摘要
本文研究了由同步带驱动的两轴拱架机器人的建模与控制问题,该类机器人提供了两个相互垂直方向的运动,即沿梁运动的工作头(x方向)和沿基座运动的梁(y方向)。两运动轴由于工作头在x轴的位置影响y轴的动力学特性而相互耦合,这一耦合的产生是由于工作头在梁上的位置决定了y轴的质量分布,也即y轴运动的振动特性。同步带驱动系统将电机扭矩转换为两运动机构的线性驱动力,目的是使工作头尽可能快地移动到目标位置并达到微米级的定位精度,但摩擦力的干扰、柔性梁和同步带驱动系统的结构振动以及两运动机构之间的动力学耦合给这一控制目标的实现增加了难度。目前,对同时具有驱动柔性和结构柔性的拱架机器人的研究还非常少。
首先,建立了拱架机器人x方向的动力学模型。为减小由同步带驱动的直线伺服定位系统的振动,构造了双闭环控制系统,基于对系统数学模型的频域分析,将系统振动分为低频振动和高频振动,这一区分对系统控制器的振动抑制策略非常重要。采用低陷滤波器抑制系统的高频振动,时滞滤波方法规划了合适的参考输入,并结合PID控制实现快速的点到点运动并保持较小的残余振动。作为一种离线规划措施,此控制器设计方法不需改变系统的任何硬件设施,能直接、有效地应用于现有的柔性驱动系统中。其次,对拱架机器人的y向动力学进行了建模,模型考虑了系统的结构柔性与驱动柔性以及两者之间的耦合作用。结构柔性具体体现为三种类型的振动:柔性梁在刚性模态下的扭转振动,一端支撑于扭簧上的柔性梁的弯曲振动和简化为一移动振荡子的贴装头的振动。基于系统的振动特性分析,提出了原型机的机械设计改进方法。
另外,分别研究了当工作头静止和移动时,柔性梁的H_∞输出反馈控制器设计方法。当工作头在x方向固定时,应用线性矩阵不等式处理方法,给出了系统的输出反馈最优控制器。当工作头沿柔性梁移动时,拱架机器人的y向动力学模型可作为一线性变参数系统处理。采用严格的等价变换将一类通用的线性变参数系统描述模型变换为一简化模型,引入变H_∞性能将控制器的设计问题转换为满足线性矩阵不等式约束的参数矩阵的求解问题,并给出了无需变参数变化率反馈的变增益全阶输出反馈H∞控制器设计方法。接着基于“H_∞性能覆盖”的概念,给出了保H_∞性能的插值方法。仿真结果表明: H_∞鲁棒控制器具有较小的调节时间且有效抑制了系统的振动和外部干扰,且本文提出的变增益H_∞控制器设计方法能有效降低控制系统的保守性。然后,针对普通变增益H_∞控制器设计过程复杂及权函数选择困难等缺陷,采用回路成形方法设计线性变参数系统的H_∞控制器,并将其应用于拱架机器人上。为了得到线性变参数系统的连续控制器,通常对选定的变参数值设计线性控制器后,需要在变参数集合内对这些线性控制器进行插值。本文给出了输出反馈线性控制器进行保稳定性插补的充分条件,确保系统指数稳定的变参数变化率的上界也可在计算出控制器插值后得出。由于此方法得出的控制器通常具有较高的阶数,为方便工程应用,对控制器进行降阶处理,采用变增益PID控制器逼近高阶鲁棒控制器,从而将最终的H_∞控制结构转化为PID+滤波器的常见形式。仿真结果验证了所提控制方法的有效性。
最后,介绍了拱架机器人在RFID封装设备中贴装模块的集成设计方法,并给出了本文理论研究成果在该机器人中的实现方法。
This dissertation mainly studies the modeling and control of two-axis belt-driven gantry robots. Such robots provide two orthogonal motions, a head sliding along a beam (x-axis motion) and the beam sliding along a frame (y-axis motion). The two axes are coupled in the sense that the x-axis position influences the y-axis dynamics. This coupling arises because the location of the head on the beam determines the mass distribution and hence the vibration characteristics for y-axis motion. Belt-pulley transmissions convert rotary motor torque into linear forces that drive the two-axis mechanism. The control objective is to move the gantry head to the target position as fast as possible, yet also settle quickly withμm accuracy. But friction force disturbances, structural vibrations in the gantry beam, transmission resonance and the coupling effect of the two-axis mechanism add difficulties to achieve this objective. At present, the study about the gantry robots which inclue both drive elasticity and structure flexibility is very few.
