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Design and analysis of a modular learning based cross-coupled control algorithm for multi-axis precision positioning systems

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Abstract

Increasing demand for micro/nano-technology related equipment resulted in growing interest for precision positioning systems. In this paper a modular controller combining cross-coupled control and iterative learning control approaches to improve contour and tracking accuracy at the same time is presented. Instead of using the standard error estimation technique, a computationally efficient and modular contour error estimation technique is used. The new controller is more suitable for tracking arbitrary nonlinear contours and easier to implement to multi-axis systems. Stability and convergence analysis for the proposed controller is presented with the necessary conditions. Effectiveness of the control design is verified with simulations and experiments on a two-axis positioning system. The resulting positioning system achieves nanometer level contouring and tracking performance.

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References

  1. R. Seifabadi, S. M. Rezaei, S. S. Ghidary, and M. Zareinejad, “A teleoperation system for micro positioning with haptic feedback,” International Journal of Control, Automation and Systems, vol. 11, no. 4, pp. 768–775, Aug. 2013. [click]

    Article  Google Scholar 

  2. L. Lihua, L. Yingehun, G. Yongfeng, and S. Akira, “Design and testing of nanometer positioning system,” Journal of Dynamic Systems, Measurement and Control, vol. 132, no. 2, pp. 021011–6, 2010. [click]

    Article  Google Scholar 

  3. S. M. Raafat, R. Akmeliawati, and W. Martono, “Intelligent robust control design of a precise positioning system,” International Journal of Control, Automation and Systems, vol. 8, no. 5, pp. 1123–1132, Oct. 2010. [click]

    Article  Google Scholar 

  4. M. Tomizuka, “Zero phase error tracking algorithm for digital control,” Journal of Dynamic Systems, Measurement and Control, vol. 109, no. 1, pp. 65–68, 1987. [click]

    Article  MATH  Google Scholar 

  5. P. Hsu, Y. Houng, and S. Yeh, “Design of an optimal unknown unknown input observer for load compensation in motion systems,” Asian Journal of Control, vol. 3, no. 3, pp. 204–215, 2001. [click]

    Article  Google Scholar 

  6. L. Qing, W. Tai-yong, D. Ying-chuan, J. Yong-xiang, and L. Bo, “Applications of position controller for cnc machines based on state observer and cross-coupled controller,” Proc. of International Conference on Computer Mechatronics, Control and Electronic Engineering (CMCE), pp. 593–596, 2010. [click]

    Google Scholar 

  7. M. Tomizuka, “Friction compensator for feed drive systems consisting of ball screw and linear ball guide,” Proc. of the 35th International MATADOR Conference, pp. 311–314, 2007. [click]

    Google Scholar 

  8. L. Wang, S. Lin, and H. Zeng, “Precision contour control of XY table based on LuGre model friction compensation,” Proc. of 2nd International Conference on Intelligent Control and Information Processing (ICI-CIP), pp. 1124–1128, 2011. [click]

    Google Scholar 

  9. K. K. Tan, H. Dou, Y. Chen, and T. H. Lee, “High precision linear motor control via relay-tuning and iterative learning based on zero-phase filtering,” IEEE Transactions on Control Systems Technology, vol. 9, no. 2, pp. 244–253, 2001. [click]

    Article  Google Scholar 

  10. K. L. Barton and A. G. Alleyne, “A cross-coupled iterative learning control design for precision motion control,” IEEE Transactions on Control System Technology, vol. 16, no. 6, pp. 1218–1231, 2008. [click]

    Article  Google Scholar 

  11. G. Pipeleers and K. L. Moore, “Reduced-Order Iterative Learning Control and a Design Strategy for Optimal Performance Tradeoffs,” IEEE Transactions on Automatic Control, vol. 57, no. 9, pp. 2390–2395, Sep. 2012. [click]

    Article  MathSciNet  Google Scholar 

  12. Z. R. Novakovic, The Principle of Self Support in Control Systems Amsterdam, Elsevier, Netherlands, vol. 8, 1992. [click]

  13. H. S. Ahn, Y. Q. Chen, and K. L. Moore, “Iterative learning control: Brief summary and categorization,” IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, vol. 37,no. 6, pp. 1099–1121, 2007. [click]

    Article  Google Scholar 

  14. Y. Koren and C. C. Lo, “Variable gain cross-coupling controller for contouring,” CIRP Annals Manufacturing Technology, vol. 40, no. 1, pp. 371–374, 1991. [click]

    Article  Google Scholar 

  15. L. Tang and R. G. Landers, “Multiaxis contour control the state of the art,” IEEE Transactions on Control Systems Technology, vol. 21, no. 6, pp. 1997–2010, Nov. 2013. [click]

