Fault Detection For Delta Operator Systems

The sampled-data systems have been developing rapidly with the development of computer technology. Delta operator approach can avoid the ill-conditioned problems caused by the conventional shift operator based theory when fast sampling. The Delta operator formulated model approaches the corresponding continuous time model as the sampling interval goes to zero, thus the design of continuous time systems can be directly applied to discrete time systems. The fault detection using Delta operator has been attracting much attention in recent years, which is significant for high speed sampled-data systems.New development of fault detection and diagnosis (FDD) for control systems is firstly reviewed in this thesis, then the problems of fault detection for the Delta operator formulated discrete time system are studied. The major contributions of the thesis are as following.(1) The problem of fault detection for the Delta operator formulated discrete time system is studied. Some sufficient conditions are developed for fault detection and isolation (FDI) of Delta operator systems. The design method of the Delta operator-based fault detection filter is proposed. When the sampling period is very small, the FDI method using Delta operator will approach the corresponding FDI results for continuous time cases, thus the related problems of fault detection for continuous time system and discrete time system can be considered in the unified Delta operator framework. A numerical example illustrates the effectiveness of the proposed approach.(2) Based on the traditional Luenberger observer using the shift operator, a new observer design approach to fault detection for Delta operator systems is proposed. Both the existence conditions and explicit expression of the desired observer are developed. The algorithm of observer-based fault detection for Delta operator systems is also given. The simulation results show the effectiveness of the proposed approach.