Firstly, the modeling for the x-axis dynamic of the gantry robot is deduced. To suppress the vibration of the linear belt-driven system and improve the transient response performance, a double closed-loop control system is constructed and the mechanical resonance of the belt-driven system is analyzed and classified into two categories: low frequency resonance and high frequency resonance, which is crucial for guiding the design of controller. A notch filter is adopted to attenuate the high-frequency vibration. A new kind of input pre-shaping method producing an appropriate reference profile accompanied with a PID controller is proposed for suppressing the low frequency vibration to ensure fast point-to-point motions with minimum residual vibration. As an off-line method, the proposed method can be easily and effectively adopted to the existing elastic-driven system without any modification of the hardware setup. Next, the y-axis dynamic of the gantry robot is modeled. The model considers the structure flexibility and drive elasticity in addition to their coupling effect. The structure flexibility is embodied through three types of vibration, namely, the torsional vibration of a flexible beam in rigid motion mode, the transverse vibration of the flexibility beam with supports on torsional spring at one end and the vibration of the head which is simplified as a moving oscillator. Based on analysis of the vibration characteristic in the system, the improvement measures of the mechanical design are proposed.
In addition, the design method of the H_∞output feedback controller for the flexible beam in y-direction with stationary and moving head is studied respectively. When the head is stationary in x-direction, the optimum output feedback controller of the system is devised based on the linear matrix inequality (LMI) approach. When the bonding head moves along the flexible beam, the dynamic model of the gantry robot in y-direction can be considered as a linear parameter-varying (LPV) system. The general LPV system is transformed into a simplified model using strict equivalent transformation. Using parameter-varying H_∞performance, the controller design is translated into the solution of parameter matrices which satisfy the constraints of LMI. And the design method of the gain scheduling full order output feedback controller without parameter-rate feedback is also proposed. In succession, based on the concept of“H_∞performance covering”, the interpolation method which meets the demands of H_∞performance preserved is introduced. Simulation results indicate that the H_∞controller provides small settling times with reduced structural vibration and disturbance attenuation. In addition, the design method of the gain-scheduling H_∞controller proposed in this dissertation can reduce the conservation of the system effectively. Then, in order to overcome the deficiency of the ordinary H_∞controller design method, such as the complication of the design procedure and difficulities of the weight selection, a loop shaping design procedure using H_∞synthesis is introduced and applied to the gantry robot. To get the continuous gain-scheduling controller of LPV system, these designed linear controllers for the selections of scheduling variable shoule be interpolated in the scheduling variable set. This dissertation provides a sufficient condition on the selections of scheduling variable for which output feedback controllers are designed such that a stability preserving interpolation of the linear controllers can be calculated. Once the interpolation is computed, an upper bound on the rate of variation of the scheduling variable to assure exponentially stability can be calculated. Because the controller achieved from this design method generally has high orders, it is necessary to reduce the controller order for the convenience of engineering applications. A gain-scheduling PID controller is presented to approximate the high-order robust controller so that the last H_∞control structure is transformed into the form of“PID+filters”. Simulation results verify the effectiveness of the proposed control method.
Lastly, the integration design methods of gantry robot which is used in RFID package equipment pre-bonding module are introduced. And the realization methods of the academic research achievements, which are proposed in this paper and will be used on the gantry robot, are also developed.
引文
[1] Yang X D. Modeling and control of two-axis belt-drive gantry robots. Ph.D Thesis of Georgia Institute of Technology, 2000.
[2]张君,朱海涛,谭定忠.十字龙门式机器人的研究.机械工程师, 2007, 1: 116-118.
