Computation of a Reference Model for Robust Fault Detection and Isolation Residual Generation

Abstract

This paper considers matrix inequality procedures to address the robust fault detection and isolation (FDI) problem for linear time‐invariant systems subject to disturbances, faults, and polytopic or norm‐bounded uncertainties. We propose a design procedure for an FDI filter that aims to minimize a weighted combination of the sensitivity of the residual signal to disturbances and modeling errors, and the deviation of the faults to residual dynamics from a fault to residual reference model, using the ℋ∞‐norm as a measure. A key step in our procedure is the design of an optimal fault reference model. We show that the optimal design requires the solution of a quadratic matrix inequality (QMI) optimization problem. Since the solution of the optimal problem is intractable, we propose a linearization technique to derive a numerically tractable suboptimal design procedure that requires the solution of a linear matrix inequality (LMI) optimization. A jet engine example is employed to demonstrate the effectiveness of the proposed approach.