直线电机系统分析与H_∞鲁棒控制
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摘要
相对于传统旋转电机系统,直线电机驱动系统可以提供更高的速度和加速度能力,因此在半导体设备邦定机中应用已经很广泛。但是,在高加速度状态下工作的直线电机系统受到各种系统不确定性的影响,而且直线电机本身的推力波动也会影响最终的定位精度。本文分析了直线电机的力涌现象和系统的不确定性,把力涌现象分为随位置变化的力涌和根位置无关的力涌。本文对基于位置的力涌进行了检测和补偿,而对于跟位置无关的力涌波动,则需要用鲁棒控制器进行抑制。之后,对含有力涌补偿回路的系统进行辨识,由于直线电机系统不会由于信号的冲击而受到破坏,所以在辨识过程中采用伪随机序列作为理想的辨识输入信号,得到5阶系统模型来显现系统不确定因素。根据此高阶模型,使用H_∞合成优化技术设计了能够容忍各种机械不确定性和电机制造不确定性的内环速度环鲁棒控制器,外环位置环控制器则采用PI控制器+前馈的方案来保证定位精度。仿真和实验结果表明该系统可以获得高速高精度的响应性能,从而满足半导体设备的需要。在结论中,总结了本人的一些关于直线电机应用的经验。基于目前的工作,还有很多事情比如摩擦补偿还需进一步研究。
Linear motor driven system has been found in wire-bonding equipments widely, for its higher speed and acceleration capability comparing with the conventional ball-lead screw driven system. Unfortunately, the linear motor driven system operated at high acceleration is subject to various mechanical uncertainty, and the force ripple of the linear motor also affects the positioning accuracy. In this thesis, the force ripple and system uncertainties are analyzed. The force ripple can be considered composited by the position based force ripple and the others. The position based force ripple was detected and compensated with the assistant of data fitting and position based FFT technique in this thesis, and the other force ripple caused by system uncertainties should be rejection by the robust control scheme. After that, the linear motor system with fore ripple compensation has been identified. Without the low acceleration units the PRBS was adopted as a ideal identification input signal in this thesis. And for representing the system uncertainty, a 5order model was obtained in the identification process. With the high order system model, the robust inner speed controller has been designed using H_∞mixed optimization technology considering for the mechanical uncertainties and the motor manufacture uncertainties. The outer position controller is a PI controller with feedforward compensation for high precision positioning. The result shows that the system can achieve high speed and high precision positioning that is satisfactory for semiconductor equipment. In the conclusion, I give some of my experience on the linear motor application, also, there are lots of work should be deal with in future.
Linear motor driven system has been found in wire-bonding equipments widely, for its higher speed and acceleration capability comparing with the conventional ball-lead screw driven system. Unfortunately, the linear motor driven system operated at high acceleration is subject to various mechanical uncertainty, and the force ripple of the linear motor also affects the positioning accuracy. In this thesis, the force ripple and system uncertainties are analyzed. The force ripple can be considered composited by the position based force ripple and the others. The position based force ripple was detected and compensated with the assistant of data fitting and position based FFT technique in this thesis, and the other force ripple caused by system uncertainties should be rejection by the robust control scheme. After that, the linear motor system with fore ripple compensation has been identified. Without the low acceleration units the PRBS was adopted as a ideal identification input signal in this thesis. And for representing the system uncertainty, a 5order model was obtained in the identification process. With the high order system model, the robust inner speed controller has been designed using H_∞mixed optimization technology considering for the mechanical uncertainties and the motor manufacture uncertainties. The outer position controller is a PI controller with feedforward compensation for high precision positioning. The result shows that the system can achieve high speed and high precision positioning that is satisfactory for semiconductor equipment. In the conclusion, I give some of my experience on the linear motor application, also, there are lots of work should be deal with in future.
引文
[1] V.D. Braembussche, P. J. Swevers, H. Van Brussel, and P. Vanherck, Accurate Tracking Control of Linear Synchronous Motor Machine Tool Axes, Mechatron., Vo1. 6, No. 5, pp. 507-521 (1996).
[2] T.M. Jahns and W.L. Soong, Pulsating Torque Minimization Techniques for Permanent Magnet AC Motor Drives-A Review, IEEE Trans. and Electron., Vo1. 43, No. 2, pp. 321-330 (1996).
[3] G. Otten, T.J.A. de Vries, J. van Amerongen, A.M. Rankers, and E.W. Gaal, Linear Motor Motion Control Using a Learning Feedforward Controller, IEEE/ASME Trans. Mechatron., Vo1. 2, No. 3, pp. 179-187 (1997).
