Analysis And Design Of 2-D Discrete Fault Detection Observer

Fault detection problem has been occupied an important place in the research of the engineering application field, especially in the field of signal processing and automatic control. And fault detection technology which is based on models as a commonly used method, mainly through the system input, output and system state space model to generate the residual error. Then detecting faults with the aid of residual error. Therefore, it is significant to increase the fault sensitivity and attenuate the effects of disturbances.Taking the2-D discrete FMⅡ model as the research object, with the aid of the Generalized Kalman-Yakubovich-Popov(GKYP) lemma for two dimensional(2-D) discrete systems to describe the limited frequency index. A fault detection observer is designed by employing two finite frequency performance indexes H_and H∞which are used to increase the fault sensitivity and attenuate the effects of disturbances. Finally, ensuring that the system is stable.Then the design methods are presented in terms of solutions to a set of linear matrix inequalities (LMIs), and can be directly solved by Matlab control toolbox. Compared with the fault detection method which is based on the transfer function model, this method is getting the state space model of the observer directly, avoiding the state space realization of2-D system.The main work of this article:designing a fault detection observer of FMII model in a limited frequency domain. The existence condition of fault detection observer is obtained with the aid of2-D GKYP lemma. And then the result of the fault detection observer can be obtained by solving a set of linear matrix inequalities (LMIs). Giving the observer existence conditions and designing method about the FMII model of fault detection in the absence of any disturbance. Numerical examples are provided to illustrate the effectiveness of the proposed method.