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In this article, a model-free extremum-seeking control (ESC) design is proposed for the operational control of mineral grinding, where both operational indices regulation and throughput maximization are considered. Operational indices regulation and throughput maximization, as two conflicting objectives, are balanced through assigning weighting matrices to obtain a specific choice from the Pareto frontier of the multiobjective optimization problem. To deal with the input constraints, due to the physical limitations and operational constraints, a saturation function is imposed on each input and an extra penalty function is introduced to punish the inputs outside the feasible regions. The integrators and the additive perturbation signals in the ESC are swapped such that dead-zone operators can be added in between and imposed on the estimated gradients to attenuate the oscillation caused by modulating signals. The stability analysis of the proposed control design is provided in the absence of dead-zone operators. A Hardware-in-the-Loop simulation experiment is carried out to show the effectiveness of the proposed ESC. [ABSTRACT FROM AUTHOR]

Operation performance of mineral grinding processes is measured by the grinding product particle size and the circulating load, as two of the most crucial operational indices that measure the product quality and operation efficiency, respectively. In this paper, a data-driven method is proposed for the operational control design of mineral grinding processes with input constraints. A reference governor is introduced to take into account the input constraints and the infeasible setpoint issue. The reference governor generates feasible setpoints that keep control inputs within allowed regions. The lookup table embedded in the reference governor mapping steady-state outputs to inputs provides feasible setpoints for output regulation and baseline for inputs. An ad hoc optimization guarantees that the input constraints are not violated, with the priority of regulating the grinding product particle size if regulation of both indices is not feasible. Since the dynamic model of the controlled plant is complicated because of the strongly nonlinear and intricately coupled nature of ball mills and hydrocyclones, a novel policy iteration algorithm is proposed for optimal regulator design without system modeling. Simulation results comparing performances of a mineral grinding process with and without the reference governor show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]