Experimental Implementation of a Nonlinear Control Method for Magnetostrictive Transducers

In this paper, we discuss the development and experimental implementation of a nonlinear control design for magnetostrictive transducers operating in hysteretic regimes. The hysteresis and constitutive nonlinearities are characterized using a homogenized energy framework based on energy relations at the lattice level employed in combination with stochastic homogenization techniques that incorporate material and field nonhomogeneities. Using this framework, we employ nonlinear optimal control theory to construct open loop inputs for tracking. We subsequently employ Pi-based perturbation feedback to ensure robustness with respect to model uncertainty and sensor noise. Experimental implementation results at frequencies up to 1000 Hz demonstrate the feasibility of the method for high speed tracking while operating in highly nonlinear operating regimes.