Bayesian optimization for automatic tuning of a MIMO controller of a flotation bank

Abstract

A flotation bank consisting of 6 cells in series where each level is controlled by a Proportional–Integral (PI) controller is tuned using Bayesian Optimization (BO) in simulation. A Multi-Input–Multi-Output (MIMO) inventory controller is tuned to optimize the level response of the entire bank. The objective function defining optimality is a trade-off between disturbance rejection and reference tracking in the form of a weighted average of the integral squared error and the integral time absolute error of the level reference tracking error for each cell. The MIMO inventory controller used is a lower diagonal matrix where each element has a PI controller structure. The controller settings selected by the BO are constrained, assuming that the plant is linear, such that only controllers which produce stable closed-loop responses will result. Structured singular value analysis is performed, before tuning, to confirm that this is the case. The BO automated tuner is able to tune multiple PI elements to provide an overall improvement of the flotation bank level control. The method is applied successfully with and without measurement noise on a simulated plant. For use in industry, since the process is simple to model, the controller can be tuned off-line in simulation. To compensate for model-plant mismatch, once the controller is implemented the BO automatic tuner can be allowed a limited number of steps to obtain the optimal controller parameters. This provides a valuable time-saving tool for a process control engineer to tune an industrial plant quickly and efficiently.