Tracking Differentiator Algorithms by Hehong Zhang & Gaoxi Xiao & Yunde Xie & Wenzhong Guo & Chao Zhai

Author:Hehong Zhang & Gaoxi Xiao & Yunde Xie & Wenzhong Guo & Chao Zhai
Language: eng
Format: epub
ISBN: 9789811593840
Publisher: Springer Singapore

4.2 Construction of Tracking Differentiator

In this section, we first present a brief outline for the construction of the continuous tracking differentiator based on time-optimal control. Then we can use the same construction principle to design the Fast algorithm based tracking differentiator directly.

As shown in Chap. 3, the double-integral system is defined as

(4.1)

where r is a constant. Note that, depending on the physical limitations of each application, the parameter r can be selected accordingly to speed up or slow down the transient profile. The resulting feedback control law that drives the state from any initial point to the origin in the shortest time is

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