An extended state observer with adjustable bandwidth for measurement noise

In this paper, a bandwidth-adjustable extended state observer(ABESO) is proposed for the systems with measurement noise. It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates noise, which conflicts with observation accuracy. Therefore, we introduce a bandwidth scaling factor such that ABESO is formulated to a 2-degree-of-freedom system. The observer gain is determined and the bandwidth scaling factor adjusts the bandwidth according to the tracking error. When the tracking error decreases, the bandwidth decreases to suppress the noise, otherwise the bandwidth does not change. It is proven that the error dynamics are bounded and converge in finite time. The relationship between the upper bound of the estimation error and the scaling factor is given. When the scaling factor is less than 1, the ABESO has higher estimation accuracy than the linear extended state observer(LESO). Simulations of an uncertain nonlinear system with compound disturbances show that the proposed ABESO can successfully estimate the total disturbance in noisy environments. The mean error of total disturbance of ABESO is 15.28%lower than that of LESO.