[3]刘永男,张国栋,于志俊.由直线运动部件组成的直角坐标装配机器人.组合机床与自动化加工技术, 2002, 7: 46-47, 52.
[4]李刚.百格拉机器人在汽车生产线上的应用.机电一体化, 2003, 7: 66, 80.
[5]郭庆鼎,蓝益鹏.双直线电机驱动的龙门移动式加工中心H∞鲁棒自适应控制.中国机械工程, 2003, 14(22): 1966-1969.
[6] Lee H H, Chun T W and Jung E H et al. Design of robust synchronizing controller for unknown servo-motor systems with H∞controller. Proc. of the 7th Korea-Russia International Symposium, 2003: 495-501.
[7] Kim S, Chu B and Hong D et al. Synchronizing fual-drive gantry of chip mounter with LQR approach. Proc. of the IEEE/ASME International Conf. on Advanced Intelligient Mechatronics, 2003: 838-843.
[8] Tan K K, Lim S S and Huang S et al. Coordinated motion control of moving gantry stages for precision applications based on observer-augmented composite controller. IEEE Trans. on Control Systems Technology, 2004, 12(6): 984-991.
[9] Haus R. Converting rotary motion to linear motion. Power Conversion and Intelligent Motion, 1996, 22(11), 72-74.
[10]熊有伦.机器人技术基础.武汉:华中科技大学出版社, 2002.
[11] SIPLACE 80S-20/80F4/F5 placement systems service manual. Siemens Corporation, 1999.
[12]丁汉,朱利民,林忠钦.面向芯片封装的高加速度运动系统的精确定位和操作.自然科学进展, 2003, 13(6): 568-574.
[13]雷源忠,雒建斌,丁汉等.先进电子制造中的重要科学问题.中国科学基金, 2002, 16(4): 204-209.
[14] Book W J. Controlled motion in an elastic world. Journal of Dynamic Systems, Measurement and Control, 1993, 115: 252~261.
[15] Shabana A A, Hwang Y L. Dynamical coupling between the joint and elastic coordinates in flexible mechanism systems. International Journal of Robotics Research, 1993, 12(3): 299-309.
[16] Jablokow A G, Nagarajan S and Turcic D A. A modal analysi solution technique to theequations of elastic mechanism systems including the rigid-body and elastic motion coupling term. ASME Journal of Mechanical Design, 1993, 115: 314-323.
[17] Liou F W, Peng K C. Experimental frequency response analysis of flexible mechanism. Mechanism and Machine Theory, 1993, 28(1): 72-81.
[18] Desoyer K, Kopacek P and Lugner P et al.. Flexible robot - a survey. Proc IFAC, 1986: 23-34.
[19] Book W J. Modeling, design and control of flexible manipulator arms: a tutorial review. Proc. the 29th IEEE Conf. on Decision and Control, 1990, 500-506.
[20] Sandor G, Zhuang X. A linearized lumped parameter approach to vibration and stress analysis of elastic linkage. Mechanism and Machine Theory, 1985, 20(5): 427-437.
[21] Sarkissyan Y, Stepanian K and Martirossian. Approximate dynamic synthesis of linkage with elastic links. 9th World Congress on the Theory of Machines and Mechanism, 1995: 1571-1574.
[22] Wojciech S. Optimal trajectories for a manipulator with flexible links. 9th World Congress on the Theory of Machines and Mechanism, 1995: 1915-1919.
[23] De Luca A, Siciliano B. Closed-form dynamic model of planar multilink lightweight robots. IEEE Trans. Sys. Man and Cybernet, 1991, 21(4): 826-839.
[24]荣莉莉,范懋基.机器人弹性手臂的模型与控制.机器人, 1992, 14(1): 32-36.
[25]徐晨,张景绘,史维祥.一个高精度单臂柔性机械手的动力学模型.机器人, 1992, 14(5): 8-11.
[26]曹彤,孙杏初.机器人弹性动力学研究及结构综合优化.机械工程学报, 1995, 31(5): 64-69.
