Design and Implementation of an Efficient Tracking Differentiator

Yunde Xie,Longhua She,Hehong Zhang,Tso-Chien Pan,Chao Zhai,Gaoxi Xiao

doi:10.1109/access.2019.2930963

Abstract

Differential signals play significant roles in control practices, but they are prone to noise corruption. A noise-tolerant time-optimal system-based tracking differentiator (TD) was first proposed by Jingqing Han, which is constructed in the form of state feedback control for a discrete-time and double-integral system. However, its performances of signal-tracking filtering and differentiation extraction are sensitive to the sampling period. To relax the sensitivity on the sampling period, a time-criterion-based feedback control algorithm is proposed to construct the TD. The control algorithm is derived by comparing the time that the initial state is driven to the switching curve or the origin with any given sampling period. The impact of the algorithm parameter setting on filtering is analyzed in the frequency domain. Meanwhile, a compensation scheme is introduced to deal with the trade-off between the filtering ability and phase delay. The simulation results show that the proposed TD has smaller static errors in signal-tracking filtering, and better differentiation acquisition compared with others. The experiments conducted on STM32F405 reveal that the proposed TD uses the shortest execution time among others for processing the same input signals.

Highlights

The differentiation of a given signal in real time is a well-known yet challenging problem in control theory and engineering [1], [2]
Proposed by Han [16], [17], the discrete-time optimal control based tracking differentiator (TD) with the noise-tolerant characteristic has widely used in filtering and differentiation acquisition [16]
Under any given sampling period, the time-criterion based feedback control is presented to construct the TD. It relaxes the strict constraint on the sampling time for the discrete time optimal control (Fhan) based TD

Summary

INTRODUCTION

The differentiation of a given signal in real time is a well-known yet challenging problem in control theory and engineering [1], [2]. Proposed by Han [16], [17], the discrete-time optimal control based tracking differentiator (TD) with the noise-tolerant characteristic has widely used in filtering and differentiation acquisition [16] The advantage of this TD is that it sets a weak condition on the stability of the systems to be constructed for TD and requires a weak condition on the input. A bigger sampling period that may be needed in some engineering scenarios may result in bigger static errors or overshoots in signal tracking and differentiation extraction, which means that, in order to make Han’s TD highly accurate in signaltracking and differentiation extraction, one has to impose strict constraints on the sampling period To relax this particular constraint and improve performances in signal-tracking and differentiation extraction, an efficient time-criterion based control algorithm is proposed in this paper to construct the TD.

PROBLEM STATEMENT

PHASE DELAY COMPENSATION

CONCLUSION