多轴协调跟踪控制系统的研究与实现
摘要
随着大规模集成电路,精密加工设备,计算机硬盘等高新技术的飞速发展,对数控系统加工速度及加工精度的要求也越来越高,所以在加工速度不断提高的同时,跟踪误差的精度问题已经成为亟待研究和解决的问题之一。
本文在分析误差来源的基础上,结合NURBS曲线的特点,设计了多轴协调跟踪控制系统。控制系统主要分为提高单轴跟踪精度和双轴轮廓精度两个部分,在提高单轴跟踪精度上,运用基于模型扰动抑制器来处理外部负载产生的干扰问题,并增加系统的强健性和稳定性。在提高单轴跟踪精度的同时间接提高轮廓精度。在提高轮廓精度上,针对NURBS等多种曲线运用带实时轮廓误差估测的交叉偶和控制算法、位置误差跟踪补偿算法及NURBS曲线速度规划实现NURBS曲线轮廓的跟踪任务,增加各轴间的协调性以降低轮廓误差,提高跟踪精度。
文中首先对X-Y实验平台进行系统辨识,建立数学模型,并归纳不同曲线轮廓误差的计算方法。其次,在NURBS曲线插补中运用快速德布尔算法,对进给速度进行合理规划。然后为提高跟踪精度,根据误差来源的分析,设计了多轴协调跟踪控制器。其中,为保证系统的稳定性,还对控制器进行了稳定性分析。
经过计算机的仿真和实验验证,表明本文提出的多轴协调跟踪控制系统能很好的改善轮廓精度,提高跟踪性能。
With the rapid development of high technology such as the large-scale integrated circuits, precision processing equipment, computer hard drivers and so on, the requirements of high-speed and high-precision processing in CNC system is increasing. Therefore, the accuracy of the tracking error and processing speed are required to be improved.
Based on the analysis of the error source and the characteristics of NURBS curve, the multi-axis coordinate tracking control system is designed in this paper, The control system mainly includes the two parts of functions: the reduction of single-axis position error and the contour error in biaxial system. In tracking error, in order to eliminate the external disturbance, model-based disturbance attenuation is employed to enhance the robust and stability of the system. The reduction of position error can improve the contour accuracy indirectly. In contour error, combining with the feedrate regulator of NURBS curve, the cross-coupled control with real-time contour error estimator and position error position compensator (PEC) are applied in this research to improve the multi-axis coordination and complete the tracking task.
Firstly, system identification of X-Y table is carried out, and the mathematic model is established, then the contour error calculation methods is introduced in the following. Secondly, the fast de-boor method is employed in NURBS interpolation. The feedrate is regulated by two stages. Finally the multi-axis coordination control system is designed on basis of machining error and the stability of control system is also analyzed. The proposed multi-axis coordinate tracking control system can improve the contour accuracy and tracking performance effectively by simulation and experimental results.
本文在分析误差来源的基础上,结合NURBS曲线的特点,设计了多轴协调跟踪控制系统。控制系统主要分为提高单轴跟踪精度和双轴轮廓精度两个部分,在提高单轴跟踪精度上,运用基于模型扰动抑制器来处理外部负载产生的干扰问题,并增加系统的强健性和稳定性。在提高单轴跟踪精度的同时间接提高轮廓精度。在提高轮廓精度上,针对NURBS等多种曲线运用带实时轮廓误差估测的交叉偶和控制算法、位置误差跟踪补偿算法及NURBS曲线速度规划实现NURBS曲线轮廓的跟踪任务,增加各轴间的协调性以降低轮廓误差,提高跟踪精度。
文中首先对X-Y实验平台进行系统辨识,建立数学模型,并归纳不同曲线轮廓误差的计算方法。其次,在NURBS曲线插补中运用快速德布尔算法,对进给速度进行合理规划。然后为提高跟踪精度,根据误差来源的分析,设计了多轴协调跟踪控制器。其中,为保证系统的稳定性,还对控制器进行了稳定性分析。
经过计算机的仿真和实验验证,表明本文提出的多轴协调跟踪控制系统能很好的改善轮廓精度,提高跟踪性能。
With the rapid development of high technology such as the large-scale integrated circuits, precision processing equipment, computer hard drivers and so on, the requirements of high-speed and high-precision processing in CNC system is increasing. Therefore, the accuracy of the tracking error and processing speed are required to be improved.
