]B A Francis, J W Helton, and G Zames. H∞optimal feedback controllers for linear multivari-able systems. IEEE Transactions on Automatic Control, 29(10):888-900, 1984.
[5]K Glover. All optimal hankel-norm approximations of linear multivariable systems and theirL∞ error bounds. InternationalJournal of Control, 39(6): 1115-1193, 1984.
[6]J Doyle. Advance in multivariable control. Lecture Notes at ONR/Honeywell Workshop, 1984.
[7]B A Francis. A course in H∞ control theory. Springer-verlag, New York, 1987.
[8]J Doyle, K Glover, P P Khargonekar, and Francis B A. State-space solutions to standard H2and H∞ control problems. IEEE Transactions on Automatic Control, 34(8):831-842, 1989.
[9]K Kimura. Conjugation and interpolation and model-matching in H∞. InternationalJournalof Control, 49:269-307, 1989.
[10]K Green, M an d Glover, D Limebeer, and Doyle J. A J-spectral factorization approach to H∞control. SAIM Journal of Control and Optimization, 28(6):1350-1371, 1990.
[11]M C Tsai and I Postlethwaite. On J-lossless coprime factorizations and H∞ control. Intera-tional Journal of Robust and Nonlinear Control, 1:47-68, 1991.
[12]俞立．鲁棒控制——线性矩阵不等式处理方法．清华大学出版社，2002．
[1]Parker直线电机编程手册．
[2]Matlab帮助手册．
[3]Pcl833卡用户手册．
[2]H Schulz and St. Hock. High-speed milling of dies and moulds--cutting conditions andtechnoligy. Annals of the CIRP, 44(1):35-38, 1995.
[3]P Fallbohmer, C A Rodriguez, and T. Ozel. High-speed machining of cast iron and alloy steelsfor die and mold manufacturing. Journal of Materials Processing Technology, 98:104-115,2000.
[4]童红峰，李江雄，吴福中，巫新海．高速加工技术及其在模具制造中的应用．模具制造， 11(6)：34-37，2002．
[5]J．H.绍克．高速切削在模具加工中的应用及发展趋势．航空制造技术，3：37-38，2000．
[6]H Schulz. High-speed machining. Annals of the CIRP, 41(2):637-643, 1992.
[7]J Tlusty. High-speed machining. Annals of the CIRP, 42(2):733-7387, 1993.
[8]S Smith and J Tlusty. Current trends in high-speed machining. Transactions of the ASMEJournal of Engineering for Industry, 119:664-666, 1997.
[9]艾兴．高速切削加工技术．北京：国防工业出版社，2003．
[10]张伯霖．高速切削技术及应用．北京：机械工业出版社，2002．
[11]杨志勇，殷国增．国产数控机床与冶金工业的发展．数控机床市场，，6，2005．
[12]邹兆东，贺艳．数控系统发展趋势．机械研究与应用，19：24-26，2006．
[13]罗然宾．数控技术和装备发展趋势及对策．装备制造技术，1，2006．
[14]周济．数控加工技术．国防工业出版社，2002．
[15]王西彬，解丽静．超高速切削技术及其新进展．中国机械工程，1：190-194，2000．
[16]刘学杰．高速切削及主要相关技术．包头钢铁学院学报，17(1)，1998．
[17]林胜．数控高速切削加工技术(上，下)．航空制造工程，2-3：16-17，14-15，1997．
[18]杨祖孝．用直线电机实现高速机床进给驱动．制造技术与机床，3：14-16，1999．
[19]Yoram Koren. Computer control of manufacturing systems. New York: McGraw-Hill, 1983.
[20]Daniel C H Yang and Tom Kong. Parametric interpolator versus linear interpolator for precisionCNC machining. Computer Aided Design, 26(3):225-234, 1994.
[21]S Bedi, I Ali, and N Quan. Advanced interpolation techniques for NC machines. Transactionsof the ASME Journal of Engineering for Industry, 115:329-336, 1993.
