Robust Fault Detection For Delta Operator Systems

The discrete sampled systems have been developing rapidly because of the computer technology. In processing high sampling data system, discrete time model using Delta operator approaches corresponding continuous time model, and the results also tend to the corresponding ones of its continuous counterpart. As the sampling rates increase, the numerical instability problems caused by the conventional shift operator(Z transform) can be well conquered by the Delta operator. In order to ensure the system safety and reliability, researches on robust fault detection for control systems are very important. This thesis is concerned with robust fault detection problem for Delta operator formulated discrete time system by using fault detection filter, threshold selection method and linear matrix inequalities(LMI).First of all, for Delta operator formulated discrete time system, the residual generator is constructed based on full-order filter, and the robust fault detection filter design is reduced to H∞filtering problem by using H∞control theory. Then the solvable condition and the solutions are derived by employing LMI method. The simulations show that when the sampling period is very small, compared to the numerical instability problems caused by the conventional shift operator, the robust fault detection filter based on Delta operator can achieve the system stability. The filter parameters and detection results are closer to the ones based on continuous systems, thus the related problems of robust fault detection for continuous time system and discrete time system can be considered in the unified Delta operator framework. Secondly, the design approach to robust H∞fault detection filter for norm-bounded uncertain Delta operator systems is studied. The simulation result shows that the designed fault detection filter has strong robustness to uncertainties. Besides, considering that the filter parameters might vary in a designed-limited bound, the non-fragile robust H∞fault detection filters for Delta operator systems and uncertain Delta operator systems are designed. The numerical examples illustrate the effectiveness of the proposed approaches and show that it’s necessary to consider the variation of the filter parameters when the fault detection filter is designed.Finally, in order to further verify the validity of the proposed schemes and apply them to practice, the proposed approach of robust H∞fault detection filter for Delta operator systems is applied on the fault detection of the elevator driving mechanical system. The simulation results show that the designed fault detection filter has high sensitivity to faults, strong robustness to noise disturbances and can detect the faults quickly.