Discretization of Preisach hysteresis model

Abstract

In order to reduce the partial derivative errors in Preisach hysteresis model caused by inaccurate experimental data, the concept and correlative method of discretization of Preisach hysteresis model are proposed, the essential of which is to centralize the distribution density of Preisach hysteresis model in local region as an integral, which is defined as the weight of a certain point in that region. For the input composed of an ascending segment and a descending segment, a method to determine the initial weights together with an additional method to determine present weights is given according to the number of input ascending segments. If the number of input ascending segments increases, the weights of the corresponding points in updating rectangle are updated by adding the initial weights of corresponding points. A prominent advantage of discrete Preisach hysteresis model is its memory efficiency. Another advantage of discrete Preisach hysteresis model is that there is no function in the model, and thus, it can be expediently operated using a computer. By generalizing the above updating rectangle method to the continuous Preisach hysteresis model, identification method of distribution density can be given as well.

Keywords

hysteresis / discretization / distribution density / output

References

[1] MarcoS, PaoloG, RiccardoM, GiovanniB P. Vibration control of a flexible space manipulator during on orbit operations [J]. Acta Astronautica, 2012, 73(2): 109-121

[2] ChoiS B, CheongC C, ShinH C. Sliding mode control of vibration in a single-link flexible arm with parameter variations [J]. J Sound Vibr, 1995, 179(5): 737-48

[3] MoudgalV G, PassinoK M, YurkovichS. Rule-based control for a flexible-link robot [J]. IEEE Trans Control Syst Technol, 1994, 2(4): 392-405

[4] YoshikawaT, HosodaK. Modeling of flexible manipulators using virtual rigid links and passive joints [J]. Int J Robot Res, 1996, 15(3): 290-299

[5] HuH, BenM R. On the classical Preisach model in piezoceramic actuators [J]. Mechatronics, 2003, 13(3): 85-94

[6] FridmanG. Second-order Preisach model of scalar hysteresis [J]. Physica B, 2000, 275(3): 173-178

[7] AmrA, AdlyA, SalwaK. Efficient modeling of hysteresis using HNN implementation of stoner-wohlfarth operators [J]. Journal of Advanced Research, 2013, 4: 403-409

[8] AdlyA A, AbdS K. Efficient implementation of vector Preisach-type models using orthogonally coupled hysteresis Operators [J]. IEEE Trans Magn, 2006, 42(4): 1518-1525

[9] KrejP O, KaneJ P, PokrovskiiclA, RachinskiiD. Properties of solutions to a class of differential models incorporating Preisach hysteresis operator [J]. Physica D, 2012, 241(22): 2010-2028

[10] FelixW A, SutorE, StefanJ. A generalized Preisach approach for piezoceramic materials incorporating uniaxial compressive stress [J]. Sensors and Actuators A: Physical, 2012, 186(2): 223-229

[11] TaoG, KokotovicP V. Adaptive control of plant with unknown hysteresis [J]. IEEE Transactions on Automatic Control, 1995, 40: 200-212

[12] GyorgyK. On the product Preisach model of hysteresis [J]. Physica B, 2000, 275(1): 40-44

[13] PavelK. Forced oscillations in Preisach systems [J]. Physica B, 2000, 275(2): 81-86

[14] MiklosK. Vector Preisach hysteresis modeling: Measurement, identification and application [J]. Physica B, 2011, 406(8): 1403-1409

[15] WangY, YingZ G, ZhuW Q. Stochastic averaging of energy envelope of Preisach hysteretic systems [J]. Journal of Sound and Vibration, 2009, 321(4): 976-993

[16] BrokateM, SprekelsJHysteresis and phase transitions [M], 1996New YorkSpringer112-231

[17] LiL, LiuX-d, HouC-Z, WangWei. Mixed Preisach hysteresis model and its properties [J]. Optics and Precision Engineering, 2008, 16(2): 279-284

[18] CrossaR K, SkiibA M, PokrovskiiA V. A time-dependent Preisach model [J]. Physica B, 2001, 306(4): 206-210

[19] TanX, BarasJ S. Modeling and control of hysteresis in magnetostrictive actuators [J]. Automatica, 2004, 40(9): 1469-1480

[20] WangY, YingZ G, ZhuW Q. Nonlinear stochastic optimal control of Preisach hysteretic systems [J]. Probabilistic Engineering, 2009, 24(3): 255-264

[21] AcrossR, KrasnoselA M, PokrovskiiA V. A time-dependent Preisach model [J]. Physica B, 2001, 306(4): 206-210