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A non-linear observer model of a semi-autogenous grinding mill is developed. The observer model distinguishes between the volumetric hold-up of water, solids, and the grinding media in the mill. Solids refer to all ore small enough to discharge through the end-discharge grate, and grinding media refers to the rocks and steel balls. The rocks are all ore too large to discharge from the mill. The observer model uses the accumulation rate of solids and the mill's discharge rate as parameters. It is shown that with mill discharge flow-rate, discharge density, and volumetric hold-up measurements, the model states and parameters are linearly observable. Although instrumentation at the mill discharge is not yet included in industrial circuits because of space restrictions, this study motivates the benefits to be gained from including such instrumentation. An extended Kalman filter is applied in simulation to estimate the model states and parameters from data generated by a semi-autogenous mill simulation model from literature. Results indicate that if sufficiently accurate measurements are available, especially at the discharge of the mill, it is possible to reliably estimate grinding media, solids and water hold-ups within the mill. Such an observer can be used as part of an advanced process control strategy.

A non-linear model-based control architecture for a single-stage grinding mill circuit closed with a hydrocyclone is proposed. The control architecture aims to achieve independent control of circuit throughput and product quality, and consists of a non-linear model predictive controller for grinding mill circuit control, and a dynamic inversion controller to control the fast sump dynamics. A particle filter is used to estimate the mill states, and an algebraic routine is used to estimate the sump states. The observers make use of real-time continuous measurements commonly available on industrial plants. Simulation results show that control objectives can be achieved by the controller despite the presence of measurement noise and disturbances.

A hybrid non-linear model predictive controller (HNMPC) is developed for a run-of-mine ore grinding mill circuit. A continuous-time grinding mill circuit model is presented with a hydrocyclone cluster as the primary classifier. The discrete-time component is the switching of hydrocyclones in the hydrocyclone cluster. The resulting model is a hybrid non-linear model with both continuous and discrete dynamics. A simulation of the HNMPC shows the advantages of using the hydrocyclone cluster as an additional manipulated variable. The advantages of the HNMPC is illustrated by comparing its performance to a non-linear MPC where no switching of hydrocyclones is possible. The genetic algorithm based HNMPC showed increased controller stability in its ability to incorporate discrete dynamics into the controller directly. The methods discussed in this paper can be used to incorporate different types of discrete dynamics into advanced grinding mill circuit controllers due to the modular presentation of the model and HNMPC controller design.

The recently developed reference-command tracking version of model predic- Email address: derik.leroux@up.ac.za (Johan D. le Roux) 1 This work was carried out while the author was a visiting professor at the University of Pretoria, South Africa. February 17, 2015 in standard MPC, the control horizon is normally restricted. However, in the MPSP technique the control horizon is extended to the prediction horizon with a minor increase in the computational time. Furthermore, the MPSP technique generally takes only a couple of iterations to converge, even when input constraints are applied. Therefore, MPSP can be regarded as a potential candidate for online applications of the nonlinear MPC philosophy to real-world industrial process plants. Preprint submitted to Journal of Process Control