Dynamic modeling and contraction metric-based tube model predictive control for mineral hydraulic collection

Efficient mineral hydraulic collection is a key issue in the mining of deep-sea minerals, where the collection efficiency is related to the lifted fluid velocity and the mineral particle velocity. In this paper, a robust control contraction metric (RCCM)-based tube model predictive control (Tube-MPC) for efficient mineral hydraulic collection is proposed. Firstly, a simplified control model is designed with empirical formula of hydrodynamic forces to avoid the computational burden in solution of the fluid equations. Secondly, a nonlinear programing problem (NLP) for efficiency optimization is formulated to calculate the nominal control law and the optimal state. To address external disturbance and model mismatch from the simplified model, a robust control contraction metric is utilized to calculate the feedback control law to track the optimal state. Finally, numerical simulations and experiments are conducted to verify the mineral hydraulic collection performance of the control strategy.