Design of an Optimal Linear Quadratic Regulator (LQR) Controller for the Ball-On-Sphere System
Автор: Usman Mohammed, Suleiman U. Hussein, Muhammad Usman, Sadiq Thomas
Журнал: International Journal of Engineering and Manufacturing @ijem
Статья в выпуске: 3 vol.10, 2020 года.
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Linear Quadratic Regulator (LQR) is one of the optimal control methods that continue to gain popularity. This paper designed an optimal LQR controller to control the system of the ball-on-sphere. System equations were derived and due to the nonlinearity of the system, the equations were linearized. After that, the coefficient matrices of the system dynamics were derived. Given some initial conditions, the response was simulated and controlled close to the desired values. An improvement of about 87% was achieved and the performance of the controller was observed to be good based on the simulation results. The results showed that LQR controller is one of the best optimal control methods because of its high performance improvement.
LQR, Controller, Ball-on-sphere, Optimal, System
Короткий адрес: https://sciup.org/15017308
IDR: 15017308 | DOI: 10.5815/ijem.2020.03.05
Список литературы Design of an Optimal Linear Quadratic Regulator (LQR) Controller for the Ball-On-Sphere System
- “Control of a Ball on Sphere System with Adaptive Neural Network Method for Regulation Purpose.” [Online]. Available: https://scialert.net/abstract/?doi=jas.2014.1984.1989. [Accessed: 07-Dec-2019].
- “Controlling a ball and wheel system using full-state-feedback linearization [Focus on Education],” IEEE Control Syst., vol. 29, no. 5, pp. 93–101, Oct. 2009.
- M. Moarref, M. Saadat, and G. Vossoughi, “Mechatronic design and position control of a novel ball and plate system,” in 2008 16th Mediterranean Conference on Control and Automation, Ajaccio, France, 2008, pp. 1071–1076.
- A. R. Ghiasi and H. Jafari, “Optimal Robust Controller Design for the Ball and Plate System,” p. 5.
- C. Graf and T. Röfer, “A Closed-loop 3D-LIPM Gait for the RoboCup Standard Platform League Humanoid,” p. 5, 2010.
- Óbuda University, Budapest, Hungary and R. Szabolcsi, “DESIGN AND DEVELOPMENT OF THE LQR OPTIMAL CONTROLLER FOR THE UNMANNED AERIAL VEHICLE,” Rev. Air Force Acad., vol. 16, no. 1, pp. 45–54, Aug. 2018.
- S. Beatty, “Comparison of PD and LQR Methods for Spacecraft Attitude Control Using Star Trackers,” in 2006 World Automation Congress, Budapest, Hungary, 2006, pp. 1–6.
- S. A. Moezi, E. Zakeri, Y. Bazargan-Lari, and M. Khalghollah, “Fuzzy Logic Control of a Ball on Sphere System,” Adv. Fuzzy Syst., vol. 2014, pp. 1–6, 2014.
- H. Purnawan, Mardlijah, and E. B. Purwanto, “Design of linear quadratic regulator (LQR) control system for flight stability of LSU-05,” J. Phys. Conf. Ser., vol. 890, p. 012056, Sep. 2017.
- F. K. Zadeh, P. Moallem, S. Asiri, and M. M. Zadeh, “LQR motion control and analysis of a prototype spherical robot,” in 2014 Second RSI/ISM International Conference on Robotics and Mechatronics (ICRoM), Tehran, Iran, 2014, pp. 890–895.
- Ahmadu Bello University/Department of Computer Engineering, Zaria, 810212, Nigeria, A. M. Yesufu, and A. D. Usman, “Effect of Friction on Ball-On-Sphere System Modelled by Bond Graph,” Int. J. Mod. Educ. Comput. Sci., vol. 9, no. 7, pp. 23–29, Jul. 2017.
- M. Keshmiri, A. F. Jahromi, A. Mohebbi, M. Hadi Amoozgar, and W.-F. Xie, “MODELING AND CONTROL OF BALL AND BEAM SYSTEM USING MODEL BASED AND NON-MODEL BASED CONTROL APPROACHES,” Int. J. Smart Sens. Intell. Syst., vol. 5, no. 1, pp. 14–35, 2012.
- S. Y. Liu, Y. Rizal, and M. T. Ho, “Stabilization of a ball and sphere system using feedback linearization and sliding mode control,” in ASCC 2011 - 8th Asian Control Conference - Final Program and Proceedings, 2011, pp. 1334–1339.
- E. Zakeri, A. Ghahramani, and S. Moezi, “Adaptive Feedback Linearization Control of a Ball on Sphere System,” p. 5.
- A. Tewari, Modern control design with MATLAB and SIMULINK. Chichester; New York: John Wiley, 2002.
