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A New Class of Non-linear Reaching Laws for Sliding Mode Control of Discrete Time Systems

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Recent Advances in Sliding Modes: From Control to Intelligent Mechatronics

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 24))

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Abstract

In this chapter we investigate the reaching law based approach to the discrete time sliding mode control of dynamical systems. We present a particular class of recently introduced controllers designed according to this approach and we thoroughly discuss their properties. The common idea of all the controllers considered in this chapter, is to obtain the desired convergence rate of the systems’ state to a vicinity of the sliding hyperplane and to maintain the state in the vicinity, once the state has entered it. The vicinity is called the quasi sliding mode band and its width may serve as a good measure of the closed loop system robustness. Furthermore, we apply the proposed controllers to the periodic review inventory management problem. Even though in this chapter we focus our attention on the inventory system control, the presented reaching laws can be effectively applied to any linear discrete time plant subject to disturbance and parameter uncertainty.

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Authors and Affiliations

  1. Institute of Automatic Control, Technical University of Lodz, 18/22 Stefanowskiego St., 90-924, Lodz, Poland

    Piotr Lesniewski & Andrzej Bartoszewicz

Authors
  1. Piotr Lesniewski
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  2. Andrzej Bartoszewicz
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Correspondence to Piotr Lesniewski .

Editor information

Editors and Affiliations

  1. RMIT University, Carlton, Victoria, Victoria, Australia

    Xinghuo Yu

  2. Hacettepe University, Beytepe, Ankara, Turkey

    Mehmet Önder Efe

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Lesniewski, P., Bartoszewicz, A. (2015). A New Class of Non-linear Reaching Laws for Sliding Mode Control of Discrete Time Systems. In: Yu, X., Önder Efe, M. (eds) Recent Advances in Sliding Modes: From Control to Intelligent Mechatronics. Studies in Systems, Decision and Control, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-319-18290-2_6

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  • DOI: https://doi.org/10.1007/978-3-319-18290-2_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18289-6

  • Online ISBN: 978-3-319-18290-2

  • eBook Packages: EngineeringEngineering (R0)

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