Optimal Tracking Using Magnetostrictive Actuators Operating in Nonlinear and Hysteretic Regimes

摘要

MANY ACTIVE MATERIALS EXHIBIT NONLINEARITIES AND HYSTERESIS WHEN DRIVEN AT FIELD LEVELS NECESSARY TO MEET STRINGENT PERFORMANCE CRITERIA IN HIGH PERFORMANCE APPLICATIONS. This often requires nonlinear control designs to effectively compensate for the nonlinear, hysteretic field-coupled material behavior. In this paper, an optimal 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 unified 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 homogenizations techniques to predict macroscopic material behavior. The constitutive model is incorporated into a finite element representation of the magnetostrictive transducer which provides the framework for developing the finite-dimensional nonlinear control design. The control design includes an open loop nonlinear component computed off-line with perturbation feedback around the optimal state trajectory. Estimation of unmeasurable states is achieved using a Kalman filter. The hybrid control technique provides the potential for real-time control implementation while providing robustness with regard to operating uncertainties and unmodeled dynamics.