Robust state estimation and fault detection combining unknown input observer and set-membership approach

Abstract

Abstract-This paper aims to propose a new robust stateestimation and fault-detection method by combining the unknown input observer (UIO) and the set-membership estimator (SME). It is known that both the SUIO and the SME can be used to estimate the states of a system. The former aims to obtain a particular value by actively decoupling the effect of unknown inputs, while the latter can obtain state-estimation sets by prediction and correction based on the set theory. Instead of particular state values, the latter can obtain state-estimation sets guaranteeing to contain system states (i.e., robust state estimation). In this paper, we propose to use the framework of the UIO to actively decouple part of unknown inputs and then further employ the set-membership estimation method to estimate state sets and detect faults. The objective of the proposed method is to reduce the conservatism of robust stateestimation sets by using the UIO to remove the contribution of part of unknown inputs to the sizes of state-estimation sets. At the end of this paper, a numerical example is used to illustrate the effectiveness and advantages of the proposed approach.

PIO Output Fault Diagnosis by ARX-Laguerre Model Applied to 2 nd Order Electrical System

“…Moreover, by exploiting (12), (13) and (14) we propose to write the measured output y m (k) from the augmented system (19), under this compact form:…”

“…In this case, the sensors and actuator faults can be considered as unknown inputs as well which are not available from measurements. Therefore, the UIO received great attention in the recent years by using geometric theory to decouple the effects from the unknown inputs [5], [19] or by exploiting the sliding mode approach for the unknown input observer [7], [9] in order to the state estimation as well as the fault. In this context, Proportional-Integral observer (PIO) is considered as an UIO with a simple structure.…”

Generalized set‐theoretic unknown input observer for LPV systems with application to state estimation and robust fault detection

“…The current paper is based on preliminary results by authors recently presented in . In , a preliminary algorithm combining active and passive robust approaches was presented, and used the set‐membership‐estimation framework and the UIO for robust estimation of state sets.…”

“…Moreover, we design SUIOs for the LPV systems to deal with the existence of nonlinearities in actual systems. In this way, we will be able to broaden the applicability and benefit from the advantages of SUIOs in SE and FD applications.The current paper is based on preliminary results by authors recently presented in [21,22]. In [22], a preliminary algorithm combining active and passive robust approaches was presented, and i;k 2 P i for i D 1; 2; : : : ; m:Remark 2.1 P is typically defined as an interval vector (i.e., a box) composed of the intervals of the components of k (P i is the interval for the i-th component of k , and i;k and i;k are the minimal and maximal bounds of i;k , respectively).According to [10,22], a UIO for the LPV system (1) can be designed aś Provided that the standard method of designing UIOs, such as the one proposed in [5], is followed to design the UIO for the LPV system based on (6), the following conditions: ƒ 1 .…”

“…The current paper is based on preliminary results by authors recently presented in [21,22]. In [22], a preliminary algorithm combining active and passive robust approaches was presented, and i;k 2 P i for i D 1; 2; : : : ; m:…”