Admissible model matching using DR-regions: fault accommodation and robustness against FDD inaccuracies
Résumé
This paper proposes a reformulation of the Admissible Model Matching (AMM) method for Fault-Tolerant Control (FTC) using Linear Matrix Inequality (LMI) regional pole placement. The essential feature of the AMM approach is that the FTC design is based on the specification of a set of admissible closed-loop behaviors whose limits represent the acceptable control performance degradation in the presence of faults. In the original formulation, this set is characterized by inequalities relating the coefficients of the closed-loop system matrix, derived ‘ad hoc' for the particular system and the provided control specification, and the FTC design problem is formulated as a non-linear constrained optimization problem. In this paper, the set of admissible behaviors is specified by restricting the closed-loop spectrum in a union of particular convex regions called DR-regions. On one hand, this allows a straightforward representation for a wide variety of practical control specifications while preserving the convexity of the problem. On the other hand, DR-regions are characterized by LMIs and the fault accommodation can be formulated in terms of several LMI (feasibility) problems. Moreover, the robustness of the solutions against errors in the fault estimations provided by the Fault Detection and Diagnosis module is characterized as well as a LMI-constrained optimization problem. The versatility and the effectiveness of the proposed method are illustrated using an example.