[4] Schrijver, E. J. van Dijk, H∞Design of Disturbance Compensators for Cogging Forces in a Linear Permanent Magnet Motor, Int. J. of Automation and Control., Vo1. 40, No. 4, pp. 36-41 (1999).
[5] Lee, T.H., K.K. Tan, S.Y. Lim, and H.F. Dou, Iterative Learning of Permanent Magnet Linear Motor with Relay Automatic Tuning, Mechatron., Vo1. 10, No. 1-2, pp. 169-190 (2000).
[6] Xu, L. and B. Yao, Adaptive Robust Precision Motion Control of Linear Motors with Ripple Force Compensations: Theory and Experiments, Proc. IEEE Conf. Contr. Appl., Anchorage, USA, pp. 373-378 (2000).
[7] Rohrig, C. and A. Jochheim, Identification and Compensation of Force Ripple in Linear Permanent Magnet Motors, Proc. Amer. Contr. Conf., Arlington, USA, pp. 2161-2166 (2001).
[8] Gieras, J.F., Status of Linear Motors in the United States, Proc. 4th Int. Symp. Linear Drives Ind. Appl., Birmingham, UK, pp. 169-176 (2003).
[9] Rohrig, C. and A. Jochheim, Motion Control of Linear Permanent Magnet Motorswith Force Ripple Compensation, Proc. 3rd Int. Symp. Linear Drives Ind. Appl., Nagano, Japan, pp. 478-483 (2001).
[10] Rohrig, C. and A. Jochheim, Motion Control of Linear Synchronous Motors with Force Ripple Compensation Uusing Current Shaping, Proc. 15th IFAC World Congr. Automat. Contr., CD-ROM, p6, Barcelona, Spanien (2002).
[11] Bianchi, N. and S. Bolognani, Force Ripple in Linear PM Motors: Causes and Remedial Strategies, Proc. 4th Int. Symp. Linear Drives Ind. Appl., Birmingham, UK, pp. 223-226 (2003).
[12] Schrijver, E. and J. van Dijk. H∞Design of Disturbance Compensators for Cogging Forces in a Linear Permanent Magnet Motor, Int. J. of Automation and Control., Vo1. 40, No. 4, pp. 36-41 (1999).
[13] Rohrig, C., Current Waveform Optimization for Force Ripple Compensation of Linear Synchronous Motors, Proc. 42nd Conf. Decis. Contr., Maui, Hawaii, Vol. 6, pp. 5891-5896 (2003). [ 14 ] K.K,Tan. Precision Motion Control With Disturbance Observer for Pulsewidth-Modulated-Driven Permanent-Magnet Linear Motors, IEEE Trans. on mag,. Vol.39.No.3, May.(2003).
[15]Ye, Yunyue, Research and Development of Linear Drive Technology in China, Proc. 4th Int. Symp. Linear Drives Ind. Appl., Birmingham, UK, pp. 177- 182 (2003).
[16] LE Series Linear Motor Systems, Motor Integration Manual LEA, LEB, LEC & LEM Linear Motors, Anorad Corporation (1999).
[17] Hanselman, D.C., Brushless Permanent-Magnet Motor Design, McGraw-Hill, New York (1994).
[18] Rohrig, C. and A. Jochheim, Identification and Compensation of Force Ripple in Linear Permanent Magnet Motors, Proc. Amer. Contr. Conf., Arlington, USA, pp. 2161-2166 (2001).
[19] Matlab Data-Fitting Toolbox User Guide,(2004).
[20] Menhaj, M.B., and N. Seifipour, A New Implementation of Discrete-time Hopfield Net with Higher Capacity and Speed of Convergence, IEEE Trans. On Neural Networks, vol. 1, pp. 436-441, (2001).
[21] Shigeo A., Convergence Acceleration of the Hopfield Neural Network by Optimizing Integration Step Sizes, IEEE Trans. On Systems,Man,Cybernetics. vol. 26, no. 1, pp. 194-201, (1996).
[22] Yamaguchi, I., et al., Experimental Demonstration of LSS System Identification by Eigensystem Realization Algorithm, Proc. Amer. Contr. Conf., pp.402-406, (1995).
[23] A. M. Elramsisi, M. A. Zohdy, and N. K. Loh, A Joint Frequency-Position Domain Structure Identification of Nonlinear Discrete-time Systems by Neural Networks, IEEE Trans. On Automat. Contr., vol. 36, no. 5, May (1991).
[24] K. Ohnishi, M. Shibata and T. Murakami, Motion Control for Advanced Mechatronics, IEEE/ASME Trans. Mechatronics, vol. 1, pp. 56–67, Mar.(1996).
