Optimal Nonlinear Adaptive Observers for State, Parameter and Fault Estimation

The demand for reliable, fast and robust techniques for detection and estimation of faults in real-world systems is constantly increasing. A nonlinear adaptive observer for state, parameter and fault estimation is developed in this work using an optimal approach. This observer is capable of estimating unknown parameters as well as sensor faults in the system. The proposed observer also accounts for existing noise and disturbance in the system. By defining appropriate cost functions for each problem, the observer is made to satisfy a performance bound. A systematic method of checking existence conditions and calculating observer gains in terms of Linear Matrix Inequalities (LMIs) is presented. Types of nonlinearities considered are fairly general and encompass sector bounded, Lipschitz and dissipative nonlinearities. The observer can identify time-varying unknown parameters, bias and gain sensor faults. Compared with the method of extended Kalman filter, the proposed observer is not computationally intensive and in its relaxed form, does not require online solution to the Ricatti equation. The observer is applied to representative state space models including a wind turbine mechanical power transmission mechanism. The considered system model is highly nonlinear and contains input disturbances as well. The results are compared with the results obtained from extended Kalman filtering and show satisfactory performance in the presence of noise and disturbances.