Skip to main content
SpringerLink
Log in

Tangential velocity tracking-based task coordinate frame approach for contouring control of biaxial motion systems

  • Original Article
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

This paper focuses on solving the contour performance reduction problem caused by inaccurate contour error estimations. We will show that the task coordinate frame (TCF) strategy for contouring control is conventionally designed based on the timed trajectory tracking scheme, and the large estimation deviation of the contour error may exhibit due to the inevitable tangential position tracking error. To address the problem, this paper proposes a novel tangential velocity tracking (TVT)-based contouring control framework for biaxial motion systems, where the contour-following task is decoupled in the tangential and normal directions of the reference contour, and the control objective is to track the desired tangential velocity commands at the foot point rather than the time-stamped position commands. It has the advantage that nearly perfect contour error estimation accuracy can be obtained by calculating the normal position tracking error. To validate the feasibility and effectiveness of the proposed contouring control framework, a TVT-based TCF approach is further developed in a systematic way. The TVT-based TCF method realizes controlling the tangential velocity tracking error and the contour error in a separate and independent way. Experimental results show that the proposed TVT-based TCF method can yield much better contouring performance than the traditional TCF method due to accurate contour error estimations.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

Data availability

Not applicable.

Code availability

Not applicable.

References

  1. Jiang YK, Chen JH, Zhou HC, Yang JZ, Hu PC, Wang JX (2022) Contour error modeling and compensation of CNC machining based on deep learning and reinforcement learning. Int J Adv Manuf Technol 118(1–2):551–570. https://doi.org/10.1007/s00170-021-07895-6

    Article  Google Scholar 

  2. Lyu D, Liu Q, Liu H, Zhao WH (2020) Dynamic error of CNC machine tools: a state-of-the-art review. Int J Adv Manuf Technol 106(5–6):1869–1891. https://doi.org/10.1007/s00170-019-04732-9

    Article  Google Scholar 

  3. Kamalzadeh A, Erkorkmaz K (2007) Accurate tracking controller design for high-speed drives. Int J Mach Tools Manuf 47(9):1393–1400. https://doi.org/10.1016/j.ijmachtools.2006.08.027

    Article  Google Scholar 

  4. 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 

  5. Dai LY, Li X, Zhu Y, Zhang M (2021) Quantitative tracking error analysis and feedforward compensation under different model-based feedforward controllers in different control architectures. IEEE Trans Industr Electron 68(1):381–390. https://doi.org/10.1109/tie.2019.2960717

    Article  Google Scholar 

  6. Yang JZ, Li ZX (2011) A novel contour error estimation for position loop-based cross-coupled control. IEEE-ASME Trans Mechatronics 16(4):643–655. https://doi.org/10.1109/TMECH.2010.2048718

    Article  Google Scholar 

  7. Poo A, Bollinger JG, Younkin GW (1972) Dynamic errors in type 1 contouring systems. IEEE Transactions on Industry Applications IA-8 (4):477–484. https://doi.org/10.1109/TIA.1972.349839

  8. 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 

  9. Koren Y (1980) Cross-coupled biaxial computer control for manufacturing systems. J Dyn Syst Meas Contr 102(4):265–272. https://doi.org/10.1115/1.3149612

    Article  MATH  Google Scholar 

  10. Yeh SS, Hsu PL (2002) Estimation of the contouring error vector for the cross-coupled control design. IEEE-ASME Trans Mechatronics 7(1):44–51. https://doi.org/10.1109/3516.990886

    Article  Google Scholar 

  11. Cheng MY, Lee CC (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 

  12. Wang Z, Hu CX, Zhu Y (2022) Accelerated iteration algorithm based contouring error estimation for multiaxis motion control. IEEE-ASME Trans Mechatronics 27(1):452–462. https://doi.org/10.1109/tmech.2021.3066188

    Article  Google Scholar 

  13. Yang M, Yang JX, Zhu LM, Yu X (2020) A novel curvature circle iterative algorithm for contour error control of multi-axis CNC machine tools. Precision Eng-J Int Soc Precision Eng Nanotechnol 65:23–31. https://doi.org/10.1016/j.precisioneng.2020.05.005

    Article  Google Scholar 

  14. El Khalick A, Uchiyama N (2011) Contouring controller design based on iterative contour error estimation for three-dimensional machining. Robotics Comput-Integr Manuf 27(4):802–807. https://doi.org/10.1016/j.rcim.2011.01.001

    Article  Google Scholar 

  15. Liu Z, Dong JC, Wang TY, Ren CZ, Guo JX (2020) Real-time exact contour error calculation of NURBS tool path for contour control. Int J Adv Manuf Technol 108(9–10):2803–2821. https://doi.org/10.1007/s00170-020-05525-1

    Article  Google Scholar 

  16. Ghaffari A, Ulsoy AG (2016) Dynamic contour error estimation and feedback modification for high-precision contouring. IEEE-ASME Trans Mechatronics 21(3):1732–1741. https://doi.org/10.1109/TMECH.2015.2494518

