@article{hatch_smith_de_salapaka_2006, title={Construction and experimental implementation of a model-based inverse filter to attenuate hysteresis in ferroelectric transducers}, volume={14}, ISSN={["1558-0865"]}, DOI={10.1109/TCST.2006.883195}, abstractNote={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}, number={6}, journal={IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY}, author={Hatch, Andrew G. and Smith, Ralph C. and De, Tathagata and Salapaka, Murti V.}, year={2006}, month={Nov}, pages={1058–1069} }
 @article{smith_hatch_mukherjee_liu_2005, title={A homogenized energy model for hysteresis in ferroelectric materials: General density formulation}, volume={16}, ISSN={["1045-389X"]}, DOI={10.1177/1045389X05054789}, abstractNote={ In this article, we construct a framework for modeling hysteresis and constitutive nonlinearities in ferroelectric compounds based on energy analysis at mesoscopic scales in combination with stochastic homogenization techniques to construct macroscopic models. In the first step of the development, previous analysis is used to construct Helmholtz and Gibbs energy relations at the lattice level. This provides local polarization relations that can be extrapolated to provide constitutive models for certain homogeneous, single crystal compounds. To incorporate material and field nonhomogeneities, as well as the effects of polycrystallinity, certain parameters in the local models are assumed to be manifestations of underlying distributions having densities which must be identified for a given compound. Two techniques for estimating the unknown densities are presented, and the accuracy of the resulting model is illustrated for both symmetric major loops and biased minor loops through fits and predictions with experimental PZT4 and PZT5H data. }, number={9}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Smith, RC and Hatch, AG and Mukherjee, B and Liu, SF}, year={2005}, month={Sep}, pages={713–732} }
 @article{smith_hatch_2005, title={Parameter estimation techniques for a class of nonlinear hysteresis models}, volume={21}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/21/4/011}, abstractNote={This paper addresses the development of parameter estimation techniques for a class of models used to characterize hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials employed in a wide range of actuators and sensors. These models are formulated as integral equations with known kernels and unknown densities to be identified through least-squares techniques. Due to the compactness of the integral operators, the resulting discretized models inherit ill-posedness which must be accommodated through regularization. The accuracy of regularized finite-dimensional models is illustrated through comparison with experimental data.}, number={4}, journal={INVERSE PROBLEMS}, author={Smith, RC and Hatch, AG}, year={2005}, month={Aug}, pages={1363–1377} }