Frequency-Shaped and Observer-Based Discrete-time Sliding Mode Control

  • Axaykumar Mehta
  • Bijnan Bandyopadhyay

Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Axaykumar Mehta, Bijnan Bandyopadhyay
    Pages 1-7
  3. Axaykumar Mehta, Bijnan Bandyopadhyay
    Pages 9-25
  4. Axaykumar Mehta, Bijnan Bandyopadhyay
    Pages 27-45
  5. Axaykumar Mehta, Bijnan Bandyopadhyay
    Pages 57-90
  6. Back Matter
    Pages 91-95

About this book

Introduction

It is well established that the sliding mode control strategy provides an effective and robust method of controlling the deterministic system due to its well-known invariance property to a class of bounded disturbance and parameter variations. Advances in microcomputer technologies have made digital control increasingly popular among the researchers worldwide. And that led to the study of discrete-time sliding mode control design and its implementation. This brief presents, a method for multi-rate frequency shaped sliding mode controller design based on switching and non-switching type of reaching law. In this approach, the frequency dependent compensator dynamics are introduced through a frequency-shaped sliding surface by assigning frequency dependent weighing matrices in a linear quadratic regulator (LQR) design procedure. In this way, the undesired high frequency dynamics or certain frequency disturbance can be eliminated. The states are implicitly obtained by measuring the output at a faster rate than the control. It is also known that the vibration control of smart structure is a challenging problem as it has several vibratory modes. So, the frequency shaping approach is used to suppress the frequency dynamics excited during sliding mode in smart structure. The frequency content of the optimal sliding mode is shaped by using a frequency dependent compensator, such that a higher gain can be obtained at the resonance frequencies. The brief discusses the design methods of the controllers based on the proposed approach for the vibration suppression of the intelligent structure. The brief also presents a design of discrete-time reduced order observer using the duality to discrete-time sliding surface design. First, the duality between the coefficients of the discrete-time reduced order observer and the sliding surface design is established and then, the design method for the observer using Riccati equation is explained. Using the proposed method, the observer for the Power System Stabilizer (PSS) for Single Machine Infinite Bus (SMIB) system is designed and the simulation is carried out using the observed states. The discrete-time sliding mode controller based on the proposed reduced order observer design method is also obtained for a laboratory experimental servo system and verified with the experimental results.

Keywords

Duality Frequency Shaping Power System Stabilizer Reduced Order Observer Sliding Mode Control Smart Structure Variable Structure Control

Authors and affiliations

  • Axaykumar Mehta
    • 1
  • Bijnan Bandyopadhyay
    • 2
  1. 1.Institute of Infrastructure Technology Research and Management (IITRAM)AhmedabadIndia
  2. 2.IDP in Systems and Control EngineeringIndian Institute of Technology BombayMumbaiIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-81-322-2238-5
  • Copyright Information The Author(s) 2015
  • Publisher Name Springer, New Delhi
  • eBook Packages Engineering
  • Print ISBN 978-81-322-2237-8
  • Online ISBN 978-81-322-2238-5
  • Series Print ISSN 2191-530X
  • Series Online ISSN 2191-5318
  • About this book
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