Extremum seeking control of grinding mill circuits based on grind curves

Abstract

Mineral processing plants include several operations to liberate the valuable minerals within raw ore material to produce a concentrate, which is processed into a usable product by a metallurgical refinery. A mineral processing plant consists of a comminution and a separation stage. During the comminution stage, the raw ore material is processed through a grinding mill circuit to liberate the valuable minerals by grinding the ore to fine particles. The product from the comminution stage is then processed at a separation stage, which separates the valuable minerals (concentrate) from the waste material (tailings).

The comminution stage plays a crucial role in the mineral processing industry. It significantly impacts the net revenue generated by a mineral processing plant due to the high operating costs associated with liberating the valuable minerals from the ore material. A grinding stage operates efficiently if it is processing the ore material at its maximum capacity, minimizing power consumption while reducing the amount of valuables lost to the tailings stream. Therefore, the ore material should be sufficiently ground for effective separation in subsequent downstream processes. Ideally, the separation stage requires a consistent stream of fine particles for effective separation.

It is challenging for plant operators to manually achieve the above-mentioned operational objectives, which motivates the need to adopt a suitable control framework and ensure an efficiently run process. The performance of a grinding mill circuit is measured by its throughput and grind quality. These performance indicators are inversely related to operational objectives. The challenge in controlling the grinding mill circuit arises in determining the optimal operating conditions to maximize the net revenue generated by the plant. The optimal operating conditions vary with different ore types and unknown disturbances, such as varying ore hardness, which can result in the comminution stage operating at sub-optimal operating conditions. Furthermore, grinding mills rely on the cascading motion of the ore material and grinding media to accelerate ore breakage. The cascading motion is a function of the fraction of the mill volume filled with ore and the mill rotating speed, which influences the breakage forces that occur between rocks. Therefore, selecting optimal operating conditions is a difficult task requiring frequent adjustments as the operating conditions vary. Grind curves are a valuable tool that establishes the relationship between the mill load filling and rotational speed to the grinding mill throughput, grind quality and power consumption for a given ore type. Generally, the curves show parabolic features and the peaks vary with changes in the ore characteristics. A model-free adaptive control strategy is proposed for optimizing the performance of a semi-autogenous grinding (SAG) mill based on grind curves to improve throughput or grind quality. The controller explores an unknown map in search of the extremum of the performance indicators along the grind curves. A perturbation-based (PESC), a time-varying parameter estimation-based (TESC), and a Nelder-Mead simplex-based (SESC) extremum seeking control method are considered to optimize the grinding mill performance.

Several optimization strategies are investigated for an open grinding mill configuration and a closed grinding mill circuit, where the closed circuit is equipped with a screen or with a hydrocyclone classifier to recirculate oversized ore material for additional grinding. The challenge lies in implementing an efficient optimization model-free control framework that will effectively maximize the performance measures of the complex, non-linear behaviour of the grinding mill circuit.