Online algorithm for third-order minimum time discrete tracking differentiator

This paper presents the third-order minimum time discrete tracking differentiator, which is to generate transient profiles of setpoint reference signal as well as the first and second derivatives, corresponding to transients of the position, velocity and acceleration. These signals contain useful information of dynamics that can improve the tracking performance of control systems. In order to accomplish the derivation of the minimum time tracking differentiator, a general algorithm is derived for solving minimum time control of discrete time systems. Then we focus on the third-order differentiator and make the implementation algorithm online applicable. The computation complexity is also evaluated by a simple formula, which judges whether the computation can be accomplished before the next time instant. Numerical examples are provided to illustrate the effectiveness of the proposed methods.