---

 In this paper an observer-based robust fault estimation scheme is proposed for a special class of Lipchitz nonlinear systems where the disturbances and faults are assumed to be coupled with the main system states. In the considered model of system, fault is assumed to enter both of the state and output equations as an unmeasured nonlinear function and coupled with the states. The disturbances and the uncertainties are considered as nonlinear functions coupled with the states. To the best of the authors’ knowledge these conditions have not been previously considered in related papers. In the proposed approach, a Luenberger observer is designed for the estimation of faults and states of system simultaneously. The effect of system disturbances is attenuated with the L2  norm. The necessary conditions for the existence of such observer is expressed in the form of Linear Matrix Inequality. The Lipchitz constant of the nonlinear function is obtained by solving the proposed Linear Matrix Inequality. Finally, the performance of the proposed method is simulated on a three-phase induction motor. The results indicate good performance of the proposed method.
 

---

In chemical processes, thermal reactors are described by nonlinear closed-loop dynamic models. Timely detection of simultaneous fouling phenomena in the heat transfer system is a concern of this art. In this work, a new incipient fault diagnosis approach is proposed for application in the closed-loop non-isothermal continuous stirred-tank reactor (CSTR) system subjected to simultaneous Gaussian and non-Gaussian noises. First, the state vector is estimated by applying the well-known particle filter estimator. Then, the primary residual signal is generated using the system measurements, and the fault vector estimation is obtained. After that, by an adaptive either fixed threshold design applied in the online monitoring devised with the proposed evaluation technique, while the fault detectability is improved, the false detection problem is restricted to the system permitted number. Bank on, preventive maintenance scheduling also incipient fault trend prediction have become possible using the Gauss-Newton identification method. Finally, in order to evaluate the proposed approach, the simultaneous fouling incipient fault diagnosis over the heat transfer unit built-in nonlinear closed-loop CSTR system is considered. Furthermore, the confusion matrix and associated evaluation indices are employed to assess the simulation results quantitatively.