{"title":"Short Time Identification of Feed Drive Systems using Nonlinear Least Squares Method","authors":"M.G.A. Nassef, Linghan Li, C. Schenck, B. Kuhfuss","volume":59,"journal":"International Journal of Mechanical and Mechatronics Engineering","pagesStart":2281,"pagesEnd":2287,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/619","abstract":"Design and modeling of nonlinear systems require the\r\nknowledge of all inside acting parameters and effects. An empirical\r\nalternative is to identify the system-s transfer function from input and\r\noutput data as a black box model. This paper presents a procedure\r\nusing least squares algorithm for the identification of a feed drive\r\nsystem coefficients in time domain using a reduced model based on\r\nwindowed input and output data. The command and response of the\r\naxis are first measured in the first 4 ms, and then least squares are\r\napplied to predict the transfer function coefficients for this\r\ndisplacement segment. From the identified coefficients, the next\r\ncommand response segments are estimated. The obtained results\r\nreveal a considerable potential of least squares method to identify the\r\nsystem-s time-based coefficients and predict accurately the command\r\nresponse as compared to measurements.","references":"[1] Y. Kakino and A. Mutsubara, \"High speed and high acceleration feed\r\ndrive system for NC machine tools,\" The Japan Society for Precision\r\nEngineering Journal, vol. 30, pp. 295-298, 1996.\r\n[2] R. Bearee, P. J. Barre, and S. Bloch, \"Influence of high speed machine\r\ntool control parameters on the contouring accuracy, application to linear\r\nand circular interpolation,\" Journal of Intelligent and Robotic Systems,\r\nvol. 40, pp. 321-342, 2004.\r\n[3] M. S. Kim, and S. C. Chung, \"A systematic approach to design high\r\nperformance feed drive system,\" International Journal of Machine tools\r\nand Manufacture, vol. 45, pp.1421-1435, 2005.\r\n[4] C. Chen, and C. Cheng, \"Integrated design for a mechatronic feed drive\r\nsystem of machine tools,\" in proc. IEEE\/ASME International Conference\r\non Advanced Intelligent Mechatronics, pp. 588-593, 2005.\r\n[5] A. Janczak, Identification of nonlinear systems using NN and polynomial\r\nmodels: A block-oriented approach. Springer-Verlag Berlin Heidelberg:\r\nBerlin, Germany, 2005, pp. 117-125.\r\n[6] J. R. Raol, G. Girija and J. Singh, Modeling and Parameter Estimation of\r\nDynamic Systems. The Institution of Engineering and Technology,\r\nLondon, United Kingdom, 2004, pp. 239-248.\r\n[7] R. Krneta, S. Antic, and D. Stojanovic, \"Recursive least squares method\r\nin parameters identification of DC motors models,\" Facta Universitatis\r\nSeries: Electronics and Energetics, vol. 18, no. 3, pp 467-478, December\r\n2005.\r\n[8] I. Eker, \"Experimental on-line identification of an electromechanical\r\nsystem,\" PubMed U.S. National Library of Medicine, PubMed journal,\r\nvol. 43, issue 1, pp.13-22, January 2004.\r\n[9] K. Wang, J. Chiasson, M. Bodson, L. M. Tolbert, \"A nonlinear\r\nleast-squares approach for identification of the induction motor\r\nparameters,\" 43rd IEEE Trans. On Automatic Control, vol. 50, issue 4,\r\npp1622 - 1628, October 2005.\r\n[10] A. Stephen, Billings, and H. L. Wei, \"Sparse model identification using a\r\nforward orthogonal regression algorithm aided by mutual information,\"\r\nIEEE trans. on neural networks, vol. 18, no. 1, January 2007.\r\n[11] R. J. Schilling, \"Approximation of nonlinear systems with radial basis\r\nfunction neural networks,\" IEEE trans. on neural networks, vol. 12, no. 1,\r\nJanuary 2001.\r\n[12] Y. Z. Tsypkin, J. D. Mason, and E. D. Avedyan, \"Neural networks for\r\nidentification of nonlinear systems under random piecewise polynomial\r\ndisturbances,\" IEEE Trans. Neural Network, vol. 10, no. 2, March 1999.\r\n[13] O. G. Rudenko, and A. A. Bessonov, \"Real-time identification of\r\nnonlinear time-varying systems using radial basis function network,\"\r\nCybernetics and Systems Analysis, vol. 39, No. 6, 2003.\r\n[14] W. Yu, \"Nonlinear system identification using discrete-time recurrent\r\nneural networks with stable learning algorithms,\" Information Sciences\r\nInt. J. vol. 158, pp.131-147, 2004.\r\n[15] G. Amirian, \"Transformation of tracking error in parallel kinematic\r\nmachining,\" Ph.D. dissertation, bime institute, Universit\u251c\u00f1t Bremen,\r\nBremen, Germany, 2008.\r\n[16] X. Desforges, and A. Habbadi, \"A neural network for parameter\r\nestimation of a DC Motor for feed-drives,\" in ICANN '97 Proc. of the 7th\r\nInternational Conference on Artificial Neural Networks, vol. 3, pp 867-\r\n872, 1997.\r\n[17] B. Kuhfuss, C. Schenck, \"Calculating the trajectories for geometric\r\nredundant machining,\" 1st International Conference on Computing and\r\nSolutions in Manufacturing Engineering, COSME, pp 16-18, 2004.\r\n[18] M. G. A. Nassef, C. Schenck, B. Kuhfuss, \"Feed drive Systems: An\r\ninvestigation using kinematic redundancy for compensation of self\r\ninduced vibrations,\" Proc. 22nd International Conference on\r\nComputer-Aided Production Engineering (CAPE), Edinburgh, Scotland,\r\nApril 2011.\r\n[19] G. Ellis, Control System Design Guide: A Practical Guide. Elsevier\r\nAcademic press: California, pp 99-107, pp. 254-256, 2004.\r\n[20] M. G. A. Nassef, C. Schenck, B. Kuhfuss, \"Simulation-Based Parameter\r\nIdentification of a reduced model Using Neural Networks,\" proc.\r\nIEEE\/ICCA International Conference on Control and Automation,\r\nDecember 2011, to be published.\r\n[21] D. W. Marquardt, \"An Algorithm for Least-Squares Estimation of\r\nNonlinear Parameters,\" Journal of the Society for Industrial and Applied\r\nMathematics, vol. 11, No. 2, pp. 431-441, January 1963.\r\n[22] W. Spendley, Nonlinear least squares fitting using a modified simplex\r\nminimization method, Optimization. Symposium of the Institute of\r\nMathematics and its Applications, University of Keele, U.K, Academic\r\nPress, London-New York, pp. 259-270, 1968.\r\n[23] W. Spendley, G. R. Hext and F. R. Himsworth, \"Sequential application of\r\nsimplex designs in optimization and evolutionary operation,\r\nTechnometrics,\" American Statistical Association and American Society\r\nfor Quality, vol. 4, pp. 441-461, 1962.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 59, 2011"}