    Article  Google Scholar 

  16. Y. Koren, “Cross-coupled biaxial computer control for manufacturing systems,” Journal of Dynamic Systems, Measurement and Control, vol. 102, no. 4, pp. 265–272, 1980. [click]

    Article  MATH  Google Scholar 

  17. M. Naumovic and M. Stojic, “Design of the observer based cross-coupled positioning servo drives,” Proc. of the IEEE International Symposium on Industrial Electronics, ISIE’ 97, vol. 2, 1997. [click]

    Google Scholar 

  18. H. Y. Chuang and C. H. Liu, “A model referenced adaptive control strategy for improving contour accuracy of multiaxis machine tools,” Proc. of the 1990 IEEE Industry Applications Society Annual Meeting, 2, Ed., pp. 1539–1544, 1990. [click]

    Chapter  Google Scholar 

  19. K. L. Barton and A. G. Alleyne, “Cross-coupled ilc for improved precision motion control: design and implementation,” Proc. of the American Control Conference, pp. 5496–5502, 2007. [click]

    Google Scholar 

  20. H. S. Li, X. Zhou, and Y. Chen, “Iterative learning control for cross-coupled contour motion systems,” Proc. of IEEE International Conference Mechatronics and Automation,, vol. 3, pp. 1468–1472, 2005. [click]

    Google Scholar 

  21. S. S. Yeh and P. L. Hsu, “Estimation of contouring error vector for the cross-coupled control design,” IEEE/ASME Transaction on Mechatronics, vol. 7, no. 1, pp. 44–51, 2002. [click]

    Article  Google Scholar 

  22. N. Gecer-Ulu, E. Ulu, and M. Cakmakci, “Learning based cross-coupled control for multi-axis high precision positioning systems,” Proc. ASME Dynamic Systems and Control Conf. (DSCC 2012), Ft. Lauderdale, FL, Oct 2012. [click]

    Google Scholar 

  23. E. Ulu, N. Gecer Ulu, and M. Cakmakci, “Development and Validation of an Adaptive Method to Generate High-Resolution Quadrature Encoder Signals,” Journal of Dynamic Systems, Measurement, and Control, vol. 136, no. 3, May 2014. [click]

  24. K. Ogata, Modern Control Engineering, Prentice Hall, 1990.

    MATH  Google Scholar 

  25. S. S. Yeh and P. L. Hsu, “Theory and applications of the robust cross-coupled control design,” Proc. of the American Control Conference, pp. 791–795, 1997. [click]

    Google Scholar 

  26. T. Y. Doh, J. R. Ryoo, and D. E. Chang, “Robust iterative learning controller design using the performance weighting function of feedback control systems,” International Journal of Control, Automation and Systems, vol 12, no. 1, pp.63–70, 2014. [click]

    Article  Google Scholar 

Download references

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Correspondence to Melih Cakmakci.

Additional information

Recommended by Associate Editor Won-jong Kim under the direction of Editor Hyouk Ryeol Choi. This research is sponsored by Scientific and Technical Research Council of Turkey (TUBITAK) through Project No: 110M251. The authors would like to thank undergraduate students Oytun Ugurel and Ersun Sozen for their support during computer aided design and drafting of the positioning system. Authors would also like to thank Dr. Sinan Filiz for sharing his experience in precision positioning systems.

Nurcan Gecer-Ulu is a graduate student in Mechanical Engineering at Bilkent University in Ankara, Turkey. She received her B.S. degree in Mechanical Engineering from M.E.T.U Ankara in 2010. Her research areas include modeling, analysis and control of dynamic systems and smart mechatronics.

Erva Ulu is a graduate student in Mechanical Engineering at Bilkent University in Ankara, Turkey. He received his B.S. degree in Mechanical Engineering from M.E.T.U Ankara in 2010. His research areas include mechatronic design, modeling, analysis and control of dynamic systems.

Melih Cakmakci is an Assistant Professor of Mechanical Engineering at Bilkent University in Ankara, Turkey. He received his B.S. degree in Mechanical Engineering from M.E.T.U Ankara in 1997. He received his M.S. and Ph.D. in Mechanical Engineering Degrees from University of Michigan, in 1999 and 2009, respectively. His research areas include modeling, analysis and control of dynamic systems, Prior to joining Bilkent University, he was a senior engineer at the Ford Scientific Research Center. He is a member of ASME, IEEE and SAE.

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Ulu, N.G., Ulu, E. & Cakmakci, M. Design and analysis of a modular learning based cross-coupled control algorithm for multi-axis precision positioning systems. Int. J. Control Autom. Syst. 14, 272–281 (2016). https://doi.org/10.1007/s12555-014-0125-1

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