Chord error constraint based integrated control strategy for contour error compensation

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 B-splines curves indicate that the proposed integrated control strategy can significantly improve the tracking and contour control accuracy in biaxial contour following tasks.

Keywords

cross-coupling controller / contour error / tracking error / position error compensator / feed rate regulator

References

[1] Koren Y. Cross-coupled biaxial computer control for manufacturing systems. Journal of Dynamic Systems, Measurement, and Control, 1980, 102(4): 265–272

[2] Koren Y, Lo C C. Variable-gain cross-coupling controller for contouring. CIRP Annals, 1991, 40(1): 371–374

[3] Zhao H, Zhu L M, Ding H. Cross-coupled controller based on high-precision contouring error estimation. Journal of Mechanical Engineering, 2014, 50(3): 158–164 (in Chinese)

[4] Wu J, Liu C, Xiong Z, . 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

[5] 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

[6] Yang J, Li Z.A novel contour error estimation for position loop-based cross-coupled control. IEEE/ASME Transactions on Mechatronics, 2011, 16(4): 643–655

[7] 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

[8] Chen H R, Cheng M Y, Wu C H, . Real time parameter based contour error estimation algorithms for free form contour following. International Journal of Machine Tools and Manufacture, 2016, 102: 1–8

[9] 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

[10] Chen W, Wang D, Geng Q, . Robust adaptive cross-coupling position control of biaxial motion system. Science China. Technological Sciences, 2016, 59(4): 680–688

[11] 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

[12] Ouyang P R, Dam T, Pano V. Cross-coupled PID control in position domain for contour tracking. Robotica, 2015, 33(6): 1351–1374

[13] Chen C S, Chen L Y. Cross-coupling position command shaping control in a multi-axis motion system. Mechatronics, 2011, 21(3): 625–632

[14] Sun W, Zhang Y, Huang Y, . Transient-performance-guaranteed robust adaptive control and its application to precision motion control systems. IEEE Transactions on Industrial Electronics, 2016, 63(10): 6510–6518

[15] 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

[16] Wu J, Han Y, Xiong Z, . Servo performance improvement through iterative tuning feedforward controller with disturbance compensator. International Journal of Machine Tools and Manufacture, 2017, 117: 1–10

[17] Cheng M Y, Su K H, Wang S F. Contour error reduction for free-form contour following tasks of biaxial motion control systems. Robotics and Computer-integrated Manufacturing, 2009, 25(2): 323–333

[18] 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

[19] Moghadam H Z, Landers R G, Balakrishnan S N. Hierarchical optimal contour control of motion systems. Mechatronics, 2014, 24(2): 98–107

[20] Tang L, Landers R G. Predictive contour control with adaptive feed rate. IEEE/ASME Transactions on Mechatronics, 2012, 17(14): 669–679

[21] 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

[22] 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

[23] 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

[24] 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

[25] Yang J, Ding H, Zhao H, . 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

[26] Yang J, Ding H, Zhao H, . 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

[27] 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

[28] Yeh S S, Hsu P L. Theory and applications of the robust cross-coupled control design. In: Proceedings of the 1997 American Control Conference. Albuquerque: IEEE, 1997

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