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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 dynamic non-linear model was fitted to the grind curve data of an industrial semi-autogenous grinding (SAG) mill by means of a step-wise procedure. Grind curves give the steady-state values of the performance variables throughput, power draw, and grind in terms of the mill filling and critical mill speed. The grind curves indicate the operable region of the grinding mill. An analysis and dynamic simulation of the model show that the model captures the main dynamics of the grinding mill. Further simulations demonstrate that the model represents the full range of steady-state conditions defined by the grind curves. In other words, the dynamic model is quantitatively accurate as it settles at the correct steady-state for the operable region of the grinding mill. Therefore, the model is suitable as a simulator to test and develop optimizing control strategies for global operating conditions rather than only for local operating conditions.

A nonlinear phenomenological model of a grinding mill is used to determine five run-of-mine (ROM) grinding milling circuit parameters. The five parameters are fraction of fines and fraction of rocks in the ore fed to the mill, rock and steel abrasion factor and power needed for a ton of fines produced. The model is analyzed according to an identifiability procedure to identify the system data needed to calculate the parameter values. It is shown that a minimum of 18 measurements for a single-stage closed circuit and a minimum of 16 measurements for a single-stage open circuit are needed to determine the five milling circuit parameters. For the closed circuit, the time signals of 8 quantities in the mill will be sufficient to determine all five parameters since the other 10 measurements are time derivatives of these signals. The measurements require the holdup quantities of states within the mill. Since these measurements are not readily available in real-time at plants, it may be difficult to estimate the parameters on-line.