Based on the analysis of the error source and the characteristics of NURBS curve, the multi-axis coordinate tracking control system is designed in this paper, The control system mainly includes the two parts of functions: the reduction of single-axis position error and the contour error in biaxial system. In tracking error, in order to eliminate the external disturbance, model-based disturbance attenuation is employed to enhance the robust and stability of the system. The reduction of position error can improve the contour accuracy indirectly. In contour error, combining with the feedrate regulator of NURBS curve, the cross-coupled control with real-time contour error estimator and position error position compensator (PEC) are applied in this research to improve the multi-axis coordination and complete the tracking task.
Firstly, system identification of X-Y table is carried out, and the mathematic model is established, then the contour error calculation methods is introduced in the following. Secondly, the fast de-boor method is employed in NURBS interpolation. The feedrate is regulated by two stages. Finally the multi-axis coordination control system is designed on basis of machining error and the stability of control system is also analyzed. The proposed multi-axis coordinate tracking control system can improve the contour accuracy and tracking performance effectively by simulation and experimental results.
引文
1. Y. Koren, CC. Lo, M. Shpitalni. CNC interpolators: Algorithms and analysis. ASME Manufacture Science and Engineering. 2000, 14:403–428
2. D.C.H.Yang, T.Kong. Parametric interpolator versus linear interpolator for precision CNC machining. Computer Aided Design. 1994, 26(3):225–33
3. M. Shapitalni, Y.Koren, and C.C. Lo. Real-Time Curve Interpolators. Computer-Aided Design. 1994, 26 (11):832–838
4. D.C.H. Yang, T. Kong. Hair. Parameteric Interpolator versus Linear Interpolator for Precision CNC Machining. Computer Aided Design. 1994, 26(3):225–234
5. R.A. O.Riosa, R.J.R. Troncosob, G.H. Ruiza and R.C. Miranda. Computationally efficient parametric analysis of discrete-time polynomial based acceleration–deceleration profile generation for industrial robotics and CNC machinery. Mechatronics. 2007, 17(9):511–523
6. S.S Yeh, P.L. Hsu. A adaptive Feedrate Interpolation for Parametric Curves with a Confined Chord Error, Computer Aided Design. 2002, 34(3):229–237
7. Z.M. Xu, J.C.Chen, Z.J. Feng. Performance Evaluation of a Real-Time Interpolation Algorithm for NURBS Curves. International Journal of Advanced Manufacturing Technology. 2002,20(4):270–276
8. M. Tikhon, T.J. Ko, S.H. Lee. NURBS Interpolator for constant material removal rate in open NC machine tools. International Journal of Machine Tools and Manufacture. 2004, 44(2):237–245
9. H.Y. Chuang, C.H. Liu. Cross-coupled adaptive feedrate control for multiaxis machine tools. ASME Journal of Dynamic Systems, Measurement, and Control. 1991, 113: 451–457
10. Y.S. Tarng, H.Y. Chuang, W.T. Hsu. Intelligent cross-coupled fuzzy feedrate controller design for CNC machine tools based on genetic algorithms. International Journal of Machine Tools and Manufacture. 1999, 39 (10):1673–1692
11. M.Y. Cheng, K.H. Su, S.F. Wang. Contour error reduction for free-form contour following tasks of biaxial motion control systems. Robotics and Computer-Integrated Manufacturing. 2009, 25:323–333
12. J. W. Jeon and Y.K. Kim. FPGA based acceleration and deceleration circuit for industrial robots and CNC machine tools. Mechatronics. 2002,12:635–642
