Design and analysis of robust residual generators for systems under feedback control

In this paper, a general approach is presented to design robust fault detection and isolation (FDI) filters for LTI uncertain systems under feedback control. A two-step design procedure is proposed to derive non-conservative robust FDI filters. The first step consists of designing an optimal FDI filter that maximizes fault sensitivity performance and simultaneously minimizes the influence of unknown inputs, for a large class of model perturbations. The design problem is formulated so that all free parameters are optimized via Linear Matrix Inequality techniques. The second step consists of a systematic post-design analysis procedure. A test is proposed to check if all FDI objectives are achieved for all specified model perturbations. The problem is formulated using an appropriate performance index over a specified frequency range. The solution is based on the generalized structured singular value. Finally, experimental results from a pilot laboratory system are presented to demonstrate the effectiveness of the proposed method.