Multi‐Rate Sampled and Delayed Output Signal Prediction‐Based Observer Design for Two‐Stage Anaerobic Digestion Process

ABSTRACT Two‐stage anaerobic digestion (TSAD) has emerged as a promising technology for both organic pollutant purification and biogas production. In industrial applications, however, TSAD process measurements are subject to multi‐rate sampling, different time delays, and sensor noise, while certain critical process states (e.g., concentrations of anaerobic microorganisms) remain unmeasurable in real time. To address these challenges, this study proposes a multi‐rate sampled and delayed output signal prediction‐based (MSDOSP) observer for TSAD processes, which simultaneously reduces measurement errors and estimates key unmeasurable states. The proposed MSDOSP observer utilizes multi‐rate sampled measurements with time delays and noise to simultaneously reconstruct accurate continuous signals and provide real‐time state estimation. The vector small‐gain theorem is employed to rigorously establish the stability conditions of the observer. Finally, the performance of the MSDOSP observer was verified on the MATLAB/Simulink platform compared with two existing methods.