[27] Readman M, Belanger P. Stabilization of the fast modes of a flexible-joint robot. International Journal of Robotics Research, 1992, 11(2): 123-134.
[28] Jankowski K, Brussel H. Inverse dynamics task control of flexible joint robots– I. Mechanism and Machine Theory, 1993, 28(6): 741-749.
[29] Jankowski K, Brussel H. Inverse dynamics task control of flexible joint robots– II. Mechanism and Machine Theory, 1993, 28(6): 741-749.
[30] Gogate S, Lin Y. Formulation and control of robots with link and joint flexibility. Robotica, 1993, 11: 273-282.
[31] Xi F, Fenton R. On flexible link manipulators: modeling and analysis using the algebra of rotations. Robotica, 1994, 12: 371-381.
[32] Xi F, Fenton R. Coupling effect of a flexible link and a flexible joint. International Journal of Robotics Research, 1994, 13(5): 443-453.
[33] Shigang Y, Yueqing Y and Shixian B. Flexible rotor beam element for the manipulator with joint and link flexibility. Mechanism and Machine Theory, 1997, 32(2): 209-219.
[34] Hace A, Jezernik K. and ?abanovi? A. Improved design of VSS controller for a linear belt-driven servomechanism. IEEE/ASME Trans. on mechatronics, 2005, 10(4): 385-390.
[35] Hace A, Jezernik K and Terbuc M. VSS motion control for a laser-cutting machine. Control Engineering Practice, 2001, 19(1): 67-77.
[36] Jayawardene T S S, Nakamura M and Goto S. Accurate control position of belt drives under acceleration and velocity constraints. International Journal of Control, Automation, and Systems, 2003, 1(4), 474-483.
[37] Lee K M, Rutherford C. Frequency reshaped quadratic control of a low-cost human-level performance belt-driven robot. Mechanics, 1999, 9: 95-110.
[38]杨玉萍,钱永明,沈世德.同步带传动纵向振动的分析.机械传动, 2002, 26(4): 38-40.
[39]杨玉萍,张小美,沈世德.同步带传动横向振动的分析研究.机械设计, 2003, 20(1): 28-30.
[40] Leamy M. Dynamic analysis of the time-varying operation of belt-drives. ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2003: 1:10.
[41] Fukada K, Morinoto S and Takeda Y et al. Dynamic model and vibration control of a robot arm with flexible timing belts. Proc. of the 1992 International Conf. on Power Electronics and Motion Control, 1992, 2: 606-611.
[42] Baicu C F, Rahn C D and Dawson D M. Backstepping boundary control of flexible-link electrically driven gantry robots. IEEE/ASME Trans. on Mechatronics, 1998, 3(1): 60-66.
[43] Choi S B, Han S S and Kim H K et al. H∞control of a flexible gantry robot arm using smart actuators. Mechatronics, 1999, 9: 271-286.
[44] Rieber J M, Taylor D G. Integrated control system and mechanical design of a compliant two-axes mechanism. Mechatronics, 2004, 14: 1069-1087.
[45] Rieber J M, Taylor D G. Gain-scheduled L2-gain based control of a flexible parameter parameter-varying robot link. 27th Annual Conf. of the IEEE Industrial Electronics Society, 2001: 552-557.
[46] He T, Kulicke and Soffa. Application of intelligent control in improving dynamics of precision motion systems used in microelectronics manufacturing. IEEE Electronics Manufacturing Technology Symposium, 2002: 410-414.
[47] Book W J. Modeling design and control of flexible manipulator arms. MIT, 1974.
[48] Bay E. Computed torque for the position control of open-chain robot. Proc. of the 1988 IEEE International Conf. on Robotics and Automation, 1988: 316-321.
[49] Bayo E, Moulin H. An efficient computation of the inverse dynamics of flexible manipulators in the time domain. Proc. of the 1989 IEEE International Conf. on Robotics and Automation, 1989: 710-715.
[50] Serna M A, Bayo E. Trajectory planning for flexible manipulators. Proc. of the 1990 IEEE International Conf. on Robotics and Automation, 1990: 910-915.
