Approximating fault detection linear interval observers usingλ‐order interval predictors

Summary Interval observers can be described by an autoregressive‐moving‐average model while λ ‐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 λ ‐order interval predictors and 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 λ − order interval predictor for a given interval observer with the same fault detection properties by the appropriate selection of the λ − order. A condition for selecting the minimal order that provides the λ − 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 λ − 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.