[22]M Shpitalni, Y Koren, and C C Lo. Realtime curve interpolators. Computer Aided Design,26(11):832-838, 1994.
[23]M Y Cheng, M C Tsai, and J C Kuo. Real-time NURBS command generators for CNC servocontrollers. International Journal of Machine Tools and Manufacture, 42:801-813,2002.
[24]Rida T. Farouki, Jairam Manjunathaiah, and Guo-Feng Yuan. G codes for the specification ofpythagorean-hodograph tool paths and associated feedrate functions on open-architecture CNCmachines. InternationalJournal of Machine tools and Manufacturing, 39:123-142, 1999.
[25]Sung Ho Nam and Min Yang Yang. A study on a generalized parametric interpolator withreal-time jerk-limited acceleration. Computer Aided Design, 2004(36):27-36,2004.
[26]Kaan Erkorkmaz and Yusuf Altintas. High speed CNC system design. part i: jerk limitedtrajectory generation and quintic spline interpolation. InternationalJournal of Machine Tools& Manufacture, 41:1323-1345,2001.
[27]叶伯生，杨叔子．任意三维抛物线的一种高速插补方法．华中理工大学学报，24(11)：15- 17，1996．
[28]叶伯生，杨叔子．CNC系统中三次参数样条曲线的插补算法．华中理工大学学报，， 24(9)：9-12，1996．
[29]Qiyi G Zhang and R B Greenway. Development and implementation of a NURBS curve motioninterpolator. Robotics and Computer-Integrated Manufaturing, 14:27-36, 1998.
[30]Rong Shine Lin. Real-time surface interpolator for 3-D parametric surface machining on 3-axis machine tools. International Journal of Machine Tools and manufacturing, 40:1516-1526,2000.
[31]M C Tsai, C W Cheng, and Cheng M Y. A real-time NURBS surface interpolator for precision three-axis CNC machining. International Journal of Machine Tools and Manufacturing,43:1217-1227,2003.
[32]周济，周艳红，周云飞．自由曲面的CNC直接插补加工技术．高技术通讯，11：30-35， 1998．
[33]王水来，周云飞，朱志红．复杂曲面实时插补系统的开发．中国机械工程，9(5)：38-41， 1998．
[34]S S Yeh and P L Hsu. The speed-controlled interpolator for machining parametric curves.Computer Aided Design, 31:347-359, 1999.
[35]Tsai Y F Farouki, R T. Exact taylor series coefficients for variable-feedrate cnc curve interpolators. Computer Aided Design, 33:155-165, 2001.
[36]Mi Ching Tsai and Chung Wei Cheng. A real-time predictor-corrector interpolator for CNC machining. Transactions of the ASME Journal of Manufacturing Science and Engineering, 125:449-460,2003.
[37]Syh Shiuh Yeh and Pau Lo Hsu. Adaptive-feedrate interpolation for parametric curves with a confined chord error. Computer Aided Design, 34:229-237, 2002.
[38]Tsehaw Yong and Ranga Narayanaswami. A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining. Computer Aided Design, 35:1249-1259,??2003．
[39]杜道山．面向模具高速切削加工全软件数控系统若干共性基础问题研究．上海交通大学 博士学位论文，2006．
[40]Rida T. Farouki, Yi Feng Tsai, and Curtis S. Wilson. Physical constraints on feedrates and feedaccelerations along curved tool paths. Computer Aided Geometric Design, 17:337-359,2000.
[41]Yi-Feng Tsai, Rida T. Farouki, and Bryan Feldman. Performance analysis of CNC interpolators for time-dependent feedrates along PH curves. Computer Aided Geometric Design, 18:245-265,2001.
[42]陈金成，徐志明，钟廷修，蒋厚宗．机床沿曲线高速加工时的运动学与动力学特性分 析．机械工程学报，38(1)：31-34，2002．
[43]Zhi Ming Xu, Jin Cheng Chen, and Zheng Jin Feng. Performance evaluation of a real-timeinterpolation algorithm for NURBS curves. International Journal of Advanced ManufacturingTechnology, 20:270-276, 2002.
