Interval observer-based fault detectability analysis using mixed set-invariance theory and sensitivity analysis approach

Abstract

This paper addresses the characterisation of the minimum detectable fault (MDF) by means of residual sensitivity integrated with the set-invariance theory when using an interval observer-based approach as a fault detection (FD) scheme. Uncertainties (disturbances and noise) are considered as of unknown but bounded nature (i.e. in the set-membership framework). A zonotopic-set representation towards reducing set operations to simple matrix calculations is utilised to bound the state/output estimations provided by the interval observer-based approach. In order to show the connection between sensitivity and set-invariance analyses, mathematical expressions of the MDF are derived when considering different types of faults. Finally, a simulation case study based on a quadruple-tank system is employed to both illustrate and discuss the effectiveness of the proposed approach. The interval observer-based FD scheme is used to test the MDF obtained from the integration of both residual sensitivity analysis and set-invariance theory in the considered case study.