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Mineral processing plants remain nowadays infamous for their low energy efficiency. Economic model predictive control (EMPC), by directly considering the energy costs, could possibly help reduce their footprint, but its environmental benefits are yet to be clearly quantified. In an attempt to cast some light on this topic, this paper compares the response to a given ore feed size and hardness disturbance sequence of an EMPC to that of basic and advanced regulatory control systems using the profits and the specific energy (power draw/ore feed rate) as metrics. The simulated circuit comprises a high-pressure grinding rolls (HPGR), a ball mill, and a flotation circuit. It is based on population balance modeling and is an extension of previous works. The basic regulatory control (BRC) system comprises only single-input–single-output control loops with proportional–integral (PI) controllers and operates at a fixed feed rate. The advanced regulatory control (ARC) system consists of PI controllers maximizing the plant feed rate with override constraint handling. The results show that (1) ARC generates more revenue and maintains a lower circuit specific energy consumption than BRC, (2) ARC can produce the same economic performance as EMPC because the constraints of the system define the economic optimum, and (3) EMPC can trade revenues for a lower circuit specific energy with a hybrid criterion that penalizes power draw. • The work compares different control systems on an HPGR grinding circuit. • A decentralized PI control system can generate equivalent revenues to an EMPC. • EMPC can trade revenues for a lower circuit specific energy. [ABSTRACT FROM AUTHOR]

[Display omitted] • An observer allows estimating the slip profile in an HPGR working gap. • It is based on force balance equations and the Coulomb friction criterion. • The observed ore showed slippage at the working gap level. Modelling the high-pressure grinding rolls mass flow rate from the continuity principle represents a difficult task, partly because the ore may slip against the rolls. In effort to increase the understanding of this phenomenon, this paper introduces a state observer to estimate the slip profile in the HPGR working gap from the force balance equations and Coulomb friction criterion. The observer is used off-line and a posteriori, i.e. it requires a series of HPGR tests conducted at different levels of specific force and roll speed. It allows observing the slip profile on a gold ore at the pilot scale. As the material enters the compression zone, it descends at a slower rate than the vertical component of the roll peripheral speed. As it progresses downward, its velocity increases. It exceeds the roll peripheral speed at the working gap level and peaks below. The pressure peaking above the working gap makes slipping possible. It leads to the material above the working gap to push onto the one below and thus accelerating it. [ABSTRACT FROM AUTHOR]

• This paper presents a steady-state high-pressure grinding rolls model. • It consists of unified previously published works. • It is calibrated on 18 pilot scale data sets. This paper unifies high-pressure grinding rolls crusher (HPGR) models of the working gap, mass flow rate, power draw, and centre and edge product particle size distribution models to produce a framework that allows the simulation of the equipment for process optimization and control studies. Calculating the model parameters requires exclusively a series of HPGR tests, but the framework prediction capabilities remain confined within the range of the calibration data set. The model inputs the specific force, the roll speed, the zero-gap and the edge width setting. It makes no restricting hypothesis regarding slip or material bypass and does not necessitate prior knowledge of the flakes density. The work presents an extensive model analysis with calibrations on 18 data sets with invariable moisture content and feed particle size distribution, which includes computing the parameter uncertainties and analyzing the residuals. Seven of these data sets are new, while the rest consists of previously published values. The analysis shows that the model performs satisfactorily for all data sets. [ABSTRACT FROM AUTHOR]

• We review the state of the art developments in process modeling and cone crusher control from 1972 to 2020. • The steady-state model of Whiten (1972) is still used today in recent works. • DEM models are limited to the mechanistic understanding of cone crushers. • Most control applications consist of PID and expert system rather than MPC. • The innovation drivers are the Industry 4.0 and sustainability and profit needs. Run-of-mine ore is usually too large to be useful for construction or metallurgy. Large particles must be reduced to specific sizes to either comply with aggregate sizing regulations, or facilitate mineral liberation; therefore, in the aggregates and mineral processing industries, run-of-mine ore is broken in crushing circuits by cone crushers. Here, we review the cone crusher literature, focusing on the modeling and control of crushing circuits. A total of 61 works published in the primary literature, ranging from 1972 to 2020, are classified and discussed with respect to the model formulation—i.e., population balance models, empirical models, or data-driven models—and control strategy—i.e., proportional-integral-derivative, model predictive control, expert system, or model-free control. The data are summarized in a table that makes locating a particular formulation or strategy quick and easy. The discussion of the current state of the art of crushing circuit modeling and control technologies consolidates the results available in the literature, as well as the challenges that we must overcome to increase crushing performance through control and optimization. The discussion of future trends brings attention to the discrete element method, model based control, plant-wide and mine-to-mill optimization, and machine learning applications for data acquisition and process optimization. [ABSTRACT FROM AUTHOR]