Output-Bias Reference Correction Using Long Short-Term Memory Networks for Model Predictive Control of Industrial Processes with Delays and Variable Parameters: Application to a Mining Thickener

Many continuous industrial processes are non-linear, multi-variable, subject to transport or reaction delays, and described by operating-point-dependent parameters. These characteristics reduce the reliability of fixed models used in model predictive control (MPC), particularly when slow disturbances, regime changes and operational constraints are dominant. This paper proposes an output-bias reference-correction framework based on Long Short-Term Memory (LSTM) networks for predictive control of industrial processes with delays and variable parameters. The dominant dynamics are represented by a fixed compact linear nominal model in deviation coordinates; this model drives a standard constrained MPC that remains structurally unchanged throughout operation. The persistent output bias between the actual process and the nominal model is learned from closed-loop data by an LSTM network. At each sampling step, the predicted bias is used to correct the future reference trajectory fed to the nominal MPC, so that the controller compensates for model–process mismatch without modifying its internal model, constraint set or solver. The final implementation uses a one-step bias predictor, selected by ablation, and it extends this one-step estimate across the MPC horizon by exponentially decayed persistence. A closed-loop bias-error bound links the LSTM identification error, the adaptive correction gain and the resulting tracking deviation. The framework is illustrated using a mining thickener, a representative process characterised by slow dynamics, delays, variable parameters and stringent safety constraints. A three-controller Monte Carlo study compares the nominal MPC, a classical offset-free MPC and the proposed LSTM-MPC, and it highlights the resulting tracking–actuation–constraint trade-off. Applied to a mining thickener, the LSTM corrector reduces the first-step output-prediction RMSE by 96.6% (FIT from (Formula presented.) to (Formula presented.)). In a 50-scenario Monte Carlo closed-loop evaluation, the LSTM-MPC outperforms the nominal MPC in 92% of scenarios on RMSE while using substantially less actuator activity than the offset-free baseline (mean input total variation: 67.0 vs. 119.4).