Hybrid predictive control of heave compensation based on CNN–Transformer–GRU

The heave motion of ships under medium sea conditions can be severe, with amplitudes often exceeding 1 m, posing significant risks to operational safety and personnel. To address this issue, this study proposes a deep learning-based method for predicting heave motion and subsequently compensating for it by treating the predicted motion as a disturbance. The CNN–Transformer–GRU neural network architecture is introduced and trained on a heave motion dataset. This model reduces prediction errors by more than 37.9% compared to conventional CNN–LSTM and Transformer-based approaches. To ensure effective and stable compensation, the predictions are incorporated as input disturbances into a model predictive control (MPC) framework. Simulation results demonstrate that the proposed controller exhibits excellent stability and robustness, maintaining relative displacement within 0.0015 m in the heave direction.