Short Time Identification of Feed Drive Systems using Nonlinear Least Squares Method
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:49757", author = "M.G.A. Nassef and Linghan Li and C. Schenck and B. Kuhfuss", title = "Short Time Identification of Feed Drive Systems using Nonlinear Least Squares Method", 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", volume = "5", number = "11", pages = "2125-6", }
