Model matching fault detection filter design for a linear discrete-time system with mixed uncertainties

Abstract

The paper discusses the design of a robust fault detection system for linear discrete-time invariant uncertain systems. The intended system consists of norm-bounded uncertainty, stochastic uncertainty, and external unknown input. Due to the mixed uncertainties, H ∞ based model matching technique is used to develop a robust system that offers maximum sensitivity to faults and minimum sensitivity to all other unknown inputs. Reference residual model is designed using co-inner-outer factorization and the fault detection system is designed so that the error between reference residual and robust residual generated by fault detection filter (FDF) is minimized in H ∞ sense. The existing condition of FDF is exploited in terms of linear matrix inequalities. A numerical example and a benchmark three-tank system are simulated to illustrate the performance of the proposed fault detection system. Results confirm the effectiveness of the proposed approach by timely detecting the occurrence of the fault.