[44]陈金成，徐志明，徐正飞，钟廷修，蒋厚宗．基于分段三次样条曲线的高速加工平滑运 动轮廓自适应算法研究．机械工程学报，38(5)：61-65，2002．
[45]刘可照．基于机床动力学特性的NURBS曲线直接插补的研究．华中科技大学硕士学位论 文，2004．
[46]刘可照，彭芳瑜，吴昊，胡建兵．基于机床动力学特性的NURBS曲线直接插补．机床与 液压，11：19-22，2004．
[47]彭芳瑜，何莹，罗忠诚，李宾．NURBS曲线机床动力学特性自适应直接插补．华中科技 大学学报(自然科学版)，33(7)：80-83，2005．
[48]黄翔，曾荣，岳伏军，廖文和．NURBS插补技术在高速加工中的应用研究．南京航空航 天大学学报，34(1)：82-85，2002．
[49]游有鹏，王珉，朱剑英．NURBS曲线高速高精度加工的插补控制．计算机辅助设计与图 形学学报，13(10)：943-947，2001．
[50]杨海成．五次样条在数控加工中的全过程应用技术．西北工业大学博士学位论文．
[51]周凯，谭仲毅．STEP-NC数控系统的NURBS曲面插补方法．制造技术与机床，12，2006．
[52]梁宏斌，王永章，李霞．自动调节进给速度的NURBS插补算法的研究与实现．计算机集 成制造系统，03，2006．
[53]徐志祥，赵国勇，赵福令，周栋梁．一种基于NURBS插补器的多轴交叉耦合控制方法． 机械科学与技术，12，2006．
[54]叶佩青，赵慎良．微小直线段的连续插补控制算法研究．中国机械工程，15(15)：1354- 1356，2004．
[55]王宇晗，肖凌剑，曾水生，吴祖育，钟胜波．小线段高速加工速度衔接数学模型．上海 交通大学学报，38：6，2004．
[56]游有鹏，王珉，朱剑英．参数曲线的自适应插补算法．南京航空航天大学学报， 32(6)：667-671，2000．
[57]Koepfer Chris. Linear motor drives - a fast track for machine tools. In Modern Machine Shop,1994.
[58]郭庆鼎，赵希梅．数控机床直线伺服驱动控制的若干问题与展望．沈阳工业大学学报， 28(3)：273-277，2006．
[59]叶云岳．直线电机原理与应用．北京：机械工业出版社，2000．
[60]张柏霖，夏红梅，黄晓明．数控机床高速化的研究与应用．中国机械工程，12(10)：1132- 1136，2001．
[61]王先逵，陈定积，吴丹．机床进给系统用直线电动机综述．制造技术与机床，8：18-20， 2001．
[62]郜业猛，杨正新，于世江，张翊诚．直线电机在数控机床进给系统中应用现状与趋势． 合肥工业大学学报(自然科学版)，25，2002．
[63]钟扬，叶云岳，赵光宙．直线感应电机的新型PID控制研究综述．微特电机，2：27-30， 2002．
[64]G Pritschow and W Philipp. Direct drives for high-dynamic machine tool axes. Annals of the CIRP, 1990, 39(1): 413-416, 39(1):413-416, 1990.
[65]邓中亮，王先逵．直线电机的智能化PID控制．电气传动，23(2)：25-29，1993．
[66]秦忆，周永鹏，邓中华．现代交流伺服系统.武汉：华中理工大学出版社，1995．
[67]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)，38(2)：44-46，1998．
[68]M Kinouchi and N Iwatusk. Application of fuzzy PI control to improve the position accuracy of a rotate-linear motor driven by two dimension, ultrasonic actuators. Microprocessors and Microsystems, 24:105-112,2000.
