Construction and Experimental Implementation of a Model-Based Inverse Filter to Attenuate Hysteresis in Ferroelectric Transducers

Abstract

Hysteresis and constitutive nonlinearities are inherent properties of ferroelectric transducer materials due to the noncentrosymmetric nature of the compounds. In certain regimes, these effects can be mitigated through restricted input fields, charge-or current-controlled amplifiers, or feedback designs. For general operating conditions, however, these properties must be accommodated in models, transducer designs, and model-based control algorithms to achieve the novel capabilities provided by the compounds. In this paper, we illustrate the construction of inverse filters, based on homogenized energy models, which can be used to approximately linearize the piezoceramic transducer behavior for linear design and control implementation. Attributes of the inverse filters are illustrated through numerical examples and experimental open loop control implementation for an atomic force microscope stage.i Report Documentation Page Form Approved OMB No. 0704-0188Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

Adaptive Control of Uncertain Linear Systems With Uncertain Hysteretic Input Nonlinearities

“…The most direct approach to dealing with hysteresis is to invert the nonlinearity [6,7]. When the hysteresis map is uncertain, the hysteresis can be inverted robustly or adaptively [8].…”

Image‐based hysteresis modeling and compensation for an AFM piezo‐scanner

“…According to the modeling mechanism, there are two types of models describing the hysteresis behavior. The first type is called constitutive model such as Jiles‐Atherton (JA) model (2 offers a numerical implementation of JA model) and homogenized energy model 3. These models are studied from a viewpoint of magnetization, thus they have explicit physical meaning.…”

“…In 11, a compensator was designed to reduce the hysteresis behavior of piezo‐scanners. In 3, based on the analysis for the homogenized energy model, an inverse filter was constructed to attenuate hysteresis and it finally obtained roughly linear input‐output behavior for ferroelectric transducers. In 12, the authors used a modified Prandtl‐Ishlinskii model to design an inverse controller that compensates for hysteretic actuator characteristics.…”

High Speed Model Implementation and Inversion Techniques for Ferroelectric and Ferromagnetic Transducers

“…Moreover, inverse models based on these techniques have been experimentally implemented (Ge and Jouaneh, 1996;Mittal and Meng, 2000;Tan et al, 2001;Nealis and Smith, 2003;Tan and Baras, 2004;Song et al, 2005;Hatch et al, 2006;Nealis and Smith, 2007).…”

“…Several classes of models for ferroelectric and ferromagnetic materials meet these criteria including homogenized energy models Smith et al, 2003aSmith et al, , b, 2006aSmith, 2005;, Preisach models (Mayergoyz, 1991;Ge and Jouaneh, 1995;Mittal and Meng, 2000;Robert et al, 2000;Webb et al, 2000;Song et al, 2005), and domain wall models (Jiles and Atherton, 1984;Dapino et al, 2000;Massad and Smith, 2003;Smith and Massad, 2003). Moreover, inverse models based on these techniques have been experimentally implemented (Ge and Jouaneh, 1996;Mittal and Meng, 2000;Tan et al, 2001;Nealis and Smith, 2003;Tan and Baras, 2004;Song et al, 2005;Hatch et al, 2006;Nealis and Smith, 2007).…”