Robust Fault Detection and Estimation in Nonlinear Systems with Unknown Constant Time‐Delays

Abstract

This paper studies the problem of fault detection and estimation in nonlinear time-delayed systems with unknown inputs, where the time-delays are supposed to be constant but unknown. A new fault detection filter, which can estimate online the time-delays, is first introduced. Then, a reference residual model is proposed to formulate the robust fault detection filter design problem as an ∞ model-matching problem. Furthermore, by a novel robust adaptive fault estimation algorithm, the classical assumption that the time derivative of the output error should be known is removed. In addition, applying a robust ∞ optimization control technique, sufficient conditions for the existence of the fault detection filter (FDF) are derived in terms of linear matrix inequality (LMI). Finally, simulation results are presented to illustrate the effectiveness of the proposed algorithm.

Fault estimation for nonlinear uncertain time‐delay systems based on unknown input observer

“…Also, in order to get closer to the natural conditions, a part of the disturbance has been considered inseparable, and the LMI has been used for optimal decupling. To confirm the improved performance of the proposed method, an evaluation with [44] has been made. In [44], which has the closest conditions to the proposed method of the present paper, a certain delayed nonlinear system (delay in both the linear and nonlinear parts) is considered, where faults and disturbances exist in both the state and the output equations.…”

“…To confirm the improved performance of the proposed method, an evaluation with [44] has been made. In [44], which has the closest conditions to the proposed method of the present paper, a certain delayed nonlinear system (delay in both the linear and nonlinear parts) is considered, where faults and disturbances exist in both the state and the output equations. In [44], a state observer for robust fault detection is designed and simulated for an abstract and impractical example.…”

“…In [44], which has the closest conditions to the proposed method of the present paper, a certain delayed nonlinear system (delay in both the linear and nonlinear parts) is considered, where faults and disturbances exist in both the state and the output equations. In [44], a state observer for robust fault detection is designed and simulated for an abstract and impractical example. The certain delayed nonlinear system and the proposed observer for state and fault approximation in [44]…”

“…In [44], a state observer for robust fault detection is designed and simulated for an abstract and impractical example. The certain delayed nonlinear system and the proposed observer for state and fault approximation in [44]…”

“…In the following figures, the estimation of states (Figures 24 and 25), the fault (Figure 26) and the estimated errors (Figures [27][28][29] with the proposed UIO and the observer in [44] with a fault in sensor 1 is shown. As depicted in the following figures, the proposed UIO-based method shows better performance (speed of convergence and accuracy) compared to the suggested observer in [44]. Furthermore, the effect of un-decoupled disturbance in the proposed UIO is less than [44].…”