[69]Kang J. Chang. Gou-Jen Wang, Chuan-Tzueng Fong. Neural-network-based self-tuning PI controller for precise motion control of PMAC motors. IEEE Transactions on Industrial Electronics, 48(2):408-415,2001.
[70]ID郎道(法)著，康景利译．论自适应控制.北京：北京理工大学出版社，1991．
[71]B Yao, M Al-Majed, and M Tomizuka. High performance robust motion control of machine tools: an adaptive robust control approach and comparative experiments. IEEE/ASME Trans Mechatronics, 2(2):63-76, 1997.
[72]B Yao and M Tomizuka. Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form. Automatica, 33(5):893-900, 1997.
[73]郭庆鼎，王军．基于在线辨识补偿的永磁直线同步电机模型参考自适应神经网络速度控 制．电气传动，4：16-19，2000．
[74]R Marino, S Peresada, and P Valigi. Adaptive input-output linearizing control of induction motors. IEEE Transactions on Automatatic Control, 38:208-221, 1993.
[75]John Y Hung, Weibing Gao, and James C. Hung. Variable structure control: a survey. IEEE Trans. Industrial Electronics, 40(1), 1993.
[76]Vl Utkin. Sliding model control design principles and applications to electric drives. IEEETrans. Ind. Electron, 40:23-36, 1993.
[77]Kawamura Atsuo and Sakamoto Kiyoshi. Chattering reduction of disturbance observer basedsliding mode control. IEEE Trans. Industry Applications, 30(2), 1994.
[78]赵金，万淑云，孙晓鹏等．交流伺服系统基于滑模变结构理论的控制方案综述．电气传 动，26(1)：2-6，1996．
[79]孙宜标，郭庆鼎，石丽梅．基于推力观测器的直线式交流伺服系统滑模变结构控制．电 工技术学报，13(2)：1-5，1998．
[80]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，16(1)：52-56，2001．
[81]D M Alter and T C Tsao. Control of linear motors for machine tool feed drives: design andimplementation of optimal feedback control. ASME J Dyn Syst. Meas. Control, 118:649-656,1996.
[82]徐月同，傅建中，陈子辰．永磁直线同步电机进给系统H∞控制策略的研究．浙江大学 学报(工学版)，39(6)：789-794，2005．
[83]B J Kang, L S Hung, S K Kuo, S C Lin, and C M Liaw. H∞2DOF control for the motionof a magnetic suspension positioning stage driven by inverter-fed linear motor. Mechatronics,13:677-696,2003.
[84]Wei Te Su and Chang Ming Liaw. Adaptive position control for a LPMSM drive based onadapted inverse model and robust disturbance observer. IEEE transactions on Power Electronics,21(2):505-517,2006.
[85]蓝益鹏，郭庆鼎．永磁直线伺服系统H∞鲁棒控制．沈阳工业大学学报，26(3)：281-283， 2004．
[86]蓝益鹏，郭庆鼎，孙宜标．永磁直线伺服系统的速度H∞控制器优化设计．电工技术学 报，5：76-80，2004．
[87]周悦，郭威，郭庆鼎，郭扬．最优预见补偿控制在PMLSM伺服系统中的应用．沈阳建 筑工程学院学报，16(1)：75-78，2000．
[88]T Fukuda and T Shibata. Theory and application of neural networks for industrial controlsystems. IEEE Trans. Ind. Electon, 39:3-20, 1992.
[89]H C Tseng and Hwang V H. Servo controller tuning with fuzzy logic. IEEE Trans. Contr. Syst.Technol, 1:262-269, 1993.
[90]P.V Goode and M.Y. Chow. Using a neural/fuzzy system to extract heuristic knowledge ofincipient faults in induction motors-part i: Methodology. IEEE Trans. Ind. Electron, 42:121-138, 1995.
[1]Les Piegl and Wayne Tiller. The NURBS Book (2nd Edition). Springer, 1997.
