429 leaching. More broadly, the Particle Size Distribution (PSD) describes the distribution of particles across their respective size ranges, typically represented in tabular form, providing a comprehensive characterization of the material’s granulometric composition. Figure 1a shows valuable mineral particles embedded within a gangue matrix and their progressive liberation through comminution. As the ore undergoes size reduction, valuable mineral exposure increases as seen on Figure 1b. The plot on Figure 1c presents the resulting P80 time-series (in microns), highlighting inherent stochastic fluctuations during mill operation caused by variations in ore properties and process conditions. Figure 1 – Physical ore fragmentation and resulting P80 time-series variability in grinding operations. Napier-Munn et al. (1996) conclude that optimization in comminution circuits is only meaningful when defined against measurable quantities (e.g., throughput, product size, or energy utilization) and evaluated within specific operating constraints. By applying mathematical and operational models, it is possible to optimize not only isolated grinding circuits but also their interaction with downstream concentration processes, and ultimately entire mine to concentrator operations. The optimization of particle size distribution (P80) remains a cornerstone of mineral processing efficiency, as it directly dictates downstream recovery rates. Maintaining P80 within an optimal range is therefore essential not only for achieving stable and efficient operation, but also for optimizing grinding performance and ensuring consistent downstream processing. However, ore grinding circuits are characterized by multivariate, non-linear, and dynamic behaviors (such as ore hardness variability) that challenge conventional control. Wills & Finch, (2016) proposed a hierarchical control system, as depicted in Figure 2, the objective of this control system structure is to decompose the global problem into simpler, structured subtasks handled by dedicated control layers following the divide-and-conquer strategy. Each control layer performs specific tasks at a different timescale, which provides a functional and temporal decomposition.
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