An enhanced nonlinear PID controller design for the CSTR system utilizing NARX-Laguerre model

This study leverages a second-order discrete-time Nonlinear AutoRegressive Exogenous (NARX)-Laguerre model to develop a nonlinear predictive proportional–integral–derivative (PID) control approach. The proposed technique employs the model predictive control (MPC) framework to dynamically adjust the PID controller parameters. This work is motivated by the limitations of conventional PID controllers in handling nonlinear dynamics and system constraints, which are frequently encountered in real-world applications. In addition, the challenge of control signal saturation is addressed, with a practical solution introduced to improve system performance. The effectiveness of this advanced PID control strategy is demonstrated through its application to a continuous stirred tank reactor (CSTR).