A New Simplified Design for Discrete-time Tracking-Differentiator

The thickness of the boundary layer of the discrete-time Tracking-Differentiator is variable, so that the control characteristic line is asymmetric. In general, the nonlinear boundary transform is used to get the control synthesis function. However, it contains square root operations, and the compute is more complex. This study is conducted to put forward a new algorithm to simplify partition boundary. In the region far from the origin, a set of symmetric and approximate boundary of the control characteristic line is considered. Additionally, the two-step reachable region is still adopted in the region near the origin. The computational complexity is greatly simplified, and the discrete-time Tracking-Differentiator using the simplified algorithm is able to track the input signal quickly without overshoot or flutter and obtain the differential signal of good characteristics.