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Contour error dynamic analysis and predictive control for multi-axis motion system

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Abstract

Contour tracking accuracy is the key performance index of a multi-axis motion control system. In the previous design of the contour error feedback controller, the independent design idea of the tracking controller and contour controller of each logic axis is often adopted, which is not easy to realize the optimal control of tracking accuracy and contour accuracy. The coupling increment of each controller is inevitable in motion control compensation, which impacts the control system’s stability. Here, we propose a predictive control method for contour error. At first, through the state space model of the feed system, the system dynamics are judged to predict the contour accuracy in the future finite time domain. Besides, the linear quadratic performance index function of contour error is established, and the performance of the control objective is continuously optimized during the limited time domain with the form of rolling optimization. A closed-loop solution is obtained, which is most suitable for the current motion situation and could add to the system to realize the optimal control considering the trajectory contour and the tracking stability of each servo axis in the subsequent few sampling cycles. Finally, utilizing comparative experiments on the three-axis motion control platform, it is verified that the proposed contour predictive control strategy not only effectively reduces the tracking error but also significantly improves the contour accuracy, which is suitable for application in a complex industrial environment.

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Data availability

All data generated and analyzed during this research are included in this published article.

Code availability

Code used during the current study is available from the corresponding author on reasonable request.

References

  1. Hu L, Zha J, Zhu YS, Wei WM, Li DY, Luo M, Niu WT, Chen YL (2021) Research progresses of basic equipment manufacturing and high-grade integrated CNC machine tools. China Mech Eng 32(16):1891–1903

    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

    Article  Google Scholar 

  3. Wang XZ, Chen FX, Zhu RF, Huang XL, Sang N, Yang GL, Zhang C (2021) A review on disturbance analysis and suppression for permanent magnet linear synchronous motor. Actuators 10(4):1–27

    Article  Google Scholar 

  4. Jia ZY, Ma JW, Song DN, Wang FJ, Liu W (2018) A review of contouring-error reduction method in multi-axis CNC machining. Int J Mach Tools Manuf 125:34–54

    Article  Google Scholar 

  5. Koren Y (1980) Cross-coupled biaxial computer control for manufacturing systems. J Dyn Syst Meas Contr 102(4):265–272

    Article  MATH  Google Scholar 

  6. Koren Y, Lo ChCh (1991) Variable-gain cross-coupling controller for contouring. CIRP Ann Manuf Technol 40(1):371–374

    Article  Google Scholar 

  7. Li B, Wang TY, Wang P (2021) Cross-coupled control based on real-time Double Circle contour error estimation for biaxial motion system. Meas Control 54(3–4):324–335

    Google Scholar 

  8. Chin JH, Cheng YM, Lin JH (2004) Improving contour accuracy by fuzzy-logic enhanced cross-coupled precompensation method. Rob Comput-Integr Manuf 20(1):65–76

    Article  MathSciNet  Google Scholar 

  9. Li XF, Zhao H, Zhao X, Ding H (2016) Dual sliding mode contouring control with high accuracy contour error estimation for five-axis CNC machine tools. Int J Mach Tools Manuf 108:74–82

    Article  Google Scholar 

  10. Chen W, Wang DD, Geng Q, Xia CL (2016) Robust adaptive cross-coupling position control of biaxial motion system. Sci China-Technol Sci 59(4):680–688

    Article  Google Scholar 

  11. Yeh SS, Hsu PL (1999) Theory and applications of the robust cross-coupled control design. J Dyn Syst Meas Contr 121(3):524–530

    Article  Google Scholar 

  12. Hu CX, Wang Z, Zhu Y, Zhang M, Liu H (2016) Performance-oriented precision LARC tracking motion control of a magnetically levitated planar motor with comparative experiments. IEEE Trans Industr Electron 63(9):5763–5773

    Article  Google Scholar 

  13. 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

    Article  Google Scholar 

  14. Berners T, Epple A, Brecher C (2018) Model predictive controller for machine tool feed drives. In 2018 4th International Conference on Control, Automation and Robotics (ICCAR) Auckland, New Zealand (pp 136-140), doi: https://doi.org/10.1109/ICCAR.2018.8384658

