IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v168y2016i2d10.1007_s10957-015-0759-z.html
   My bibliography  Save this article

Motion Controller Design of Wheeled Inverted Pendulum with an Input Delay Via Optimal Control Theory

Author

Listed:
  • Yusheng Zhou

    (Nanjing University of Aeronautics and Astronautics)

  • Zaihua Wang

    (Nanjing University of Aeronautics and Astronautics)

Abstract

This paper investigates the control of Back-and-Forth motion to fetch object and Lower-Raise-Head motion to avoid obstacle of the wheeled inverted pendulum system with an input delay. In controlling the Back-and-Forth motion, the linear optimal control theory is used because the tilt angle of the pendulum is forced to be small enough by minimizing a quadratic performance criterion with large weight of tilt angle error, and the controller is represented by using predictor-based feedback. In controlling the Lower-Raise-Head motion, linearized models do not work due to the strong nonlinearity caused by big tilt angle for avoiding obstacle. Without considering yaw movement, the wheeled inverted pendulum system is decoupled, the subsystem governing the state of the tilt angle is transformed into a simple linear system by using feedback linearization. With a properly chosen trajectory tracking target, the control of Lower-Raise-Head motion is solved on the basis of optimal trajectory tracking control for linear subsystems with an input delay. Numerical simulations illustrate the effectiveness of the proposed approaches.

Suggested Citation

  • Yusheng Zhou & Zaihua Wang, 2016. "Motion Controller Design of Wheeled Inverted Pendulum with an Input Delay Via Optimal Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 625-645, February.
  • Handle: RePEc:spr:joptap:v:168:y:2016:i:2:d:10.1007_s10957-015-0759-z
    DOI: 10.1007/s10957-015-0759-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-015-0759-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-015-0759-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. S. F. P. Saramago & V. Steffen, 2001. "Trajectory Modeling of Robot Manipulators in the Presence of Obstacles," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 17-34, July.
    2. M. S. Mahmoud & M. Zribi, 1999. "H∞-Controllers for Time-Delay Systems Using Linear Matrix Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 100(1), pages 89-122, January.
    3. J. D. Chen, 2005. "LMI-Based Robust H∞ Control of Uncertain Neutral Systems with State and Input Delays," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 553-570, September.
    4. Yusheng Zhou & Zaihua Wang, 2014. "Optimal Feedback Control for Linear Systems with Input Delays Revisited," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 989-1017, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yusheng Zhou & Zaihua Wang & Kwok-wai Chung, 2019. "Turning Motion Control Design of a Two-Wheeled Inverted Pendulum Using Curvature Tracking and Optimal Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 634-652, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Jenq-Der, 2007. "Delay-dependent robust H∞ control of uncertain neutral systems with state and input delays: LMI optimization approach," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 595-606.
    2. O. M. Kwon & J. H. Park & S. M. Lee, 2008. "Exponential Stability for Uncertain Dynamic Systems with Time-Varying Delays: LMI Optimization Approach," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 521-532, June.
    3. J. D. Chen, 2006. "LMI Approach to Robust Delay-Dependent Mixed H 2/H ∞ Controller of Uncertain Neutral Systems with Discrete and Distributed Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 383-403, December.
    4. J. D. Chen, 2009. "Delay-Dependent Nonfragile H ∞ Observer-Based Control for Neutral Systems with Time Delays in the State and Control Input," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 445-460, May.
    5. J. D. Chen, 2007. "Robust H ∞ Output Dynamic Observer-Based Control Design of Uncertain Neutral Systems," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 193-211, January.
    6. Karimi, Hamid Reza & Zapateiro, Mauricio & Luo, Ningsu, 2009. "Stability analysis and control synthesis of neutral systems with time-varying delays and nonlinear uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 595-603.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:168:y:2016:i:2:d:10.1007_s10957-015-0759-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.