Koopman Operator Based Model Predictive Control of the Grinding Process

As a critical stage in mineral processing, the grinding process plays a pivotal role in determining the concentrate grade, recovery rate, and overall economic efficiency. Owing to its nonlinear dynamics and inherent uncertainties, traditional control methods face significant challenges in achieving precise optimization. The Koopman operator provides a mathematical framework for representing nonlinear systems in a high-dimensional linear space, thereby facilitating the application of linear control techniques. This study employs the Koopman operator in conjunction with Extended Dynamic Mode Decomposition (EDMD) to develop a high-dimensional linear model of the grinding process. Leveraging this model, a Model Predictive Control (MPC) strategy is formulated to enhance process optimization. The proposed approach effectively manages input-output constraints and mitigates computational complexity through quadratic programming, thereby enhancing control accuracy and stability. Experimental results validate the efficacy of the proposed method in optimizing nonlinear grinding processes. This study presents an efficient and interpretable framework for intelligent optimization control of the grinding process.