LQR Controller Based on BAT Algorithm for Rotary Double Parallel Inverted Pendulum
DOI:
https://doi.org/10.59247/jfsc.v3i2.304Keywords:
LQR Controller, BAT Algorithm, Rotary Double Parallel Inverted Pendulum, Swarm IntelligenceAbstract
This paper presents an enhanced approach to stabilizing the Rotary Double Parallel Inverted Pendulum (RDPIP) through a combination of the LQR method and the BAT algorithm. Traditionally, selecting appropriate Q and R matrices relies on designers' intuitions or trial-and-error processes, often resulting in suboptimal performance. By leveraging the BAT algorithm’s swarm intelligence, the proposed method automatically optimizes the cost function to yield improved control performance. Key improvements include shorter stabilization time, reduced overshoot, and minimized oscillations. Simulation results show that the BAT-enhanced LQR controller significantly outperforms traditional design in terms of convergence speed and system damping. These findings underscore the potential of metaheuristic algorithms in refining classical control strategies for complex, nonlinear systems.
References
Fahmizal, Geonoky, and H. Maghfiroh, “Rotary Inverted Pendulum Control with Pole Placement,” J. Fuzzy Syst Control, vol. 1, no. 3, pp. 90–96, 2023, https://doi.org/10.59247/jfsc.v1i3.152.
N.-C. Tran et al., “LQR Control for Experimental Double Rotary Inverted Pendulum,” J. Fuzzy Syst Control, vol. 2, no. 2, pp. 104–108, 2024, https://doi.org/10.59247/jfsc.v2i2.212.
P.-H. Huynh et al., “Model Predictive Control for Rotary Inverted Pendulum: Simulation and Experiment,” J. Fuzzy Syst Control, vol. 2, no. 3, pp. 215–222, 202, https://doi.org/10.59247/jfsc.v2i3.263.
M. Abdullah et al., “Swing up and stabilization control of rotary inverted pendulum based on energy balance, fuzzy logic, and LQR controllers,” Measurement and Control, vol. 54, no. 9-10, pp. 1356-1370, 2021, https://doi.org/10.1177/00202940211035406.
I. Chawla and A. Singla, "Real-Time Control of a Rotary Inverted Pendulum using Robust LQR-based ANFIS Controller," International Journal of Nonlinear Sciences and Numerical Simulation, vol. 19, no. 3-4, pp. 379-389, 2018, https://doi.org/10.1515/ijnsns-2017-0139.
Chawla et al., "Robust LQR Based ANFIS Control of x-z Inverted Pendulum," Amity International Conference on Artificial Intelligence, pp. 818-823, 2019, https://doi.org/10.1109/AICAI.2019.8701333.
M. -T. Vo et al., "Linear Quadratic Regulators Optimal Control of Rotary Double Parallel Inverted Pendulum," International Conference on Control, Robotics and Informatics, pp. 14-18, 2023, https://doi.org/10.1109/ICCRI58865.2023.00009.
C.-H. Nguyen et al., “ANFIS-based LQR Control for Rotary Double Parallel Inverted Pendulum,” J. Fuzzy Syst Control, vol. 2, no. 2, pp. 109–116, 2024, https://doi.org/10.59247/jfsc.v2i2.214.
Q. Yong et al, “Balance control of twowheeled self-balancing mobile robot based on TS fuzzy model,” Proceedings of 2011 6th International Forum on Strategic Technology, pp. 406-409, 2011, https://doi.org/10.1109/IFOST.2011.6021051.
M. Park et al, “Swing-up and LQR stabilization of a rotary inverted pendulum,” Artificial Life and Robotics, vol. 16, pp. 94-97, 2011, https://doi.org/10.1007/s10015-011-0897-9.
R. Xiaogang et al., “Design and LQ Control of a two-wheeled self-balancing robot,” 2008 27th Chinese Control Conference, pp. 275-279, 2008, https://doi.org/10.1109/CHICC.2008.4605775.
M. T. Vo et al, “Combining Passivity Based Control and Linear Quadratic Regulator to Control a Rotary Inverted Pendulum,” Journal of Robotics and Control (JRC), vol. 4, no. 4, pp. 479-490, 2023, https://doi.org/10.18196/jrc.v4i4.18498.
N. Kawasaki and E. Shimemura, “Determining quadratic weighting matrices to locate poles in a specified region,” Automatica, vol. 19, no. 5, pp. 557-560, 1983, https://doi.org/10.1016/0005-1098(83)90011-0.
N. Kawasaki et al, “On the quadratic weights of an LQ-problem shifting only the specified poles,” Proceedings of the Society of Instrument and Control Engineers, vol. 25, no. 11, pp. 1248–1250, 1989, https://doi.org/10.9746/sicetr1965.25.1248.
F. J. Kraus and V. Kučera, “Linear quadratic and pole placement iterative design,” 1999 European Control Conference (ECC), pp. 653 658, 1999, https://doi.org/10.23919/ECC.1999.7099379.
F. J. Kraus and V. Kučera, "Linear quadratic and pole placement iterative design," 1999 European Control Conference (ECC), pp. 653-658, 1999, https://doi.org/10.23919/ECC.1999.7099379.
B. D. Anderson and J. B. Moore. Optimal control: linear quadratic methods. Courier Corporation. 2007. https://books.google.co.id/books?hl=id&lr=&id=fW6TAwAAQBAJ.
C. N. Xuan and T. Le Tran, “Design of State Feedback Controller with Optimal Parameters Using BAT algorithm for Reaction Wheel Pendulum,” 2021 International Conference on Advanced Technologies for Communications (ATC), pp. 172-177, 2021, https://doi.org/10.1109/ATC52653.2021.9598306.
X. S. Yang. Nature-inspired metaheuristic algorithms. Luniver press. 2010. https://books.google.co.id/books?hl=id&lr=&id=iVB_ETlh4ogC.
X. S. Yang, “A new metaheuristic bat-inspired algorithm,” In Nature inspired cooperative strategies for optimization (NICSO 2010), pp. 65-74, 2010, https://doi.org/10.1007/978-3-642-12538-6_6.
Thamir, Luay, “Bat Algorithm Based an Adaptive PID Controller Design for Buck Converter Model,” Journal of Engineering, vol. 26, pp. 62-82, 2020, https://doi.org/10.31026/j.eng.2020.07.05.
G. Li, H. Xu, and Y. Lin, “Application of bat algorithm based time optimal control in multi-robots formation reconfiguration,” Journal of Bionic Engineering, vol. 15, no. 1, pp. 126-138, 2018, https://doi.org/10.1007/s42235-017-0010-8.
O. B. Alzain et al., "optimization of Sliding Mode Control based on BAT-Algorithm for the DFIG-WT," International Conference on Computer, Control, Electrical, and Electronics Engineering (ICCCEEE), pp. 1-7, 2021, https://doi.org/10.1109/ICCCEEE49695.2021.9429587.
C. Abdelghani et al., "Robust design of fractional order PID Sliding Mode based Power System Stabilizer in a power system via a new metaheuristic Bat algorithm," International Workshop on Recent Advances in Sliding Modes (RASM), pp. 1-5, 2015, https://doi.org/10.1109/RASM.2015.7154651.
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Copyright (c) 2025 Thanh-Tri-Dai Le, Ngoc-Kien Nguyen, Phuc-Truong Le, Minh-Nguyen-Bao Bui, Trong-Tin Nguyen, Chi-Anh Tran, Phuong-Tu Doan, Duc-Nhan Dao, Van-Dong-Hai Nguyen, Thanh-Tung Nguyen

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