Fuzzy Intervals‐Based Supervisory Control for Nonlinear Cement Grinding Process

ABSTRACT Controlling nonlinear systems remains a complex challenge, even when their dynamic models are known, due to inherent uncertainties and unpredictable behaviors that affect system performance and stability. This complexity has led to the growing adoption of multi‐controller strategies supervised by advanced controllers, offering substantial advancements over the years. These strategies have evolved from simple approaches to sophisticated techniques that integrate artificial intelligence and machine learning, significantly improving the robustness, performance, and adaptability of control systems across various industries. This paper describes a novel supervisory control approach for a nonlinear cement ball mill grinding system. The proposed approach combines two controllers under the guidance of a fuzzy supervisor: A Proportional‐Integral‐Derivative (PID) controller, fine‐tuned through the Grey Wolf Optimization (GWO) algorithm to achieve a rapid and precise dynamic response, and a Fuzzy Logic Controller (FLC), which delivers robust performance during steady‐state operation while dealing with the uncertainties associated with the process. The supervisory system employs advanced fuzzy aggregation operators, specifically the 2‐additive fuzzy Choquet integral, and the fuzzy arithmetic mean, to evaluate tracking error and its variation. These evaluations dynamically determine the contributions of the PID and FLC controllers, ensuring smooth transitions while augmenting the benefits of each controller. Comparative analyzes with recent control methods highlight the superiority of the proposed approach in achieving a more stable and efficient cement grinding process. This innovative approach ensures flexible and robust management of the studied system, enhancing its overall performance while being easy to implement. It also provides better adaptation to system variations and increased robustness against uncertainties and disturbances.