Flatness-based algebraic fault diagnosis for distributed-parameter systems

Abstract

This paper presents a flatness-based approach to the fault diagnosis for a large class of parabolic and biharmonic distributed-parameter systems (DPS). The inputs, outputs and disturbances of the faulty DPS can be defined in-domain or at a boundary. Time-varying additive actuator and sensor faults of polynomial form are considered. In the presence of disturbances with polynomial form, fault identification is achieved in finite-time by evaluating an algebraic expression depending on the known inputs and measurements. This expression results from applying integral transformations to the faulty DPS. It is shown that the corresponding integral kernels follow from the flatness-based realization of a set-point change for a DPS. The solvability of the latter results in fault identifiability conditions. For bounded disturbances of unknown form acting on the DPS, a threshold for secured finite-time fault detection is introduced. The results of the paper are demonstrated for a cantilever beam subject to in-domain actuator and boundary sensor faults. For polynomial type and bounded stochastic disturbances fault detection is verified for the faulty beam in simulations.