Constrained model predictive control of an industrial high-rate thickener

Abstract

High-rate thickeners are used in the mining industry to improve water recovery from slurries and increase their solids ratio. High-rate thickeners operate under strict constraints and several disturbances. To control this process, a constrained model predictive control (MPC) is developed in this paper. For process identification, a historical data-driven methodology is used and a vector autoregressive with exogenous variables (VARX) model structure is considered. The model takes underflow slurry density as both a state variable and the process output, along with turbidity, bed level, rake torque, and cone pressure as additional state variables. It takes feed slurry and flocculant flow rates as manipulated inputs and considers inlet slurry density, slurry circulation flow rate, and underflow slurry flow rate as disturbances. The VARX model structural parameters (orders and delays) and coefficients are estimated using a bilevel optimization method. From the model obtained, a discrete state-space representation is derived. This latter is augmented to obtain a standard formulation without delays. The MPC is then formulated considering the process constraints. To evaluate the control performance, simulations are conducted and a baseline comparison is established using proportional integral (PI) control. Simulation results demonstrate that the proposed control method outperforms the baseline method by providing reduced settling times (−32%), minimized peak errors (−20%), and constraints handling ability. Accordingly, the proposed MPC is implemented in an industrial environment and compared to existing manual control based on an object linking and embedding (OLE) for process control (OPC) architecture. Finally, the industrial results show that the proposed control method effectively stabilizes the underflow slurry density and handles process constraints, resulting in a minimized average error (−90%) and a reduced standard deviation (−50%) compared to existing manual control.