State estimation and diagnosis of systems described by multiple model: Application to a biological reactor
Résumé
Applying the methods of analysis and synthesis of linear systems to nonlinear systems presents a number of challenges especially in the construction steps of observer and control law. The structure of multiple model (MM) or polytopic linear model, which was the subject of much attention in the last two decades, provides some answers to these challenges. In the first part of the presentation, we specify how to write a multiple model and its use for monitoring the system. Here, the multiple model structure is based on the principle of reducing complexity of nonlinear systems, building sub-linear models which are then interpolated using appropriate weighting functions. In this paper, the MM is obtained by applying a method that is characterized by no loss of information. It is then explain how to build a dedicated observer adapted to this structure, how to detect and isolate a fault, how to synthesize a fault tolerant control. In the second part of the presentation, we show how the MM structure can be applied to a reactor for water purification. After separation into several time scales, a singularly perturbed standard is obtained. Then, an equivalent MM can be written. The classic form of MM is slightly modified in order to separate the different time scales. Thus, a proportional integral observer for unknown inputs can be constructed using the form MM into two time scales. Because of the limited number of sensors, this approach is attractive due to the choice of fast variables as unknown inputs. This observer can reconstruct the slow and fast state variables simultaneously. We conclude the discussion of some lines of research.