Optimal Tracking Using Magnetostrictive Actuators Operating in Nonlinear and Hysteretic Regimes

Many active materials exhibit nonlinearities and hysteresis when driven at fleld levels necessary to meet stringent performance criteria in high performance applications. This often requires nonlinear control designs to efiectively compensate for the nonlinear, hysteretic fleld-coupled material behavior. In this paper, an opti-mal control design is developed to accurately track a reference signal using magnetostrictive transducers. The methodology can be directly extended to transducers employing piezoelectric materials or shape memory alloys (SMAs) due to the unifled nature of the constitutive model employed in the control design. The constitutive model is based on a framework that combines energy analysis at lattice length scales with stochastic homoge-nizations techniques to predict macroscopic material behavior. The constitutive model is incorporated into a flnite element representation of the magnetostrictive transducer which provides the framework for developing the flnite-dimensional nonlinear control design. The control design includes an open loop nonlinear component computed ofi-line with perturbation feedback around the optimal state trajectory. Estimation of unmeasurable states is achieved using a Kalman fllter. The hybrid control technique provides the potential for real-time control implementation while providing robustness with regard to operating uncertainties and unmodeled dynamics