Dynamic Simulation and Model Based Real-Time Optimization of SAG Mills Using Genetic Algorithms

This paper presents a dynamic simulator of the semi-autogenous grinding operation deduced from first principles (non-stationary population balances) coupled to a Model-Based Real-Time Optimization (MBRTO) system to study optimizing strategies for an industrial semi-autogenous mill using genetic algorithms. For the design of the MBRTO both a validated first-principle steady-state model adapted on-line and a dynamic model were used to study the transient effect. The objective function considered is to maximize the ore throughput or the fine-product rate by changing the power-draw. For these purposes, these two performance indexes were introduced as fitness functions in the genetic algorithms. The three decision variables used were the ore feed rate, the water feed rate and the mill rotating velocity. The optimization problem was solved using a classical genetic algorithm with constant population. Constraints in the power draw and the filling level were handled by assigning a penalty function to the fitness function. Simulation results using industrial data for a large 1800 t/h copper-ore mill show the effectiveness of the system in finding the optimum controller set-points as a function of the process-operating constraints; mainly maximum ore feed rate, power draw and filling level. Starting from non- optimum conditions, the optimizer is able to improve the global performance index by 50% relative to a base case.