### Abstract

In previous work we had proposed a low (6) dimensional model for a thin magnetostrictive actuator that was suitable for real-time control. One of the main results of this modeling effort was the separation of the rate-independent hysteretic effects from the rate-dependent linear effects. The hysteresis phenomenon may also be captured by a (modified) Preisach operator with the magnetic field H as the input. If one can find an inverse for the Preisach operator, then the composite system can be approximately linearized. In this paper, we complete the proof of the existence of an inverse theorem due to Brokate and Sprekels and propose a new algorithm for computation of the inverse. Previous algorithms used linearization of the operating point. As numerical differentiation is involved, this approach can cause divergence. Our algorithm does not linearize the Preisach operator, but makes use of its monotone increasing property. Convergence of the algorithm is proved using the contraction mapping principle.

Original language | English |
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Pages (from-to) | 404-414 |

Number of pages | 11 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 3984 |

State | Published - 2000 |

Event | Smart Structures and Materials 2000 - Mathematics and Control in Smart Structures - Newport Beach, CA, USA Duration: Mar 6 2000 → Mar 9 2000 |

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## Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*,

*3984*, 404-414.