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Advances in Model Predictive Control for Flotation
Paulina Quintanilla, Stephen Neethling, Pablo Brito-Parada
Advanced Mineral Processing Research Group, Department of Earth Science and Engineering,
Imperial College London, UK
Daniel Navia
Universidad Técnica Federico Santva María, Chile
ABSTRACT: Model Predictive Control (MPC) strategies rely on the model that represents the dynamics of
the process, which has often hindered its application in flotation. We present a new dynamic flotation model
that incorporates froth physics, and which is suitable for MPC. Unlike other flotation models for control, our
model includes important variables related to froth stability and pulp-froth interface physics, and incorporates
phenomenological equations for froth recovery and entrainment. The model is the basis for an economic MPC
strategy that was implemented in both simulations and a laboratory-scale flotation rig, with encouraging results
for its exploitation in industrial flotation circuits.
INTRODUCTION
Advances in flotation control and optimisation are of great
relevance since even small increases in metallurgical recov-
ery lead to large economic benefits (Ferreira and Loveday,
2000, Maldonado et al., 2007). The implementation of
advanced flotation control and optimisation strategies,
however, poses many challenges since flotation perfor-
mance is affected by many variables that interact with each
other. Disturbances that are not easily measured further
complicate the implementation of efficient strategies.
Effective control is difficult due to the complex and
dynamic nature of the phenomena taking place in flota-
tion cells (Quintanilla et al., 2021a). Process disturbances
include changes in feed flowrate, particle size distribu-
tion, and feed grade, among many others. The standard
control method used in flotation is Proportional-Integral
(PI) control, which is commonly used for regulatory con-
trol. However, PI controllers alone are usually ineffective
in optimising key performance indicators, especially under
process disturbances, leading to suboptimal outcomes.
Advanced control and optimisation strategies, particularly
Model Predictive Control (MPC), have gained significant
attention for improving process performance in froth flota-
tion. MPC uses a dynamic model of the process to predict
future behaviour and optimise control actions, balancing
performance while satisfying constraints. However, despite
the potential benefits of MPC strategies in flotation, their
full utilisation has been hindered by the complexity of
modelling process dynamics and instabilities. The kinetic
models used in previous studies (e.g., Maldonado et al.
(2007) Putz &Cipriano (2015) Riquelme et al. (2016))
are insufficient in modelling complex froth phase phenom-
ena, which are critical drivers of flotation performance.
New advancements in flotation modelling for control that
incorporate the froth phase phenomena can be found in
Oosthuizen et al. (2021), and Quintanilla et al. (2021b, c).
Economic model predictive control (E-MPC) is a strat-
egy to optimise control actions based on economic objec-
tives. As such, it is a promising solution for enhancing
flotation performance. E-MPC introduces the economic
optimisation layer into traditional model predictive con-
trol, allowing for direct integration of process economics