Abstract
As the traditional cross-coupling control method cannot meet the requirements for tracking accuracy and contour control accuracy in large curvature positions, an integrated control strategy of cross-coupling contour error compensation based on chord error constraint, which consists of a cross-coupling controller and an improved position error compensator, is proposed. To reduce the contour error, a PI-type cross-coupling controller is designed, with its stability being analyzed by using the contour error transfer function. Moreover, a feed rate regulator based on the chord error constraint is proposed, which performs speed planning with the maximum feed rate allowed by the large curvature position as the constraint condition, so as to meet the requirements of large curvature positions for the chord error. Besides, an improved position error compensation method is further presented by combining the feed rate regulator with the position error compensator, which improves the tracking accuracy via the advance compensation of tracking error. The biaxial experimental results of non-uniform rational Bsplines curves indicate that the proposed integrated control strategy can significantly improve the tracking and contour control accuracy in biaxial contour following tasks.
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References
Koren Y. Cross-coupled biaxial computer control for manufacturing systems. Journal of Dynamic Systems, Measurement, and Control, 1980, 102(4): 265–272
Koren Y, Lo C C. Variable-gain cross-coupling controller for contouring. CIRP Annals, 1991, 40(1): 371–374
Zhao H, Zhu L M, Ding H. Cross-coupled controller based on highprecision contouring error estimation. Journal of Mechanical Engineering, 2014, 50(3): 158–164 (in Chinese)
Wu J, Liu C, Xiong Z, et al. Precise contour following for biaxial systems via an A-type iterative learning cross-coupled control algorithm. International Journal of Machine Tools and Manufacture, 2015, 93: 10–18
Su K H, Cheng M Y. Contouring accuracy improvement using cross-coupled control and position error compensator. International Journal of Machine Tools and Manufacture, 2008, 48(12–13): 1444–1453
Yang J, Li Z. A novel contour error estimation for position loopbased cross-coupled control. IEEE/ASME Transactions on Mechatronics, 2011, 16(4): 643–655
Shih Y T, Chen C S, Lee A C. A novel cross-coupling control design for bi-axis motion. International Journal of Machine Tools and Manufacture, 2002, 42(14): 1539–1548
Chen H R, Cheng M Y, Wu C H, et al. Real time parameter based contour error estimation algorithms for free form contour following. International Journal of Machine Tools and Manufacture, 2016, 102: 1–8
Yan M T, Lee M H, Yen P L. Theory and application of a combined self-tuning adaptive control and cross-coupling control in a retrofit milling machine. Mechatronics, 2005, 15(2): 193–211
Chen W, Wang D, Geng Q, et al. Robust adaptive cross-coupling position control of biaxial motion system. Science China. Technological Sciences, 2016, 59(4): 680–688
Srinivasan K, Kulkarni P K. Cross-coupled control of biaxial feed drive servomechanisms. Journal of Dynamic Systems, Measurement, and Control, 1990, 112(2): 225–232
Ouyang P R, Dam T, Pano V. Cross-coupled PID control in position domain for contour tracking. Robotica, 2015, 33(6): 1351–1374
Chen C S, Chen L Y. Cross-coupling position command shaping control in a multi-axis motion system. Mechatronics, 2011, 21(3): 625–632
Sun W, Zhang Y, Huang Y, et al. Transient-performance-guaranteed robust adaptive control and its application to precision motion control systems. IEEE Transactions on Industrial Electronics, 2016, 63(10): 6510–6518
El Khalick M A, Uchiyama N. Discrete-time model predictive contouring control for biaxial feed drive systems and experimental verification. Mechatronics, 2011, 21(6): 918–926
Wu J, Han Y, Xiong Z, et al. Servo performance improvement through iterative tuning feedforward controller with disturbance compensator. International Journal of Machine Tools and Manufacture, 2017, 117: 1–10
Cheng M Y, Su K H, Wang S F. Contour error reduction for freeform contour following tasks of biaxial motion control systems. Robotics and Computer-Integrated Manufacturing, 2009, 25(2): 323–333
Chen C S, Fan Y H, Tseng S P. Position command shaping control in a retrofitted milling machine. International Journal of Machine Tools and Manufacture, 2006, 46(3–4): 293–303
Moghadam H Z, Landers R G, Balakrishnan S N. Hierarchical optimal contour control of motion systems. Mechatronics, 2014, 24(2): 98–107
Tang L, Landers R G. Predictive contour control with adaptive feed rate. IEEE/ASME Transactions on Mechatronics, 2012, 17(14): 669–679
Rahaman M, Seethaler R, Yellowley I. A new approach to contour error control in high speed machining. International Journal of Machine Tools and Manufacture, 2015, 88: 42–50
Barton K L, Alleyne A G. A cross-coupled iterative learning control design for precision motion control. IEEE Transactions on Control Systems Technology, 2008, 16(6): 1218–1231
Tsai M S, Yen C L, Yau H T. Iterative learning control based on a hybrid tracking and contour error algorithm. In: Proceedings of 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics. Singapore: IEEE, 2009, 650–655
Song D N, Zhong Y G, Ma J W. Third-order contour-error estimation for arbitrary free-form paths in contour-following tasks. Precision Engineering, 2019, 60: 85–92
Yang J, Ding H, Zhao H, et al. A generalized on-line estimation and control of five-axis contouring errors of CNC machine tools. International Journal of Machine Tools and Manufacture, 2015, 88: 9–23
Yang J, Ding H, Zhao H, et al. A generalized online estimation algorithm of multi-axis contouring errors for CNC machine tools with rotary axes. International Journal of Advanced Manufacturing Technology, 2016, 84(5–8): 1239–1251
Cheng M Y, Tsai M C, Kuo J C. Real-time NURBS command generators for CNC servo controllers. International Journal of Machine Tools and Manufacture, 2002, 42(7): 801–813
Yeh S S, Hsu P L. Theory and applications of the robust crosscoupled control design. In: Proceedings of the 1997 American Control Conference. Albuquerque: IEEE, 1997
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This work was supported by the National Science and Technology Major Project of China (Grant No. 2015ZX04005006), and the Science and Technology Major Project of Zhongshan City, China (Grant Nos. 2016F2FC0006 and 2018A10018).
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Zhang, T., Wu, C. & Zou, Y. Chord error constraint based integrated control strategy for contour error compensation. Front. Mech. Eng. 15, 645–658 (2020). https://doi.org/10.1007/s11465-020-0601-7
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DOI: https://doi.org/10.1007/s11465-020-0601-7