Near optimal interval observers bundle for uncertain bioreactors

In this paper we design an interval observer for the estimation of unmeasured variables of uncertain bioreactors. The observer is based on a bounded error observer, as proposed in [1], that considers a loose approximation of the growing rate. We first show how to generate guaranteed upper and lower bounds on the state, provided that known intervals for the initial condition and the uncertainties are available. These so called “framers” depend on a tuning gain. They can be run in parallel and the envelope provides the best estimate. An optimality criterion is introduced leading to the definition of an optimal observer. We show that this criterion provides straightforwardly a gain set containing the best framers. The method is applied to the estimation of the total biomass of an industrial wastewater treatment plant, demonstrating its efficiency.

[1]  Alex M. Andrew,et al.  Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics , 2002 .

[2]  E. Walter,et al.  Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics , 2001 .

[3]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[4]  Sippe G. Douma,et al.  Relations between uncertainty structures in identification for robust control , 2005, Autom..

[5]  V. Lemesle,et al.  Hybrid bounded error observers for uncertain bioreactor models , 2005, Bioprocess and biosystems engineering.

[6]  Olivier Bernard,et al.  Nonlinear observers for a class of biological systems: application to validation of a phytoplanktonic growth model , 1998, IEEE Trans. Autom. Control..

[7]  Eric Walter,et al.  Guaranteed Nonlinear State Estimator for Cooperative Systems , 2004, Numerical Algorithms.

[8]  E Roca,et al.  An integrated system to remote monitor and control anaerobic wastewater treatment plants through the internet. , 2005, Water science and technology : a journal of the International Association on Water Pollution Research.

[9]  A. Kurzhanski,et al.  Ellipsoidal Calculus for Estimation and Control , 1996 .

[10]  Olivier Bernard,et al.  Nonlinear adaptive control for bioreactors with unknown kinetics , 2004, Autom..

[11]  Maurício C. de Oliveira,et al.  H[sub 2] and Hinfinity Robust Filtering for Discrete-Time Linear Systems , 2000, SIAM J. Control. Optim..

[12]  Lihua Xie,et al.  Robust Kalman filtering for uncertain discrete-time systems , 1994, IEEE Trans. Autom. Control..

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

[14]  Jean-Luc Gouzé,et al.  Near optimal interval observers bundle for uncertain bioreactors , 2007 .

[15]  M. Darouach,et al.  Full-order observers for linear systems with unknown inputs , 1994, IEEE Trans. Autom. Control..

[16]  D. Dochain,et al.  Interval observers for biochemical processes with uncertain kinetics and inputs. , 2005, Mathematical biosciences.

[17]  Giorgio Battistelli,et al.  Design of state estimators for uncertain linear systems using quadratic boundedness , 2006, Autom..

[18]  Benoît Chachuat,et al.  Probabilistic observers for a class of uncertain biological processes , 2006 .

[19]  J. Gouzé,et al.  Interval observers for uncertain biological systems , 2000 .

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

[21]  Alain Rapaport,et al.  Parallelotopic and practical observers for non-linear uncertain systems , 2003 .

[22]  Alain Rapaport,et al.  Output tracking of continuous bioreactors through recirculation and by-pass , 2006, Autom..

[23]  Benoît Chachuat,et al.  Design of Probabilistic Observers for Mass-Balance Based Bioprocess Models , 2004 .

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