Designing an efficient observer for the non-linear lipschitz system to troubleshoot and detect secondary faults considering linearizing the dynamic error

The presence of faults in a system leads to a lower value for efficiency, accuracy and speed, and, in some cases, even a complete breakdown. Thus, early fault detection is a major factor in efficiency and productivity of the procedure. In recent decades, many research studies have been conducted on troubleshooting and secondary fault detection. The current work presents an efficient and novel observer design capable of stabilizing the residue and dynamic error for the nonlinear Lipschitz systems with faults as well as a troubleshooting analysis and determining the formation of secondary faults in defective systems. The observer is designed based on linearizing dynamic error considering uncertainty, disturbance, and defects by employing non-linear gain factors instead of using state transformation. The dynamic error and residue stabilization of a non-linear faulty system have been discussed as well as the likelihood of secondary fault generation. The results indicate that the observer is able to determine fault-emergence, fault-disappearance and secondary fault formation well and quite fast.