A Study of Adaptive Model Predictive Control for Rotary Inverted Pendulum
DOI:
https://doi.org/10.59247/jfsc.v3i2.302Keywords:
Rotary Inverted Pendulum, Adaptive Control, Model Predictive Control, Kalman Filter, Linear Time-varyingAbstract
This paper proposes an Adaptive Model Predictive Control (MPC) approach for the rotary inverted pendulum (RIP). The method combines Linear Time-Varying (LTV) models at each sampling instant with a Linear Time-Varying Kalman Filter (LTVKF) for state estimation. By predicting and adapting to dynamic system changes, the controller achieves trajectory tracking performance comparable to non-adaptive MPC. However, the Adaptive MPC extends the arm’s operating range by up to 1.5 times, making it a promising solution for strongly nonlinear or time-varying systems like the RIP.
References
S. N. Vassilyev, A. Y. Kelina, Y. I. Kudinov, and F. F. Pashchenko, “Intelligent control systems,” Procedia Computer Science, vol. 103, pp. 623-628, 2017, https://doi.org/10.1016/j.procs.2017.01.088.
H. F. Murcia and A. E. González, "Performance comparison between PID and LQR control on a 2-wheel inverted pendulum robot," 2016 IEEE Colombian Conference on Robotics and Automation (CCRA), Bogota, Colombia, 2016, pp. 1-6, 2016, https://doi.org/10.1109/CCRA.2016.7811420.
T.-D. Chu and C.-K. Chen, "Design and Implementation of Model Predictive Control for a Gyroscopic Inverted Pendulum," Applied Sciences, vol. 7, no. 12, 2017. https://doi.org/10.3390/app7121272.
E. Kreindler, “Contributions to the theory of time-optimal control,” Journal of the Franklin Institute, vol. 275, no. 4, pp. 314-344, 1963, https://doi.org/10.1016/0016-0032(63)90689-6.
R. E. Kalman, "A new approach to linear filtering and prediction problems," J. Fluids Eng., vol. 82, no. 1, pp. 35-45, 1960, https://doi.org/10.1115/1.3662552.
R. Ortega et al. Euler-Lagrange systems (pp. 15-37). Springer London. 1998. https://doi.org/10.1007/978-1-4471-3603-3_2.
S. J. Qin and T. A. Badgwell, "A survey of industrial model predictive control technology," Control Engineering Practice, vol. 11, no. 7, pp. 733-764, 2003, https://doi.org/10.1016/S0967-0661(02)00186-7.
L. Chrif and Z. M. Kadda, "Aircraft control system using LQG and LQR controller with optimal estimation-Kalman filter design," Procedia Engineering, vol. 80, pp. 245-257, 2014, https://doi.org/10.1016/j.proeng.2014.09.084.
A. Ingabire and A. A. Sklyarov, "Control of longitudinal flight dynamics of a fixedwing UAV using LQR, LQG and nonlinear control," in E3S Web of Conferences, vol. 104, p. 02001, 2019, https://doi.org/10.1051/e3sconf/201910402001.
A. Niknezhadi et al., "Design and implementation of LQR/LQG strategies for oxygen stoichiometry control in PEM fuel cells based systems," Journal of Power Sources, vol. 196, no. 9, pp. 4277-4282, 2011, https://doi.org/10.1016/j.jpowsour.2010.11.059.
H. H. Phuc et al., "Model Predictive Control for Rotary Inverted Pendulum: Simulation and Experiment," Journal of Fuzzy Systems and Control, vol. 2, no. 3, pp. 215-222, 2024, https://doi.org/10.59247/jfsc.v2i3.263.
S. Jung and J. T. Wen, "Nonlinear model predictive control for the swing-up of a rotary inverted pendulum," J. Dyn. Sys., Meas., Control, vol. 126, no. 3, pp. 666-673, 2004, https://doi.org/10.1115/1.1789541.
J. He, Y. Li, Z. Wei, and Z. Huang, "Gain-Scheduled Model Predictive Control for Cart–Inverted-Pendulum with Friction and Disturbances," Appl. Sci., vol. 13, no. 24, p. 13080, 2023, https://doi.org/10.3390/app132413080.
J. -S. Kim, "Recent advances in adaptive MPC," ICCAS 2010, pp. 218-222, 2010, https://doi.org/10.1109/ICCAS.2010.5669892.
P. H. Huynh, et al., “A Survey Of Lqg Over Mpc And Lqr Control For Rotary Inverted Pendulum,” Robotica & Management, vol. 29, no. 2, 2024, https://doi.org/10.24193/rm.2024.2.2.
L. S. Shieh et al., "Discrete-continuous model conversion," Applied Mathematical Modelling, vol. 4, no. 6, pp. 449-455, 1980, https://doi.org/10.1016/0307-904X(80)90177-8.
M. Bujarbaruah, X. Zhang, U. Rosolia and F. Borrelli, "Adaptive MPC for Iterative Tasks," 2018 IEEE Conference on Decision and Control (CDC), 2018, https://doi.org/10.1109/CDC.2018.8618694.
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Copyright (c) 2025 Phuc-Hoang Huynh, Khac-Chan-Nguyen Le, Truong-Phuc Nguyen, Hoang-Dang-Khoa Tran, Su-Truong Dang, Thanh-Quyen Nguyen, Thang-Phong Le, Huu-Hanh Nguyen, Pham-Hong-Linh Tran, Hau-Phuong Nguyen, Hoang-Son Nguyen, Tai-Truong Nguyen, Hai-Thanh Nguyen

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