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book: Stabilisation and Motion Control of Unstable Objects
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Stabilisation and Motion Control of Unstable Objects

  • Alexander M. Formalskii
Language: English
Published/Copyright: 2016
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De Gruyter Studies in Mathematical Physics

About this book

Systems with mechanical degrees of freedom containing unstable objects are analysed in this monograph and algorithms for their control are developed, discussed, and numerically tested. This is achieved by identifying unstable modes of motion and using all available resources to suppress them. By using this approach the region of states from which a stable regime can be reached is maximised.

The systems discussed in this book are models for pendula and vehicles and find applications in mechatronics, robotics as well as in mechanical and automotive engineering.

  • Starting from a theoretical analysis control algorithms for a selection of unstable mechanical example systems are developed.
  • Efficacy of these algorithms is analysed numerically as well as, for some examples, by experiment.

Author / Editor information

Alexander Formalskii, Lomonosov State University, Moscow, Russia.

Reviews

"The book can serve as an excellent basis for a graduate course on control and stabilization of multi-body mechanical systems. It provides a researcher with a comprehensive account of approaches and methods of designing controls stabilizing unstable equilibria. It will be a valuable reference to the classical and modern literature on the subject."
Oleg N. Kirillov in: Mathematical Reviews Clippings, July 2018, MR3726859

Topics

  • Publicly Available

    Frontmatter

    I
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  • Publicly Available

    Contents

    V
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    Preface to English Edition

    IX
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    Preface

    XI
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  • Part I: Devices containing a single-link pendulum
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    1. A pendulum with stationary pivot

    5
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    2. A pendulum with wheel-based pivot

    21
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    3. A pendulum with a flywheel

    31
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    4. Wheel rolling control by means of a pendulum

    50
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    5. Optimal swinging and damping of a swing

    58
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    6. Pendulum control that minimizes energy consumption

    71
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  • Part II: Double physical pendulum
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    7. Local stabilization of an inverted pendulum by means of a single control torque

    91
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    8. Optimal control design for swinging and damping a double pendulum

    110
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    9. Global stabilization of an inverted pendulum controlled by torque in the inter-link joint

    126
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    10. Global stabilization of an inverted pendulum controlled by torque in the pivot

    134
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    11. Multi-link pendulum on a moving base

    145
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  • Part III: Ball on a beam
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    12. Stabilization of a ball on a straight beam

    165
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    13. Stabilization of a ball on a curvilinear beam

    176
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  • Part IV: Gyroscopic stabilization of a two-wheel bicycle
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    14. Bicycle design

    189
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    15. Designing a control law to stabilize the bicycle tilt

    198
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  • Part V: Avoiding undesired vibrations
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    16. Bang-bang control and fluent control

    209
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    17. Trapezoidal control for a system with compliant elements

    217
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    Bibliography

    229
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    Index

    237
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
November 13, 2015
eBook ISBN:
9783110375893
Hardcover published on:
November 3, 2015
Hardcover ISBN:
9783110375824
Pages and Images/Illustrations in book
Front matter:
16
Main content:
239
Illustrations:
83
Coloured Illustrations:
5
https://doi.org/10.1515/9783110375893
eBook ISBN: 9783110375893
Hardcover ISBN: 9783110375824
Keywords for this book
Stabilisierung; Optimale Kontrolle; Pendel; Gyroskop
Audience(s) for this book
Scientists in physics, applied mathematics, and mechanics as well as engineers in control, robotics, and mechatronics.
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