Systematic Multimodeling Methodology Applied to an Activated Sludge Reactor Model

Abstract

In this article, an analytical method is used to obtain multiple model (MM) forms strictly equivalent to a given nonlinear model. The proposed method induces no information loss, contrary to existing order reduction methods. Several MMs formally equivalent to the initial model may be obtained, due to the intermediate quasi-LPV forms. Thus some criteria are given, using the linear matrix inequality (LMI) formulation, in order to chose the most suitable MM for analysis or control purpose. This method is applied to an activated sludge reactor model.

State and parameter estimation for nonlinear systems: A Takagi-Sugeno approach

“…It allows to extend the use of some tools developed in the linear framework to the nonlinear systems, for the stability study, the control design and observer synthesis. A systematic procedure to transform a nonlinear system by rewriting it into a T-S form, without any loss of information is known as the sector nonlinearity transformation (SNT) [13], [9]. This transformation advantage is to be analytical and systematic.…”

Nonlinear joint state and parameter estimation: Application to a wastewater treatment plant

“…This form allows a better comparison of x(t) withx(t), since µ i (x(t)) µ j (θ(t)) not only appears in (14), but also in (16). Let us define:…”

“…A systematic and exact transformation of a nonlinear system into a T-S form, without any loss of informations, is known as the Sector Nonlinearity Transformation (SNT) [19], [14]. Even if SNT leads to T-S models with unmeasurable premise variables, most of the works on T-S systems are devoted to models with known premise variables, since the estimation or diagnosis is obviously easier when the premise variables are accessible.…”

A New Strategy of Validities’ Computation for Multimodel Approach: Experimental Validation

“…The first one is only based on the measures of inputs/outputs of the system from which are estimated the different models' parameters [5], [10], [11]. For the second and the third method, we supposed to have a nonlinear mathematical model, the base-models are obtained either by linearization around the different operating points [1], or by convex polytopic transformation [6], [12].…”