IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i4p913-d1064889.html
   My bibliography  Save this article

Complex Fractional-Order LQIR for Inverted-Pendulum-Type Robotic Mechanisms: Design and Experimental Validation

Author

Listed:
  • Omer Saleem

    (Department of Electrical Engineering, National University of Computer and Emerging Sciences, Lahore 54770, Pakistan)

  • Faisal Abbas

    (Centre for Continuous Manufacturing and Advanced Crystallization, University of Strathclyde, Glasgow G1 1XQ, UK)

  • Jamshed Iqbal

    (School of Computer Science, Faculty of Science and Engineering, University of Hull, Hull HU6 7RX, UK)

Abstract

This article presents a systematic approach to formulate and experimentally validate a novel Complex Fractional Order (CFO) Linear Quadratic Integral Regulator (LQIR) design to enhance the robustness of inverted-pendulum-type robotic mechanisms against bounded exogenous disturbances. The CFO controllers, an enhanced variant of the conventional fractional-order controllers, are realised by assigning pre-calibrated complex numbers to the order of the integral and differential operators in the control law. This arrangement significantly improves the structural flexibility of the control law, and hence, subsequently strengthens its robustness against the parametric uncertainties and nonlinear disturbances encountered by the aforementioned under-actuated system. The proposed control procedure uses the ubiquitous LQIR as the baseline controller that is augmented with CFO differential and integral operators. The fractional complex orders in LQIR are calibrated offline by minimising an objective function that aims at attenuating the position-regulation error while economising the control activity. The effectiveness of the CFO-LQIR is benchmarked against its integer and fractional-order counterparts. The ability of each controller to mitigate the disturbances in inverted-pendulum-type robotic systems is rigorously tested by conducting real-time experiments on Quanser single-link rotary pendulum system. The experimental outcomes validate the superior disturbance rejection capability of the CFO-LQIR by yielding rapid transits and strong damping against disturbances while preserving the control input economy and closed-loop stability of the system.

Suggested Citation

  • Omer Saleem & Faisal Abbas & Jamshed Iqbal, 2023. "Complex Fractional-Order LQIR for Inverted-Pendulum-Type Robotic Mechanisms: Design and Experimental Validation," Mathematics, MDPI, vol. 11(4), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:913-:d:1064889
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/4/913/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/4/913/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Soukaina Krafes & Zakaria Chalh & Abdelmjid Saka, 2018. "A Review on the Control of Second Order Underactuated Mechanical Systems," Complexity, Hindawi, vol. 2018, pages 1-17, December.
    2. Omer Saleem & Khalid Mahmood-ul-Hasan, 2019. "Robust stabilisation of rotary inverted pendulum using intelligently optimised nonlinear self-adaptive dual fractional-order PD controllers," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(7), pages 1399-1414, May.
    3. Xin Wang & Seyed Mehdi Abtahi & Mahmood Chahari & Tianyu Zhao, 2022. "An Adaptive Neuro-Fuzzy Model for Attitude Estimation and Control of a 3 DOF System," Mathematics, MDPI, vol. 10(6), pages 1-16, March.
    4. Mihailo Micev & Martin Ćalasan & Diego Oliva, 2020. "Fractional Order PID Controller Design for an AVR System Using Chaotic Yellow Saddle Goatfish Algorithm," Mathematics, MDPI, vol. 8(7), pages 1-22, July.
    5. Hojin Lee & Jeonghwan Gil & Sesun You & Yonghao Gui & Wonhee Kim, 2021. "Arm Angle Tracking Control with Pole Balancing Using Equivalent Input Disturbance Rejection for a Rotational Inverted Pendulum," Mathematics, MDPI, vol. 9(21), pages 1-16, October.
    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. Khanh Hieu Nguyen & Sung Hyun Kim, 2023. "Peak-to-Peak Stabilization of Sampled-Data Systems Subject to Actuator Saturation and Its Practical Application to an Inverted Pendulum," Mathematics, MDPI, vol. 11(22), pages 1-19, November.
    2. Omer Saleem & Shehryaar Ali & Jamshed Iqbal, 2023. "Robust MPPT Control of Stand-Alone Photovoltaic Systems via Adaptive Self-Adjusting Fractional Order PID Controller," Energies, MDPI, vol. 16(13), pages 1-20, June.

    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. Emad A. Mohamed & Mokhtar Aly & Masayuki Watanabe, 2022. "New Tilt Fractional-Order Integral Derivative with Fractional Filter (TFOIDFF) Controller with Artificial Hummingbird Optimizer for LFC in Renewable Energy Power Grids," Mathematics, MDPI, vol. 10(16), pages 1-33, August.
    2. Mokhtar Aly & Emad A. Mohamed & Abdullah M. Noman & Emad M. Ahmed & Fayez F. M. El-Sousy & Masayuki Watanabe, 2023. "Optimized Non-Integer Load Frequency Control Scheme for Interconnected Microgrids in Remote Areas with High Renewable Energy and Electric Vehicle Penetrations," Mathematics, MDPI, vol. 11(9), pages 1-31, April.
    3. Abdelhakim Idir & Laurent Canale & Yassine Bensafia & Khatir Khettab, 2022. "Design and Robust Performance Analysis of Low-Order Approximation of Fractional PID Controller Based on an IABC Algorithm for an Automatic Voltage Regulator System," Energies, MDPI, vol. 15(23), pages 1-20, November.
    4. Othman A. M. Omar & Mostafa I. Marei & Mahmoud A. Attia, 2023. "Comparative Study of AVR Control Systems Considering a Novel Optimized PID-Based Model Reference Fractional Adaptive Controller," Energies, MDPI, vol. 16(2), pages 1-19, January.
    5. Abdulsamed Tabak, 2023. "Novel TI λ DND 2 N 2 Controller Application with Equilibrium Optimizer for Automatic Voltage Regulator," Sustainability, MDPI, vol. 15(15), pages 1-16, July.
    6. RamaKoteswara Rao Alla & Kandipati Rajani & Ravindranath Tagore Yadlapalli, 2023. "Design of FOPID controller for higher order MIMO systems using model order reduction," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(5), pages 1660-1670, October.
    7. Hady H. Fayek & Eugen Rusu, 2022. "Novel Combined Load Frequency Control and Automatic Voltage Regulation of a 100% Sustainable Energy Interconnected Microgrids," Sustainability, MDPI, vol. 14(15), pages 1-16, August.
    8. Aravindh Dharmarajan & Parivallal Arumugam & Sakthivel Ramalingam & Kavikumar Ramasamy, 2023. "Equivalent-Input-Disturbance Based Robust Control Design for Fuzzy Semi-Markovian Jump Systems via the Proportional-Integral Observer Approach," Mathematics, MDPI, vol. 11(11), pages 1-16, June.

    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:gam:jmathe:v:11:y:2023:i:4:p:913-:d:1064889. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.