Enhancing batch reactor temperature control: a hybrid PID-MPC approach for magnesium stearate production from palm stearin

Abstract A hybrid Proportional-Integral-Derivative Model Predictive Controller (PID-MPC) is developed to regulate the temperature of a batch reactor to obtain high yield of product in the novel production of magnesium stearate from magnesium hydroxide and palm stearin, with palm stearin serving as a sustainable, renewable alternative to existing source of stearic acid. Previous studies indicate that a reaction temperature of 180 °C yields an optimum yield of magnesium stearate highlighting the critical role of precise temperature control in optimizing reactor performance. In this study, a PID controller was initially tuned using the Ziegler-Nichols (ZN) method, yielding proportional, integral, and derivative gains of 0.6, 3.75, and 0.024, respectively. The MPC design was then integrated with the PID controller, utilizing a prediction horizon of 60, a control horizon of 20, and a sampling time of 0.216 s. Simulations were conducted using MATLAB R2024a’s Simulink toolbox to evaluate the performance of the hybrid PID-MPC controller in comparison to single PID and MPC controllers in both servo and regulatory cases. The hybrid PID-MPC controller outperformed the standalone PID and MPC controller in the absence of process disturbance, demonstrating minimal overshoot and a faster settling time. While the Mean Absolute Error (MAE) and Mean Squared Error (MSE) for both the hybrid PID-MPC and single MPC controllers were similar where both approaching to zero. In the presence of constraint, it excelled in disturbance and noise rejection, achieving the lowest MAE (1.245) and MSE (1.551), highlighting its superior robustness and control performance compared to single controllers ensuring high quality and yield of magnesium stearate of 68.16 % using palm stearin. These findings demonstrate that the hybrid PID-MPC approach provides highly robust and efficient temperature control, even under the influence of disturbances, positioning it as a great solution for enhancing the performance and optimization of batch reactor operations in producing high yield of magnesium stearate using renewable palm stearin.