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Adaptive nonlinear contour coupling control for a machine tool system

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Abstract

The quality of products from a machine tool system is largely determined by the tolerances maintained, which is a function of how well the desired contour is tracked. To mitigate contour errors in a three-axis machine tool feed drive system, the control development in this paper is based on an error system that is transformed into tangential, normal, and binormal components to the desired contour (i.e., a cross-coupling controller (CCC)). Unlike previous CCCs, the controller developed in this paper does not assume exact knowledge of the inertia and friction matrices. Specifically, an adaptive estimate is developed to compensate for uncertain friction and inertial parameters. Lyapunov-based methods are used to craft the adaptive estimate and to prove global asymptotic contour tracking. Experimental results of the proposed controller on the xy-axes of the high speed milling machine showed improvement of the contouring accuracy compared to proportional-derivative controller and a benchmark CCC.

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References

  1. Tomizuka M (1987) Zero phase error tracking algorithm for digital control. J Dyn Syst Meas Control 109:65–68

    Article  MATH  Google Scholar 

  2. Weck M, Ye G (1990) Sharp corner tracking using the IKF control strategy. Ann CIRP 39(1):437–441

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  4. Koren Y, Lo CC (1991) Variable-gain cross-coupling controller for contouring. Ann CIRP 104:371–374

    Article  Google Scholar 

  5. Yeh S-S, Hus P-L (1999) Analysis and design of the integrated controller for precise motion systems. IEEE Trans Control Syst Technol 7(6):706–717

    Article  Google Scholar 

  6. Yeh S-S, Hus P-L (2003) Analysis and design of integrated control for multi-axis motion systems. IEEE Trans Control Syst Technol 11(3):375–382

    Article  Google Scholar 

  7. Yeh S-S, Hus P-L (2002) Estimation of the contouring error vector for the cross-coupled control design. IEEE Trans Mechatron 7(1):44–51

    Article  Google Scholar 

  8. Kulkarni PK, Srinivasan K (1989) Optimal contouring control of multi-axial drive servomechanisms. ASME Trans J Eng Ind 111:140–148

    Article  Google Scholar 

  9. Srinivasan K, Kulkarni PK (1990) Cross-coupled control of biaxial feed drive servomechanisms. ASME Trans J Dyn Syst Meas Control 112(2):225–232

    Article  Google Scholar 

  10. Chen S-L, Liu H-L, Ting SC (2002) Contouring control of biaxial systems based on polar coordinates. IEEE/ASME Trans Mechatron 7(3):329–345

    Article  Google Scholar 

  11. Yeh Z-M, Tarng YS, Lin YS (1997) Cross-coupled fuzzy logic control for multiaxis machine tools. Mechatronics 7(8):663–681

    Article  Google Scholar 

  12. Tarng YS, Chuang HY, Hus WT (1999) Intelligent cross-coupled fuzzy federate controller design for CNC machine tools based on genetic algorithms. Int J Mach Tool Manuf 39:1673–1692

    Article  Google Scholar 

  13. Chuang HY, Liu CH (1991) Cross-coupled adaptive feedrate control for multiaxis machine tools. ASME Trans J Dyn Syst Meas Control 113:451–457

    Article  Google Scholar 

  14. Tomizuka M, Hu J, Chiu T-C, Kamano T (1992) Synchronization of two motion control axes under adaptive feedforward control. ASME Trans J Dyn Syst Meas Control 114:196–203

    Article  MATH  Google Scholar 

  15. Chiu GT-C, 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 

  16. Chiu GT-C, Yao B (1997) Adaptive robust control tracking of machine tool feed drive system—a task coordinate frame approach. In: Proc. of the American control conf., Albuquerque, New Mexico, pp 2731–2735

    Google Scholar 

  17. Xu L, Yao B (2000) Coordinated adaptive robust contour tracking of linear-motor-driven tables in task space. In: Proc. of the 39th IEEE conf. on decision and control, Sydney, Australia, pp 2430–2435

  18. Lewis F, Abdallah C, Dawson D (1993) Control of robot manipulators. MacMillan, New York

    Google Scholar 

  19. Frenet F (1847) Sur les courbes à double courbure, Thèse, Toulouse. Abstract in J de Math, vol 17 (1852)

  20. Kreyszig E (1991) Formulae of Frenet. In: Differential geometry. Dover, New York, pp 40–43

    Google Scholar 

  21. Serret JA (1851) Sur quelques formules relatives à la théorie des courbes à double courbure. J de Math 16

  22. Gray A (1997) The fundamental theorem of space curves, modern differential geometry of curves and surfaces with mathematica, 2nd edn. CRC, Boca Raton, pp 219–222

    Google Scholar 

  23. Lee J (2005) Design of controllers for improving contour accuracy in a high-speed milling machine. Ph.D. dissertation, Univ. Florida

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Correspondence to Jinho Lee.

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Lee, J., Dixon, W.E. & Ziegert, J.C. Adaptive nonlinear contour coupling control for a machine tool system. Int J Adv Manuf Technol 61, 1057–1065 (2012). https://doi.org/10.1007/s00170-011-3760-1

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  • DOI: https://doi.org/10.1007/s00170-011-3760-1

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