[25] P. M. Young, Controller Design with Real Parametric Uncertainty, Inter. J. C, vol. 65, pp. 469–509, (1996).
[26] Matlab System Identification Toolbox,(2006).
[27] LENNART, LJUNG, System Identification—Theory for the User, Second Edition, Prentice-hall, Jan.(2002).
[28] K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Robust Control, Upper Saddle River, NJ: Prentice-Hall(1996).
[29] J. Doyle, Analysis of Feedback Systems with Structured Uncertainty, IEE Proc. Part D, vol. 129, no. 6, pp. 242–250, Nov. (1982).
[30] Matlab Robust Control Toolbox,(2001).
[31] J. Doyle, K. Glover, P. Khargonekar, and B. Francis, State Space Solutions to H2and H∞Control Problems, IEEE Trans.Auto., vol. 34, no. 8, pp. 831–847, August (1989).
[32]李忠明,刘卫国,稀土永磁电机,北京:国防工业出版社,(1999).
[33] Ronald Rohner, Linear Motor. US 6316848 B1,Nov 13, pp.5(2001).
[34] Danaher Motion, Platinum DDL Motors Catlaog, (November 2004)
[35] K V. I. Johannes, M. A. Green, and C. A. Brockley. The Role of The Rate of Application of The Tangential Force in Determining The Static Friction Coefficient, Wear, 24:381–385, (1973).
[36] E. Rabinowicz. The Nature of The Static and Kinetic Coefficients of Friction, Int. J. of Automation and Control., 22H11I:1373–79, (1951).
[37] R. S. H. Richardson and H. Nolle. Surface Friction Under Time-Dependent Loads, Wear, 37H1I:87–101, (1976).
[38] J. Courtney-Pratt and E. Eisner. The Effect of A Tangential Force on The Contact of Metallic Bodies, In Proc. R.S, Vol. A238, pp. 529–550, (1957).
[39] THK Product Catalog,(2008)
[40] Danaher Motion Control Reference,(2006).
[2] T.M. Jahns and W.L. Soong, Pulsating Torque Minimization Techniques for Permanent Magnet AC Motor Drives-A Review, IEEE Trans. and Electron., Vo1. 43, No. 2, pp. 321-330 (1996).
[3] G. Otten, T.J.A. de Vries, J. van Amerongen, A.M. Rankers, and E.W. Gaal, Linear Motor Motion Control Using a Learning Feedforward Controller, IEEE/ASME Trans. Mechatron., Vo1. 2, No. 3, pp. 179-187 (1997).
[4] Schrijver, E. J. van Dijk, H∞Design of Disturbance Compensators for Cogging Forces in a Linear Permanent Magnet Motor, Int. J. of Automation and Control., Vo1. 40, No. 4, pp. 36-41 (1999).
[5] Lee, T.H., K.K. Tan, S.Y. Lim, and H.F. Dou, Iterative Learning of Permanent Magnet Linear Motor with Relay Automatic Tuning, Mechatron., Vo1. 10, No. 1-2, pp. 169-190 (2000).
[6] Xu, L. and B. Yao, Adaptive Robust Precision Motion Control of Linear Motors with Ripple Force Compensations: Theory and Experiments, Proc. IEEE Conf. Contr. Appl., Anchorage, USA, pp. 373-378 (2000).
[7] Rohrig, C. and A. Jochheim, Identification and Compensation of Force Ripple in Linear Permanent Magnet Motors, Proc. Amer. Contr. Conf., Arlington, USA, pp. 2161-2166 (2001).
[8] Gieras, J.F., Status of Linear Motors in the United States, Proc. 4th Int. Symp. Linear Drives Ind. Appl., Birmingham, UK, pp. 169-176 (2003).
[9] Rohrig, C. and A. Jochheim, Motion Control of Linear Permanent Magnet Motorswith Force Ripple Compensation, Proc. 3rd Int. Symp. Linear Drives Ind. Appl., Nagano, Japan, pp. 478-483 (2001).
[10] Rohrig, C. and A. Jochheim, Motion Control of Linear Synchronous Motors with Force Ripple Compensation Uusing Current Shaping, Proc. 15th IFAC World Congr. Automat. Contr., CD-ROM, p6, Barcelona, Spanien (2002).
[11] Bianchi, N. and S. Bolognani, Force Ripple in Linear PM Motors: Causes and Remedial Strategies, Proc. 4th Int. Symp. Linear Drives Ind. Appl., Birmingham, UK, pp. 223-226 (2003).
