  In this paper, the parallel multi-extended state observers (ESOs) based
active disturbance rejection control approach is proposed to achieve desired
tracking performance by automatically selecting the estimation values leading
to the least tracking error. First, the relationship between the estimation
error of ESO and the tracking error of output is quantitatively studied for
single ESO with general order. In particular, the algorithm for calculating the
tracking error caused by single ESO's estimation error is constructed.
Moreover, by timely evaluating the least tracking error caused by different
ESOs, a novel switching ADRC approach with parallel multi-ESOs is proposed. In
addition, the stability of the algorithm is rigorously proved. Furthermore, the
proposed ADRC is applied to the high-speed precision motion stage which has
large nonlinear uncertainties and elastic deformation disturbances near the
dead zone of friction. The experimental results show that the parallel
multi-ESOs based ADRC has higher tracking performance than the traditional
single ESO based ADRC.
