OPTIMAL-CONTROL OF A BALL MILL GRINDING CIRCUIT .1. GRINDING CIRCUIT MODELING AND DYNAMIC SIMULATION

Mineral grinding circuits can be controlled with a set of proportional-integral (PI) controllers or alternatively by specialized controllers which make use of optimal control theory. The latter control strategy is superior in the sense that feed solid and water addition rates are manipulated in concert to achieve a specified control objective. A dynamic model is needed for optimal control, and for PI control the model can be used for off-line tuning. Off-line tuning circumvents the problem of on-line tuning, during which transients persist for a long time, resulting in lost production. The key elements of the full dynamic model are the population balance model of the ball mill and an empirical model of the hydrocyclone. The model development and its verification for both steady- and unsteady-state responses are shown. On-line computations with the full dynamic model require the solution of 37 differential equations at every sampling instant. In addition, optimal control calculations may overburden the control computer. Therefore, a simplified model using just three state variables is shown to be adequate for dynamic predictions. In Part II the full dynamic model is used in off-line tuning and the simplified model is used in the optimal controller. Both model predictions and pilot scale ball mill circuit responses are shown.