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Optimal Fuzzy Proportional‐Integral‐Derivative Control for a Class of Fourth‐Order Nonlinear Systems using Imperialist Competitive Algorithms

Author

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  • S. Hadipour Lakmesari
  • Z. Safipour
  • M. J. Mahmoodabadi
  • Yousef Ibrahim
  • Saleh Mobayen

Abstract

The proportional integral derivative (PID) controller has gained wide acceptance and use as the most useful control approach in the industry. However, the PID controller lacks robustness to uncertainties and stability under disturbances. To address this problem, this paper proposes an optimal fuzzy‐PID technique for a two‐degree‐of‐freedom cart‐pole system. Fuzzy rules can be combined with controllers such as PID to tune their coefficients and allow the controller to deliver substantially improved performance. To achieve this, the fuzzy logic method is applied in conjunction with the PID approach to provide essential control inputs and improve the control algorithm efficiency. The achieved control gains are then optimized via the imperialist competitive algorithm. Consequently, the objective function for the cart‐pole system is regarded as the summation of the displacement error of the cart, the angular error of the pole, and the control force. This control concept has been tested via simulation and experimental validations. Obtained results are presented to confirm the accuracy and efficiency of the suggested method.

Suggested Citation

  • S. Hadipour Lakmesari & Z. Safipour & M. J. Mahmoodabadi & Yousef Ibrahim & Saleh Mobayen, 2022. "Optimal Fuzzy Proportional‐Integral‐Derivative Control for a Class of Fourth‐Order Nonlinear Systems using Imperialist Competitive Algorithms," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:3554897
    DOI: 10.1155/2022/3554897
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    References listed on IDEAS

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    1. Duc Ngoc Nguyen & Tuan Anh Nguyen & Xiaoping Liu, 2022. "A Novel Hybrid Control Algorithm Sliding Mode-PID for the Active Suspension System with State Multivariable," Complexity, Hindawi, vol. 2022, pages 1-14, June.
    2. 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.
    3. Hadipour Lakmesari, S. & Mahmoodabadi, M.J. & Yousef Ibrahim, M., 2021. "Fuzzy logic and gradient descent-based optimal adaptive robust controller with inverted pendulum verification," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Miguel Gabriel Villarreal-Cervantes & Jesús Said Pantoja-García & Alejandro Rodríguez-Molina & Saul Enrique Benitez-Garcia, 2021. "Pareto optimal synthesis of eight-bar mechanism using meta-heuristic multi-objective search approaches: application to bipedal gait generation," International Journal of Systems Science, Taylor & Francis Journals, vol. 52(4), pages 671-693, March.
    5. Duc Ngoc Nguyen & Tuan Anh Nguyen, 2022. "A Novel Hybrid Control Algorithm Sliding Mode‐PID for the Active Suspension System with State Multivariable," Complexity, John Wiley & Sons, vol. 2022(1).
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