Determination of Model, Implement and Compare New Two Optimal Adaptive Fault Diagnosis Observers with Six Observers

This chapter presents the design of new optimal adaptive diagnosis observers (OAD) and (OAL) where they are designed for additive fault and disturbance; the gain matrix of the observer (OAD) verifies the proposed Lyapunov condition while the gain matrix of (OAL) verifies the proposed Lyapunov condition using the LMI technique. Matlab software is efficient to verify the performance of the observers by comparing them with six different considerable linear observers Luenberger Observer (LO), Kalman (Filter) Observer (KO), Unknown Input Observer (UIO), Augmented Robust Observer (ARO), High Gain Observer (HGO) and Sensitive High Gain Observer (SHGO). The assumed disturbance and faults are white noise, coloured noise, and non-Gaussian fault while a MIMO DC servomotor has been used as a benchmark in the performance assessments; the comparison results show that each observer detects well and they need more tuning according to plant type to increase its activity. However, the new observers (OAD) and (OAL) are the best in diagnosing fault and disturbance using the proposed fault diagnosis rule of each one as well as they have high states estimation performance.