A Sliding Mode Multiobserver Based on an Uncoupled Multimodel: An Application on a Transesterification Reaction

Abstract

This paper concerns the design of robust sliding mode multiobserver for nonlinear systems. A discrete uncoupled multimodel structure is retained for the modeling of nonlinear systems. Unlike the classically used multimodel structures, the retained uncoupled multimodel is known by its flexibility of modeling, thus, the structures of the partial models are adapted to the complexity of the local models in each operating zone. Sufficient conditions are provided, in terms of linear matrix inequalities (LMIs), to ensure the asymptotic stability of the proposed sliding mode multiobserver. A convergence analysis is achieved to obtain the convergence radius. A numerical example and a real time application on a transesterification reactor are carried out to illustrate, once again, the performance of the proposed sliding mode multiobserver in terms of precision and rapidity of convergence.

Fault detection using sliding mode multiobserver for nonlinear systems: Validation on a real chemical process

“…Otherwise, when each partial model has its own independent state vector, an uncoupled multimodel structure is obtained. Hence, this last structure allows the obtention of a more flexible multimodel representation (Montacer et al, 2019(Montacer et al, , 2020.…”

A discrete output feedback 2-SMC using Linear Matrix Inequalities and adaptive switching gain approaches: Real application on a chemical reactor

“…As demonstrated in Messaoud et al (2009), Messaoud and Ben Abdennour (2017) and Montacer et al (2018), the considered reactor is a highly nonlinear systems. Its static characteristic shows that the transesterification reaction has three operation zones: heating, reaction, and cooling.…”

Indirect Measurement of Variables in a Heterogeneous Reaction for Biodiesel Production

“…They also allow for formalizing and incorporating the The goal of the observer is to obtain an accelerated process dynamic, allowing us to predict (estimate) the behavior of variables; then, a mathematical model is required. Usually, the models considered are based on the general equation of the transesterification reaction [7] since it describes the different steps to transform triglycerides in biodiesel and crude glycerol, regardless of the reaction phase (homogeneous or heterogeneous transesterification); kinetics, conversion rate, reaction mechanism, and mass and energy balance are usually included in the models for variables' estimation [5,[8][9][10]. Once the models are formulated, it is necessary to adapt their structure according to the state space theory, since this is the basis for observer development.…”