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Journal of Systems Science and Complexity

, Volume 32, Issue 4, pp 1039–1052 | Cite as

A Prescribed Performance Adaptive Control for Hysteresis Hammerstein System

  • Xuehui GaoEmail author
  • Wei Zhao
  • Shubo Wang
  • Minlin Wang
  • Xuemei Ren
Article
  • 24 Downloads

Abstract

A prescribed performance adaptive control (PPAC) is proposed for Hammerstein system where nonlinearity is described by backlash-like hysteresis. In order to simplify the controller design as well as guarantee the precision of the controlled system, the tracking error is transformed into performance error by two steps. The first step is to transform the tracking error into scalar error, but it magnifies the tracking error decreasing the accuracy of the controlled system. Therefore, a new S(z) is proposed for prescribed performance function (PPF) and the second step is transforming the scalar error into performance error by the proposed PPF, which guarantees the scalar error converges to a prescribed bound to improve the control accuracy. Finally, Lambert W function is introduced for the Lyapunov function candidate to guarantee the closed-loop system bounded and the tracking error converged. Simulations demonstrate the effectiveness of the proposed approaches.

Keywords

Hammerstein hysteresis Lambert W function prescribed performance 

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Copyright information

© The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2019

Authors and Affiliations

  • Xuehui Gao
    • 1
    Email author
  • Wei Zhao
    • 2
  • Shubo Wang
    • 3
  • Minlin Wang
    • 2
  • Xuemei Ren
    • 2
  1. 1.Department of Mechanical and Electrical EngineeringShandong University of Science and TechnologyTai’anChina
  2. 2.School of AutomationBeijing Institute of TechnologyBeijingChina
  3. 3.College of Automation and Electrical EngineeringQingdao UniversityQingdaoChina

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