[2]Daniel C H Yang and Tom Kong. Parametric interpolator versus linear interpolator for precisioncnc machining. Computer Aided Design, 26(3):225-234, 1994.
[3]M Y Cheng, M C Tsai, and J C Kuo. Real-time nurbs command generators for cnc servocontrollers. International Journal of Machine Tools and Manufacture, 42:801-813,2002.
[4]施法中．计算机辅助几何设计与非均匀有理B样条．高等教育出版社，2001．
[5]李爱平．现代机床的控制技术．同济大学出版社，1999．
[6]苏步青，华宣积，忻元龙．实用微分几何引论．北京：科学技术出版社，1986．
[7]Dong Il Kim, Jae Wook Jeon, and Sungwun Kim. Software acceleration/deceleration methods for industrial robots and cnc machine tools. Mechatronics, 4(1):37-53, 1994.
[8]Jae Wook Jeon and Young Youl Ha. A generalized approach for the acceleration and deceleration of industrial robots and cnc machine tools. IEEE Transactions On Industrial Electronics, 47(1):133-139,2000.
[9]Jae Wook Jeon. Efficient acceleration and deceleration techqique for short distance movementin industrial robots and cnc machine tools. Electronics Letters, 36(8):766-768, 2000.
[10]G Pritschow. Control techniques of machine tools and industrial robots. Institute of controltechnology for machine tools and manufacturing units, 1997.
[11]F C Wang and P K Wright. Open architecture controller for machine tools.part 2: A real time quintic spline interpolator. Journal of machufacturing science and Engineering, 120(2):425-432, 1998.
[12]陈金成．多轴联动高性能数控加工的运动优化与复杂轨迹实时控制策略研究．PhD thesis， 上海交通大学，2001．
[13]Yi Feng Tsai. Real-time CNC interpolators for precision machining of complex shapes with Pythagorean-hodograph curves. PhD thesis, The University of Michigan, 2000.
[14]迟永琳，明良玉，吴祖育，蔡建国．基于windows nt和linux的开放式数控系统．上海交 通大学学报，37(1)：44-46，2003．
[15]S S Yeh and P L Hsu. The speed-controlled interpolator for machining parametric curves. Computer Aided Design, 31:347-359, 1999.
[16]Syh Shiuh Yeh and Pau Lo Hsu. Adaptive-feedrate interpolation for parametric curves with a confined chord error. Computer Aided Design, 34:229-237, 2002.
[17]Tsehaw Yong and Ranga Narayanaswami. A parametric interpolator with confined chord errors, acceleration and deceleration for nc machining. Computer Aided Design, 35:1249-1259, 2003.
[1]苏步青，华宣积，忻元龙．实用微分几何引论．北京：科学技术出版社，1986．
[2]Herbert Schulz and Toshimichi Moriwaki. High-speed machining. Annals of the CIRP,41(2):637-643, 1992.
[3]S Smith and J Tlusty. Current trends in high-speed machining. Transactions of the ASMEJournal of Engineering for Industry, 119:664-666, 1997.
[4]J Tlusty. High-speed machining. Annals of the CIRP, 42(2):733-7387, 1993.
[5]杨楸，唐恒龄，廖伯瑜．机床动力学．机械工业出版社，北京，1983．
[6]M A Elbestawi and R Sagherian. Parameter adaptive control in peripheral milling. Interna-tional Journal of Machine Tools and Manufacture, 27(3):399-414, 1987.
[7]陈金成，徐志明，钟廷修，蒋厚宗．机床沿曲线高速加工时的运动学与动力学特性分 析．机械工程学报，38(1)：31-34，2002．
[8]Zhi Ming Xu, Jin Cheng Chen, and Zheng Jin Feng. Performance evaluation of a real-timeinterpolation algorithm for NURBS curves. International Journal of Advanced ManufacturingTechnology, 20:270-276, 2002.