    Article  Google Scholar 

  17. Wang Z, Hu CX, Zhu Y, He SQ, Zhang M, Mu HH (2018) Newton-ILC contouring error estimation and coordinated motion control for precision multiaxis systems with comparative experiments. IEEE Trans Industr Electron 65(2):1470–1480. https://doi.org/10.1109/TIE.2017.2733455

    Article  Google Scholar 

  18. Hu CX, Wang Z, Zhu Y, Zhang M (2018) Accurate three-dimensional contouring error estimation and compensation scheme with zero-phase filter. Int J Mach Tools Manuf 128:33–40. https://doi.org/10.1016/j.ijmachtools.2018.01.001

    Article  Google Scholar 

  19. Jia ZY, Song DN, Ma JW, Zhao XX, Su WW (2017) Adaptive estimation and nonlinear variable gain compensation of the contouring error for precise parametric curve following. Sci China-Technol Sci 60(10):1494-+. https://doi.org/10.1007/s11431-017-9042-x

  20. Shi R, Lou YJ (2019) Three-dimensional contouring control: a task polar coordinate frame approach. IEEE Access 7:63626–63637. https://doi.org/10.1109/ACCESS.2019.2916911

    Article  Google Scholar 

  21. Chiu GTC, Tomizuka M (2001) Contouring control of machine tool feed drive systems: A task coordinate frame approach. IEEE Trans Control Syst Technol 9(1):130–139. https://doi.org/10.1109/87.896754

    Article  Google Scholar 

  22. Lou YJ, Meng H, Yang JZ, Li ZX, Gao J, Chen X (2014) Task polar coordinate frame-based contouring control of biaxial systems. IEEE Trans Industr Electron 61(7):3490–3501. https://doi.org/10.1109/TIE.2013.2282609

    Article  Google Scholar 

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

    Article  Google Scholar 

  24. Yao B, Hu CX, Wang QF (2012) An orthogonal global task coordinate frame for contouring control of biaxial systems. IEEE-ASME Trans Mechatronics 17(4):622–634. https://doi.org/10.1109/TMECH.2011.2111377

    Article  Google Scholar 

  25. Shi R, Lou YJ, Zhang X, Li JG (2018) A novel task coordinate frame reduced-dimension 3-D contouring control. IEEE Trans Autom Sci Eng 15(4):1852–1863. https://doi.org/10.1109/TASE.2018.2819420

    Article  Google Scholar 

  26. Erkorkmaz K, Altintas Y (2001) High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation. Int J Machine Tools Manuf 41(9):1323–1345. https://doi.org/10.1016/S0890-6955(01)00002-5

    Article  Google Scholar 

  27. Yeung C-H, Altintas Y, Erkorkmaz K (2006) Virtual CNC system. Part I. System architecture. Int J Machine Tools Manuf 46(10):1107–1123. https://doi.org/10.1016/j.ijmachtools.2005.08.002

    Article  Google Scholar 

  28. Wan M, Xiao QB, Liu Y, Zhang WH (2020) A new decoupled tangential contouring control scheme for multi-dimensional motion. Mechanism Machine Theory 151.https://doi.org/10.1016/j.mechmachtheory.2020.103944

  29. Kim S (2019) Moment of inertia and friction torque coefficient identification in a servo drive system. IEEE Trans Industr Electron 66(1):60–70. https://doi.org/10.1109/TIE.2018.2826456

    Article  Google Scholar 

  30. 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 

Download references

Funding

This work was supported by the National Natural Science Foundation of China (grant numbers 51605328 and 51975402).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Tianjin University, Jinnan District, No.135 YaGuan Road, Tianjin, 300354, People’s Republic of China

    Runji Ke, Taiyong Wang, Jingchuan Dong & Libo Cao

  2. Renai College, Tianjin University, Tianjin, 301636, People’s Republic of China

    Taiyong Wang

Authors
  1. Runji Ke
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Taiyong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jingchuan Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Libo Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Runji Ke: conceptualization, software, validation, formal analysis, data curation, writing — original draft, and writing — review and editing. Taiyong Wang: conceptualization, funding acquisition, supervision, and resources. Jingchuan Dong: conceptualization, funding acquisition, supervision, and resources. Libo Cao: methodology, investigation, review, and data curation.

Corresponding author

Correspondence to Jingchuan Dong.

Ethics declarations

Ethics approval

ApprovaL.

Consent to participate

ConsenT.

Consent for publication

ConsenT.

Conflict of interest

The authors declare 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

Ke, R., Wang, T., Dong, J. et al. Tangential velocity tracking-based task coordinate frame approach for contouring control of biaxial motion systems. Int J Adv Manuf Technol 124, 3489–3504 (2023). https://doi.org/10.1007/s00170-022-10744-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-022-10744-9

Keywords

Search

Navigation