Flatness-based algebraic fault identification for a wave equation with dynamic boundary conditions

Abstract

This paper presents a fault identification approach for a boundary controlled wave equation with dynamic boundary conditions. The faulty system is subject to an additive time-varying actuator fault and an unknown in-domain disturbance. These signals are assumed to be the solution of a finite-dimensional signal model so that polynomial and trigonometric faults as well as disturbances can be taken into account. By making use of integral transformations an algebraic expression is derived to obtain the fault from the known input and output in finite time. The kernels determining the integral transformations are obtained by solving the so-called kernel equations. This problem is traced back to the flatness-based realization of a setpoint change for an ODE-PDE casacade. From this, a condition for fault identification is derived. A simulation example demonstrates the proposed approach.