[51] Trautt T A, Bayo E. Cancelling vibration in flexible articulated structures using non-casual inverse dynamics. IEE Proc. of Control Theory and Applications, 2000: 596-604.
[52] Yigit A S. On the stability of PD control for a two-link rigid-flexible manipulator, ASME Transaction, Journal of Dynamic Systems. Measurement and Control, 1994, 116: 208-215.
[53] Goldenberg A A, Rakhsha F. Feedforward control of a single-link flexible robot. Mechanism and Machine Theory, 1986, 21(4): 325-335.
[54] Sakawa Y. Modeling and feedback control of flexible arm. Journal of Robotics System, 1985, 2(4): 453-472.
[55]金栋平,胡海岩.结构碰撞振动的建模与模态截断.固体力学学报, 2001, 22(2): 205-208.
[56] Singer N C, Seering W P. Preshaping command inputs to reduce system vibration. Journal of Dynamic Systems Measurement and Control-Transaction of the ASME, 1990, 112: 76-82.
[57] Singhose, William E and Seering et al. Improving repeatability of coordinate measuring machines with shaped command signals. Precision Engineering, 1996,18: 138-146.
[58] Pao, Lucy Y. Multi-input shaping design for vibration reduction. Automatic, 1999, 35: 81-89.
[59] Alice G, Kapucu S and Baysec S. On preshaped reference inputs to reduce swing of suspended objects transported with robot manipulators. Mechatronics, 2000, 10: 609-626.
[60] Singhose W, Pao L. A comparison of input shaping and time-optimal flexible-body control. Control Engineering Practice, 1997, 5: 459-467.
[61] Saad M M., Dugard L, Hammad S H. A suitable generalized predictive adaptive controller case study: control of a flexible arm. Automatic, 1993, 29(3): 589-608.
[62] Meng C H, Chen J S. Dynamic modeling and payload-adaptive control of flexible manipulator. Proc. of the 1988 IEEE International Conf. on Robotics and Automation, 1988: 488-493.
[63] Sasiadek J Z, Sinivansan R. Dynamic modeling and control of a single-link flexible manipulator. Journal of Guidance, 1989, 12(6): 838-844.
[64] Nathan P J, Singh S N. Sliding mode control and elastic mode stabilization of a roboticarm with flexible links. ASME Trans., Journal of Dynamic Systems, Measurement, and Control, 1991, 113: 669-676.
[65] Sicilano B, Book W. A singular perturbation approach to control of light weight manipulators. International Journal of Robotics Research, 1988, 7(4): 79-90.
[66] Vardegrift M W, Lewis F L, Zhu S Q. Flexible-link robot arm control by a feedback linearization/singular perturbation approach. Journal of Robotic Systems, 1994, 11(7): 591-603.
[67] Lin Y J. Intelligent control of flexible robot manipulator utilizing fuzzy logic. Proc. of the 1992 ASME Winter Annual Meeting, 1992: 85-91.
[68] Moudgal V G, et al. Rule-based control for a flexible-link robot. IEEE Trans. on Control System Techniques, 1994, 2(4): 392-405.
[69] Greene K, Michael E. Indirect adaptive control of a two-link robot arm using regularization neural networks. Proc. of the 1991 International Conf. on Industrial Electronics, Control and Instrumentation, 1991: 252-258.
[70] Doyle J C, Stein G. Multivariable feedback design: concepts for a classical/modern synthesis. IEEE Trans. Automatic Control, 1981, 26(1): 4-16.
[71] Apkarian P, Adams R J. Advanced gain-scheduling techniques for uncertain systems. IEEE Trans. on Control Systems Technology, 1998, 6(1): 21-32.
[72] Apkarian P, Biannic J. Gain scheduled control of missile via linear matrix inequalities. J. of Guidance, Control and Dynamics, 1995, 18(3): 532-538.
[73] Apkarian P, Gahinet P and Becker G. Self-scheduled H∞control of linear parameter-varying systems: a design example. Automatica, 1995, 31(9): 1251-1261.
[74] Shamma J S, Athans M. Analysis of gain scheduled control for nonlinear plants. IEEE Trans. on Automatic Control, 1990, 35(8): 898-907.
