Robust fractional-order fast terminal sliding mode control with fixed-time reaching law for high-performance nanopositioning

Geng Wang, Yongsheng Zhou, Lei Ni, Sumeet S. Aphale* (Corresponding Author)

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


For high-performance trajectory tracking at the nanometer scales, this paper presents a new fast terminal sliding mode controller, which combines a recursive integerorder non-singular high-order sliding manifold and a fractional-order fast fixed-time reaching law to ensure globally fast convergence, and adopts a time-delay-estimation (TDE) based disturbance estimator deeming the designed controller robust to parameter uncertainty. Stability of the designed controller is verified through the Lyapunov framework, where the full analyses of convergence region and settling time are also presented. The tracking performance is experimentally verified on a piezostack driven nano-positioning platform. To showcase the performance improvements, measured closed-loop performance of the proposed controller is contrasted with those obtained using three benchmark control approaches namely the basic Proportional-Integral-Derivative (PID), the popular Positive Position Feedback with Integral action (PPF+I), and the traditional Linear Sliding Mode Controller (LSMC).
Original languageEnglish
Pages (from-to)2596-2614
Number of pages20
JournalInternational Journal of Robust and Nonlinear Control
Issue number4
Early online date7 Dec 2022
Publication statusPublished - 10 Mar 2023

Bibliographical note

Open Access via the Wiley Agreement
This work is supported by the China Scholarship Council under Grant No. 201908410107 and by the National Natural Science Foundation of China under Grant No. 51505133. The authors also thank the anonymous reviewers for their insightful and constructive comments.

Data Availability Statement

All the codes presented in this manuscript can be furnished on reasonable requests to the corresponding author.


  • high-order sliding mode
  • fractional calculus
  • fast fixed-time convergence
  • time delay estimation
  • nanopositioning


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