@inproceedings{lewis_mcmahan_smith_2014, title={Model calibration for beam models in the presence of model discrepancy}, DOI={10.1115/smasis2014-7722}, abstractNote={Piezoelectric, magnetic and shape memory alloy (SMA) materials offer unique capabilities for energy harvesting and reduced energy requirements in aerospace, aeronautic, automotive, industrial and biomedical applications. However, all of these materials exhibit creep, rate-dependent hysteresis, and constitutive nonlinearities that must be incorporated in models and model-based control designs to achieve their full potential. Furthermore, models and control designs must be constructed in a manner that incorporates parameter and model uncertainties and permits predictions with quantified uncertainties. In this presentation, we compare the Euler-Bernoulli and Timoshenko beam models for a cantilever beam with an applied PZT patch to illustrate parameter estimation in the presence of model discrepancy.}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, 2014, vol 1}, author={Lewis, A. L. and McMahan, J. A. and Smith, Ralph}, year={2014} }
 @inproceedings{mcmahan_smith_2014, title={ncertainty quantification for robust control design of smart material systems}, DOI={10.1115/smasis2013-3166}, abstractNote={The objective in robust control design is to provide mechanisms to achieve tracking or stabilization objectives in the presence of unmodeled dynamics. This is usually achieved by assuming worst case model discrepancies which can significantly degrade control authority if the uncertainty bounds are overly conservative. In this paper, we use uncertainty quantification techniques to construct densities for control outputs that can be used to derive optimal robust control designs. We illustrate the performance of these techniques in the context of systems with smart material actuators and sensors.}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems - 2013, vol 1}, author={McMahan, J. A. and Smith, Ralph}, year={2014} }
 @article{mcmahan_crews_smith_2013, title={Inversion algorithms for the homogenized energy model for hysteresis in ferroelectric and shape memory alloy compounds}, volume={24}, DOI={10.1177/1045389x12471868}, abstractNote={Ferroelectric and ferromagnetic materials have the advantage of broadband and dual actuator and sensor capabilities. Ferroelastic compounds such as shape memory alloys have large energy densities and are biocompatible. However, to take full advantage of these properties, it is necessary to employ models and control designs that account for the rate-dependent hysteresis, creep, and constitutive nonlinearities inherent to the materials. Inverse compensation is one technique that achieves this purpose. We present an inversion algorithm based on a binary search of a discretized input grid and apply this to the homogenized energy model for modeling hysteresis. The inversion algorithm is shown to provide a reasonable balance between accuracy and computational speed. Numerical examples are presented for three specific cases of the homogenized energy model.}, number={15}, journal={Journal of Intelligent Material Systems and Structures}, author={McMahan, J. A. and Crews, J. H. and Smith, Ralph}, year={2013}, pages={1796–1821} }
 @article{crews_mcmahan_smith_hannen_2013, title={Quantification of parameter uncertainty for robust control of shape memory alloy bending actuators}, volume={22}, ISSN={["1361-665X"]}, DOI={10.1088/0964-1726/22/11/115021}, abstractNote={In this paper, we employ Bayesian parameter estimation techniques to derive gains for robust control of smart materials. Specifically, we demonstrate the feasibility of utilizing parameter uncertainty estimation provided by Markov chain Monte Carlo (MCMC) methods to determine controller gains for a shape memory alloy bending actuator. We treat the parameters in the equations governing the actuator’s temperature dynamics as uncertain and use the MCMC method to construct the probability densities for these parameters. The densities are then used to derive parameter bounds for robust control algorithms. For illustrative purposes, we construct a sliding mode controller based on the homogenized energy model and experimentally compare its performance to a proportional-integral controller. While sliding mode control is used here, the techniques described in this paper provide a useful starting point for many robust control algorithms.}, number={11}, journal={SMART MATERIALS AND STRUCTURES}, author={Crews, John H. and McMahan, Jerry A. and Smith, Ralph C. and Hannen, Jennifer C.}, year={2013}, month={Nov} }
 @inproceedings{mcmahan_smith_2013, title={Sliding mode control for inverse compensated hysteretic smart systems}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, vol 1}, author={McMahan, J. A. and Smith, R. C.}, year={2013}, pages={335–344} }
 @article{mcmahan_smith_2012, title={Sliding Mode Control Design for Hysteretic Ferroelectric Materials}, volume={8342}, ISSN={["0277-786X"]}, DOI={10.1117/12.914631}, abstractNote={Ferroelectric materials are attractive for use in a wide range of applications due to their unique transduction capabilities. However, taking full advantage of these capabilities requires a control design which accounts for the materials' inherent hysteretic behavior. A common approach is to partially cancel the hysteretic effects in the system by employing an approximate inversion algorithm in the control input, resulting in an almost linear system. Using a recently developed modification to the homogenized energy model for ferroelectric materials, we combine this method with a sliding mode control design to track a reference trajectory even in the presence of modeling and inversion errors. Numerical simulations illustrate the effectiveness of the design.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2012}, author={McMahan, Jerry A. and Smith, Ralph C.}, year={2012} }
 @inproceedings{mcmahan_smith_2012, title={Sliding mode control based on an inverse compensator design for hysteretic smart systems}, DOI={10.1109/cdc.2012.6426815}, abstractNote={Ferroelectric (e.g., PZT), ferromagnetic (e.g., Terfenol-D) and ferroelastic (e.g., shape memory alloy (SMA)) materials offer unique design and control capabilities for a range of present and emerging control applications. However, all of these materials exhibit creep, rate-dependent hysteresis, and constitutive nonlinearities that must be incorporated in model-based control designs to achieve stringent tracking requirements. In this paper, we employ a recently-developed extension of the homogenized energy model (HEM) to characterize rate-dependent hysteresis behavior and construct an approximate model inverse for sliding mode control design. We illustrate this in the context of an actuator employing the ferroelectric material PZT but note that the general framework is also applicable to magnetic and shape memory alloy transducers. Through numerical examples, we illustrate the effectiveness of the HEM inverse-based sliding mode design for tracking a reference trajectory in the presence of modeling and inversion errors.}, booktitle={2012 ieee 51st annual conference on decision and control (cdc)}, author={McMahan, J. A. and Smith, R. C.}, year={2012}, pages={985–990} }
 @article{mcmahan_smith_2011, title={Adaptive Control Design for Hysteretic Smart Systems}, volume={7978}, ISSN={["1996-756X"]}, DOI={10.1117/12.884621}, abstractNote={Ferroelectric and ferromagnetic actuators are being considered for a range of industrial, aerospace, aeronautic and biomedical applications due to their unique transduction capabilities. However, they also exhibit hysteretic and nonlinear behavior that must be accommodated in models and control designs. If uncompensated, these effects can yield reduced system performance and, in the worst case, can produce unpredictable behavior of the control system. In this paper, we address the development of adaptive control designs for hysteretic systems. We review an MRAC-like adaptive control algorithm used to track a reference trajectory while computing online estimates for certain model parameters. This method is incorporated in a composite control algorithm to improve the tracking capabilities of the system. Issues arising in the implementation of these algorithms are addressed, and a numerical example is presented, comparing the results of each method.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2011}, author={McMahan, Jerry A. and Smith, Ralph C.}, year={2011} }