Interval Observer for Fault Identifi cation in Discrete-Time Dynamic Systems

The paper considers the problem of fault estimation (identification) in nonlinear discrete-time stationary systems described by linear dynamic models under external disturbances based on interval observers. To solve the problem, a reduced order model of the original system of minimal dimension than that of the original system insensitive or having minimal sensitivity to the external disturbances is designed. This model is based on diagonal Jordan canonical form allowing obtaining one-dimensional model. Based on this model, the interval observer is designed consisting of two subsystems. The first subsystem generates the lower bound of the set of admissible values of the prescribed function of the system state vector while the second system generates the upper bound. The relations describing such subsystems are derived. The prescribed function is such that forms one component of the system output vector containing the variable which is a result of the fault occurred in the system. This is necessary to introduce a feedback in the interval observer which is created by the estimated system output. Based on the interval observer description, the variable is introduced connecting the lower and upper bounds and real value of the prescribed function which can be measured. Based on the introduced variable, the relation connecting the lower and upper bounds and real value of the prescribed function in neighboring moments of time is constructed. This relation is based for fault estimation. Since measurement noises are absent and the reduced order model is insensitive to the disturbances, all obtained relations are precise, and the resulting formula for fault estimation is precise one as well. The theoretical results are illustrated by an example of electro actuator model where the value of fault is estimated. Simulation results based on the package Matlab show the effectiveness of the developed theory.