(382c) Robust Fault Tolerant Control of Hydraulic Pipeline Systems

We study the application of the fault tolerant control for hydraulic pipeline systems described by the so-called water hammer equations [1]. By taking the benefits of backstepping transformations [2] and the superposition principle, novel observers are proposed to realize fault detection and estimation while fault detectability analysis is facilitated in backstepping coordinates. Moreover, fault detectability conditions are given and namely once a fault occurs the detection residual (the difference between the measured physical output and the estimated output) exceeds the predefined threshold. Upon a fault detection, the integration of novel plant state observer design and the design of novel adaptive tuning update law is proposed without consideration model uncertainties and external disturbances present [2]. Nevertheless, due to the coupling between the fault parameters and state/input, the conventional observer cannot undertake the tasks of fault estimations upon the fault detection. By decoupling the observation error system, this paper first develops a novel approach to solve the actuator fault detection and estimation simultaneously. In the proposed approach, only detection residual is needed. However, the observer error system cannot be transformed into the desired form for the solution of the sensor estimation problem. Later, the observer is modified based on superposition principle, and novel methods are proposed with available detection residual. The developed methods cannot only address both fault detection and estimation issues but also complete plant state estimation in presence of faults. In particular, bounded model uncertainties and disturbances are considered, and by applying proposed methods the state estimation error and fault parameter estimation error are ultimately bounded. Based on resulting fault detection and estimation, a novel robust output regulation scheme is proposed to complete output tracking issues. Finally, a representative example is given to verify theoretical results.

[1] Van Pham, T., Georges, D., & Besancon, G. (2014). Predictive control with guaranteed stability for water hammer equations. IEEE transactions on automatic control, 59(2), 465-470.

[2] Diagne, A., Diagne, M., Tang, S., & Krstic, M. (2017). Backstepping stabilization of the linearized Saint-Venant–Exner model. Automatica, 76, 345-354.

[3] Xu, X., and Dubljevic, S., Adaptive fault detection and estimation for a class of PIDE systems based on boundary observers, Automatica, Under review, 2018.