A T-S Fuzzy Approach with Extended LMI Conditions for Inverted Pendulum on a Cart
Received: 31 October 2023 | Revised: 1 December 2023 | Accepted: 6 December 2023 | Online: 8 February 2024
Corresponding author: Thi Van Anh Nguyen
Abstract
The Inverted Pendulum On a Cart (IPOC) system poses a challenge in control engineering due to its inherent instability, nonlinearity, and underactuation. This addresses the fundamental issues arising from its underactuated nature and introduces an approach that combines Takagi-Sugeno (T-S) fuzzy control with an awareness of real-world constraints to create a control system ensuring both stability and practicality. By aligning theoretical insights with extended considerations, the Linear Matrix Inequality (LMI)-based control design is demonstrated in a comprehensive framework. Theorems are introduced and validated, leading to the derivation of LMI conditions. The simulation results are assessed with accompanying comments to demonstrate the effectiveness of the theorems. Through this integration of T-S fuzzy control with additional considerations, the paper aims to bridge the gap between theory and practical applications, advancing the field of control engineering.
Keywords:
Takagi-Sugeno fuzzy, inverted pendulum on a cart, linear matrix inequality, decay rate, constraint on the outputDownloads
References
S. Hadipour Lakmesari, M. J. Mahmoodabadi, and M. Yousef Ibrahim, "Fuzzy logic and gradient descent-based optimal adaptive robust controller with inverted pendulum verification," Chaos, Solitons & Fractals, vol. 151, Oct. 2021, Art. no. 111257.
E. Susanto, A. Surya Wibowo, and E. Ghiffary Rachman, "Fuzzy Swing Up Control and Optimal State Feedback Stabilization for Self-Erecting Inverted Pendulum," IEEE Access, vol. 8, pp. 6496–6504, 2020.
T. Johnson, S. Zhou, W. Cheah, W. Mansell, R. Young, and S. Watson, "Implementation of a Perceptual Controller for an Inverted Pendulum Robot," Journal of Intelligent & Robotic Systems, vol. 99, no. 3, pp. 683–692, Sep. 2020.
S.-J. Huang, S.-S. Chen, and S.-C. Lin, "Design and Motion Control of a Two-Wheel Inverted Pendulum Robot," International Journal of Mechanical and Mechatronics Engineering, vol. 13, no. 3, pp. 194–201, Feb. 2019.
G. Curiel-Olivares, J. Linares-Flores, J. F. Guerrero-Castellanos, and A. Hernández-Méndez, "Self-balancing based on Active Disturbance Rejection Controller for the Two-In-Wheeled Electric Vehicle, Experimental results," Mechatronics, vol. 76, Jun. 2021, Art. no. 102552.
T. Zielinska, G. R. R. Coba, and W. Ge, "Variable Inverted Pendulum Applied to Humanoid Motion Design," Robotica, vol. 39, no. 8, pp. 1368–1389, Aug. 2021.
M. A. Sen and M. Kalyoncu, "Optimal Tuning of a LQR Controller for an Inverted Pendulum Using the Bees Algorithm," Journal of Automation and Control Engineering, pp. 384–387, 2016.
B. Abeysekera and W. K. Wanniarachchi, "Modelling and Implementation of PID Control for Balancing of an Inverted Pendulum," International Journal of Automation, Control and Intelligent Systems, vol. 4, no. 4, pp. 43–53, Dec. 2018.
S. Irfan, A. Mehmood, M. T. Razzaq, and J. Iqbal, "Advanced sliding mode control techniques for Inverted Pendulum: Modelling and simulation," Engineering Science and Technology, an International Journal, vol. 21, no. 4, pp. 753–759, Aug. 2018.
G. S. Maraslidis, T. L. Kottas, M. G. Tsipouras, and G. F. Fragulis, "Design of a Fuzzy Logic Controller for the Double Pendulum Inverted on a Cart," Information, vol. 13, no. 8, Aug. 2022, Art. no. 379.
B. Kasmi and A. Hassam, "Comparative Study between Fuzzy Logic and Interval Type-2 Fuzzy Logic Controllers for the Trajectory Planning of a Mobile Robot," Engineering, Technology & Applied Science Research, vol. 11, no. 2, pp. 7011–7017, Apr. 2021.
S. Hadipour Lakmesari, M. J. Mahmoodabadi, and M. Yousef Ibrahim, "Fuzzy logic and gradient descent-based optimal adaptive robust controller with inverted pendulum verification," Chaos, Solitons & Fractals, vol. 151, Oct. 2021, Art. no. 111257.
I. H. Hamad, A. Chouchaine, and H. Bouzaouache, "A Takagi-Sugeno Fuzzy Model for Greenhouse Climate," Engineering, Technology & Applied Science Research, vol. 11, no. 4, pp. 7424–7429, Aug. 2021.
N. V. Hai, N. V. Tiem, L. H. Lan, and T. H. Vo, "Pantograph Catenary Contact Force Regulation Based on Modified Takagi-Sugeno Fuzzy Models," Engineering, Technology & Applied Science Research, vol. 13, no. 1, pp. 9879–9887, Feb. 2023.
R. V. Gandhi and D. M. Adhyaru, "Takagi-Sugeno fuzzy regulator design for nonlinear and unstable systems using negative absolute eigenvalue approach," IEEE/CAA Journal of Automatica Sinica, vol. 7, no. 2, pp. 482–493, Mar. 2020.
A. I. Roose, S. Yahya, and H. Al-Rizzo, "Fuzzy-logic control of an inverted pendulum on a cart," Computers & Electrical Engineering, vol. 61, pp. 31–47, Jul. 2017.
K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. John Wiley & Sons, Ltd, 2001.
Downloads
How to Cite
License
Copyright (c) 2023 Thi Van Anh Nguyen, Ngoc Hiep Tran
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.