13. K. Ohishi, M. Nakao, K. Ohnishi, and K. Miyachi, Microprocessor-controlled DC motor for load-insensitive position servo system. IEEETrans. Ind. Electron. 1987, 34: 44–49
14. T. Umeno and Y. Hori. Robust speed control of servomotors using modern two degrees-of-freedom controller design. IEEE Trans. Ind.Electron. 1991, 38:363–368
15. S. Endo, H. Kobayashi, C. J. Kempf, S. Kobayashi, M. Tomizuka, and Y. Hori. Robust digital tracking controller design for high-speed positioning systems. Contr. Eng. Practice. 1996, 4(4): 527–536
16. C. J. Kempf and S. Kobayashi. Discrete-time disturbance observer design for systems with time-delay. Proc. AMC’96-Mie. 1996, 1: 332–337
17. S. Komada, K. Nomura, M. Ishida, and T. Hori. Robust force control based on compensation for parameter variations of dynamic environment. IEEE Trans. Ind. Electron. 1993, 40: 89–95
18. J. S. Ko, J. H. Lee, S. K. Chung, and M. J. Youn. A robust digital position control of brushless DC motor with dead beat load torque observer. IEEE Trans. Ind. Electron. 1993, 40:512–520
19. J. Zhang and T. H. Barton. Robustness enhancement of DC drives with a smooth optimal sliding-mode control. IEEE Trans. Ind. Electron. 1991, 27: 686–693
20. Y. Fujimoto and A. Kawamura. Robust servo-system based on two-degree-of-freedom control with sliding mode. IEEE Trans. Ind. Electron. 1995, 42: 272–280
21. Y. Z. Tsypkin and F. Fujii. Internal model principle in internal model control. Proc. 32nd SICE Annu. Conf. 1993, 1055–1059
22. T. Umeno and Y. Hori. Robust speed control of servomotors using modern two degrees-of-freedom controller design. IEEE Trans. Ind. Electron. 1991, 38:363–368
23. S. Hara. Parameterization of stabilizing controllers for multivariable servo systems with two degrees of freedom. International Journal of Control. 1987, 45: 779-790
24. T. Umeno, T Kaneko, and Y. Hori. Robust servosystem design withtwo degrees of freedom and its application to novel motion control of robot manipulators. IEEE Trans. Ind. Electron. 1993,40: 473–485
25. Y. Zhao and H. Kimura. Two-degrees-of freedom dead-beat control system with robustness. Int. J. Contr. 1988,48(1): 303–315
26. K.J. Astrom and B. Wittenmark. Adaptive control, second edition
27. M.T. Yana, M.H. Leea and P.L. Yenb. Theory and application of a combined self-tuning adaptive control and cross-coupling control in a retrofit milling machine. Mechatronics. 2005, 15:193-211
28. B.Yao. High Performance Adaptive Robust Control of Nonlinear systems:A general Framework and New Schemes. Proceedings of the 36th conference on decision&control. 1997, 6(5):2489-2494
29. B.K.Choi, C.H. Choi and H. Lim. Model-Based Disturbance Attenuation for CNC Machining Centers in Cutting Process. IEEE/ASME Transactions Mechatronics. 1999, 4(2):157-168
30. O. Masory. Improving contouring accuracy of NC/CNC systems with additional velocity feedforward loop. ASME Journal of Engineering for Industry. 1986, 108: 227–230
31. M. Tomizuka. Zero phase error tracking algorithm for digital control. ASME Journal of Dynamic Systems, Measurement, and Control. 1987, 109:65–68
32. C.C. Lo, C.Y. Chung. Tangential-contouring controller for biaxial motion control. ASME Journal of Dynamic Systems, Measurement and Control. 1999,121:126–129
33. G.T.-C. Chiu, M. Tomizuka. Contouring control of machine tool feed drive systems: a task coordinate frame approach. IEEE Transactions on Control Systems Technology. 2001,9 (1):130–139
34. Y. Koren. Cross-Coupled Biaxial Computer for Manufacturing Systems. Journal of Dynamic System, Measurement and Control. Transactions of the ASME. 1980, 102: 265~272
