Paper:

# Adaptive Control for Feed Drives Considering Coupling Effects Among Multiple Axes

## Naoki Uchiyama and Kazunori Mori

Department of Mechanical Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku, Toyohashi, Aichi 441-8580, Japan

Most feed drive controller design ignores coupling effects among multiple axes. Inertia force caused by movement at one axis affects contact force between mechanical components at other axes, so friction magnitude changes at contact points, and considering this coupling effect in controller design could improve control performance. Because coupling effects are generally unknown, we propose adaptive controller design expanding on our previous design and demonstrate its effectiveness by comparative experiments with an adaptive controller that neglects coupling effects.

*Int. J. Automation Technol.*, Vol.4, No.1, pp. 45-52, 2010.

- [1] K. Srinivasan and T.-C. Tsao, “Machine Tool Feed Drives and Their Control —A Survey of the State of the Art,” Trans. of ASME, J. of Manufacturing Science and Engineering Vol.119, pp. 743-748, 1997.
- [2] R. Ramesh, M. A. Mannan, and A. N. Poo, “Tracking and Contour Error Control in CNC Servo Systems,” Int. J. of Machine Tools and Manufacture Vol.45, pp. 301-326, 2005.
- [3] Y. Koren, “Cross-Coupled Biaxial Control for Manufacturing Systems,” ASME J. of Dynamic Systems, Measurement, and Control Vol.102, pp. 265-272, 1980.
- [4] P. K. Kulkarni and K. Srinivasan, “Optimal Contouring Control of Multi-Axis Feed Drive Servomechanism,” ASME J. of Engineering for Industry Vol.111, pp. 140-148, 1989.
- [5] Y. S. Tarng, H. Y. Chuang, and W. T. Hsu, “An Optimisation Approach to the Contour Error Control of CNC Machine Tool Using Genetic Algorithms,” Int. J. of Advanced Manufacturing Technology Vol.13, pp. 359-366, 1997.
- [6] Y. S. Tarng, H. Y. Chuang, and W. T. Hsu, “Intelligent Cross-Coupled Fuzzy Feedrate Controller Design of CNC Machine Tools Based on Genetic Algorithms,” Int. J. of Machine Tools and Manufacture Vol.39, pp. 1673-1692, 1999.
- [7] G. T.-G. Chiu and M. Tomizuka, “Coordinate Position Control of Multi-Axis Mechanical Systems,” ASME J. of Dynamic Systems, Measurement, and Control Vol.120, pp. 389-393, 1998.
- [8] R. J. McNab and T.-C. Tsao, “Receding Time Horizon Linear Quadratic Optimal Control for Multi-Axis Contour Tracking Motion Control,” ASME J. of Dynamic Systems, Measurement, and Control, Vol.122, pp. 375-381, 2000.
- [9] Q. Zhong, Y. Shi, J. Mo, and S. Huang, “A Linear Cross-Coupled Control System for High-Speed Machining,” Int. J. of Advanced Manufacturing Technology Vol.19, pp. 558-563, 2002.
- [10] X. Ye, X. Chen, X. Li, and S. Huang, “A Cross-Coupled Path Precompensation Algorithm for Rapid Prototyping and Manufacturing,” Int. J. of Advanced Manufacturing Technology Vol.20, pp. 39-43, 2002.
- [11] Y.-T. Shih, C.-S. Chen, and A.-C. Lee, “A Novel Cross-Coupling Control Design for Bi-Axis Motion,” Int. J. of Machine Tools and Manufacture Vol.42, pp. 1539-1548, 2002.
- [12] Y.-M. Cheng and J.-H. Chin, “Machining Contour Errors as Ensembles of Cutting,” Feeding and Machine Tool Structure Effects, Int. J. of Machine Tools and Manufacture Vol.43, pp. 1001-1014, 2003.
- [13] C.-S. Chen, Y.-H. Fan, and S. P. Tseng, “Position Command Shaping Control in a Retrofitted Milling Machine,” Int. J. of Machine Tools and Manufacture Vol.46, pp. 293-303, 2006.
- [14] C.-C. Lo and C.-Y. Chung, “Tangential Contouring Controller for Biaxial Motion Control,” ASME J. of Dynamic Systems, Measurement, and Control Vol.121, pp. 126-129, 1999.
- [15] H.-C. Ho, J. Y. Yen, and S. S. Lu, “A Decoupled-Path Following Control Algorithm Based upon the Decomposed Trajectory Error,” Int. J. of Machine Tools and Manufacture Vol.39, pp. 1619-1630, 1999.
- [16] G. T.-C. Chiu and M. Tomizuka, “Contouring Control of Machine Tool Feed Drive Systems: a Task Coordinate Frame Approach,” IEEE Trans. on Control System Technology Vol.9, No.1, pp. 130-139, 2001.
- [17] C.-C. Peng and C.-L. Chen, “Biaxial Contouring Control with Friction Dynamics using a Contour Index Approach,” Int. J. of Machine Tools and Manufacture Vol.47, pp. 1542-1555, 2007.
- [18] N. Uchiyama, “Contouring Control of Biaxial Feed Drive Systems with Non-Linear Friction Compensation,” Proceedings of the Institution of Mechanical Engineers, Part I: J. of Systems and Control Engineering, Vol.222, pp. 153-162, 2008.
- [19] M. Tomizuka, “Zero Phase Error Tracking Algorithm for Digital Control,” Trans. of ASME, J. of Dynamic Systems, Measurement, and Control Vol.109, pp. 65-68, 1987.
- [20] C.-S. Chen, Y.-H. Fan, and S. P. Tseng, “Position Command Shaping Control in a Retrofitted Milling Machine,” Int. J. of Machine Tools and Manufacture Vol.46, pp. 293-303, 2006.
- [21] K. Erkorkmaz and Y. Altintas, “High Speed CNC System Design. Part III: High Speed Tracking and Contouring Control of Feed Drives,” Int. J. of Machine Tools and Manufacture Vol.41, pp. 1637-1658, 2001.
- [22] T.-C. Tsao and M. Tomizuka, “Adaptive Zero Phase Tracking Algorithm for Digital Control,” Trans. of ASME, J. of Dynamic Systems, Measurement, and Control Vol.109, pp. 349-354, 1987.
- [23] S.-S. Yeh and P.-L. Hsu, “An Optimal and Adaptive Design of the Feedforward Motion Controller,” IEEE/ASME Trans. on Mechatronics 4/4, pp. 428-439, 1999.
- [24] D. Torfs, J. D. Schutter, and J. Swevers, “Extended Bandwidth Zero Phase Error Tracking Control of Nonminimal Phase Systems,” Trans. of ASME, J. of Dynamic Systems, Measurement, and Control Vol.114, pp. 347-351, 1992.
- [25] L. Guo and M. Tomizuka, “High-Speed and High-Precision Motion Control with an Optimal Hybrid Feedforward Controller,” IEEE/ASME Trans. on Mechatronics 2/2, pp. 110-122, 1997.
- [26] N. Uchiyama, “Adaptive Two-Degree-of-Freedom Control of Feed Drive Systems,” Int. J. of Machine Tools and Manufacture Vol.48, pp. 437-445, 2008.
- [27] M. Tomizuka and R. Horowitz, “Model Reference Adaptive Control of Mechanical Manipulators,” IFAC Adaptive Systems in Control and Signal Processing, San Francisco, USA, pp. 27-32, 1983.
- [28] I. D. Landau, R. Lozano, and M. M’Saad, “Adaptive Control,” Springer, 1998.