A Multivariable Dynamic Suboptimal Control Strategy for Mineral Processes with Large Uncertainties in Model and Inputs

Abstract

A suboptimal control method is developed - on the basis of one presented previously by two of the same authors - which provides a practical way for achieving suboptimal dynamic control for multivariable processes in which the stochastic disturbances acting on the plant produce such an uncertainty on its behaviour, that the application of optimizing control strategies becomes difficult. The method uses dynamic multiple input-multiple output adaptive models, where the optimizing control variables are among the inputs, and the outputs are among the variables appearing in the performance functional. A proof is given for this method which, on the one hand, may be implemented by computing the controls to be applied. However, it also has a very practical implementation based on the properties shown by the proof. Indeed, the dynamic adaptive models are used to find the maximum change of the variation of the performance functional with respect to the small set of candidate optimal controls shown to exist at each stage. This is one of the features which makes the method applicable to processes such as flotation. The method has been tested by simulation using both a simple model to exemplify its essential characteristics, and a detailed phenomenological model of a grinding-rougher-first cleaner flotation plant to which stochastic disturbances have been applied to approach a realistic plant behaviour. Comparison by simulation with a static optimization method found in the literature successfully applied to flotation plants, shows an improvement in the speed of response, so that either the time to reach an optimal condition is reduced, or at least the performance functional has a higher value whenever a stationary condition is not reached. Robustness is incorporated using a measure of the adaptive model validity.