  15. Yang JX, Zhang HT, Ding H (2017) Contouring error control of the tool center point function for five-axis machine tools based on model predictive control. Int J Adv Manuf Technol 88:2909–2919

    Article  Google Scholar 

  16. Wang YW, Zhang WA, Dong H, Yu L (2019) A GESO based MPC approach to contour error control of networked motion control system. Int J Syst Sci 50(11):2216–2225

    Article  MATH  Google Scholar 

  17. Yeh SS, Hsu PL (2002) Estimation of the contouring error vector for the cross-coupled control design. IEEE-ASME Trans Mechatron 7(1):44–51

    Article  Google Scholar 

  18. Yeh SS, Hsu PL (2003) Analysis and design of integrated control for multi-axis motion systems. IEEE Trans Control Syst Technol 11(3):375–382

    Article  Google Scholar 

  19. El KMA, Uchiyama N, Sano S (2013) Sliding mode contouring control design using nonlinear sliding surface for three-dimensional machining. Int J Mach Tools Manuf 65:8–14

    Article  Google Scholar 

  20. 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):1494–1504

    Article  Google Scholar 

  21. 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

    Article  Google Scholar 

  22. Uzunovic T, Baran EA, Golubovic E, Sabanovic A (2016) A novel hybrid contouring control method for 3-DOF robotic manipulators. Mechatronics 40:178–193

    Article  Google Scholar 

  23. Cho CN, Song YH, Kim HJ (2018) Neural network-based real time PID gain update algorithm for contour error reduction. Int J Precis Eng Manuf 19(11):1619–1625

    Article  Google Scholar 

  24. Zhang Dailin, Chen Youping, Xie Jingming(2012) Cross coupling control design for three-dimensional contouring control system based on layered modeling method. 2012 12th International Conference on Control Automation Robotics & Vision (ICARCV), Guangzhou, China (pp 1636-1641), doi:  https://doi.org/10.1109/ICARCV.2012.6485436

  25. Zhang DL, Yang JX, Chen YH, Chen YP (2015) A two-layered cross coupling control scheme for a three-dimensional motion control system. Int J Mach Tools Manuf 98:12–20

    Article  Google Scholar 

  26. 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

    Article  Google Scholar 

  27. Shi R, Lou YJ (2019) Three-dimensional contouring control: a task polar coordinate frame approach. IEEE Access 7:63626–63637

    Article  Google Scholar 

  28. Jiang JL, Li BR, Lin FY, Zhang H (2022) Ye PQ (2022) Prediction and compensation strategy of contour error in multi-axis motion system. Int J Adv Manuf Technol 119:163–175

    Article  Google Scholar 

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Funding

This work is supported by National Natural Science Foundation of China (Grant No.51875312).

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Authors and Affiliations

  1. Beijing Institute of Aerospace Control Devices, Beijing, China

    Jiali Jiang & Qingyu Dong

  2. Department of Mechanical Engineering, Tsinghua University, Beijing, China

    Bingran Li, Hui Zhang & Peiqing Ye

  3. China Astronautics Standards Institute, Beijing, China

    Shengxin Jiang

Authors
  1. Jiali Jiang
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  2. Bingran Li
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  3. Qingyu Dong
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  4. Hui Zhang
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  5. Peiqing Ye
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  6. Shengxin Jiang
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Contributions

Jiali Jiang: experiment and writing; Bingran Li: operation instruction, experiment, and reviewing; Qingyu Dong: investigation and reviewing; Hui Zhang: investigation and editing; Peiqing Ye: investigation and reviewing; Shengxin Jiang: reviewing and editing.

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Correspondence to Jiali Jiang.

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Jiang, J., Li, B., Dong, Q. et al. Contour error dynamic analysis and predictive control for multi-axis motion system. Int J Adv Manuf Technol 126, 5501–5514 (2023). https://doi.org/10.1007/s00170-023-11415-z

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  • DOI: https://doi.org/10.1007/s00170-023-11415-z

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