Unknown Inputs Observer-Based Output Feedback Predictive Controller for an Activated Sludge Process

ABSTRACT

This paper investigates the control problem of an activated sludge process despite the non-measurable states and the unknown inputs (UIs). Precisely, our objective is to control the global nitrogen concentration ($S_N$) at the settler output, with partial state measurement and UIs. For this MIMO system, a nonlinear predictive controller based on a high-gain observer is proposed. First a state feedback (full information) predictive control low is designed in order to maintain the global nitrogen concentration in accordance with the standard imposed by the European standards for water quality. Then, a high-gain observer-based UI is designed whose aim is to estimate the non-measurable states (the concentrations of the readily biodegradable substrate $S_s$ and the ammonia $S_{N{H}_4}$) and the UIs (the concentrations of substrate soluble in water and the ammoniacal nitrogen entering the reactor: $S_{s_{in}}$ and $S_{N{H}_{4in}}$) despite their variable behavior. Finally, estimated states and inputs are used to generate the output feedback predictive control. Simulation results validate the objective of the paper.

KEYWORDS:

• Activated sludge process
• Nonlinear system
• Predictive control
• Unknown inputs observer

Additional information

Notes on contributors

Feten Smida

Feten Smida received her engineering diploma and master's degree,in electrical-automatic engineering from the National School of Engineer of Gabes,Tunisia in 2008 and in automatic and signal processing from the National School of Engineer of Monastir, Tunisia, in 2010, respectively. She is currently a PhD candidate at electrical engineering in National Engineering School of Monastir. Her research interests are focused on nonlinear control and unknown inputs observation.

Taoufik Ladhari

Taoufik Ladhari received the electrical engineering diploma from INSAT Tunis (2003), in DEA in Automatic Systems from UPS-LAAS Toulouse, France (2004), then the PhD degree in process engineering from the National High School of Mines of Saint-Etienne, France(2007). He is currently Assistant Professor at ENIM. His research interests are in the control and state estimation of nonlinear systems, optimization of bioprocess, and biomedical system. E-mail: [email protected]

Salim Hadj Saïd

Salim Hadj Said received his PhD and his academic accreditation in electric engineering from ENIT in 2009 and ENIM in 2015, respectively. He is currently an assistant professor of Automatic at Preparatory Institute for Engineering Studies of Monastir (IPEIM), Tunisia. His research interests include robust observation, predictive and back-stepping control. E-mail: [email protected]

Faouzi M'sahli

Faouzi M'Sahli received his BS and MS degrees from ENSET, Tunis, Tunisia, in 1987 and 1989, respectively. In 1995, he obtained his PhD degree in electrical engineering from ENIT, Tunisia. He is currently a professor of Electrical Engineering at National School of Engineers, Monastir, Tunisia. His research interests include modeling, identification, and predictive and adaptive control of linear and nonlinear systems. He has published over 80 technical papers and co-author of a book Identification et commande numérique des procédés industriels, Technip editions, Paris. E-mail: [email protected]