Fault Tolerant Observer Design for a Class of Re-Entrant Manufacturing Systems

This paper investigates the fault-tolerant observer design problem for a class of re-entrant manufacturing systems (RMSs) in the presence of workstation faults during the production process. A hyperbolic hybrid partial differential equation (HHPDE) continuum model is constructed to describe the dynamics of RMSs suffering from unexpected workstation faults, by considering that machinery failures of workstations lead to discarding of defective products. In the case that the faults are known, a fault-tolerant impulsive observer is designed for state estimation of the RMSs. In the case that the fault information is uncertain, a diagnostic observer based residual evaluation logic is developed for fault detection first. Upon detecting the faults, an adaptive impulsive observer is then proposed to simultaneously estimate both the system states and the faults. In addition, by using a piecewise Lyapunov function candidate, sufficient stability conditions that guarantee the exponential input-to-state stability (EISS) of the estimation error are formulated in terms of linear matrix inequalities (LMIs). Finally, the feasibility and effectiveness of the proposed strategy are validated through numerical simulations.