Extremum seeking control for optimization of an open-loop grinding mill using grind curves

Abstract

A semi-autogenous grinding mill is simulated with gradient and non-gradient based extremum seeking controllers to maximize the mill performance using grind curves. Grind curves map the essential performance measures of a grinding mill to the mill load and rotational speed. The curves vary with the changes in the feed ore characteristic but show generic parabolic features with extremums. The extremum seeking controllers search along the unknown input–output map to steer the process towards an unknown optimum. In this study, a classical perturbation-based method, a time-varying parameter estimation-based method and the Nelder–Mead simplex method are employed as extremum seeking control (ESC) methods to search along the grind curves to either optimize the mill throughput or grind by means of manipulating the mill feed or rotational speed. The proposed extremum seeking controller could reduce the need for a plant operator to manually select the optimal operating conditions that maximize the performance measures of a grinding mill. Since the controller is agnostic to the process model, the grinding mill can be optimized without the need for a detailed process model. The simulated results show that the extremum seeking controllers steer the mill operating conditions toward the steady-state optimum and can be used to satisfy operational objectives. However, the slow grinding mill dynamics result in a long convergence rate when the initial conditions are far from the optimal operating conditions.