A nonlinear observer design for an activated sludge wastewater treatment process

Abstract

This paper treats the problem of estimating simultaneously the state and the unknown inputs of a class of nonlinear discrete-time systems. An observer design method for nonlinear Lipschitz discrete-time systems is proposed. By assuming that the linear part of this class of systems is time-varying, the state estimation problem of nonlinear system is transformed into a state estimation problem for LPV system. The stability analysis is performed using a Lyapunov function that leads to the solvability of linear matrix inequalities (LMIs). Performances of the proposed observer are shown through the application to an activated sludge process model.

New dynamical observers design for linear descriptor systems

“…In [2], the modelling and control of mechatronics systems is treated by using a descriptor systems approach. In [3] a non‐linear observer for descriptor systems is designed to estimate the state variables and the unknown inputs in a wastewater treatment plant. Biological complex systems are modelled by descriptor systems in [4] and discrete‐time descriptor systems are used in [5] to design observers for state estimation in an experimental hydraulic tank system.…”

Unknown Inputs Nonlinear Observer for an Activated Sludge Process

“…In [21] the authors resorted to a linear matrix inequality (LMI) to determine the values of the gain matrix of the asymptotic and classic observer, those are applied to a linearized bioprocess model. In the same framework a nonlinear observer which actually utilized both LMI and Lyapunov function was studied in [22]. In [11], the authors applied one classical Luenberger observer which was dedicated to continuous nonlinear models after linearization and it allows the estimation of nitrate and ammonia concentrations.…”

Fault diagnosis for discrete-time descriptor linear systems

“…So that represents the physical phenomena that the model by ordinary differential equations can not describe. These systems were introduced by Luenberger (1977) from a control theory point of view and since, great efforts have been made to investigate descriptor systems theory and their applications (see Müller and Hou (1993); Müller (2005); Liu et al (2008); Boulkroune et al (2009);Darouach (2009) ;Zhou and Lu (2009); Darouach (2012); Araujo et al (2012)). The main contribution of this paper is the new observer structure, which is more general than those presented in Darouach et al (2010) and Wu et al (2009).…”