Fault detection for parabolic systems with distributed inputs and outputs using the modulation function approach

摘要

An algebraic method to the fault detection for parabolic systems with distributed inputs and outputs is presented in this contribution. The modulation functions method is used to derive an algebraic expression for the fault detection, that only depends on known signals. This allows the detection of the absolute value of piecewise constant faults without a system approximation, despite the occurrence of disturbances. It is shown that the modulation function can be described by a distributed-parameter signal model with a distributed input. For its derivation a systematic approach is proposed, which involves the introduction of suitable in-domain pointwise and boundary measurements. Then, the modulation function follows from solving a trajectory planning problem for its signal model. The results of the paper are illustrated for the actuator and sensor fault detection of a heat conductor.