35. K. Srinivasan, P.K. Kulkarni. Cross-coupled control of biaxial feed drive servomechanisms. ASME Journal of Dynamic Systems, Measurement and Control. 1990, 112:225–232
36. S.S. Yeh, P.L. Hsu. Theory and applications of the robust cross-coupled control design. ASME Journal of Dynamic Systems, Measurement and Control. 1999, 121:524–530
37. Y.T. Shin, C.S. Chen, A.C. Lee. A novel cross-coupling control design for bi-axis motion. International Journal of Machine Tools and Manufacture. 2002,42 (14):1539–1548
38. C.S. Chen, Y.H. Fan, S.P. Tseng. Position command shaping control in a retrotted milling machine, International Journal of Machine Tools and Manufacture. 2006,46 (3-4) :293–303
39. M.Y. Cheng, C.C. Lee. Motion controller design for contour following tasks based on real-time contour error estimation. IEEE Transactions on Industrial Electronics. 2007, 54 (3): 1686–1695
40. J.H. Chin and T.C. Lin. Cross-coupled precompensation method for the contouring accuracy of computer numerically controlled machine tools. International Journal of Machine Tools and Manufacture. 1997, 37(7):947–967
41. J.H. Chin, Y.M. Cheng, J.H. Lin. Improving contour accuracy by fuzzy-logic en-hanced cross-coupled precompensation method. Robotics and Computer-Integrated Manufacturing. 2004, 20(1): 65–76
42. K. L. Barton and A. G. Alleyne. A cross–coupled iterative learning control design for precision motion control. IEEE Transactions on control system technology. 2008, 16(6):1218-1231
43. S.K. Jeonga and S.S. You. Precise position synchronous control of multi-axis servo system. Mechatronics. 2008, 18:129-140
44. S. Jee and Y. Koren. Adaptive fuzzy logic controller for feed drives of a CNC machine tool. Mechatronics. 2004, 14:299-326
45. K. H. Su and M. Y. Cheng. Contouring accuracy improvement using cross-coupled control and position error compensator. International Journal of Machine Tools & Manufacture. 2008, 48:1444– 1453
46. O. Masory. Improving contouring accuracy of NC/CNC systems with additional velocity feedforward loop. ASME Journal of Engineering for Industry. 1986, 108:227–230
47. Y. Koren, C.C. Lo, Shpitalni M. CNC interpolators: Algorithms and analysis. ASME Manufacture Science and Engineering. 1993,64:83–92
48. L. Piegl. On NURBS: a survey. IEEE Computer Graphics & Application. 1991,11 (1): 55–71
49. F.Z. Shi. CAD and NURBS. High-school education publisher, 2001:211~245.
50. G.Q. Liu, Q.D. Guo. Model-based Disturbance Attenuation for Linear Motor Servo System. Power Electronics and Motion Control Conference. 2006, 2:1~3
2. D.C.H.Yang, T.Kong. Parametric interpolator versus linear interpolator for precision CNC machining. Computer Aided Design. 1994, 26(3):225–33
3. M. Shapitalni, Y.Koren, and C.C. Lo. Real-Time Curve Interpolators. Computer-Aided Design. 1994, 26 (11):832–838
4. D.C.H. Yang, T. Kong. Hair. Parameteric Interpolator versus Linear Interpolator for Precision CNC Machining. Computer Aided Design. 1994, 26(3):225–234
5. R.A. O.Riosa, R.J.R. Troncosob, G.H. Ruiza and R.C. Miranda. Computationally efficient parametric analysis of discrete-time polynomial based acceleration–deceleration profile generation for industrial robotics and CNC machinery. Mechatronics. 2007, 17(9):511–523
6. S.S Yeh, P.L. Hsu. A adaptive Feedrate Interpolation for Parametric Curves with a Confined Chord Error, Computer Aided Design. 2002, 34(3):229–237
7. Z.M. Xu, J.C.Chen, Z.J. Feng. Performance Evaluation of a Real-Time Interpolation Algorithm for NURBS Curves. International Journal of Advanced Manufacturing Technology. 2002,20(4):270–276
