Underwater dynamic hysteresis modeling and feedforward control of flexible caudal fin actuated by macro fiber composites

Underwater bionic robotics and vehicles that use flexible structures as power sources have attracted considerable attention. Thus, the underwater dynamic behaviors of the flexible structure of a variable cross-section actuated by smart actuators must be further investigated. In this study, underwater dynamic hysteresis modeling and feedforward compensation of a flexible caudal fin driven by macro fiber composites (MFC) at different frequencies were investigated. The MFC-actuated flexible caudal fin is considered a Euler–Bernoulli beam. A revised hydrodynamic function governed by the thickness of the viscous layer and the gap-to-width ratio of the cross-section was developed. Then, a characteristic-frequency-dependent extended transform function model is proposed for the hydrodynamic response of a non-uniform beam. An asymmetric hysteresis model is presented to characterize the rate-independent hysteresis behavior of the MFC actuators. Further, the underwater dynamic equation of the MFC-actuated caudal fin with hysteresis is obtained by connecting the two established models in series. Experiments demonstrate the dynamic behavior between the underwater responses of the caudal fin and the input voltages have an ellipse-like shape and vary in shape and size with oscillating frequency. The ellipse-like dynamic hysteresis loop first grows, reaching its maximum at the resonant frequency, and then decreases, because of the frequency-dependent dynamic behavior. Meanwhile, a phase shift of approximately 90°between the input voltage and underwater dynamic response was observed at the resonant state. Furthermore, the experimental results demonstrate that the proposed model can describe the nonlinear underwater dynamic hysteresis behavior of the proposed caudal fin at different frequencies. The trajectory tracking performances are remarkably improved over a broad frequency range with the proposed compensator. Consequently, the effectiveness of the proposed dynamic model and compensation method was demonstrated. These results are helpful for robotic fish or autonomous underwater vehicles propelled by oscillating foils actuated by smart actuators, including MFC.