Skip to main content
Log in

Research on a novel integrated control strategy for contour error compensation of biaxial CNC machining

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

In the applications of multi-axis computer-numerical-control (CNC) precision machining, one of the important issues in the multi-axis contour following task is to reduce the contour error in the machining process. A popular method to solve this problem is the cross-coupling control (CCC). As the traditional CCC method cannot meet the requirements for tracking accuracy and contour control accuracy for large curvature positions, a novel integrated control strategy of cross-coupling contour error compensation, which consists of an improved real-time contour error estimation algorithm based on arc length parameters, an improved position error compensator (PEC) and a single neuron cross-coupling controller, is proposed. To improve the accuracy of contour error estimation for large curvature trajectories, an improved real-time estimation algorithm of contour error based on arc length parameters is proposed. The method first finds the nearest interpolation point by backtracking method and calculates the backward reference point by using the method based on arc length parameters. Then, the obtained backward reference point is used as the desired command point by arc approximation method to find the estimated value of contour error. Moreover, a single-neuron adaptive cross-coupling controller is designed, which continuously adjusts the weights through a single-neuron learning algorithm to reach the effect of improving the control accuracy. In addition, an improved PEC method is further presented, which improves the tracking accuracy by compensating the tracking error in advance. The feasibility of the proposed integrated control strategy is verified with several non-uniform rational B-spline (NURBS) parametric curve contour following experiments. Moreover, experimental results indicate that the proposed integrated control strategy can significantly improve the tracking and contour control accuracy of biaxial contour following tasks compared with None CCC method and CCC method and has better contour control performance in large curvature positions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Data availability

The authors have no financial or proprietary interests in any data and material discussed in this article.

Code availability

The authors have no financial or proprietary interests in any code discussed in this article.

References 

  1. Cheng MY, Su KH, Wang SF (2007) Motion controller design for contour-following tasks based on real-time contour error estimation. IEEE Trans Industr Electron 54(3):1686–1695. https://doi.org/10.1109/TIE.2007.894691

    Article  Google Scholar 

  2. Koren Y (1980) Cross-coupling biaxial computer control for manufacturing systems. ASME J Dyn Sys Meas Control 102(4):265–272. https://doi.org/10.1115/1.3149612

    Article  Google Scholar 

  3. Koren Y, Lo CC (1991) Variable-gain cross-coupling controller for contouring. CIRP Ann 40(1):371–374. https://doi.org/10.1016/S0007-8506(07)62009-5

    Article  Google Scholar 

  4. Zhang T, Wu CC, He YW (2022) Zou YB & Liao CL (2022) Gain parameters optimization strategy of cross-coupling controller based on deep reinforcement learning. Eng Optim 54(5):727–742. https://doi.org/10.1080/0305215X.2021.1897801

    Article  MathSciNet  Google Scholar 

  5. Chen SL, Liu HL, Ting SC (2002) Contouring control of biaxial systems based on polar coordinates. IEEE/ASME Trans Mechatron 7(3):329–345. https://doi.org/10.1109/TMECH.2002.802723

    Article  Google Scholar 

  6. Yang J, Li ZA (2010) novel contour error estimation for position loop-based cross-coupled control. IEEE/ASME Trans Mech 16(4):643–655. https://doi.org/10.1109/TMECH.2010.2048718

    Article  Google Scholar 

  7. Shih YT, Chen CS, Lee AC (2002) A novel cross-coupling control design for bi-axis motion. Int J Mach Tools Manuf 42(14):1539–1548. https://doi.org/10.1016/S0890-6955(02)00109-8

    Article  Google Scholar 

  8. Zhao GY, An HJ, Zhao QZ (2013) Contour error coupled-control strategy based on line interpolation and curve interpolation. J Comput 8(6):1512–1519. https://doi.org/10.4304/jcp.8.6.1512-1519

    Article  Google Scholar 

  9. Xu HN (2017) Research on contour control for feeding servo system of CNC machine tools. Tianjin University, Tianjin (In Chinese)

    Google Scholar 

  10. Li B, Wang TY, Wang P (2021) Cross-coupling control based on real-time double circle contour error estimation for biaxial motion system. Measure Control 54(3–4):324–335. https://doi.org/10.1177/0020294021993830

    Article  Google Scholar 

  11. Chen HR, Cheng MY, Wu CH, Su KH (2016) Real time parameter based contour error estimation algorithms for free form contour following. Int J Mach Tools Manuf 102:1–8. https://doi.org/10.1016/j.ijmachtools.2015.11.009

    Article  Google Scholar 

  12. Yan MT, Lee MH, Yen PL (2005) Theory and application of a combined self-tuning adaptive control and cross-coupling control in a retrofit milling machine. Mechatronics 15(2):193–211. https://doi.org/10.1016/j.mechatronics.2004.07.011

    Article  Google Scholar 

  13. Chen W, Wang DD, Geng Q, Xia CL (2016) Robust adaptive cross-coupling position control of biaxial motion system. SCI CHINA Technol Sci 59:680–688. https://doi.org/10.1007/s11431-015-5988-8

    Article  Google Scholar 

  14. Chen CS, Chen LY (2011) Cross-coupling position command shaping control in a multi-axis motion system. Mechatronics 21(3):625–632. https://doi.org/10.1016/j.mechatronics.2011.01.004

    Article  Google Scholar 

  15. Sun D (2003) (2003) Position synchronization of multiple motion axes with adaptive coupling control. Automatica 39(6):997–1005. https://doi.org/10.1016/S0005-1098(03)00037-2

