February  2013, 6(1): 101-119. doi: 10.3934/dcdss.2013.6.101

The Preisach hysteresis model: Error bounds for numerical identification and inversion

1. 

Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 11567 Praha 1, Czech Republic

Received  March 2011 Revised  July 2011 Published  October 2012

A structure analysis of the Preisach model in a variational setting is carried out by means of an auxiliary hyperbolic equation with memory variable playing the role of time, and amplitude of cycles as spatial variable. Using this representation, we propose an algorithm and derive error estimates for the identification of the Preisach density function and for an approximate inversion of the Preisach operator.
Citation: Pavel Krejčí. The Preisach hysteresis model: Error bounds for numerical identification and inversion. Discrete & Continuous Dynamical Systems - S, 2013, 6 (1) : 101-119. doi: 10.3934/dcdss.2013.6.101
References:
[1]

M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions,'', Appl. Math. Sci., (1996). Google Scholar

[2]

M. Brokate and A. Visintin, Properties of the Preisach model for hysteresis,, J. Reine Angew. Math., 402 (1989), 1. Google Scholar

[3]

D. Davino, A. Giustiniani and C. Visone, Fast inverse Preisach models in algorithms for static and quasistatic magnetic-field computations,, IEEE Transactions on Magnetics, 44 (2008), 862. Google Scholar

[4]

K. H. Hoffmann and G. H. Meyer, A least squares method for finding the Preisach hysteresis operator from measurements,, Numer. Math., 55 (1989), 695. Google Scholar

[5]

S. K. Hong, H. K. Jung and H. K. Kim, Analytical formulation for the Everett function,, Journal of Magnetics, 2 (1997), 105. Google Scholar

[6]

M. A. Krasnosel'skii and A. V. Pokrovskii, "Systems with Hysteresis,'', Nauka, (1983). Google Scholar

[7]

P. Krejčí, Hysteresis and periodic solutions of semilinear and quasilinear wave equations,, Math. Z, 193 (1986), 247. Google Scholar

[8]

P. Krejčí, On Maxwell equations with the Preisach hysteresis operator: the one-dimensional time-periodic case,, Apl. Math., 34 (1989), 364. Google Scholar

[9]

P. Krejčí, Hysteresis memory preserving operators,, Appl. Math., 36 (1991), 305. Google Scholar

[10]

P. Krejčí, "Hysteresis, Convexity and Dissipation in Hyperbolic Equations,'', Gakuto Int. Ser. Math. Sci. Appl., (1996). Google Scholar

[11]

P. Krejčí, Kurzweil integral and hysteresis,, Journal of Physics: Conference Series, 55 (2006), 144. Google Scholar

[12]

F. Preisach, Über die magnetische Nachwirkung,, Z. Physik, 94 (1935), 277. doi: 10.1007/BF01349418. Google Scholar

[13]

A. Visintin, "Differential Models of Hysteresis,'', Springer, (1994). Google Scholar

[14]

C. Visone and M. Sjöström, Exact invertible hysteresis models based on play operators,, Physica B, 343 (2004), 148. Google Scholar

show all references

References:
[1]

M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions,'', Appl. Math. Sci., (1996). Google Scholar

[2]

M. Brokate and A. Visintin, Properties of the Preisach model for hysteresis,, J. Reine Angew. Math., 402 (1989), 1. Google Scholar

[3]

D. Davino, A. Giustiniani and C. Visone, Fast inverse Preisach models in algorithms for static and quasistatic magnetic-field computations,, IEEE Transactions on Magnetics, 44 (2008), 862. Google Scholar

[4]

K. H. Hoffmann and G. H. Meyer, A least squares method for finding the Preisach hysteresis operator from measurements,, Numer. Math., 55 (1989), 695. Google Scholar

[5]

S. K. Hong, H. K. Jung and H. K. Kim, Analytical formulation for the Everett function,, Journal of Magnetics, 2 (1997), 105. Google Scholar

[6]

M. A. Krasnosel'skii and A. V. Pokrovskii, "Systems with Hysteresis,'', Nauka, (1983). Google Scholar

[7]

P. Krejčí, Hysteresis and periodic solutions of semilinear and quasilinear wave equations,, Math. Z, 193 (1986), 247. Google Scholar

[8]

P. Krejčí, On Maxwell equations with the Preisach hysteresis operator: the one-dimensional time-periodic case,, Apl. Math., 34 (1989), 364. Google Scholar

[9]

P. Krejčí, Hysteresis memory preserving operators,, Appl. Math., 36 (1991), 305. Google Scholar

[10]

P. Krejčí, "Hysteresis, Convexity and Dissipation in Hyperbolic Equations,'', Gakuto Int. Ser. Math. Sci. Appl., (1996). Google Scholar

[11]

P. Krejčí, Kurzweil integral and hysteresis,, Journal of Physics: Conference Series, 55 (2006), 144. Google Scholar

[12]

F. Preisach, Über die magnetische Nachwirkung,, Z. Physik, 94 (1935), 277. doi: 10.1007/BF01349418. Google Scholar

[13]

A. Visintin, "Differential Models of Hysteresis,'', Springer, (1994). Google Scholar

[14]

C. Visone and M. Sjöström, Exact invertible hysteresis models based on play operators,, Physica B, 343 (2004), 148. Google Scholar

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