Attemps of modeling the mineral particle size by using stochastic signals in a balls mill grinding circuit

A full treatment of nonlinear systems such as the ball mill grinding circuit might include stochastic ingredients since the inclusion of several input as well output variables could interact among them, thereby producing a phenomenology which would differ notably of the ones as perceived traditionally. In effect, such interactions could not be described in a fully deterministic scenario due to the lack of information of the phenomenology and dynamics of variables whose temporal evolution turns out to be of importance. This fact might be faced under a stochastic approach which would consider in one hand those representative parameters of the circuit and which are known to priori, and on the other hand the ones which are associated to random behaviors of "hidden" functions as result of the interaction of variables. Thus, in this report a mathematical methodology based on convoluted integrals that in some extent might describe the complexity of the system even in the case when interactions take place, is presented. The analysis and discussion is based from simulations of the temporal evolution of the most relevant variable of the balls mill grinding circuit such as the particle size mineral. According to the results, the incorporation of interactions might be of importance when a certain precision on the set point in robust schemes of control is desired.