    Article  MathSciNet  Google Scholar 

  16. Sun D (2009) Tong MC (2009) A synchronization approach for the minimization of contouring errors of CNC machine tools. IEEE Trans Autom Sci Eng 6(4):720–729. https://doi.org/10.1109/TASE.2009.2021970

    Article  Google Scholar 

  17. Su KH, Cheng MY (2008) Contouring accuracy improvement using cross-coupling control and position error compensator. Int J Mach Tools Manuf 48(12–13):1444–1453. https://doi.org/10.1016/j.ijmachtools.2008.04.008

    Article  Google Scholar 

  18. Cheng MY, Su KH, Wang SF (2009) Contour error reduction for free-form contour following tasks of biaxial motion control systems. Robotics and Computer-Integrated Manufacturing 25(2):323–333. https://doi.org/10.1016/j.rcim.2008.01.003

    Article  Google Scholar 

  19. Moghadam HZ, Landers RG (2014) Balakrishnan SN (2014) Hierarchical optimal contour control of motion systems. Mechatronics 24(2):98–107. https://doi.org/10.1016/j.mechatronics.2013.12.007

    Article  Google Scholar 

  20. Zhang T, Wu CC, Zou YB (2020) Chord error constraint based integrated control strategy for contour error compensation. Front Mech Eng 15:645–658. https://doi.org/10.1007/s11465-020-0601-7

    Article  Google Scholar 

  21. Sun WC, Zhang YF, Huang YP, Gao HJ, Kaynak O (2016) Transient-performance-guaranteed robust adaptive control and its application to precision motion control systems. IEEE Trans Industr Electron 63(10):6510–6518. https://doi.org/10.1109/TIE.2016.2542787

    Article  Google Scholar 

  22. El Khalick M, AUchiyama N, (2011) Discrete-time model predictive contouring control for biaxial feed drive systems and experimental verification. Mechatronics 21(6):918–926. https://doi.org/10.1016/j.mechatronics.2010.11.011

    Article  Google Scholar 

  23. Wu JH, Han Y, Xiong ZH, Ding H (2017) Servo performance improvement through iterative tuning feedforward controller with disturbance compensator. Int J Mach Tools Manuf 117:1–10. https://doi.org/10.1016/j.ijmachtools.2017.02.002

    Article  Google Scholar 

  24. Chen CS, Fan YH, Tseng SP (2006) Position command shaping control in a retrofitted milling machine. Int J Mach Tools Manuf 46(3–4):293–303. https://doi.org/10.1016/j.ijmachtools.2005.05.018

    Article  Google Scholar 

  25. Tang L, Landers RG (2012) Predictive contour control with adaptive feed rate. IEEE/ASME Trans Mechatron 17(4):669–679. https://doi.org/10.1109/TMECH.2011.2119324

    Article  Google Scholar 

  26. Barton KL, Alleyne AG (2008) A cross-coupling iterative learning control design for precision motion control. IEEE Trans Control Syst Technol 16(6):1218–1231. https://doi.org/10.1109/TCST.2008.919433

    Article  Google Scholar 

  27. Yu YZ, Lin N, Chi RG (2022) Data-driven adaptive tuning of iterative learning control. Trans Inst Meas Control 44(15):3016–3027. https://doi.org/10.1177/01423312221099381

    Article  Google Scholar 

  28. Rahaman M, Seethaler R, Yellowley I (2015) A new approach to contour error control in high speed machining. Int J Mach Tools Manuf 88:42–50. https://doi.org/10.1016/j.ijmachtools.2014.09.002

    Article  Google Scholar 

  29. Cheng MY, Tsai MC, Kuo JC (2002) Real-time NURBS command generators for CNC servo controllers. Int J Mach Tools Manuf 42(7):801–813. https://doi.org/10.1016/S0890-6955(02)00015-9

    Article  Google Scholar 

  30. Song DN, Zhong YG, Ma JW (2019) Third-order contour-error estimation for arbitrary free-form paths in contour-following tasks. Precis Eng 60:85–92. https://doi.org/10.1016/j.precisioneng.2019.07.009

    Article  Google Scholar 

  31. Yang J, Altintas Y (2015) A generalized on-line estimation and control of five-axis contouring errors of CNC machine tools. Int J Machine Tools Manufact 88:9–23. https://doi.org/10.1016/j.ijmachtools.2014.08.004

  32. Yang JX, Ding H, Zhao H, Yan SJ (2016) A generalized online estimation algorithm of multi-axis contouring errors for CNC machine tools with rotary axes. Int J Adv Manuf Technol 84(5–8):1239–1251. https://doi.org/10.1007/s00170-015-7783-x

    Article  Google Scholar 

Download references

Funding

This work was supported by the Program of Brought in Urgently-Needed Talents for Principally Supported Regions of Shandong Province and the Taishan Industrial Experts Program, P. R. China. Authors Jun Zhao and Yongliang Lu have received research support from the Shandong Deed Precision Machine Tool Co., Ltd.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jun Zhao.

Ethics declarations

Consent to participate

All authors consent to participate in the study.

Consent for publication

All authors consent to the publication of this article.

Competing interests

The authors declarse no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lu, Y., Zhao, J., Zhang, Z. et al. Research on a novel integrated control strategy for contour error compensation of biaxial CNC machining. Int J Adv Manuf Technol 130, 385–402 (2024). https://doi.org/10.1007/s00170-023-12645-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-023-12645-x

Keywords

Navigation