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This paper proposes an observer-based residual generator (OBRG) for diagnosing faults in a continuous non-affine system with polynomial non-linearities up to any finite degree where the fault and an unknown input affect both the system and part of the output. Firstly, given certain assumptions and the use of defined extended vectors, a parameterized polynomial system is considerred for which a compact set of sufficient conditions is given for the existence of a candidate OBRG. Conditions for error stability (by a Lyapunov method) and detectability are given. The calculation steps in the design of the OBRG are shown to involve the solution of three linear equations (with parameterizations) and the calculation of a set of constant matrices (for detectability of faults). A result is then given establishing that the design holds for a much wider class of systems. The residual design is applied to a real three-tank system.

The design of a high-gain observer-based residual is considered for a class of non-linear systems. Input–output maps are derived for use in residual design to increase design flexibility. An invest...

This paper proposes a robust fault detection observer (RFDO) for a continuous non-linear system with polynomial non-linearities up to any finite degree. The observer error and residual are robust with respect to unknown inputs. Sufficient conditions are given, in an efficient algebraic compact form, for a RFDO (observer and residual) to exist. Useable results on detectablility conditions are proved. Numerical prodedures for the design of a RFDO and a sub-optimal RFDO (SORFDO) are given. The theory is illustrated with an application to a (benchmark) three-tank system. One linear and three non-linear models are considered with corresponding RDFOs (including a sub-optimal RFDO), and the performances of the corresponding residuals are compared under two initial conditions for a scenario consisting of a leak (fault) and a disturbance.

A bilinear fault detection filter (BFDF) is proposed for bilinear systems with unknown inputs. Sufficient conditions are given for the existence of a BFDF and a strict BFDF for which the latter is sensitive to all faults. A particular choice of observer structure is shown to give explicit solutions both for the observer gain matrix and for establishing fault sensitivity. Structured actuator and component faults give rise to residuals with known directions enabling these faults to be easily isolated. A numerical example is used to demonstrate the BFDF design.

A nonlinear observer is considered for a class of discrete nonlinear descriptor systems subject, to unknown inputs and faults. This class is partly characterized by globally Lipschitz nonlinearities, and a member system may be singular and possibly non-causal. The structure proposed for the observer makes it useful for both state estimation for feedback controls and residual generation for fault detection. Results on the existence of solutions are given and some useful bounds are derived which are important in the observer design. The proposed nonlinear observer is based on a transformed system and on the solution of a Riccati equation. The existence, convergence properties and robustness of the observer are investigated by the use of a quadratic Lyapunov function. A design algorithm is given and applied to the estimation of the states of a flexible joint robot.

A bilinear fault detection observer is proposed for bilinear systems with unknown input. A sufficient condition for the existence of the observer is given. The residual generated by this observer is decoupled from the unknown input. The method is applied to a hydraulic test rig to detect and isolate a large group of simulated faults. The effectiveness of the method in fault detection and isolation for the hydraulic system is demonstrated by real data simulation.