[12] Schrijver, E. and J. van Dijk. H∞Design of Disturbance Compensators for Cogging Forces in a Linear Permanent Magnet Motor, Int. J. of Automation and Control., Vo1. 40, No. 4, pp. 36-41 (1999).
[13] Rohrig, C., Current Waveform Optimization for Force Ripple Compensation of Linear Synchronous Motors, Proc. 42nd Conf. Decis. Contr., Maui, Hawaii, Vol. 6, pp. 5891-5896 (2003). [ 14 ] K.K,Tan. Precision Motion Control With Disturbance Observer for Pulsewidth-Modulated-Driven Permanent-Magnet Linear Motors, IEEE Trans. on mag,. Vol.39.No.3, May.(2003).
[15]Ye, Yunyue, Research and Development of Linear Drive Technology in China, Proc. 4th Int. Symp. Linear Drives Ind. Appl., Birmingham, UK, pp. 177- 182 (2003).
[16] LE Series Linear Motor Systems, Motor Integration Manual LEA, LEB, LEC & LEM Linear Motors, Anorad Corporation (1999).
[17] Hanselman, D.C., Brushless Permanent-Magnet Motor Design, McGraw-Hill, New York (1994).
[18] Rohrig, C. and A. Jochheim, Identification and Compensation of Force Ripple in Linear Permanent Magnet Motors, Proc. Amer. Contr. Conf., Arlington, USA, pp. 2161-2166 (2001).
[19] Matlab Data-Fitting Toolbox User Guide,(2004).
[20] Menhaj, M.B., and N. Seifipour, A New Implementation of Discrete-time Hopfield Net with Higher Capacity and Speed of Convergence, IEEE Trans. On Neural Networks, vol. 1, pp. 436-441, (2001).
[21] Shigeo A., Convergence Acceleration of the Hopfield Neural Network by Optimizing Integration Step Sizes, IEEE Trans. On Systems,Man,Cybernetics. vol. 26, no. 1, pp. 194-201, (1996).
[22] Yamaguchi, I., et al., Experimental Demonstration of LSS System Identification by Eigensystem Realization Algorithm, Proc. Amer. Contr. Conf., pp.402-406, (1995).
[23] A. M. Elramsisi, M. A. Zohdy, and N. K. Loh, A Joint Frequency-Position Domain Structure Identification of Nonlinear Discrete-time Systems by Neural Networks, IEEE Trans. On Automat. Contr., vol. 36, no. 5, May (1991).
[24] K. Ohnishi, M. Shibata and T. Murakami, Motion Control for Advanced Mechatronics, IEEE/ASME Trans. Mechatronics, vol. 1, pp. 56–67, Mar.(1996).
[25] P. M. Young, Controller Design with Real Parametric Uncertainty, Inter. J. C, vol. 65, pp. 469–509, (1996).
[26] Matlab System Identification Toolbox,(2006).
[27] LENNART, LJUNG, System Identification—Theory for the User, Second Edition, Prentice-hall, Jan.(2002).
[28] K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Robust Control, Upper Saddle River, NJ: Prentice-Hall(1996).
[29] J. Doyle, Analysis of Feedback Systems with Structured Uncertainty, IEE Proc. Part D, vol. 129, no. 6, pp. 242–250, Nov. (1982).
[30] Matlab Robust Control Toolbox,(2001).
[31] J. Doyle, K. Glover, P. Khargonekar, and B. Francis, State Space Solutions to H2and H∞Control Problems, IEEE Trans.Auto., vol. 34, no. 8, pp. 831–847, August (1989).
[32]李忠明,刘卫国,稀土永磁电机,北京:国防工业出版社,(1999).
[33] Ronald Rohner, Linear Motor. US 6316848 B1,Nov 13, pp.5(2001).
[34] Danaher Motion, Platinum DDL Motors Catlaog, (November 2004)
[35] K V. I. Johannes, M. A. Green, and C. A. Brockley. The Role of The Rate of Application of The Tangential Force in Determining The Static Friction Coefficient, Wear, 24:381–385, (1973).
[36] E. Rabinowicz. The Nature of The Static and Kinetic Coefficients of Friction, Int. J. of Automation and Control., 22H11I:1373–79, (1951).
[37] R. S. H. Richardson and H. Nolle. Surface Friction Under Time-Dependent Loads, Wear, 37H1I:87–101, (1976).
[38] J. Courtney-Pratt and E. Eisner. The Effect of A Tangential Force on The Contact of Metallic Bodies, In Proc. R.S, Vol. A238, pp. 529–550, (1957).
[39] THK Product Catalog,(2008)
[40] Danaher Motion Control Reference,(2006).