Short Time Identification of Feed Drive Systems using Nonlinear Least Squares Method

Authors: M.G.A. Nassef, Linghan Li, C. Schenck, B. Kuhfuss

Abstract:

Design and modeling of nonlinear systems require the knowledge of all inside acting parameters and effects. An empirical alternative is to identify the system-s transfer function from input and output data as a black box model. This paper presents a procedure using least squares algorithm for the identification of a feed drive system coefficients in time domain using a reduced model based on windowed input and output data. The command and response of the axis are first measured in the first 4 ms, and then least squares are applied to predict the transfer function coefficients for this displacement segment. From the identified coefficients, the next command response segments are estimated. The obtained results reveal a considerable potential of least squares method to identify the system-s time-based coefficients and predict accurately the command response as compared to measurements.

Keywords: feed drive systems, least squares algorithm, onlineparameter identification, short time window

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328760

References:

[1] Y. Kakino and A. Mutsubara, "High speed and high acceleration feed drive system for NC machine tools," The Japan Society for Precision Engineering Journal, vol. 30, pp. 295-298, 1996.
[2] R. Bearee, P. J. Barre, and S. Bloch, "Influence of high speed machine tool control parameters on the contouring accuracy, application to linear and circular interpolation," Journal of Intelligent and Robotic Systems, vol. 40, pp. 321-342, 2004.
[3] M. S. Kim, and S. C. Chung, "A systematic approach to design high performance feed drive system," International Journal of Machine tools and Manufacture, vol. 45, pp.1421-1435, 2005.
[4] C. Chen, and C. Cheng, "Integrated design for a mechatronic feed drive system of machine tools," in proc. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 588-593, 2005.
[5] A. Janczak, Identification of nonlinear systems using NN and polynomial models: A block-oriented approach. Springer-Verlag Berlin Heidelberg: Berlin, Germany, 2005, pp. 117-125.
[6] J. R. Raol, G. Girija and J. Singh, Modeling and Parameter Estimation of Dynamic Systems. The Institution of Engineering and Technology, London, United Kingdom, 2004, pp. 239-248.
[7] R. Krneta, S. Antic, and D. Stojanovic, "Recursive least squares method in parameters identification of DC motors models," Facta Universitatis Series: Electronics and Energetics, vol. 18, no. 3, pp 467-478, December 2005.
[8] I. Eker, "Experimental on-line identification of an electromechanical system," PubMed U.S. National Library of Medicine, PubMed journal, vol. 43, issue 1, pp.13-22, January 2004.
[9] K. Wang, J. Chiasson, M. Bodson, L. M. Tolbert, "A nonlinear least-squares approach for identification of the induction motor parameters," 43rd IEEE Trans. On Automatic Control, vol. 50, issue 4, pp1622 - 1628, October 2005.
[10] A. Stephen, Billings, and H. L. Wei, "Sparse model identification using a forward orthogonal regression algorithm aided by mutual information," IEEE trans. on neural networks, vol. 18, no. 1, January 2007.
[11] R. J. Schilling, "Approximation of nonlinear systems with radial basis function neural networks," IEEE trans. on neural networks, vol. 12, no. 1, January 2001.
[12] Y. Z. Tsypkin, J. D. Mason, and E. D. Avedyan, "Neural networks for identification of nonlinear systems under random piecewise polynomial disturbances," IEEE Trans. Neural Network, vol. 10, no. 2, March 1999.
[13] O. G. Rudenko, and A. A. Bessonov, "Real-time identification of nonlinear time-varying systems using radial basis function network," Cybernetics and Systems Analysis, vol. 39, No. 6, 2003.
[14] W. Yu, "Nonlinear system identification using discrete-time recurrent neural networks with stable learning algorithms," Information Sciences Int. J. vol. 158, pp.131-147, 2004.
[15] G. Amirian, "Transformation of tracking error in parallel kinematic machining," Ph.D. dissertation, bime institute, Universität Bremen, Bremen, Germany, 2008.
[16] X. Desforges, and A. Habbadi, "A neural network for parameter estimation of a DC Motor for feed-drives," in ICANN '97 Proc. of the 7th International Conference on Artificial Neural Networks, vol. 3, pp 867- 872, 1997.
[17] B. Kuhfuss, C. Schenck, "Calculating the trajectories for geometric redundant machining," 1st International Conference on Computing and Solutions in Manufacturing Engineering, COSME, pp 16-18, 2004.
[18] M. G. A. Nassef, C. Schenck, B. Kuhfuss, "Feed drive Systems: An investigation using kinematic redundancy for compensation of self induced vibrations," Proc. 22nd International Conference on Computer-Aided Production Engineering (CAPE), Edinburgh, Scotland, April 2011.
[19] G. Ellis, Control System Design Guide: A Practical Guide. Elsevier Academic press: California, pp 99-107, pp. 254-256, 2004.
[20] M. G. A. Nassef, C. Schenck, B. Kuhfuss, "Simulation-Based Parameter Identification of a reduced model Using Neural Networks," proc. IEEE/ICCA International Conference on Control and Automation, December 2011, to be published.
[21] D. W. Marquardt, "An Algorithm for Least-Squares Estimation of Nonlinear Parameters," Journal of the Society for Industrial and Applied Mathematics, vol. 11, No. 2, pp. 431-441, January 1963.
[22] W. Spendley, Nonlinear least squares fitting using a modified simplex minimization method, Optimization. Symposium of the Institute of Mathematics and its Applications, University of Keele, U.K, Academic Press, London-New York, pp. 259-270, 1968.
[23] W. Spendley, G. R. Hext and F. R. Himsworth, "Sequential application of simplex designs in optimization and evolutionary operation, Technometrics," American Statistical Association and American Society for Quality, vol. 4, pp. 441-461, 1962.