21 Citations (SciVal)
39 Downloads (Pure)


Back-stepping design method is widely used in high-performance tracking control tasks As is known to all, the controller based on back-stepping design will become complex as the model order increases, which is the so called “explosion of terms” problem. In this paper, a tracking differentiator (TD) based back-stepping controller is proposed to handle the “explosion of terms” problem. Instead of calculating the derivatives of intermediate control variables through tedious analytical expressions, for the proposed method, the tracking differentiator is embedded into each recursive procedure to generate the substitute derivative signal for every intermediate control variable. As a result, the complexity of implementation procedure of back-stepping controller is significantly reduced. The discrepancies between the derivative substitutes and the real derivatives are considered. And the effects on control performances caused by the discrepancies are analyzed. In addition to giving the theoretical results and the stability proofs with Lyapunov methods, the developed controller design method is evaluated through a series of experiments with a hydraulic robot arm position serve system. The control performance of the proposed controller is verified by the experiments results.

Original languageEnglish
Pages (from-to)208-220
Number of pages13
JournalISA Transactions
Early online date19 Feb 2021
Publication statusPublished - 1 Jan 2022

Bibliographical note

Funding Information:
This work was funded in part by the National Research and Development Program of China (Grand No. 2019YFB2004502 ), the Key Research and Development Projects of Shanxi Province (Grand No. 201903D121069 ), the Research Project Supported by Shanxi Scholarship Council of China (Grand No. HGKY2019016 ), and the Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems Grand GZKF-201720 .

Publisher Copyright:
© 2021 ISA

Copyright 2021 Elsevier B.V., All rights reserved.


  • Back-stepping design
  • Explosion of complexity
  • Hydraulic position controller
  • Nonlinear control
  • Tracking differentiator (TD)

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Instrumentation
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Applied Mathematics


Dive into the research topics of 'Tracking differentiator based back-stepping control for valve-controlled hydraulic actuator system'. Together they form a unique fingerprint.

Cite this