Fuzzy Observer-Based Control Design for Rotary Inverted Pendulum Using Takagi-Sugeno Model
Main Article Content
Abstract
The paper introduces fuzzy observer-based control for rotary inverted pendulum systems, renowned for their inherent instability and complexity. We leverage the Takagi-Sugeno (T-S) fuzzy model, which involves the incorporation of local linear models described by fuzzy rules, thus enabling precise and stable control. The Takagi-Sugeno (T-S) fuzzy model, a versatile framework renowned for its suitability in complex control systems, is central to our approach. The significance of observers in accurately estimating unmeasurable states is underlined, with a focus on elucidating the theoretical foundations of fuzzy observers and their role in bolstering control robustness. Additionally, we introduce the integration of Linear Matrix Inequalities (LMIs) and Parallel Distributed Compensation (PDC) for efficient determination of observer and control gains. These advanced tools work in tandem to empower T-S observer control, ensuring both precision and robustness. This paper shows the potential of fuzzy observer-based control and achieving stability and high-performance control of rotary inverted pendulum systems. The effectiveness of the proposed method is validated through simulation results.
Keywords
Takagi-Sugeno fuzzy model, observer control, linear matrix inequality, rotary inverted pendulum
Article Details
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References
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[8] Y. J. Kim, Y. G. Lee, S. H. Lee and O. M. Kwon, T-S fuzzy controller design for Rotary Inverted Pendulum with input delay using Wirtinger-based integral inequality, In Proc. 22nd International Conference on Control, Automation and Systems (ICCAS), Jeju, Republic of Korea, pp. 890-895, 2022, https://doi.org/10.23919/ICCAS55662.2022.10003811
[9] V. N. Giap, S. -C. Huang, Q. D. Nguyen and T. -J. Su, Disturbance observer-based linear matrix inequality for the synchronization of Takagi-Sugeno fuzzy chaotic systems, in IEEE Access, vol. 8, pp. 225805-225821, 2020, https://doi.org/10.1109/ACCESS.2020.3045416
[10] Valentino, M. C., Faria, F. A., Oliveira, V. A., & Alberto, L. F. Sufficient conditions in terms of linear matrix inequalities for guaranteed ultimately boundedness of solutions of switched Takagi-Sugeno fuzzy systems using the S-procedure. Information Sciences, vol. 572, pp. 501-521, 2021, https://doi.org/10.1016/j.ins.2021.04.103
[11] Chen, C. W., Modeling and fuzzy PDC control and its application to an oscillatory TLP structure. Mathematical Problems in Engineering, vol. 2010, Article ID 120403, 13 pages, 2010. https://doi.org/10.1155/2010/120403
[12] Rajesh, R., & Kaimal, M. R., T–S fuzzy model with nonlinear consequence and PDC controller for a class of nonlinear control systems. Applied Soft Computing, vol. 7, no. 3, pp. 772-782, June 2007, https://doi.org/10.1016/j.asoc.2006.01.014
[2] Li, Y., Xin, X., & Yan, Y. A signal compensation-based balance control for the rotary inverted pendulum system. Journal of Vibration and Control, 2023. Online https://doi.org/10.1177/107754632311962
[3] Bhourji, R. S., Mozaffari, S., & Alirezaee, S. Reinforcement learning DDPG–PPO agent-based control system for rotary inverted pendulum. Arabian Journal for Science and Engineering, pp. 1-14, 2023, https://doi.org/10.1007/s13369-023-07934-2 [4] Hamza, M. F., Yap, H. J., Choudhury, I. A., Isa, A. I., Zimit, A. Y., & Kumbasar, T. Current development on using Rotary Inverted Pendulum as a benchmark for testing linear and nonlinear control algorithms. Mechanical Systems and Signal Processing, vol. 116, no. 1, pp. 347-369, 2019, https://doi.org/10.1016/j.ymssp.2018.06.054
[5] Hazem, Z. B., Fotuhi, M. J., & Bingül, Z. Development of a Fuzzy-LQR and Fuzzy-LQG stability control for a double link rotary inverted pendulum. Journal of the Franklin Institute, vol. 357, no. 15, pp. 10529-10556, 2020, https://doi.org/10.1016/j.jfranklin.2020.08.030 [6] AYDIN, M., & Yakut, O., Fuzzy sliding mode control with moving sliding surface of rotary inverted pendulum. Journal of Advanced Research in Natural and Applied Sciences, vol. 8, no. 3, pp. 355-369, 2022, https://doi.org/10.28979/jarnas.1015366
[7] Nguyen, T. V. A., Dong, B. T., & BUI, N. T. Enhancing stability control of inverted pendulum using Takagi– Sugeno fuzzy model with disturbance rejection and input–output constraints. Scientific Reports, vol. 13, no. 14412, 2023, https://doi.org/10.1038/s41598-023-41258-3
[8] Y. J. Kim, Y. G. Lee, S. H. Lee and O. M. Kwon, T-S fuzzy controller design for Rotary Inverted Pendulum with input delay using Wirtinger-based integral inequality, In Proc. 22nd International Conference on Control, Automation and Systems (ICCAS), Jeju, Republic of Korea, pp. 890-895, 2022, https://doi.org/10.23919/ICCAS55662.2022.10003811
[9] V. N. Giap, S. -C. Huang, Q. D. Nguyen and T. -J. Su, Disturbance observer-based linear matrix inequality for the synchronization of Takagi-Sugeno fuzzy chaotic systems, in IEEE Access, vol. 8, pp. 225805-225821, 2020, https://doi.org/10.1109/ACCESS.2020.3045416
[10] Valentino, M. C., Faria, F. A., Oliveira, V. A., & Alberto, L. F. Sufficient conditions in terms of linear matrix inequalities for guaranteed ultimately boundedness of solutions of switched Takagi-Sugeno fuzzy systems using the S-procedure. Information Sciences, vol. 572, pp. 501-521, 2021, https://doi.org/10.1016/j.ins.2021.04.103
[11] Chen, C. W., Modeling and fuzzy PDC control and its application to an oscillatory TLP structure. Mathematical Problems in Engineering, vol. 2010, Article ID 120403, 13 pages, 2010. https://doi.org/10.1155/2010/120403
[12] Rajesh, R., & Kaimal, M. R., T–S fuzzy model with nonlinear consequence and PDC controller for a class of nonlinear control systems. Applied Soft Computing, vol. 7, no. 3, pp. 772-782, June 2007, https://doi.org/10.1016/j.asoc.2006.01.014