Approximating fault detection linear interval observers using l-order interval predictors

Interval observers can be described by an ARMA model while l-order interval predictors by a MA model. Since an ARMA model can be approximated by a MA model, this allows establishing the equivalence between interval observers and interval predictors. This paper deals with the fault detection application and focuses on the equivalence between the l-order predictor and the interval observer with the same fault detection performance. The predictor approach is developed to obviate the wrapping effect commonly encountered with interval observer approaches. Given a particular linear interval observer, a l-order interval predictor can be found such that its behaviour is equivalent regarding fault detection and besides, it does not suffer from the wrapping effect. Thus, if the interval observer fulfils the isotonicity property, this l-order interval predictor can be computed using two point-wise trajectories corresponding to the upper and lower bound of each uncertain parameter. Finally, an example based on an industrial servo actuator will be used to illustrate the derived results.