Nonlinear observer design for two‐time‐scale systems

Comparative Analysis of a Family of Sliding Mode Observers under Real-Time Conditions for the Monitoring in the Bioethanol Production

Online monitoring of fermentation processes is a necessary task to determine concentrations of key biochemical compounds, diagnose faults in process operations, and implement feedback controllers. However, obtaining the signals of all-important variables in a real process is a task that may be difficult and expensive due to the lack of adequate sensors, or simply because some variables cannot be directly measured. From the above, a model-based approach such as state observers may be a viable alternative to solve the estimation problem. This work shows a comparative analysis of the real-time performance of a family of sliding-mode observers for reconstructing key variables in a batch bioreactor for fermentative ethanol production. These observers were selected for their robust performance under model uncertainties and finite-time estimation convergence. The selected sliding-mode observers were the first-order sliding mode observer, the proportional sliding mode observer, and the high-order sliding mode observer. For estimation purposes, a power law kinetic model for ethanol production by Saccharomyces cerevisiae was performed. A hybrid methodology allows the kinetic parameters to be adjusted, and an approach based on inference diagrams allows the observability of the model to be determined. The experimental results reported here show that the observers under analysis were robust to modeling errors and measurement noise. Moreover, the proportional sliding-mode observer was the algorithm that exhibited the best performance.

Indirect Monitoring of Anaerobic Digestion for Cheese Whey Treatment

Efficient monitoring is an open problem in the operation of anaerobic digestion processes, due to the lack of accurate, low-cost, and proper sensors for the on-line monitoring of key process variables. This paper presents two approaches for the indirect monitoring of the anaerobic digestion of cheese whey wastewater. First, the observability property is addressed using conventional and nonconventional techniques, including an observability index. Then, two model-based observer techniques, an extended Luenberger observer, a sliding mode observer, and a data-driven technique based on fractal analysis are formulated and discussed. The performance and capabilities of the proposed methodologies are illustrated on a validated model with experimental data of the anaerobic digestion of cheese whey. Experimental pH measurements are used for the data-driven approach based on fractal analysis. The experimental data sets correspond to experimental conditions (pH > 7.5 and temperature (T) = 40 °C) favoring volatile fatty acid (VFA) production (30 g/L) with simultaneously acceptable biogas production (3420 mL). Results also show that the proposed observers were able to predict satisfactory key process variables. On the other hand, the fractal analysis provides reliable qualitative trends of VFA production and chemical oxygen demand (COD) consumption.