A Variable Parameter Linear Tracking Differentiator and Its Application in Large Ground-based Telescopes

Abstract

Abstract This paper is concerned with the characteristics of a tracking differentiator (TD) in arranging transition process for the physical system. In order to overcome disadvantages of linear TD (LTD) in practice, a novel variable parameter linear tracking differentiator (VLTD) is proposed. By designing the speediness factor as a function of the tracking error, the VLTD can track a large range of set values with reasonable speed and acceleration. Analysis shows that VLTD can converge to its set value under certain conditions. Meanwhile, the speed and acceleration bounds are added to the VLTD, which guarantees that the proposed transition signal really plays a transitional role. The numerical simulation results emphasize necessity for adding speed and acceleration bounds to the VLTD. By comparing VLTD with the nonlinear TD (NLTD) in the simulations and experiments, VLTD can achieve almost the same performance as the NLTD while it is easier to be implemented.