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Takagi-Sugeno (T-S) type of polytopic models have been used prominently in the literature to analyze nonlinear systems. With the sector nonlinearity approach, an exact representation of a nonlinear system within a sector could be obtained in a T-S form. Hence, a number of observer design strategies have been proposed for nonlinear systems using the T-S framework. In this work, a design strategy for adaptive observers is presented for a type of T-S systems with unknown parameters. The proposed approach improves upon the existing literature in two folds: reduce the computational burden and provide an algorithmic procedure that would seamlessly connect the state estimation and parameter estimation parts of the observer design. Lyapunov approach is used for the stability analysis and the design procedure. The results are illustrated on a simulation example.

International audience; In this paper, the problem of observers for Takagi-Sugeno (TS) models with unmeasurable premise variables is investigated and a new design approach is proposed. The idea, is motivated by the immersion techniques and auxiliary dynamics generation, and consists in the transformation of the TS system with state dependent weighting functions in a new TS system with weighting functions depending only on the measured variables. This result aims to relax the strong conditions used in the design of observers for TS systems with unmeasurable premise variables. Illustrative examples are provided to discuss the performances of the proposed approach.

Air Handling Units (AHU) are responsible for efficiently transferring the energy produced for heating or cooling to the occupant area in the building. This energy transfer dynamics is modeled as a bilinear system. Such a structure poses problems to develop observers either with asymptotically vanishing error or with guaranteed error bounds. Takagi-Sugeno based polytopic models allow modeling of such nonlinear systems as well as to extend the results from linear system theory. Parameter estimation of such models with guaranteed error bounds is presented in Bezzaoucha et al. (2013). The present work applies this nonlinear parameter estimation technique on the energy balance model of a heat exchanger, the key component in an AHU. Three parameter estimation scenarios are proposed and extension to the theoretical results in the reference from an implementation point of view are given. Simulation results are provided to show the feasibility of the approach.

Process monitoring needs the development of data analysis tools aiming at recognizing, at each time instant, system operating mode using the measurement collected on the system. This communication aims at presenting a method relying on measurement analysis, able to identify operating modes without the knowledge of the mathematical models describing these modes. The proposed method relies on the writing of a global model combining, in a multiplicative way, the models describing the different modes. The parameters of this global model are then numerically identified from the available set of measurements. The sensitivity analysis of the global model with regard the input/output variables then provides an indicator to identify, at each instant, the current operating mode. The proposed method is applied on a simplified model of a grinding mill.