[75] Apkarian P, Gahinet P. A convex characterization of gain-scheduled H∞controllers. IEEE Trans. on Automatica Control, 1995, 40(5): 853-863.
[76]胡东.变增益控制理论及其应用.南京航空航天大学博士学位论文, 1999.
[77] Shamma J S, Athans M. Gain scheduling: potential hazards and possible remedies. IEEE Control System Magazine, 1992, 12(3): 101-107.
[78] Jiang J. Optimal gain scheduling controller for a diesel engine. IEEE Control System Magazine, 1994, 14(4): 42-48.
[79] Becker G, Packard A K. Robust performance of linear parameterically varying systems using parameterically-dependent linear feedback. System and Control Letters, 1994, 23: 205-215.
[80] Apkarian P, Tuan H D. Parameterized LMIs in control theory. SIAM Journal on Control and Optimization, 2000, 38(4): 1241-1264.
[81]虞忠伟,陈辉堂,陈启军.基于保H∞性能插值的变增益输出反馈控制.自动化学报, 2003, 29(5): 773-779.
[82] Yu Z W, Chen H T and Woo P Y. Reduced order gain scheduled output/state feedback control based on H∞performance preserved interpolation. IEEE Trans. on Control Systems Technology, 2005, 13(4): 670-681.
[83] Yang D C, Tai H C et al. Experimental approach to selecting H∞weighting functions for DC servos. Journal of Dynamic Systems, Measurement and Control, 1997, 119: 101-105.
[84] McFarlane D, Glover K. A loop shaping design procedure using H∞synthesis. IEEE Trans. on Automatic Control, 1992, 37(6): 759-769.
[85] Fujita M, Hatake K and Matsumura. Loop shaping based robust control of a magnetic bearing. IEEE Control Systems Magzine, 1993, 13(4): 57-65.
[86] Choi C T, Kim J S and Peak K N. Robust loop shaping H∞control of servo systems. IEEE Int. Conf. on Systems, Man and Cybernetics, 1995, 1: 547-552.
[87] Tan W, Niu Y and Liu J Z. Robust control for a nonlinear boiler-turbine system. Control Theory and Applications, 1999, 16(6): 863-867.
[88] Civita M L, Papageorgiou G et al. Integrated modeling and robust control for full-envelope flight of robotic helicopters. IEEE Int. Conf. on Robotics and Automation, 2003, 552-557.
[89] Maekawa Y, Yubai K and Hirai J. Design of gain-scheduling controller based on interpolation of loop shaping H∞controller. The 9th IEEE Int. Workshop on Advanced Motion Control, 2006, 29-32.
[90] Nichols R A, Reichert R T and Rugh W J. Gain scheduling for H-infinity controllers: a flight control example. IEEE Trans. on Control Systems Technology, 1993, 1(2): 69-79.
[91] Hyde R A, Glover K. The application of scheduled H∞controllers to a VSTOL aircraft. IEEE Trans. on Automatic Control, 1993, 38(7): 1021-1039.
[92] Stilwell D J, Rugh W J. Interpolation of observer state feedback controllers for gain scheduling. IEEE Trans. on Automatic Control, 1999, 44(6): 1225-1229.
[93] Stilwell D J, Rugh W J. Stability preserving interpolation methods for the synthesis of gain scheduled controllers. Automatica, 2000, 36: 665-671.
[94] Kulkarni A S, EI-Sharkawi M A. Intelligent precision position control of elastic drive systems. IEEE Transactions on Energy Conversion, 2001, 16(1): 26-31.
[95] Chang P, Park J. A concurrent design of input shaping technique and a robust control for high-speed/high-precision control for a chip mounter. Control Engineering Practice, 2001, 9(12): 1279-1285.
[96] Park H, Chang P and Kim S. Time-varying input shaping technique applied to vibration reduction of an industrial robot. International Conference on Intelligent Robots and Systems, 1999, 1: 285-290.
[97] Singhose W and Pao L. A comparison of input shaping and time-optimal flexible-body control. Control Engineering Practice, 1997, 5: 459-467.
