What is Disturbance

This chapter studies the problem of fault estimation using a fast adaptive fault diagnosis observer. Note that the advance of observer-based fault diagnosis is outlined and the idea of fault class estimation is introduced and studied. A new form of the estimator bloc considered for this purpose is an Unknown Input Observer (UIO). This observer is designed for an unknown input and fault free system, which is obtained by coordinate transformations of original systems with unknown inputs (disturbance) and faults. Stability of the adaptive estimation is provided by a Lyapunov function ending with solving the Linear Matrix Inequalities (LMI). Due to technological advances in the field of electronic devices, the family of robots is of particular interest. To overcome the drawback of robots' model responses when including a fault, a robust observer is adopted for a Pioneer robot to improve the fault estimation and thereafter to repair its trajectory.