Robust Residual Generation by the Assignment of Observer Eigenstructure

Abstract

In Chapter 3, various approaches for generating robust residual via unknown input observers have been introduced. The underlying principle of these approaches is to make the state estimation error be independent of disturbances (or unknown inputs). The residual is defined as the (weighted) output estimation error which is a linear transformation of the state estimation error. The residual generated by UIOs is also independent of disturbances, if the disturbance term does not appear in the output equation or the disturbance term in the output equation has been nulled. In model-based FDI, the state estimation is not necessarily needed, because the required information is the diagnostic signal - residual. Hence, it is not necessary to de-couple the state estimation error from disturbances in model-based FDI. A direct approach to design disturbance de-coupled residuals is then required. In this approach, the residual itself is de-coupled from disturbances, however the state estimation error may not be. It can be expected that existing conditions for such a direct approach could be relaxed compared with those required for UIOs.