[98] Yang B B, Tan C A and Bergman L A. Direct numerical procedure for solution of moving oscillator problems. Journal of Engineering Mechanics, 2000, 126(5): 462-469.
[99] Chen C H, Wang K W. An integrated approach toward the modeling and dynamic analysis of high-speed spindles. PartⅡ: Dynamics under moving end load. Journal of Vibration and Acoustics, 1994, 116: 514-522.
[100] Argento A. A spinning beam subjected to a moving deflection load. PartⅠ: Response and resonance. Journal of Sound and Vibration, 1995, 182(4): 595-615.
[101]师汉民.机械振动系统-分析﹒测试﹒建模﹒对策(下册).武汉:华中科技大学出版社, 2004.
[102] Zames G and Francis B A. Feedback, minimax sensitivity and optimal robustness. IEEE Trans. on Automatica Control, 1983, 28(5): 585-601.
[103]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.
[104] Gahinet P. On the game Riccati equations arising in H∞control problems. Proc. 31st Conf. on Decision and Control, 1992: 935-936.
[105] Gahinet P, Laub A J. Reliable computation ofγopt in singular H∞control. Proc. 33rd Conf. on Decision and Control, 1994: 1527-1532.
[106] Safonov M G, Limebeer D J N. Simplifying the H∞theory via loop shifting. Proc. 27th Conf. on Decision and Control, 1988: 1399-1404.
[107] Gahinet P, Apkarian P. A linear matrix inequality approach to H∞control. Journal of Robust and Nonlinear Control, 1994, 4(4): 421-448.
[108] Becker G. Additional results on parameter-dependent controllers for LPV systems. Proc. of the IFAC, 1996: 351-356.
[109] Safonov M G, Chiang R Y and Limebeer D J N. Optimal Hankel model reduction for nonminimal systems. IEEE Trans. on Automatic Control, 1990, 34(4): 496-502.
[110] Cheang S U, Chen W J. Stabilizing control of an inverted pendulum system based on H∞loop shaping design procedure. Proc. of the 3rd World Congress on Intelligent Control and Automation, 2000, 3385-3388.
[111] Huang Y M, Xia Y C and Wang Y. Robust H∞controller design by loop shaping approach. Proc. of the 3rd World Congress on Intelligent Control and Automation, 2000, 3377-3380.
[112] Rugh W J. Analytical framework for gain scheduling. IEEE Control Systems, 1991, 11(1): 79-84.
[113] Ulrike G.安全可靠的RFID.现代制造, 2004, (27): 50-51.
[114] Three Bond Co., LTD. Micro-capsule type anisotropic conductive adhesive for mounting bare chips. http://www.threebond.com/, 2001.
[115] DELO Industrial Adhesives Co. Adhesives for flip-chip contacting. http://www.delo.de/products.html, 2003.
[116]郭江华,王水弟等.倒装芯片凸焊点的UBM.半导体技术, 2001, 26(6): 60-64.
[117]肖久梅,黄继华.微电子互连用导电胶研究进展.中国胶粘剂, 2004, 13(6): 43-48.
[118] James E M, Jeahuck L and Johan L. Isotropic conductive adhesive interconnect technology in electronics packaging applications. International Conf. on Polymers and Adhesives in Microelectronics and Photonics, 2005: 45-52.
[119] Joachim P. New flip chip technology utilizing non-conductive adhesive adapted for high volume chip card module production. IEEE/SEMI Int’l Electronics Manufacturing Technology Symposium, 2004, 165-170.
[120] Myung J Y, Jeong I H, Hyung K C et al. Flip chip interconnection with anisotropic conductive adhesives for RF and high-frequency applications.IEEE Trans. on Component and Packaging Technologies, 2005, 28(24): 789-796.
[121]张军,陈旭.各向异性导电胶粘接可靠性研究进展.电子元件与材料, 2004, 23(1): 35-37.
[122]刘辉. RFID标签封装设备中机器视觉系统设计与实现.华中科技大学硕士学位论文, 2006.