Control Applications for Smart Systems Exhibiting Hysteretic Nonlinearities

Smart materials offer unique transduction capabilities, making them attractive for use in actuators for a wide range of existing and emerging applications. Meeting high performance objectives which fully utilize these capabilities requires control designs which account for the rate-dependent hysteresis and creep inherent to the materials. Using the Homogenized Energy Model (HEM) to quantify this behavior, this dissertation examines the problem of developing and implementing tracking control algorithms that prescribe the output trajectory of a ferroelectric actuator. We summarize the HEM and describe its numerical approximation. Inverse compensation is a standard technique for systems with inputs preceded by hysteresis operators such as Preisach or Prandtl-Ishlinskii models. By compensating for the hysteresis using such an algorithm, design is simplified by permitting the use of linear or simplified nonlinear controllers. We develop an inversion algorithm for the compensation of the HEM, providing compensation not only for the effects of hysteresis, but also for input rate-dependence and creep. The computational cost of the algorithm is bounded in terms of the computational cost of computing the HEM forward in time. Simulation results demonstrate the effectiveness of the algorithm for several variations of the HEM. While the inverse compensation algorithm attenuates the effects of hysteresis and other nonlinear behaviors in the system, it does not eliminate them, nor does it account for modeling error. To accommodate these non-ideal terms in the inverse-compensated system, a sliding mode controller is designed. Sliding mode controls specify discontinuous control laws which are capable of tracking a reference trajectory in the presence of bounded model uncertainties like the inversion error and modeling error. Simulation results verify the expected behavior of the resulting closed loop system. Experimental results of a related controller for a shape memory alloy system which uses a novel method of determining the controller parameters are also presented. The sliding mode controller achieves robust tracking in the sense that good tracking performance is achieved even in the presence of model uncertainties as long as bounds on the uncertainties are known and high input activity due to the discontinuous control law can be tolerated. Adaptive control takes a different approach to dealing with uncertainty in a system. An adaptive control law assumes that a system is adequately modeled but is uncertain due to model parameters which are imperfectly identified or slowly-varying. By extending the state of the model to include estimates of these model parameters, an adaptation law is developed which can adjust the estimates online and yield good tracking results. We improve upon a previously developed adaptive control algorithm for systems with unknown hysteresis by adding terms to the adaptation law to accelerate convergence.;The improved convergence is verified by simulation results. The field of uncertainty quantification has experienced rapid growth, providing many techniques for efficiently propagating parametric uncertainty through a dynamic model. Until recently, these techniques have largely been limited to analyzing or predicting the effects of uncertainties on model outputs. Recent research has investigated the combination of efficient methods for uncertainty propagation using generalized polynomial chaos (GPC) expansions with control parameterization methods. This results in a nonlinear program which determines optimal controls that minimize some choice of statistical norm, such as average output error or output error variance. We apply such an approach to the tracking control of a ferroelectric actuator. This implementation framework provides a first step towards using quantitative knowledge of system uncertainty to improve the control of hysteretic smart systems, with the simulation results suggesting research directions which may improve the usefulness of such an approach.