Identification of Nonlinear Cascade Systems with Time-Varying Backlash

Jozef Vörös

doi:10.2478/v10187-011-0014-2

Abstract

Recursive identification of cascade systems with time-varying input backlash and linear dynamic system is presented. A new analytic form of backlash characteristic description is used, hence all the parameters in the cascade model equation are separated and their estimation is solved as a quasi-linear problem using the recursive least squares method with internal variable estimation. Simulation studies are included.

References

BAI, E. W.: Identification of Linear Systems with Hard Input Nonlinearities of Known Structure, Automatica 38 (2002), 853-860.10.1016/S0005-1098(01)00281-3
Search in Google Scholar
BARREIRO, A.—BANOS, A.: Input-Output Stability of Systems with Backlash, Automatica 42 (2006), 1017-1024.10.1016/j.automatica.2006.02.017
Search in Google Scholar
CERONE, V.—REGRUTO, D.: Bounding the Parameters of Linear Systems with Input Backlash, IEEE Trans. Automatic Control 52 (2007), 531-536.10.1109/TAC.2007.892375
Search in Google Scholar
CHEN, H. F.: Recursive System Identification, Acta Mathematica Scientia 29 B (2009), 650-672.10.1016/S0252-9602(09)60062-X
Search in Google Scholar
CHEN, H. T.—HWANG, S. H.—CHANG, C. T.: Iterative Identification of Continuous-Time Hammerstein and Wiener Systems Using a Two-Stage Estimation Algorithm, Industrial & Engineering Chemistry Research 48 (2009), 1495-1510.10.1021/ie800149w
Search in Google Scholar
CHIDAMBARAM, M.: Computer Control of Processes, CRC Press, New York, 2001.
Search in Google Scholar
DING, F.—CHEN, T.: Identification of Hammerstein Nonlinear ARMAX Systems, Automatica 41 (2005), 1479-1489.10.1016/j.automatica.2005.03.026
Search in Google Scholar
DING, F.—CHEN, T.—IWAI, Z.: Adaptive Digital Control of Hammerstein Nonlinear Systems with Limited Output Sampling, SIAM Journal on Control and Optimization 45 (2007), 2257-2276.10.1137/05062620X
Search in Google Scholar
DING, F.—SHI, Y.—CHEN, T.: Gradient-Based Identification Methods for Hammerstein Nonlinear ARMAX Models, Nonlinear Dynamics 45 (2006), 31-43.10.1007/s11071-005-1850-z
Search in Google Scholar
DING, F.—SHI, Y.—CHEN, T.: Auxiliary Model-Based Least-Squares Identification Methods for Hammerstein Output-Error Systems, Systems & Control Letters 56 (2007), 373-380.10.1016/j.sysconle.2006.10.026
Search in Google Scholar
DOLANC, G.—STRMCNIK, S.: Identification of Nonlinear Systems Using a Piecewise-Linear Hammerstein Model, Systems & Control Letters 54 (2005), 145-158.10.1016/j.sysconle.2004.08.002
Search in Google Scholar
DONG, R.—TAN, Q.—TAN, Y.: Recursive Identification Algorithm for Dynamic Systems with Output Backlash and its Convergence, Int. J. Appl. Math. Comput. Sci. 19 (2009), 631-638.10.2478/v10006-009-0050-2
Search in Google Scholar
GIRI, F.—ROCHDI, Y.—CHAOUI, F. Z.—BROURI, A.: Identification of Hammerstein Systems in Presence of Hysteresis-Backlash and Hysteresis-Relay Nonlinearities, Automatica 44 (2008), 767-775.10.1016/j.automatica.2007.07.005
Search in Google Scholar
HASIEWICZ, Z.—MZYK, G.: Combined Parametric-Nonparametric Identification of Hammerstein Systems, IEEE Trans. on Automatic Control 49 (2004), 1370-1375.10.1109/TAC.2004.832662
Search in Google Scholar
HASIEWICZ, Z.—PAWLAK, M.—SLIWINSKI, P.: Nonparametric Identification of Nonlinearities in Block-Oriented Systems by Orthogonal Wavelets with Compact Support, IEEE Trans. Circuits and Systems I 52 (2005), 427-442.10.1109/TCSI.2004.840288
Search in Google Scholar
HÄGGLUND, T.: Automatic On-Line Estimation of Backlash in Control Loops, Journal of Process Control 17 (2007), 489-499.10.1016/j.jprocont.2007.01.002
Search in Google Scholar
JANCZAK, A.: Neural Network Approach for Identification of Hammerstein Systems, Int. J. Control 76 (2003), 1749-1766.10.1080/00207170310001633259
Search in Google Scholar
JANCZAK, A.: Identification of Nonlinear Systems Using Neural Networks and Polynomial Models: A Block-Oriented Approach, Lecture Notes in Control and Information Sciences, Vol. 310, Springer-Verlag, Heidelberg, Berlin, 2005.10.1007/b98334
Search in Google Scholar