8. M. Tikhon, T.J. Ko, S.H. Lee. NURBS Interpolator for constant material removal rate in open NC machine tools. International Journal of Machine Tools and Manufacture. 2004, 44(2):237–245
9. H.Y. Chuang, C.H. Liu. Cross-coupled adaptive feedrate control for multiaxis machine tools. ASME Journal of Dynamic Systems, Measurement, and Control. 1991, 113: 451–457
10. Y.S. Tarng, H.Y. Chuang, W.T. Hsu. Intelligent cross-coupled fuzzy feedrate controller design for CNC machine tools based on genetic algorithms. International Journal of Machine Tools and Manufacture. 1999, 39 (10):1673–1692
11. M.Y. Cheng, K.H. Su, S.F. Wang. Contour error reduction for free-form contour following tasks of biaxial motion control systems. Robotics and Computer-Integrated Manufacturing. 2009, 25:323–333
12. J. W. Jeon and Y.K. Kim. FPGA based acceleration and deceleration circuit for industrial robots and CNC machine tools. Mechatronics. 2002,12:635–642
13. K. Ohishi, M. Nakao, K. Ohnishi, and K. Miyachi, Microprocessor-controlled DC motor for load-insensitive position servo system. IEEETrans. Ind. Electron. 1987, 34: 44–49
14. T. Umeno and Y. Hori. Robust speed control of servomotors using modern two degrees-of-freedom controller design. IEEE Trans. Ind.Electron. 1991, 38:363–368
15. S. Endo, H. Kobayashi, C. J. Kempf, S. Kobayashi, M. Tomizuka, and Y. Hori. Robust digital tracking controller design for high-speed positioning systems. Contr. Eng. Practice. 1996, 4(4): 527–536
16. C. J. Kempf and S. Kobayashi. Discrete-time disturbance observer design for systems with time-delay. Proc. AMC’96-Mie. 1996, 1: 332–337
17. S. Komada, K. Nomura, M. Ishida, and T. Hori. Robust force control based on compensation for parameter variations of dynamic environment. IEEE Trans. Ind. Electron. 1993, 40: 89–95
18. J. S. Ko, J. H. Lee, S. K. Chung, and M. J. Youn. A robust digital position control of brushless DC motor with dead beat load torque observer. IEEE Trans. Ind. Electron. 1993, 40:512–520
19. J. Zhang and T. H. Barton. Robustness enhancement of DC drives with a smooth optimal sliding-mode control. IEEE Trans. Ind. Electron. 1991, 27: 686–693
20. Y. Fujimoto and A. Kawamura. Robust servo-system based on two-degree-of-freedom control with sliding mode. IEEE Trans. Ind. Electron. 1995, 42: 272–280
21. Y. Z. Tsypkin and F. Fujii. Internal model principle in internal model control. Proc. 32nd SICE Annu. Conf. 1993, 1055–1059
22. T. Umeno and Y. Hori. Robust speed control of servomotors using modern two degrees-of-freedom controller design. IEEE Trans. Ind. Electron. 1991, 38:363–368
23. S. Hara. Parameterization of stabilizing controllers for multivariable servo systems with two degrees of freedom. International Journal of Control. 1987, 45: 779-790
24. T. Umeno, T Kaneko, and Y. Hori. Robust servosystem design withtwo degrees of freedom and its application to novel motion control of robot manipulators. IEEE Trans. Ind. Electron. 1993,40: 473–485
25. Y. Zhao and H. Kimura. Two-degrees-of freedom dead-beat control system with robustness. Int. J. Contr. 1988,48(1): 303–315
26. K.J. Astrom and B. Wittenmark. Adaptive control, second edition
27. M.T. Yana, M.H. Leea and P.L. Yenb. Theory and application of a combined self-tuning adaptive control and cross-coupling control in a retrofit milling machine. Mechatronics. 2005, 15:193-211
28. B.Yao. High Performance Adaptive Robust Control of Nonlinear systems:A general Framework and New Schemes. Proceedings of the 36th conference on decision&control. 1997, 6(5):2489-2494
