A Robust State Estimation Framework Employing a Nonlinear PI2 Observer for Photobioreactor Monitoring

This work proposes an integral-enhanced nonlinear PI2 state observer for the robust estimation of unmeasured states in nonlinear dynamic systems, with experimental validation on a flat-panel photobioreactor. The observer is designed as a virtual sensor to reconstruct key biological variables using a reduced set of online measurements and known operating conditions. Compared with a conventional extended Luenberger observer, the proposed structure improves estimation accuracy and robustness against constant disturbances and model mismatch, which are common in bioprocess applications. The experimental results show a clear performance advantage during transient growth phases while highlighting that the method relies on a locally valid model structure and appropriate gain tuning. Overall, the proposed observer provides a practical and scalable monitoring tool for nonlinear systems where the direct measurement of critical state is not feasible.