LQR and Fuzzy-PID Control Design on Double Inverted Pendulum

Erlyana Trie Damayanti, Mardlijah Mardlijah, Ridho Nur Rohman Wijaya

Abstract


Double inverted pendulum is a non-linear and unstable system. Double inverted pendulum can be stabilized in the upright position by providing control to the system. In this research we compare two types of controllers namely Linear Quadratic Regulator (LQR) and Fuzzy-PID. The objective is to determine the control strategy that provides better performance on the position of the cart and pendulum angle. We modelled the system which is then linearized and given control. From the simulation results, it is proven that LQR and Fuzzy-PID controllers have been successfully designed to stabilize the double inverted pendulum. However, when given a disturbance in the form of noise step, the LQR controller has not been able to achieve the desired reference for up to 20 seconds. In another hand, the Fuzzy-PID controller is able to achieve the desired reference after 8 seconds. Therefore, it can be concluded that the Fuzzy-PID controller when applied to the Double Inverted pendulum system has better performance than the LQR controller.

Keywords


Control; Double Inverted Pendulum; LQR; Fuzzy; PID

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References


[1] Y. Y. Lim, C. L. Hoo, and Y. M. Felicia Wong, “Stabilising an Inverted Pendulum with PID Controller,” in MATEC Web of Conferences, EDP Sciences, Feb. 2018.

[2] M. Rabah, A. Rohan, and S. H. Kim, “Comparison of position control of a gyroscopic inverted pendulum using PID, fuzzy logic and fuzzy PID controllers,” International Journal of Fuzzy Logic and Intelligent Systems, vol. 18, no. 2, pp. 103–110, Jun. 2018, doi: 10.5391/IJFIS.2018.18.2.103.

[3] M. Khrisna, “Control Optimal Double Inverted Pendulum Menggunakan Sistem Kendali LQR.” [Online]. Available: https://www.researchgate.net/publication/355118786

[4] 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 (Switzerland), vol. 13, no. 8, Aug. 2022, doi: 10.3390/info13080379.

[5] R. Bhareszy, F. Hadary, and P. Studi Teknik Elektro Jurusan Teknik Elektro, “KESTABILAN DINAMIS SISTEM DOUBLE INVERTED PENDULUM DENGAN PERSAMAAN LAGRANGE.”

[6] N. S. Bhangal, “Design and Performance of LQR and LQR based Fuzzy Controller for Double Inverted Pendulum System,” Journal of Image and Graphics, vol. 1, no. 3, pp. 143–146, 2013, doi: 10.12720/joig.1.3.143-146.

[7] D. A. P. A. Pritandi, “Perancangan Kontroler PID-Fuzzy untuk Sistem Pengaturan Cascade Level dan Flow pada Basic Process Rig 38-100,” Jurnal Teknik ITS, vol. 5, no. 2, 2016, doi: 10.12962/j23373539.v5i2.16179.

[8] A. Kossoski, F. C. Correa, A. M. Tusset, and J. M. Balthazar, “PID-Fuzzy control design for a nonlinear inverted pendulum,” Journal of Applied Instrumentation and Control, vol. 9, no. 1, 2021, doi: 10.3895/jaic.v9n1.13589.

[9] E. S. Varghese, A. K. Vincent, and V. Bagyaveereswaran, “Optimal control of inverted pendulum system using PID controller, LQR and MPC,” in IOP Conference Series: Materials Science and Engineering, Institute of Physics Publishing, Dec. 2017. doi: 10.1088/1757-899X/263/5/052007.

[10] K. Ogata, Modern Control Engineering Fifth Edition, vol. 17, no. 3. 2009.

[11] T. D. Madyanto, I. Santoso, and I. Setiawan, “Pengontrolan Suhu Menggunakan Metode FUZZY-PID pada Model Sistem Hipertermia,” 2010, [Online]. Available: http://ejournal.undip.ac.id/index.php/transmisi

[12] B. Elkinany, M. Alfidi, R. Chaibi, and Z. Chalh, “T-S Fuzzy System Controller for Stabilizing the Double Inverted Pendulum,” Advances in Fuzzy Systems, vol. 2020, doi: 10.1155/2020/8835511.

[13] S. Hadi, “Penerapan Konsep Usaha dan Energi Dalam Persfektif Sains dan AlQur’an,” Jurnal Penelitian Fisika dan Terapannya (JUPITER), vol. 3, no. 2, p. 61, Feb. 2022, doi: 10.31851/jupiter.v3i2.7570.

[14] S. Side, W. Sanusi, N. K. Rustan, J. Matematika, F. Matematika, and I. Pengetahuan, “Model Matematika SIR Sebagai Solusi Kecanduan Penggunaan Media Sosial,” 2020. [Online]. Available: http://www.ojs.unm.ac.id/jmathcos

[15] Subiono, “Sistem Linear dan Kontrol Optimal.” Surabaya: Institut Teknologi Sepuluh Nopember, 2023




DOI: https://doi.org/10.18860/ca.v9i1.22070

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