Robust Model-Based Fault Diagnosis for Dynamic Systems

Design of a Robust Polytopic Unknown Input Observer for FDI: Application for Systems described by a Multi-Model Representation

“…The nonlinear model has been discretized through a Tustin method in order to provide discrete linear models represented in equation (11). Disturbance matrices of modeling error E i are directly obtained by a second order linearization and an unique matrix E * is computed through an optimization technique based on Singular Value Decomposition as proposed in [1]. An unique actuator fault on the manipulated variablesV Vr is considered, fault matrices F i are related with the column of B i .…”

“…The modeling errors matrix are noted as E i ∈ R n×q and are supposed to be full column rank for each operating point and d k ∈ R q is the associated modeling error vector. These matrices E i can be obtained from a second-order Taylor expansion or through an identification procedure as treated in [1]. In the following, we consider that D i = 0.…”

“…One way to achieve a fault diagnosis robust to modeling errors is to make disturbance de-coupling conditions hold true (in an optimal sense) for all disturbance distribution matrices. This can be done by using a single optimal disturbance distribution matrix E * to approximate all of them as proposed by [1]. This optimal matrix E * with full column rank makes possible de-coupling residual from modeling errors between different OP.…”

“…Fault detection and isolation (FDI) refers to the task of inferring the occurrence of faults in a process and finding the root causes of the faults. Fault diagnosis based on analytical models is developed for exact and uncertain linear mathematical description of the system, several books are dedicated to these topics: [1] and [2]. FDI on nonlinear systems remains a challenge due to the problem of discriminating between disturbances and faults through a wide range of operating conditions.…”

“…Indeed, these methods consider a particular multi-model approach where each model is dedicated to a specified fault. A fuzzy logic development is also mentioned in [1] for diagnosis but only with Kalman or Luenberger filters which do not permit to deal with modeling errors. Moreover, the activation functions for each model may be not robust to faults.…”