A data-driven optimal control approach for solution purification process

Solution purification holds a critical position in hydrometallurgy. With its inherent complexity and the mixed raw material supply, solution purification process exhibits various working conditions, and has nonlinear, time-varying dynamics. At current stage, a comprehensive and precise model of a solution purification process is still costly to obtain. More specifically, the model structure could be derived by applying physical and chemical principles, while the accurate model parameters cannot be obtained under certain working conditions due to reasons like insufficient data samples. This, in turn, introduces obstacles in achieving the optimal operation. In order to circumvent the modeling difficulty, this paper proposes a ‘Process State Space’ descriptive system to re-describe the optimal control problem of solution purification process, accordingly establishes a two-layer receding horizon framework for developing a data-driven optimal control of solution purification process. In the optimal control scheme, on the ‘optimization’ layer, by utilizing the ‘multiple-reactors’ characteristic of solution purification process, a ‘gradient’ optimization strategy is proposed to transform the dosage minimization problem into obtaining the optimal variation gradient of the outlet impurity concentrations along the reactors. On the ‘control’ layer, a model-free input constrained adaptive dynamic programming algorithm is devised and applied to calculate the optimal dosages for each reactor by learning from the real-time production data. Case studies are performed to illustrate the effectiveness and efficiency of the proposed approach. The results and problems need future research are also discussed.