A bi-bandwidth extended state observer for a system with measurement noise and its application to aircraft with abrupt structural damage

In this paper, we address the problem of disturbance estimation for a class of linear systems with both fast time-varying uncertainty and measurement noise. A novel bi-bandwidth extended state observer (BESO) is proposed to achieve fast disturbance tracking and satisfactory noise suppression. The direction information of the estimation errors is used through a directional switching operator (DSO) to dynamically tune the bandwidth of the BESO. Sufficient conditions for the stability of the BESO are given, and the error dynamics are proven to be bounded and to converge in finite time. A comprehensive comparison of the BESO and three other representative approaches is presented, which shows that the BESO achieves a performance improvement of greater than 13%. A closed-loop control application for a structurally damaged aircraft is also provided to demonstrate the effectiveness and efficiency of the BESO.