Actuator Fault Detection and Estimation for a Class of Hyperbolic PDEs Using Filter-Based Observer

This paper is concerned with simultaneous actuator fault detection and estimation problems for a class of hyperbolic partial integral-differential equations (PIDEs) with boundary controlled and boundary observation. Based on a Luenberger-type observer, the paper studies fault detectability and gives detectability conditions. In presence of actuator fault, the traditional boundary observer based backstepping techniques can only detect a fault occurrence rather than estimate the fault parameter. In this case, this paper developed two novel plant state observers equipped with corresponding fault parameter estimator (parameter tuning update law). The first observer is designed without consideration of model uncertainties or external disturbances based on the observation error system and the fault parameter tuning update law is developed in cooperation with a simple error target system obtained through backstepping transformation. Moreover, with consideration of bounded model uncertainties and disturbances, this paper also developed a filter-based observer. It can also be seen that the second method is easily extended for sensor fault estimation. For both proposed methods, only the boundary measurement and input signals are needed. Finally, a representative example is given to verify theoretical results of this paper.