SUMMARYIn this paper, robust fault detection based on adaptive threshold generation of a non-linear system described by means of a linear parameter-varying (LPV) model is addressed. Adaptive threshold is generated using an interval LPV observer that generates a band of predicted outputs taking into account the parameter uncertainties bounded using intervals. An algorithm that propagates the uncertainty based on zonotopes is proposed. The design procedure of this interval LPV observer is implemented via pole placement using linear matrix inequalities. Finally, the minimum detectable fault is characterized using fault sensitivity analysis and residual uncertainty bounds. Two examples, one based on a quadruple-tank system and another based on a two-degree of freedom helicopter, are used to assess the validity of the proposed fault detection approach.᭧

In this paper, a Fault Tolerant Control (FTC) strategy for Linear Parameter Varying (LPV) systems that can be used in the case of actuator faults is proposed. The idea of this FTC method is to adapt the faulty plant instead of adapting the controller to the faulty plant. This approach can be seen as a kind of virtual actuator. An integrated FTC design procedure for the fault identification and fault-tolerant control schemes using LPV techniques is provided as well. Fault identification is based on the use of an Unknown Input Observer (UIO). The FTC controller is implemented as a state feedback controller and designed using polytopic LPV techniques and Linear Matrix Inequality (LMI) regions in such a way as to guarantee the closed-loop behavior in terms of several LMI constraints. To assess the performance of the proposed approach, a two degree of freedom helicopter is used.

In this paper, robust fault detection is addressed based on evaluating the residual energy that it is compared against worst-case value (threshold) generated considering parametric modelling uncertainty using interval models. The evaluation of the residual/threshold energy can be done either in the time or frequency domain. This paper proposes methods to compute such energy in the two domains. The first method generates the adaptive threshold in the time domain through determining the worst-case time evolution of the residual's energy using a zonotope-based algorithm. The second method evaluates the worst-case energy evolution in the frequency domain using the Kharitonov polynomials. Results obtained using both approaches are related through the Paserval's Theorem. Finally, two application examples (a smart servoactuator and a two degrees of freedom helicopter) will be used to assess the validity of the proposed approaches and compare the results obtained.

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