Estimating Actuator Fault Through the Utilization of a Proportional Integral Observer with Quadratic Lyapunov Functions

This study introduces a fault estimation observer for nonlinear systems, employing a proportional-integral approach, convex optimization techniques, and quadratic Lyapunov functions. The operational conditions of this system are expressed as linear matrix inequalities. It also incorporates an H∞ performance criterion to enhance its robustness against sensor noise and external disturbances. This observer is adept at accurately estimating both the system's state and actuator faults, even in the presence of disturbances. The practicality and effectiveness of the proposed methodology are demonstrated through its implementation in a three-tank hydraulic system.