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Advances in Variable Structure Systems and Sliding Mode Control—Theory and Applications pp 101–132Cite as

Practical Stability Phase and Gain Margins Concept

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Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 115))

Abstract

A new concept of chattering characterization for the systems driven by finite-time convergent controllers (FTCC) in terms of practical stability margins is presented. Unmodeled dynamics of order two or more incite chattering in FTCC driven systems. In order to analyze the FTCC robustness to unmodeled dynamics the novel paradigm of Tolerance Limits (TL) is introduced to characterize the acceptable emerging chattering. Following this paradigm a new notions of Practical Stability Phase Margin (PSPM) and Practical Stability Gain Margin (PSGM) as a measure of robustness to cascade unmodeled dynamics is introduced. Specifically, PSPM and PSGM are defined as the values that have to be added to the phase and gain of dynamically perturbed system driven by FTCC so that the characteristics of the emerging chattering reach TL. For practical calculation of PSPM and PSGM, the Harmonic Balance (HB) method is employed and a numerical algorithm to compute Describing Functions (DFs) for families of FTCC (specifically, for nested, and quasi-continuous Higher Order Sliding Mode (HOSM) controllers) was proposed. A database of adequate DFs was developed. A numerical algorithm for solving HB equation using the Newton–Raphson method was suggested to obtain predicted chattering parameters. Finally, computational algorithms that identify PSPM and PSGM for the systems driven by FTCC were proposed. The algorithm of a cascade linear compensator design that corrected the FTCC, making the values of PSPM and PSGM to fit the prescribed quantities, was presented. In order to design the flight-certified FTCC for attitude for the F-16 jet fighter, the proposed technique was employed in a case study. The prescribed robustness to cascade unmodeled dynamics was achieved.

L. Fridman gratefully acknowledges the financial support from by Programa de Apoyo a Proyectos de Investigacion e Innovacion Tecnologica (UNAM) 113216, and DGAPA PASPA Program.

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Author information

Authors and Affiliations

  1. The Department of Electrical and Computer Engineering, University of Alabama in Huntsville, Huntsville, AL, USA

    Yuri Shtessel & Chandrasekhara Bharath Panathula

  2. The Department of Control Engineering and Robotics, Universidad Nacional Autonoma de Mexico, 04510, Mexico City, CDMX, Mexico

    Leonid Fridman

  3. Tecnologico de Monterrey, Campus Ciudad de Mexico, MX, Mexico

    Antonio Rosales

Authors
  1. Yuri Shtessel
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  2. Leonid Fridman
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  3. Antonio Rosales
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  4. Chandrasekhara Bharath Panathula
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Corresponding author

Correspondence to Leonid Fridman .

Editor information

Editors and Affiliations

  1. School of Automation, Southeast University, Nanjing, China

    Shihua Li

  2. Research & Innovation Portfolio, RMIT University, Melbourne, Victoria, Australia

    Xinghuo Yu

  3. Division of Electrical Engineering, National Autonomous University of Mexico, Mexico City, Distrito Federal, Mexico

    Leonid Fridman

  4. Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne, Victoria, Australia

    Zhihong Man

  5. School of Automation, Southeast University, Nanjing, China

    Xiangyu Wang

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Shtessel, Y., Fridman, L., Rosales, A., Panathula, C.B. (2018). Practical Stability Phase and Gain Margins Concept. In: Li, S., Yu, X., Fridman, L., Man, Z., Wang, X. (eds) Advances in Variable Structure Systems and Sliding Mode Control—Theory and Applications. Studies in Systems, Decision and Control, vol 115. Springer, Cham. https://doi.org/10.1007/978-3-319-62896-7_4

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  • DOI: https://doi.org/10.1007/978-3-319-62896-7_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62895-0

  • Online ISBN: 978-3-319-62896-7

  • eBook Packages: EngineeringEngineering (R0)

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