Modeling of Hysteresis and Backlash for a Smart Fin with a Piezoelectric Actuator

This work presents a dynamic model of a smart fin that is activated by a piezoelectric bimorph actuator, which is made by bonding two MFCs. The actuator is completely enclosed within the fin. Earlier research has indicated that the use of a linear model for the fin dynamics does not fully describe the fin. This work presents a more realistic approach to this problem by incorporating additional components into the model. Therefore, a proportional damping matrix is introduced. It is also observed that experimental results exhibit hysteresis and backlash. A Bouc-Wen hysteresis model, combined with four backlash operators, is proposed. These backlash operators are used to model the observed saturation and the non-symmetry of the response. HFSGA is used to identify the optimal set of parameters for the damping matrix constants, the Bouc-Wen model, and the backlash operators. One input case is considered for training the genetic algorithm. The results show that proposed model can predict the hysteresis of the smart fin-actuator system under various operational conditions.