KALAŠ, V.—JURIŠICA, L.—ŽALMAN, M.—ALMÁSSY, S.—SIVIČEK, P.—VARGA, A.—KALAŠ, D.: Nonlinear and Numerical Servosystems, Alfa/SNTL, Bratislava, 1985. (in Slovak)
Search in Google Scholar
LACY, S. L.—BERNSTEIN, D. S.: Subspace Identification for Non-Linear Systems with Measured-Input Non-Linearities, Int. J. Control 78 (2005), 906-926.10.1080/00207170500214095
Search in Google Scholar
LIU, Y.—BAI, E. W.: Iterative Identification of Hammerstein Systems, Automatica 43 (2007), 346-354.10.1016/j.automatica.2006.09.004
Search in Google Scholar
LJUNG, L.—SÖDERSTRÖM, T.: Theory and Practice of Recursive Identification, MIT Press, Cambridge, MA, 1983.
Search in Google Scholar
MZYK, G.: Generalized Kernel Regression Estimate for the Identification of Hammerstein Systems, Int. J. Applied Mathematics and Computer Science 17 (2007), 189-197.10.2478/v10006-007-0018-z
Search in Google Scholar
NORDIN, M.—GALIC, J.—GUTMAN, P. O.: New Models for Backlash and Gear Play, Int. J. Adapt. Control Signal Processing 11 (1997), 49-63.10.1002/(SICI)1099-1115(199702)11:1<49::AID-ACS394>3.0.CO;2-X
Search in Google Scholar
NORDIN, M.—GUTMAN, P. O.: Controlling Mechanical Systems with Backlash - a Survey, Automatica 38 (2002), 1633-1649.10.1016/S0005-1098(02)00047-X
Search in Google Scholar
PUPEIKIS, R.: On the Identification of Hammerstein Systems Having Saturation-Like Functions with Positive Slopes, Informatica 17 (2006), 55-68.10.15388/Informatica.2006.123
Search in Google Scholar
SELMIC, R. R.—LEWIS, F. L.: Neural Net Backlash Compensation with Hebbian Tuning Using Dynamic Inversion, Automatica 37 (2001), 1269-1277.10.1016/S0005-1098(01)00066-8
Search in Google Scholar
SLIWINSKI, P.—ROZENBLIT, J.—MARCELLIN, M. W.—KLEMPOUS, R.: Wavelet Amendment of Polynomial Models in Hammerstein Systems Identification, IEEE Trans. Automatic Control 54 (2009), 820-825.10.1109/TAC.2008.2009620
Search in Google Scholar
SUN, L.—LIU, W.—SANO, A.: Identification of a Dynamical System with Input Nonlinearity, IEE Proceedings - Control Theory Applications 146 (1999), 41-51.10.1049/ip-cta:19990371
Search in Google Scholar
TAO, G.—CANUDAS de WIT, C., (Eds.):: Special Issue on Adaptive Systems with Non-Smooth Nonlinearities, Int. J. Adapt. Control Signal Processing 11 (1997).10.1002/(SICI)1099-1115(199702)11:1<1::AID-ACS390>3.0.CO;2-1
Search in Google Scholar
TAO, G.—KOKOTOVIC, P. V.: Adaptive Control of Systems with Backlash, Automatica 29 (1993), 323-335.10.1016/0005-1098(93)90126-E
Search in Google Scholar
TAO, G.—KOKOTOVIC, P. V.: Adaptive Control of Systems with Unknown Output Backlash, IEEE Trans. Automatic Control 40 (1995), 326-330.10.1109/9.341803
Search in Google Scholar
TAO, G.—KOKOTOVIC, P. V.: Adaptive Control of Systems with Unknown Non-Smooth Non-Linearities, Int. J. Adapt. Control Signal Processing 11 (1997), 81-100.10.1002/(SICI)1099-1115(199702)11:1<81::AID-ACS396>3.0.CO;2-A
Search in Google Scholar
VÖRÖS, J.: Parameter Identification of Discontinuous Hammerstein Systems, Automatica 33 (1997), 1141-1146.10.1016/S0005-1098(97)00009-5
Search in Google Scholar
VÖRÖS, J.: Modeling and Parameter Identification of Systems with Multisegment Piecewise-Linear Characteristics, IEEE Trans. Automatic Control 47 (2002), 184-188.10.1109/9.981742
Search in Google Scholar
VÖRÖS, J.: Recursive Identification of Hammerstein Systems with Discontinuous Nonlinearities Containing Dead-Zones, IEEE Trans. Automatic Control 48 (2003), 2203-2206.10.1109/TAC.2003.820146
Search in Google Scholar
VÖRÖS, J.: Modeling and Identification of Systems with Backlash, Automatica 46 (2010), 369-374.10.1016/j.automatica.2009.11.005
Search in Google Scholar
WANG, J.—SANO, A.—CHEN, T.—HUANG, B.: Identification of Hammerstein Systems without Explicit Parameterization of Nonlinearity, Int. J. Control 82 (2009), 937-952.10.1080/00207170802382376
Search in Google Scholar
ZHANG, X.—TAN, Y.: Modelling of Ultrasonic Motor with Dead-Zone Based on Hammerstein Model Structure, Journal of Zhejiang University - Science A 9 (2008), 58-64.10.1631/jzus.A071146
Search in Google Scholar

Identification of Nonlinear Cascade Systems with Time-Varying Backlash

Abstract

Paradigm

My account