Link between high gain observer-based residual and parity space one

The first step of the fault detection and isolation (FDI) procedure is to design a set of residuals that reflect the discrepancy between the actual behavior of the system and the expected behaviour given by its model. To design these residuals, two approaches can be used. The first approach, namely parity space approach, rests on analytical redundancy relations whereas the second uses observers. The two approaches have been widely compared in the linear frame. This paper extends this comparison to nonlinear systems. More precisely it is proven that, for a class of nonlinear MISO systems, a relationship exists between residuals which are generated using high-gain observers and parity residuals. The example of a series DC motor is used to illustrate the result.