Research on a multimodel adaptive optimal control method for the mineral flotation process

The mineral flotation process plays a pivotal role in the extraction and purification of nonferrous metal ores such as copper and silver. However, its inherent characteristics—strong nonlinearity, substantial disturbances, and frequent operating condition changes—pose major challenges to traditional control strategies, which often fail to achieve dynamic adaptability and global optimality. This research aims to develop an intelligent control framework capable of maintaining high concentrate grades and system stability under fluctuating production conditions.

To address process variability and model mismatch, a multimodel adaptive optimal control method based on adaptive dynamic programming (ADP) is proposed. First, a multicondition modeling framework is established using recurrent neural networks (RNNs), with the beluga whale optimization (BWO) algorithm employed to globally optimize RNN learning rates. This BWO-RNN modeling approach significantly enhances the generalization capability and fitting accuracy across different operating scenarios. In the control stage, a parallel ADP tracking controller within an augmented state-space framework is adopted, enabling real-time policy iteration to compute the optimal control law. Furthermore, a cumulative error–based model-switching mechanism is introduced to dynamically select the most suitable submodel and controller in response to changing process conditions, thereby ensuring robust system performance and seamless controller transitions.

The proposed framework was validated using simulation data from a copper–silver flotation plant. Compared to traditional model-based control and (particle swarm optimization) PSO-optimized RNNs, the BWO-RNN model achieved higher fitness values and shorter training times. In control experiments involving transitions among three typical operating conditions, the multimodel ADP controller demonstrated superior tracking accuracy for copper and silver concentrate grades, with lower overshoot and faster response times than baseline controllers. In addition, the model-switching strategy effectively suppressed oscillations and maintained stability even under abrupt changes in operating conditions, demonstrating strong robustness. The overall control cost was reduced by 4.3%, indicating improved reagent efficiency and operational economy.

This study presents a novel adaptive control framework integrating a multimodel structure, BWO-RNN–based data-driven modeling, ADP-based optimal tracking control, and a dynamic model-switching mechanism. The proposed method effectively addresses the nonlinear, time-varying, and disturbance-prone characteristics of the flotation process. Simulation results confirm its capability to achieve stable and accurate concentrate grade tracking across diverse operational scenarios, offering a promising approach for industrial deployment in mineral flotation systems. Future work will focus on extending the framework to real-time online identification and practical field implementation in industrial flotation plants.