Fault diagnosis for distributed parameter systems using the modulation functions

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Increasing requirements for technological processes lead to the application of sophisticated control systems. Therefore, fault diagnosis gains more and more importance to ensure the safety of various technological processes. Many results for the solution of this problem can be found for lumped parameter systems, whereas the fault diagnosis of distributed parameter systems (DPS) is still an area of active research. Thereby, most approaches rely on observer-based techniques. This, of course, has the disadvantage that either the DPS or the resulting infinite-dimensional observer has to be approximated. In any case, the resulting fault diagnosis system has a large order to keep the related approximation error sufficiently small. This hinders the implementation of such fault diagnosis methods. In the proposer's research group, a new method for the fault diagnosis for parabolic systems with constant faults was developed, that does not suffer from these shortcomings. The main idea is to derive an algebraic expression for the fault that only depends on known input and output signals. This fault detection equation results from applying the so-called modulation function approach to the DPS. With this, it can be shown that the modulation function follows from realizing a set-point transition problem for a distributed parameter signal model. As a consequence, the fault detection problem can be traced back to a feedforward control problem for DPS. For the latter powerful methods were recently developed in the literature. Hence, the new approach makes it possible that they also become available for solving fault detection problems.The main objective of this research project is the extension of the previously obtained results to a general and systematic approach for the fault diagnosis of DPS. Thereby, time-varying faults, disturbances, and model uncertainties have to be taken into account. Subsequently, the extension of these results to other classes of DPS such as hyperbolic, biharmonic or fractional systems is planned. In order to enlarge the applicability of fault diagnosis methods for real world problems the project also investigates DPS with higher spatial domains and complex geometry. The obtained theoretical results will be verified in simulations as well as by utilizing experimental setups.