Tracking differentiator based back-stepping control for valve-controlled hydraulic actuator system

Chengwen Wang, Xinhao Ji, Zhenyang Zhang, Bin Zhao, Long Quan, A. R. Plummer

Research output: Contribution to journalArticlepeer-review


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
JournalISA Transactions
Early online date19 Feb 2021
Publication statusE-pub ahead of print - 19 Feb 2021


  • 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

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