Thomas R. Braun

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

Ferroelectric and ferromagnetic materials are employed as both actuators and sensors in a wide variety of applications including fluid pumps, nanopositioning stages, sonar transducers, vibration control, ultrasonic sources, and high-speed milling. They are attractive because the resulting transducers are solid-state and often very compact. However, the coupling of field to mechanical deformation, which makes these materials effective transducers, also introduces hysteresis and time-dependent behavior that must be accommodated in device designs and models before the full potential of compounds can be realized. In this article, we present highly efficient modeling techniques to characterize hysteresis and constitutive nonlinearities in ferroelectric and ferromagnetic compounds and model inversion techniques which permit subsequent linear control designs.

Experimental validation of a homogenized energy model for magnetic after-effects

In this letter, we experimentally validate the ability of a recently developed ferromagnetic hysteresis model to characterize magnetic after-effects in ferromagnetic materials. The modeling framework, which combines energy analysis at the lattice level with stochastic homogenization techniques to accommodate material, stress, and field nonhomogeneities, quantifies after-effects through a balance of the Gibbs and relative thermal energies. Attributes of the framework are illustrated through fits to experimental steel data.

Efficient implementation algorithm for a homogenized energy model with thermal relaxation

In this paper, we present a new algorithm to implement the homogenized energy hysteresis model with thermal relaxation for both ferroelectric and ferromagnetic materials. The approach conserves most of the accuracy of the original algorithm, but enables all erfc and exp functions to be calculated in advance, thereby requiring that only basic mathematical operations be performed in real time. This is done without a signicant increase in memory usage. Using this approach, execution time of the model has been seen to improve by a factor of 70 for some applications, whereas the error only increases by five ten thousandths (0.05%) of the saturation polarization/magnetization. The model with negligible relaxation is also given, as it is used to illustrate some optimizations. Emphasis is placed on the ecient computation of these models, and theoretical development is left to the references.

Efficient inverse compensation for hysteresis via homogenized energy models

Ferroelectric and magnetic transducers are utilized in large number of applications, including nanopositioning, fluid pumps, high-speed milling, and vibration control/suppression. However, the physical mechanisms which make these materials highly effective transducers inherently introduce nonlinear, hysteretic behavior that must be incorporated in models and control designs. This significantly complicates control designs and limits the effectiveness of linear control algorithms when directly applied to the system. One solution is to employ an exact or approximate inverse model which converts a desired output to the corresponding input. This alleviates the complex input-output relation, allowing a linear control to be applied. Linearization of the actuator dynamics in this manner permits subsequent use of linear control designs to achieve high accuracy, high speed tracking as well as vibration attenuation and positioning objectives.

A reptation model for magnetic materials

Reptation, or accommodation, is manifested in ferromagnetic materials in a variety of operating regimes and hence must be incorporated in models used for comprehensive material characterization or model-based control design. Because the microscopic mechanisms which cause reptation are complex, we characterize the effect in a phenomenological macroscopic manner within the context of a homogenized energy framework for ferromagnetic hysteresis. Attributes of the model are illustrated through comparison with experimental data.

High speed inverse model implementation for real-time control of ferroelectric and ferromagnetic transducers operating in nonlinear and hysteretic regimes

Ferroelectric (e.g., PZT), ferromagnetic, and ferroelastic (e.g., shape memory alloy) materials exhibit varying degrees of hysteresis and constitutive nonlinearities at all drive levels due to their inherent domain structure. At low drive levels, these nonlinear effects can be mitigated through feedback mechanisms or certain amplifier architectures (e.g., charge or current control for PZT) so that linear models and control designs provide sufficient accuracy. However, at the moderate to high drive levels where actuators and sensors utilizing these compounds often prove advantageous, hysteresis and constitutive nonlinearities must be incorporated into models and control designs to achieve high accuracy, high speed control specifications. In this paper, we employ a homogenized energy framework to characterize hysteresis in this combined class of ferroic compounds. We then use this framework to construct highly efficient inverse models that can be used to approximately linearize actuator dynamics for subsequent linear control design. For applications such as high speed tracking (e.g., kHz rates) or broadband vibration attenuation, the efficiency of the inverse construction proves crucial for realtime control implementation. We demonstrate aspects of the inverse model implementation in the context of rod models used to characterize PZT and magnetic actuators presently employed in applications ranging from nanopositioning to high speed milling of automotive components.