This presentation will focus on model development, uncertainty quantification, and control issues associated with emerging applications in which smart materials provide unique capabilities as actuators, sensors, or functional units. Three examples include macro-fiber composites (MFC) utilizing the piezoelectric material PZT, magnetic Terfenol-D transducers, and shape memory alloy (SMA) devices. MFC are presently being considered for applications ranging from flow control to remote deployment and control of membrane mirrors whereas magnetic transducers provide high-speed, high-accuracy milling capabilities. Shape memory alloys are presently being considered for applications ranging from jet noise reduction to conformable catheters for laser ablation treatments of atrial fibrillation.
For all of these materials, we characterize inherent hysteresis and nonlinear dynamics using the homogenized energy model (HEM) framework. To determine uncertainty bounds for the model parameters, we employ statistical parameter estimation and bootstrapping techniques to construct covariance matrices and densities for the parameters. We then propagate these uncertainties through the models to construct densities and confidence intervals for the model outputs. To provide high speed, high accuracy tracking capabilities, we employ a hybrid control design comprised of a nonlinear optimal open loop signal with an outer feedback loop. As demonstrated by experimental results, this design has been implemented at rates up to 1 kHz for magnetic transducers operating in highly nonlinear and hysteretic regimes.
Ralph Smith is a Professor in the North Carolina State University Department of Mathematics, Associate Director of the Center for Research in Scientific Computing (CRSC), and a member of the Operations Research Program. His research focuses on the mathematical modeling of smart materials, numerical analysis and numerical methods for physical systems, parameter estimation, and control theory.