This article proposes to consider the basic thermodynamics based formulation of the energy balance equation for chemical systems with a limited number of simplifying assumptions. The objective is to show, via the design of one typical mass and energy balance state observer, how such design can be modified by considering the proposed thermodynamically based model formulation. The objective is also to emphasise the difference and the links between the energy balance-based temperature equation largely used in process control. The design of the asymptotic observer is illustrated with two examples: one CSTR in liquid phase and another one in gaseous phase.

This paper proposes a nonlinear finite-time converging observer for a class of nonlinear systems. The estimate is recovered from the present and delayed estimates provided by two independent dynamical systems converging to a function of the state with linear error dynamics. The estimation is carried out using only the Jacobian matrix of both transformations determined by solving two systems of partial derivative equations. The results are illustrated on a bioreactor model.

In this paper we propose an observer for a dynamical system for which the states on the frontier of its domain are not observable, and all trajectories converge to the frontier. The proposed case study, a bioreactor in batch operating conditions with a single microbial reaction and gas production, is standard and largely encountered in practical situations. We show also how to extend this observer to obtain an observer in higher dimension that is robust with respect to unbiased noise.