Simplified grinding mill circuit models for use in process control

Abstract

A grinding mill circuit forms a crucial part in the energy-intensive comminution process of extracting valuable metals and minerals from mined ore. The ability to control the grinding mill circuit is of primary importance to achieve the desired product specification with regards to quality and production rate. In order to achieve control objectives an accurate dynamic model of the milling circuit is required. Phenomenological models are preferred over linear-time-invariant models since the latter cannot describe the non-linear behaviour of the process. However, the available phenomenological models of grinding mill circuits are usually complex, use large parameter sets and are mostly aimed towards steady-state design of grinding mill circuits. This study investigates simplified non-linear dynamic models of grinding mill circuits suitable for process controller design. In the first part of this study, the number of size classes in a cumulative rates model of a grinding mill circuit is reduced to determine the minimum number required to provide a reasonably accurate model of the circuit for process control. Each reduced size class set is used to create a non-linear cumulative rates model which is linearized to design a linear model predictive controller. The accuracy of a model is determined by the ability of the corresponding model predictive controller to control important process variables in the grinding mill circuit as represented by the full non-linear cumulative rates model. The second part of the study validates a simple and novel non-linear model of a run-of-mine grinding mill circuit developed for process control and estimation purposes. This model is named the Hulbert-model and makes use of the minimum number of states and parameters necessary to produce responses that are qualitatively accurate. It consists of separate feeder, mill, sump and hydrocyclone modules that can be connected to model different circuit configurations. The model uses five states: rocks, solids, fines, water and steel balls. Rocks are defined as too large to be discharged from the mill, whereas solids, defined as particles small enough to leave the mill, consist of out-of-specification coarse ore and in-specification fine ore fractions. The model incorporates a unique prediction of the rheology of the slurry within the mill. A new hydrocyclone model is also presented. The Hulbert-model parameters are fitted to an existing plant’s sampling campaign data and a step-wise procedure is given to fit the model to steady-state data. Simulation test results of the model are compared to sampling campaign data of the same plant at different steady-state conditions.