Hardware-in-the-Loop Multiobjective Extremum-Seeking Control of Mineral Grinding

Abstract

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.