Iterative Learning Model Predictive Control of Underwater Flexible Structure With Harmonic Actuation by Macrofiber Composites

The precise trajectory tracking of underwater flexible structures driven by smart materials is essential for bionic underwater propulsion systems, thus attracting increasing attention. In this work, we introduce a compound controller that combines an iterative learning model predictive control (ILMPC) with a dynamic hysteresis compensator. This approach realizes effective trajectory tracking of an underwater flexible structure through harmonic actuation of macrofiber composites (MFC) across a relatively broad frequency range. We present a dynamic hysteresis model that includes a state space model and a modified Prandtl–Ishlinskii (MPI) model. Experimental results indicate that the proposed hysteresis model effectively captures the underwater dynamic hysteresis nonlinearity of the MFC-actuated structure. Then, we develop the ILMPC method, which integrates model predictive control and iterative learning to reject real-time hydrodynamic disturbances and model uncertainties. To generate effective input trajectories, we design a generalized objective function that allows for independent adjustment of the weighting factors for manipulated variables to time indexes and interactive predictive horizons. We also discuss the convergence and robustness of the ILMPC. Experiments demonstrate the effectiveness of the proposed compound controller over a broad frequency range. These findings are meaningful for MFC-actuated flexible structures in applications of autonomous underwater vehicles, robotic fish, and other applications.