Abstract
A combined PD and hierarchical fuzzy control is proposed for the low-speed control of the C-axis of CNC turning centers considering the effects of transmission flexibility and complex nonlinear friction. Learning of the hierarchical structure and parameters of the suggested control strategy is carried out by using the genetic algorithms. The proposed algorithm consists of two phases: the first one is to search the best hierarchy, and the second to tune the consequent center values of the constituent fuzzy logic systems into the hierarchy. For the least total control rule number, the hierarchical fuzzy controller is chosen to include only the simple two-input/one-output fuzzy systems, and both binary and decimal genes are used for the selection, crossover and mutation of the genetic algorithm. The proposed approach is validated by the computer simulation. Each generation consists of 30 individuals: ten reproduced from its parent generation, ten generated by crossover, and the other ten by mutation. In the simulations, the C-axis is assumed to be driven by a vector-controlled AC induction motor, and the dynamic friction model suggested by Canudas de Wit et al. in 1995 is used.
Similar content being viewed by others
References
Slocum, A. H.: Precision Machine Design, Prentice-Hall, Englewood Cliffs, NJ, 1992.
Dupont, P. E.: Avoiding stick-slip through PD control, IEEE Trans. Automat. Control 39(5) (1994), 1094–1097.
Armstrong-Helouvry, B.: Control of Machines with Friction, Kluwer Academic Publishers, Boston, MA, 1991.
Kato, S., Yamaguchi, K., and Matsubayashi, T.: Stick-slip motion of machine tool slideway, ASME J. Engrg. Indust. (1974), 557–566.
Campbell, S. A.: The Science and Engineering of Microelectronic Fabrication, Oxford University Press, New York, 1996.
Aronson, R. B.: Machine tool 101: Part 7 – machine tools of the future, Manufacturing Engineering (July 1994), 39–45.
Yang, S. and Tomizuka, M.: Adaptive pulse width control for precise positioning under the influence of stiction and Coulomb friction, ASME J. Dynamic Systems Meas. Control 110 (1988), 221–227.
Dahl, P.: A solid friction model, Technical Report TOR-0158(3107–18)-1, Aerospace Corporation, El Segundo, CA, 1968.
Bo, L. C. and Pavelescu, D.: The friction-speed relation and its influence on the critical velocity of the stick-slip motion, Wear 82(3) (1982), 277–289.
Hess, D. P. and Soom, A.: Friction at a lubricated line contact operating at oscillating sliding velocities, J. Tribology 112 (1990), 149–152.
Canudas de Wit, C., Olsson, H., Åström, K. J., and Lischinsky, P.: A new model for control of systems with friction, IEEE Trans. Automat. Control 40(3) (1995), 419–425.
Tung, E. D., Anwar, G., and Tomizuka, M.: Low velocity friction compensation and feedforward solution based on repetitive control, ASME J. Dynamic SystemsMeas. Control 115 (1993), 279–284.
Lin, L. C. and Uen, S. M.: A fuzzy learning approach to intelligent stick-slip friction compensation for motion control, in: Proc. of R.O.C. Automatic Control Conf., Taichung, Taiwan, 1995, pp. 50–56.
Lin, L. C. and Lin, Y. J.: Fuzzy-enhanced adaptive control for flexible drive system with friction using genetic algorithms, J. Intelligent Robotic Systems 23 (1998), 379–405.
Holland, J. H.: Outline for a logical theory of adaptive systems, J. Assoc. Comput. Machin. 3 (1962), 297–314.
Goldberg, D. E.: Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, MA, 1989.
Grefenstette, J. J.: Genetic Algorithms for Machine Learning, Kluwer Academic Publishers, Boston, MA, 1994.
Mitchell, M.: An Introduction to Genetic Algorithms, MIT Press, Cambridge, MA, 1996.
Shimojima, K., Fukuda, T., and Hasegawa, Y.: Self-tuning fuzzy modeling with adaptive membership function, rules, and hierarchical structure based on genetic algorithm, Fuzzy Sets Systems 71 (1995), 295–309.
Man, K. F., Tang, K. S., and Kwong, S.: Genetic algorithms: concepts and applications, IEEE Trans. Industr. Electronics 43(5) (1996), 519–533.
Gupta, M. M., Kiszka, L., and Trojan, G. M.: Multivariable structure of fuzzy control systems, IEEE Trans. Systems Man Cybernet. 16 (1986), 638–656.
Raju, G. V. S., Zhou, J., and Kisner, R. A.: Hierarchical fuzzy control, Internat. J. Control 54(5) (1991), 1201–1216.
Linkens, D. A. and Nyongesa, H. O.: A hierarchical multivariable fuzzy controller for learning with genetic algorithms, Internat. J. Control 63(5) (1996), 865–883.
Wang, L. X.: A Course in Fuzzy Systems and Control, Prentice-Hall, Englewood Cliffs, NJ, 1997.
Boldea, I. and Nasar, S. A.: Vector Control of AC Drives, CRC Press, Boca Raton, FL, 1992.
Yager, R. R. and Filev, D. P.: Essentials of Fuzzy Modeling and Control, Wiley, New York, 1994.
Ge, S. S., Lee, T. H., and Zhu, G.: Genetic algorithm tuning of Lyapunov-based controllers: An application to a single-link flexible robot system, IEEE Trans. Industr. Electronics 43(5) (1996), 567–574.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lin, LC., Lee, GY. Hierarchical Fuzzy Control for C-Axis of CNC Turning Centers Using Genetic Algorithms. Journal of Intelligent and Robotic Systems 25, 255–275 (1999). https://doi.org/10.1023/A:1008035612395
Issue Date:
DOI: https://doi.org/10.1023/A:1008035612395