State Estimation in a Biodigester via Nonlinear Logistic Observer: Theoretical and Simulation Approach

The state variables in a biodigester are predicted using an unstructured model, and this study offers an analytical design of a Non-Linear Logistic Observer (NLLO), subsequently comparing its performance to that of other prominent state estimators. Because of variables such as temperature, pH, high pressure, volumetric organic load (VOC), and hydraulic retention time (HRT), among others, biodigester samples can be affected by the use of physical sensors, which are not always practical owing to their sensitivity to the type of sampling and external disturbances. The use of virtual sensors represents one approach to solving this issue. In this work, we suggest experimentally validating a mathematical model, then analytically designing a novel NLLO observer, and finally comparing the results to those obtained using a sliding-mode estimator and a Luenberger observer. By including online CH4 and CO2 measurements as inputs to the proposed observer, the local observability analysis demonstrated that all state variables were recoverable. After showing how well the suggested observer performs in numerical experiments, a proof based on the Lyapunov theory is offered. The primary innovation of this study is the incorporation of a novel algorithm that has been empirically validated and has output resilience to input parametric perturbations.