Observer-based fault diagnosis using multiple-model and LMI techniques
The ever-increasing complexity of technical processes requires a higher performance, safety and reliability. For this reason, fault detection and isolation (FDI), which consists of residual generation and residual evaluation, has received more attention in the last years. Most technical processes are represented by a nonlinear system; however it is possible to apply FDI techniques only for a few classes of nonlinear systems. In the last years, the idea of using an aggregation of local models (multiple-models), as a means to capture the global dynamic characteristics of nonlinear systems, has been successfully integrated in the field of FDI. These multiple-models have been used as an alternative for dealing with nonlinear systems. An advantage of using multiple-models for FDI is that the theory for linear systems can be used for nonlinear systems. This thesis mainly focuses on the design of robust FDI schemes for nonlinear systems using multiple-model approaches. The considered approaches are (i) the Takagi-Sugeno (TS) fuzzy model (ii) linear systems with polytopic uncertainty. Three robust FDI schemes based on TS fuzzy models are presented. The first scheme generalizes the linear unknown input observer to a class of nonlinear systems described by TS fuzzy models. The objective of this scheme is to decouple the unknown inputs for residual generation. The second scheme handles nonlinear systems affected by stochastic disturbances; this scheme minimizes the expected steady state estimation error using linear matrix inequality (LMI) techniques. The last one simultaneously enhances the robustness to unknown inputs without sacrificing the fault detection sensitivity. For linear systems with polytopic uncertainty, a robust fault detection filter is designed considering a reference model. The residuals can be evaluated with a threshold based on this filter. The effectiveness of each proposed robust FDI scheme is demonstrated with the help of four application examples.