Interval Method of Nonlinear System Diagnosis

The problems of transforming the original nonlinear system into the special linear system (reducing model) and fault diagnosis are studied. The transformation is realized based on Li derivative, and the model insensitive to the external disturbances is derived. Such a model allows to obtain a linear equation for the error that is important for solving some practical problems. To solve the problem of fault diagnosis, the interval observers are used. The advantage of the interval observer is that they allow to take into account many types of uncertainties: the external disturbances, measurement noise, and parametric uncertainties. The interval observer is based on the reducing model which initially is designed in the identification canonical form, and then it is transformed into the diagonal Jordan canonical form with negative eigenvalues since such a form has properties necessary to design the interval observer. The interval diagnostic observer creates two residuals such that when there are no faults, one residual is non-positive, the second one is non-negative. If zero lies between these residuals, a decision that there are no faults is made. The theoretical results are illustrated by an example of electro actuator model where the value of active resistor of the motor winding is estimated under the assumption that if the resistor is in its tolerance, then the fault is absent. Simulation results based on the package Matlab show the effectiveness of the developed theory.