Design and Comparison of Fractional-Order Controllers in Flotation Cell Banks and Flotation Columns Used in Copper Extraction Processes

This work explores efficiency improvements in the copper flotation stage, a complex nonlinear, multivariable process subject to numerous perturbations. The primary objective is to design a fractional-order PID (FOPID) control strategy and a fractional-order model reference adaptive control (FOMRAC) system. The parameters for these controllers are optimized using the particle swarm optimization (PSO) algorithm with an objective function tailored to the control goals. This study employs models of both a bank series of five flotation cells and a flotation column. Their performance results are compared against traditional controllers, such as an integer-order PID and MRAC. The findings reveal that fractional-order controllers offer notable advantages over their integer-order counterparts, showing improved performance metrics with minimal changes to the existing control framework. This research highlights the effectiveness of fractional control in enhancing flotation processes and introduces a novel application of fractional control techniques in this area.