LMI-Based H ∞ Nonlinear State Observer Design for Anaerobic Digestion Model

This note deals with the design of an H∞ nonlinear state observer for the anaerobic digestion model. Positively, the designed observer is an unified one that can be used for different class of systems, mainly linear systems, Linear Parameter Varying (LPV) systems with known and bounded parameters, and nonlinear Lipschitz systems. Applying the Lyapunov theory and the H∞ criterion, Linear Matrix Inequality (LMI) condition is synthesised and solved to obtain the designed observer gains. The novelty of our work consists in the relaxation of the synthesized LMI condition through the inclusion of additional decision variables. This was possible due to the use of a suitable reformulation of the Young’s inequality. Stability, effectiveness and potency of the theoretical results are confirmed by the simulation results.

[1]  Finn Haugen,et al.  State estimation and model-based control of a pilot anaerobic digestion reactor , 2014 .

[2]  D. Dochain,et al.  On-Line Estimation and Adaptive Control of Bioreactors , 2013 .

[3]  Mohamed Darouach,et al.  Invariant observer applied to anaerobic digestion model , 2016, 2016 IEEE 21st International Conference on Emerging Technologies and Factory Automation (ETFA).

[4]  Brahim Cherki,et al.  An invariant observer for a chemostat model , 2014, Autom..

[5]  Jonathan Hess.  Modélisation de la qualité du biogaz produit par un fermenteur méthanogène et stratégie de régulation en vue de sa valorisation , 2007 .

[6]  Mondher Farza,et al.  Nonlinear observers for parameter estimation in bioprocesses , 1997 .

[7]  Irini Angelidaki,et al.  Anaerobic digestion model No. 1 (ADM1) , 2002 .

[8]  Boumediène Benyahia,et al.  MODÉLISATION ET OBSERVATION DES BIOPROCÉDÉS À MEMBRANES : A PPLICATION À LA DIGESTION ANAÉROBIE , 2012 .

[9]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[10]  Michel Zasadzinski,et al.  H∞ circle criterion observer design for Lipschitz nonlinear systems with enhanced LMI conditions , 2016, 2016 American Control Conference (ACC).

[11]  John F. Andrews,et al.  A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates , 1968 .

[12]  Jérôme Harmand,et al.  A generic and systematic procedure to derive a simplified model from the anaerobic digestion model No. 1 (ADM1) , 2015 .

[13]  A Genovesi,et al.  Dynamical model development and parameter identification for an anaerobic wastewater treatment process. , 2001, Biotechnology and bioengineering.

[14]  Annisa Aditsania,et al.  Anaerobic Digestion Model No . 1 ( ADM 1 ) , 2016 .

[15]  Petar V. Kokotovic,et al.  Observer-based control of systems with slope-restricted nonlinearities , 2001, IEEE Trans. Autom. Control..

[16]  Jean-Luc Gouzé,et al.  Closed loop observers bundle for uncertain biotechnological models , 2004 .

[17]  G Stephanopoulos,et al.  Studies on on‐line bioreactor identification. I. Theory , 1984, Biotechnology and bioengineering.

[18]  J. Steyer,et al.  Modeling microbial diversity in anaerobic digestion through an extended ADM1 model. , 2009, Water research.

[19]  Hang-Sik Shin,et al.  Variation of ADM1 by using temperature-phased anaerobic digestion (TPAD) operation. , 2009, Bioresource technology.

[20]  Stefano Marsili-Libelli,et al.  Shock load modelling in the anaerobic digestion process , 1996 .

[21]  Ali Zemouche,et al.  Observers for a class of Lipschitz systems with extension to Hinfinity performance analysis , 2008, Syst. Control. Lett..

[22]  Laurent Dewasme,et al.  State and Input Estimation of an Anaerobic Digestion Reactor using a Continuous-discrete Unknown Input Observer , 2015 .

[23]  K. Fiaty,et al.  Implementation of observer for on-line estimation of concentration in continuous-stirred membrane bioreactor: Application to the fermentation of lactose , 1999 .