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The states and unknown parameters of a non-linear model of a grinding mill circuit are shown to be identifiable from manipulated, controlled and measurable variables. All the states in the mill and sump, the breakage rates in the mill, the mill and cyclone parameters and the mill power draw parameters can be algebraically expressed in terms of known variables. Theoretically, the tiered approach to estimate all states and parameters enables model-fitting without the need for unnecessary assumptions regarding model parameters. The analysis shows the necessity of accurate density and flow-rate measurements across the circuit, and especially the cyclone, to estimate all states and parameters. The aim is to enable non-linear model-based control through model characterisation using available real-time plant measurements.

A commonly used continuous grinding mill circuit model is expanded to a hybrid model which contains both continuous and discrete dynamics. The discrete dynamics in the grinding mill circuit are as a result of switching individual cyclones in a cluster of cyclones. With the additional discrete dynamics an investigation was conducted to establish whether the switching of cyclones can be used as an additional manipulated variable. A nonlinear model predictive controller was implemented using the hybrid grinding mill model. Through simulations it is shown that the switching of cyclones can be used to extend the range of control for the product particle size. When applying a substantial disturbance it was found that certain setpoints could not be reached by the NMPC controller, however by switching in an additional cyclone the particle size setpoint could be reached. Simulation results are given to show that the discrete switching of hydrocyclones can be considered as a manipulated variable for hybrid model based controllers to achieve additional controller benefits.

This paper presents the design and application of fractional single-input–single-output (SISO) controllers to a grinding mill circuit, which is a multiple-input–multiple-output (MIMO) process. Two kinds of controllers are presented: fractional order proportional-integral (FOPI) controllers, and a combination of FOPI and fractional order model reference adaptive controllers (FOMRAC). The parameters of the controller are tuned using off-line particle swarm optimization. In the presence of disturbances and process noise, the SISO fractional controllers achieve similar or better performance compared to linear model predictive control (LMPC).

The states and unknown parameters of a simplified non-linear grinding mill circuit model for process control was estimated from real plant data by means of an Extended Kalman Filter. The output of the model as calculated from the states and parameters estimated by the Extended Kalman Filter closely follow the actual output of the plant. The continuous estimate of states and parameters from plant data allows for the continuous update of a process model used for process control. This limits model-plant mismatch which deteriorates controller performance.