Cascade PID-LQR Control Strategy for Nonlinear Flexible Inverted Pendulum System

Thi-Hong-Lam Le*, Khanh-Hung Pham, Dinh-Luan Pham, Gia-Dat Tong, Le-Thanh-Dat Nguyen, Trinh-Anh-Tuan Ngo, Xuan-Tuan Le, Minh-Tuan Nguyen

1 Ho Chi Minh City University of Technology and Education (HCMUTE)
Vo Van Ngan St., No.01, Thu Duc city, Ho Chi Minh City, 700000, Vietnam
* Corresponding author. E-mail: lamlth@hcmute.edu.vn

Robotica & Management, Vol. 29, No. 1, pp. 03-08
DOI: https://doi.org/10.24193/rm.2024.1.1

Abstract: This study presents a simulation-based investigation into the application of a Cascade Proportional-Integral-Derivative (PID) combined with Linear Quadratic Regulator (LQR) control scheme for managing the complexities of a Nonlinear Flexible Inverted Pendulum System (NFIPS). The NFIPS, characterized by nonlinear dynamics and structural flexibility, demands a sophisticated control strategy to achieve stable and precise performance. The proposed Cascade PID-LQR scheme integrates the advantages of PID for addressing nonlinearities and LQR for optimizing linearized dynamics. Through comprehensive simulations, the effectiveness of the proposed control scheme is evaluated, emphasizing its potential in enhancing stability, response speed, and robustness. The study contributes valuable insights into the application of advanced control methodologies in handling nonlinear and flexible systems, paving the way for further exploration and practical implementations in related domains such as robotics and mechatronics.

Keywords: Nonlinear flexible inverted pendulum, NFIPS, cascade PID-LQR controller, stabilization control.

Full text

References

[1] Faizan F., Fari F., Rehan M., Mughal S., Qadri M.T.: “Implementation of Discrete PID on Inverted Pendulum”, 2010 2nd International Conforence on Education Technology and Computer (ICETC), pp. 48-51, 2010, DOI: 10.1109/ICETC.2010.5529304.

[2] Wang J.J.: “Simulation studies of inverted pendulum based on PID controllers”, Simulation Modelling Practice and Theory, pp. 440-449, 2011, DOI: https://doi.org/10.1016/j.simpat.2010.08.003.

[3] Chakraborty K., Mukherjee R.R., Mukherjee S.: “Tuning Of PID Controller Of Inverted Pendulum Using Genetic Algorithm”, International Journal of Soft Computing and Engineering (IJSCE), Vol. 1 2, pp. 21-24, 2013, DOI: https://doi.org/10.1007/978-981-10-4762-6_38.

[4] Razzaghi K., Jalali A.A.: “A New Approach on Stabilization Control of an Inverted Pendulum Using PID Controller”, Advanced Materials Research, Vol. 403-408, pp. 4674-4680, 2012, DOI: 10.4028/www.scientific.net/AMR.403-408.4674.

[5] Sen M.A., Kalyoncu M.: “Optimisation of a PID Controller for an Inverted Pendulum Using the Bees Algorithm”, Applied Mechanics and Materials, Vol. 789-790, pp. 1039-1044, 2015,
DOI:10.4028/www.scientific.net/AMM.789-790.1039.

[6] Wongsathan C., Sirima C.: “Application of GA to Design LQR Controller for an Inverted Pendulum System”, International Conference on Robotics and Biomimetics, Bangkok, 2009, DOI: 10.1109/ROBIO.2009.4913127.

[7] Banerjee R., Pal A.: “Stabilization Of Inverted Pendulum On Cart Based On Pole Placement and LQR”, International Conference on Advanced Mechatronic Systems (ICAMechS), Luoyang, China, 2013, DOI: 10.1109/ICCSDET.2018.8821196.

[8] El-Hawwary M.I., Elshafei A.L., Emar H.M., Fattah H.A.A.: “Adaptive Fuzzy Control of the Inverted Pendulum Problem”, Ieee Transactions On Control Systems Technology, Vol. 14, p. 1135-1144, NO. 6, November 2006, DOI: 10.1109/TCST.2006.880217.

[9] Meena R.I.B., Girgis E.: “Optimal fractional-order adaptive fuzzy control on inverted pendulum model”, International Journal of Dynamics and Control, Vol. 9, p. 288–298, 2020,
DOI: https://doi.org/10.1007/s40435-020-00636-9.

[10] De Carvalho Jr. A., Justo J.F., Angélico B.A., De Oliveira A.M., Da Silva Filho D.J.I.: “Rotary Inverted Pendulum Identification for control by Paraconsistent Neural Network”, IEEE Journals & Magazine, Vol. 9, p. 74155-74167, 2021,
DOI: 10.1109/ACCESS.2021.3080176.

[11] Gao H., Li X., Gao C., Wu J.: “Neural Network Supervision Control Strategy for Inverted pendulum tracking control”, Discrete Dynamics in Nature and Society, Vol.2021, p. 1–14, 2021, DOI: https://doi.org/10.1155/2021/5536573.

[12] Hayase T., Suematsu Y.: “Control of a flexible inverted pendulum”, Advanced Robotics, vol. 8, p. 1–12, 1993.

[13] Franco E., Astolf A., y Baen F.R.: “Robust balancing control of flexible inverted-pendulum systems”, Mechanism and Machine Theory, vol. 130, pp. 539-551, 2018, DOI: https://doi.org/10.1016/j.mechmachtheory.2018.09.001

[14] Jiali T., Gexu R.: “Modeling and Simulation of a Flexible Inverted Pendulum System”, Tsinghua Science & Technology, Vol. 14, p. 22–26, 2009, DOI: 10.1016/S1007-0214(10)70025-0.

[15] Apkarian H.J., Lacheray H., Martin P.: “Laboratory guide: Linear Flexible Inverted Pendulum Experiment, Markham” Ontario: MATLAB SIMULINK, 2012. Retrived from: https://www.made-for-science.com/de/quanser/?df=made-for-science-quanser-linear-flexible-inverted-pendulum-coursewarestud-matlab.pdf