Wide Band Modeling and Parameter Identification for Magnetostrictive Actuators

Smart materials, such as magnetostrictive and piezoelectric materials and shape memory alloys, display certain coupling phenomena between applied electromagnetic or thermal fields and their mechanical properties. This leads to complicated constitutive behaviors of actuators built from these materials and limits their effective use. In this paper, we introduce a model for magnetostrictive actuators that effectively captures phenomenological behavior over the frequency range 0-800 Hz. The model includes rate-independent hysteresis, classical eddy current losses, excess losses, magneto-elastic coupling and inertial effects. In related work, we had shown the existence, uniqueness and stability of weak solutions to this model for voltage inputs in the space L²(0,T) cap L^infin (0,T) and external mechanical forces in the space L²(0,T). In this paper, we also propose a method for identifying parameters related to the eddy current and excess losses. Our method holds the hysteresis loss per cycle at a constant value as the frequency of the input voltage is changed, which then allows the identification of the parameters related to eddy and excess losses using linear programming. Our theoretical analysis indicates that the lead resistance cannot be assumed to have a constant value at frequencies higher than 800 Hz, which means that the skin effect becomes important at higher frequencies.