Fault Detection For Generalized Systems Based On KYP Lemma

In real life, with the increasing demand for safety and reliability, the fault detection of control system has become a hot issue in the present research. Through the extraction and separation of all kinds of characteristic signals of the system, the fault of the system is detected by the means of analysis, experience and observation.Generalized systems have many unique properties which are different from normal systems. The generalized systems not only have the dynamic constraints which are described by differential equations, but also have the static constraints described by algebraic equations, which are more general than the normal systems with dynamic constraints. However, generalized systems do not necessarily meet the requirements of fault detection method in the traditional sense, which brings difficulty to the generalized systems fault detection and some related stability analysis. Therefore, the research on fault detection of the generalized systems has received extensive attention.In this paper, based on the stability condition and KYP lemma, the fault detection of singular systems with bounded disturbances is studied. The performance H_ index is introduced to measure the sensitivity of residual signal to the fault, and the performance index H∞ is used to measure the robustness of the residual signal to the disturbance. The LMI condition is transformed into the corresponding time domain by using the KYP lemma. The state error system is asymptotically stable and satisfies the given performance H_ / H∞ index. The main results are as follows:Firstly, a special kind of fault observer is designed for the fault detection of actuator faults in a continuous time singular systems with bounded disturbances. The condition of the existence of the fault detection observer and the condition of the observer gain are obtained by the LMI condition of the residual signal performance H_/H∞ index and the admissible condition of the generalized systems.Secondly, fault detection for continuous time singular systems with bounded disturbances is studied. A special kind of fault observer is designed for a class of singular systems. For this kind of error dynamic system, the LMI condition of the residual signal performance H_ /H∞ index and the admissible condition of the generalized system is given, and the condition of the existence of the fault detection observer is obtained.Thirdly, fault detection of singular systems with bounded disturbances is considered. The constrained equivalent model of the generalized systems is obtained by the constrained equivalent transformation. Based on the constrained equivalent model, a special class of special observer with transition vector is designed, and the LMI condition of fault detection performance index and fault detection is given. By using KYP lemma, the problem of fault detection is transformed into linear matrix inequality problem.The observer design for each part of the fault detection is given a specific example, which illustrates the effectiveness of our proposed method.