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Adaptive Sliding Mode Control

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Advances in Sliding Mode Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 440))

Abstract

The main obstacles for application of Sliding Mode Control are two interconnected phenomena: chattering and high activity of control action. It is well known that the amplitude of chattering is proportional to the magnitude of a discontinuous control. These two problems can be handled simultaneously if the magnitude is reduced to a minimal admissible level defined by the conditions for the sliding mode to exist. Here an adaptation methodology is discussed for obtaining the minimum possible value of control based on two approaches developed in recent publications:

  • The σ - adaptation, providing adequate adjustments of the magnitude of a discontinuous control within the “reaching phase”, that is, when the state trajectories are out of a sliding surface;

  • Dynamic adaptation or the adaptation within a sliding mode (on a sliding surface), based on the, so-called, equivalent control obtained by the direct measurements of the output signals of a first-order low-pass filter containing in the input the discontinuous control with the specially adapted magnitude value.

The application of these methodologies is illustrated by the corresponding adaptive versions of the Super Twist controller. It is shown that the adaptation based on the equivalent control application enables reducing of the control action magnitude to the minimum possible value keeping the property of finite-time convergence.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, The Ohio State University, Columbus, OH, USA

    Vadim I. Utkin

  2. Dept. Control Automatico, CINVESTAV-IPN, Mexico City, Mexico

    Alexander S. Poznyak

Authors
  1. Vadim I. Utkin
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  2. Alexander S. Poznyak
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Corresponding author

Correspondence to Vadim I. Utkin .

Editor information

Editors and Affiliations

  1. , Interdisciplinary Programme in Systems, Indian Institute of Technology Bombay, ACRE Building 114 B, Mumbai, 400 076, Maharashtra, India

    B Bandyopadhyay

  2. , Dept. of Electrical Engineering, Indian Institute of Technology Delhi, Room No : II/335, New Delhi, 110 016, India

    S Janardhanan

  3. , Department of Electronics, University of Kent, Jennison Building - Room 1.54, Kent, CT2 7NT, United Kingdom

    Sarah K. Spurgeon

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© 2013 Springer-Verlag Berlin Heidelberg

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Utkin, V.I., Poznyak, A.S. (2013). Adaptive Sliding Mode Control. In: Bandyopadhyay, B., Janardhanan, S., Spurgeon, S. (eds) Advances in Sliding Mode Control. Lecture Notes in Control and Information Sciences, vol 440. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36986-5_2

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  • DOI: https://doi.org/10.1007/978-3-642-36986-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36985-8

  • Online ISBN: 978-3-642-36986-5

  • eBook Packages: EngineeringEngineering (R0)

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