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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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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.
    2. 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.

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