ARX/NARX Modeling and PID Controller in a UV/H2O2 Tubular Photoreactor for Aqueous PVA Degradation

Water-soluble polymers are widely employed as additives in many different industries. The need to treat sewage contaminated with water-soluble polymers is essential to prevent persistent pollutants from entering our environment. The advanced oxidation process (AOP), UV/H2O2 process, is used in this study to degrade polyvinyl alcohol (PVA) in aqueous solutions. However, a suitable modeling approach and a control scheme are required to remove the PVA polymer and reduce hydrogen peroxide (H2O2) residual in the treated effluent within a safe level to prevent adverse effects on the aquatic system as well as subsequent biological processes. This study presents black-box modeling for identifying the dynamics of polyvinyl alcohol (PVA) degradation in a series of UV/H2O2 photo-reactors, where the process input and response variables are inlet hydrogen peroxide concentrations and effluent pH, respectively. Data processing, model development, and process simulation are performed using MATLAB R2019b software. In this study, the linear AutoRegressive with eXogenous input (ARX), non-linear ARX (NARX), and Hammerstein-Wiener models are considered as base system models, where the sigmoid-network-based NARX produced the best representation with 82.24% of the trainset and 76.28% of the validation-set of the process dynamics. The design of PID controllers tuned using ARX and sigmoid-network-based NARX models are discussed, and the controller performance is analyzed for set-point tracking and disturbance rejection through simulation studies. The closed-loop response of ARX-PID and NARX-PID are deemed adequate. In fact, the NARX-PID performs much better for the studied process achieving an integrated absolute error (IAE) of 0.6211 with a settling time of 4.63 h, whereas the ARX-PID has lower IAE (0.4238) and produces a more aggressive controlled output response robust in disturbance rejection. Thus, ARX-PID is adequate for frequent process disturbances but less for process set-point tracking.