High-precision tracking differentiator via generalized discrete-time optimal control

Hehong Zhang; Yunde Xie; Longhua She; Chao Zhai; Gaoxi Xiao

doi:10.1016/j.isatra.2019.05.002

High-precision tracking differentiator via generalized discrete-time optimal control

ISA Trans. 2019 Dec:95:144-151. doi: 10.1016/j.isatra.2019.05.002. Epub 2019 May 14.

Authors

Hehong Zhang¹, Yunde Xie², Longhua She³, Chao Zhai⁴, Gaoxi Xiao⁵

Affiliations

¹ Interdisciplinary Graduate School, Nanyang Technological University, Singapore.
² Beijing Maglev Transportation Development Co.,Ltd, Beijing 10024, China. Electronic address: xieyunde@maglev.cn.
³ Beijing Maglev Transportation Development Co.,Ltd, Beijing 10024, China.
⁴ School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore.
⁵ School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. Electronic address: egxxiao@ntu.edu.sg.

PMID: 31122694
DOI: 10.1016/j.isatra.2019.05.002

Abstract

An enhanced discrete-time tracking differentiator (TD) with high precision based on discrete-time optimal control (DTOC) law is proposed. This law takes the form of state feedback for a double-integral system that adopts the Isochronic Region approach. There, the control signal sequence is determined by a linearized criterion based on the position of the initial state point on the phase plane. The proposed control law can be easily extended to the TD design problem by combining the first-state variable of the double-integral system with the desired trajectory. To improve the precision of the discretization model, we introduced a zero-order hold on the control signal. We also discuss the general form of DTOC law by analysing the relationship between boundary transformations and boundary characteristic points. After comparing the simulation results from three different TDs, we determined that this new TD achieves better performance and higher precision in signal-tracking filtering and differentiation acquisition than do existing TDs. Also the comparisons of the computational complexities between the proposed DTOC law and normal one are demonstrated. For confirmation of its utility, we processed raw phasor measurement units data via the proposed TD. In the absence of complex power system modelling and historical data, it was verified that the proposed TD is suitable for applications of real-time synchrophasor estimations, especially when the states are corrupted by noise.

Keywords: Computational complexity; Differentiation acquisition; Discrete-time optimal control (DTOC); Estimation; Filtering; Tracking; Tracking differentiator (TD).