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Implementation of a Controller to Eliminate the Limit Cycle in the Inverted Pendulum on a Cart

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  • Mayra Antonio-Cruz
  • Victor Manuel Hernández-Guzmán
  • Ramón Silva-Ortigoza
  • Gilberto Silva-Ortigoza

Abstract

A frequency response-based linear controller is implemented to regulate the inverted pendulum on a cart at the inverted position. The objective is to improve the performance of the control system by eliminating the limit cycle generated by the dead-zone, induced by static friction, at the actuator of the mechanism. This control strategy has been recently introduced and applied by the authors to eliminate the limit cycle in the Furuta pendulum and the pendubot systems. Hence, the main aim of the present paper is to study the applicability of the control strategy to eliminate the limit cycle in the inverted pendulum on a cart. The successful results that are obtained in experiments corroborate that the approach introduced by the authors to eliminate the limit cycle in the Furuta pendulum and pendubot is also valid for the inverted pendulum on a cart.

Suggested Citation

  • Mayra Antonio-Cruz & Victor Manuel Hernández-Guzmán & Ramón Silva-Ortigoza & Gilberto Silva-Ortigoza, 2019. "Implementation of a Controller to Eliminate the Limit Cycle in the Inverted Pendulum on a Cart," Complexity, Hindawi, vol. 2019, pages 1-13, February.
    • Handle: RePEc:hin:complx:8271584
    DOI: 10.1155/2019/8271584
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    References listed on IDEAS

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    1. Verduzco, Fernando, 2007. "Control of oscillations from the k-zero bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 492-504.
    2. Ahmad Taher Azar & Fernando E. Serrano, 2016. "Stabilization of Mechanical Systems with Backlash by PI Loop Shaping," International Journal of System Dynamics Applications (IJSDA), IGI Global, vol. 5(3), pages 21-46, July.
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    Cited by:

    1. Elisabeth Tansiana Mbitu & Seng-Chi Chen, 2020. "Designing Limit-Cycle Suppressor Using Dithering and Dual-Input Describing Function Methods," Mathematics, MDPI, vol. 8(11), pages 1-14, November.

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