A Simplified Algorithm for Setting the Observer Parameters for Second-Order Systems with Persistent Disturbances...

Area of Science:

• Control Systems Engineering
• Bioprocess Engineering

Background:

• State observers are essential for estimating system states not directly measured.
• Robust observers are needed to handle uncertainties and disturbances in real-world systems.
• Accurate estimation is vital in applications like bioprocess monitoring.

Purpose of the Study:

• To determine the convergence region properties of a robust observer for second-order systems.
• To propose a novel algorithm for setting observer parameters under persistent disturbances.
• To apply the observer to estimate key parameters in microalgae photobioreactor cultures.

Main Methods:

• Analysis of observer error dynamics considering bounded disturbances.
• Derivation of the observer error convergence region width.
• Development of a simplified observer parameter tuning algorithm.
• Application to a microalgae culture model.

Main Results:

• The observer error convergence region width is expressed by observer parameters and disturbance terms.
• A minimum point and vertical asymptote for the convergence width were identified and characterized.
• The proposed algorithm simplifies parameter setting by avoiding complex conditions like Riccati equations or LMIs.
• The algorithm effectively estimates biomass and substrate uptake rates in a photobioreactor model.

Conclusions:

• A robust observer with a well-defined convergence region was developed for second-order systems.
• The new algorithm offers a simpler and more practical approach to observer parameter tuning.
• The method is validated through its successful application in a bioprocess engineering context.