Approximating fault detection linear interval observers using -order interval predictors

摘要

Interval observers can be described by an autoregressive-moving-average model while -order interval predictors by a moving-average model. Because an autoregressive-moving-average (ARMA) model can be approximated by a moving-average 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 -orderintervalpredictorsand the interval observers from the point of view of the fault detection performance. The paper also proves that it is possible to obtain an equivalent -order interval predictor for a given interval observer with the same fault detection properties by the appropriate selection of the -order. A condition for selecting the minimal order that provides the -order interval predictor equivalent to a given interval observer is derived. Moreover, because the wrapping effect could be avoided by tuning properly the interval observer, we can find an equivalent -order interval predictor such that it also avoids the wrapping effect. Finally, an example based on an industrial servo actuator will be used to illustrate the derived results. Copyright (c) 2016 John Wiley & Sons, Ltd.