[9]陈金成，徐志明，徐正飞，钟廷修，蒋厚宗．基于分段三次样条曲线的高速加工平滑运 动轮廓自适应算法研究．机械工程学报，38(5)：61-65，2002．
[10]刘可照．基于机床动力学特性的NURBS曲线直接插补的研究．华中科技大学硕士学位论 文，2004．
[11]刘可照，彭芳瑜，吴昊，胡建兵．基于机床动力学特性的NURBS曲线直接插补．机床与 液压，11：19-22，2004．
[12]彭芳瑜，何莹，罗忠诚，李宾．NURBS曲线机床动力学特性自适应直接插补．华中科技 大学学报(自然科学版)，33(7)：80-83，2005．
[13]陈金成．多轴联动高性能数控加工的运动优化与复杂轨迹实时控制策略研究．上海交通 大学博士学位论文，2001．
[1]吴大榕．电机学(上).北京：电力工业出版社，1981．
[2]吴大榕．电机学(下)．北京：电力工业出版社，1981．
[3]陈坚．交流电机数学模型及调速系统.北京：国防工业出版社，1989．
[4]王成元．矢量控制交流何服驱动电动机．机械工业出版社，1995．
[5]陈文纯．电机瞬变过程.北京：机械工业出版社，1982．
[6]叶云岳．直线电机原理与应用．北京：机械工业出版社，2000．
[7]纳斯尔S A，波尔达Ⅰ(著)，龙遐令等(译)．直线电机．北京：科学出版社，1982．
[8]邓中华秦忆，周永鹏．现代交流何服系统.武汉：华中理工大学出版社，1995．
[9]郝晓弘，靳方义．永磁无刷直流方波电机控制特性及其伺服系统控制策略．电气传动自 动化，21(3)：25-29，1999．
[10]符曦.高磁场永磁式电动机及其驱动系统.北京：机械工业出版社，1997．
[11]唐任远．现代永磁电机理论与设计．北京：机械工业出版社，1997．
[12]郭庆鼎，王成元．直线交流伺服系统的精密控制技术．出版社：机械工业出版社，2000．
[1]郭庆鼎，王成元．直线交流伺服系统的精密控制技术．出版社：机械工业出版社，2000．
[2]申铁龙．H∞控制理论与应用．北京：清华大学出版社社，1996．
[3]B A Francis, J W Helton, and G Zames. On h∞optimal sensitivity theory for SISO feedbacksystems. IEEE Transactions on Automatic Control, 29:9-16, 1984.
[4]B A Francis, J W Helton, and G Zames. H∞optimal feedback controllers for linear multivari-able systems. IEEE Transactions on Automatic Control, 29(10):888-900, 1984.
[5]K Glover. All optimal hankel-norm approximations of linear multivariable systems and theirL∞ error bounds. InternationalJournal of Control, 39(6): 1115-1193, 1984.
[6]J Doyle. Advance in multivariable control. Lecture Notes at ONR/Honeywell Workshop, 1984.
[7]B A Francis. A course in H∞ control theory. Springer-verlag, New York, 1987.
[8]J Doyle, K Glover, P P Khargonekar, and Francis B A. State-space solutions to standard H2and H∞ control problems. IEEE Transactions on Automatic Control, 34(8):831-842, 1989.
[9]K Kimura. Conjugation and interpolation and model-matching in H∞. InternationalJournalof Control, 49:269-307, 1989.
[10]K Green, M an d Glover, D Limebeer, and Doyle J. A J-spectral factorization approach to H∞control. SAIM Journal of Control and Optimization, 28(6):1350-1371, 1990.
[11]M C Tsai and I Postlethwaite. On J-lossless coprime factorizations and H∞ control. Intera-tional Journal of Robust and Nonlinear Control, 1:47-68, 1991.
[12]俞立．鲁棒控制——线性矩阵不等式处理方法．清华大学出版社，2002．
[1]Parker直线电机编程手册．
[2]Matlab帮助手册．
[3]Pcl833卡用户手册．