29. B.K.Choi, C.H. Choi and H. Lim. Model-Based Disturbance Attenuation for CNC Machining Centers in Cutting Process. IEEE/ASME Transactions Mechatronics. 1999, 4(2):157-168
30. O. Masory. Improving contouring accuracy of NC/CNC systems with additional velocity feedforward loop. ASME Journal of Engineering for Industry. 1986, 108: 227–230
31. M. Tomizuka. Zero phase error tracking algorithm for digital control. ASME Journal of Dynamic Systems, Measurement, and Control. 1987, 109:65–68
32. C.C. Lo, C.Y. Chung. Tangential-contouring controller for biaxial motion control. ASME Journal of Dynamic Systems, Measurement and Control. 1999,121:126–129
33. G.T.-C. Chiu, M. Tomizuka. Contouring control of machine tool feed drive systems: a task coordinate frame approach. IEEE Transactions on Control Systems Technology. 2001,9 (1):130–139
34. Y. Koren. Cross-Coupled Biaxial Computer for Manufacturing Systems. Journal of Dynamic System, Measurement and Control. Transactions of the ASME. 1980, 102: 265~272
35. K. Srinivasan, P.K. Kulkarni. Cross-coupled control of biaxial feed drive servomechanisms. ASME Journal of Dynamic Systems, Measurement and Control. 1990, 112:225–232
36. S.S. Yeh, P.L. Hsu. Theory and applications of the robust cross-coupled control design. ASME Journal of Dynamic Systems, Measurement and Control. 1999, 121:524–530
37. Y.T. Shin, C.S. Chen, A.C. Lee. A novel cross-coupling control design for bi-axis motion. International Journal of Machine Tools and Manufacture. 2002,42 (14):1539–1548
38. C.S. Chen, Y.H. Fan, S.P. Tseng. Position command shaping control in a retrotted milling machine, International Journal of Machine Tools and Manufacture. 2006,46 (3-4) :293–303
39. M.Y. Cheng, C.C. Lee. Motion controller design for contour following tasks based on real-time contour error estimation. IEEE Transactions on Industrial Electronics. 2007, 54 (3): 1686–1695
40. J.H. Chin and T.C. Lin. Cross-coupled precompensation method for the contouring accuracy of computer numerically controlled machine tools. International Journal of Machine Tools and Manufacture. 1997, 37(7):947–967
41. J.H. Chin, Y.M. Cheng, J.H. Lin. Improving contour accuracy by fuzzy-logic en-hanced cross-coupled precompensation method. Robotics and Computer-Integrated Manufacturing. 2004, 20(1): 65–76
42. K. L. Barton and A. G. Alleyne. A cross–coupled iterative learning control design for precision motion control. IEEE Transactions on control system technology. 2008, 16(6):1218-1231
43. S.K. Jeonga and S.S. You. Precise position synchronous control of multi-axis servo system. Mechatronics. 2008, 18:129-140
44. S. Jee and Y. Koren. Adaptive fuzzy logic controller for feed drives of a CNC machine tool. Mechatronics. 2004, 14:299-326
45. K. H. Su and M. Y. Cheng. Contouring accuracy improvement using cross-coupled control and position error compensator. International Journal of Machine Tools & Manufacture. 2008, 48:1444– 1453
46. O. Masory. Improving contouring accuracy of NC/CNC systems with additional velocity feedforward loop. ASME Journal of Engineering for Industry. 1986, 108:227–230
47. Y. Koren, C.C. Lo, Shpitalni M. CNC interpolators: Algorithms and analysis. ASME Manufacture Science and Engineering. 1993,64:83–92
48. L. Piegl. On NURBS: a survey. IEEE Computer Graphics & Application. 1991,11 (1): 55–71
49. F.Z. Shi. CAD and NURBS. High-school education publisher, 2001:211~245.
50. G.Q. Liu, Q.D. Guo. Model-based Disturbance Attenuation for Linear Motor Servo System. Power Electronics and Motion Control Conference. 2006, 2:1~3