[01] Buddhika Abeysekera, Department of Physics, University of Sri Jayewardenepura, Nugegoda, Sri Lanka. [02] Indika Wanniarachchi, Department of Physics, University of Sri Jayewardenepura, Nugegoda, Sri Lanka.

Inverted pendulum (IP) has become a popular topic among physicist and control engineers due to advanced applications related to this particular pendulum. Two wheel balancing robots, rockets and missile guidance systems are some complex applications of the IP. The IP is highly unstable and to maintain the vertical upright position, an active control system is needed. Proportional, Integral and Derivative (PID) controller is one of the best controlling methods used in various dynamic control systems recently because of the simplicity and applicability. In this paper, two PID controllers are used to balance the IP and an error optimization method is used for filtering unwanted sensor responses. The PID controllers have been designed for controlling of each sub-system. PID gain parameters are tuned separately and manually using trial and error approach. Mathematical model of this IP is developed to determine the dynamic properties of the IP system and through this model, state space model of the IP system is developed. With the help of state space model, Kalman filter is developed and used to optimize the error in sensor readings. Then control system of the IP based on the PID controllers and the Kalman filter (control algorithm) is implemented on a microcontroller based platform in order to balance the inverted pendulum on a trolley using the mechanical system which is controlled by the microcontroller. Main objective of this control system is to balance the IP in an upright position in the middle of the two rails. Behavior of the IP system with this control algorithm is monitored through the real-time data acquisition system. The data of the IP system is used to contrast the IP behavior with each PID gain parameter through a graphical representation. With proper gain parameters, the IP system shows best smooth behavior of it.

Inverted Pendulum, Kalman Filter, Lagrangian, Microcontroller, PID, Space State Modeling

[01] N. M. A. Ghani, F. Naim and T. P. Yon, "Two Wheels Balancing Robot with Line Following," International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, vol. 5, no. 7, pp. 1402, 1405, 2011. [02] B. Kada and Y. Ghazzawi, "Robust PID Controller Design for an UAV Flight Control System," WCECS, vol. II, 2011. [03] V. Balaji, M. Balaji, M. Chandrasekaran, A. khand and I. Elamvazuthi, "Optimization of PID Control for High Speed Line Tracking Robots," Procedia Computer Science, no. 76, pp. 147-152, 2015. [04] M. Nour, J. Ooi and K. Y. Chan, "Fuzzy Logic Control vs. Conventional PID Control of an Inverted Pendulum Robot," IEEE, pp. 1-6, 2007. [05] T. Sugihara, Y. Nakamura and H. Inoue, "Realtime Humanoid Motion Generation through ZMP Manipulation based on Inverted Pendulum Control," CREST Japan Science and Technology Corporation (JST), 2007. [06] J.-J. Wang, "Simulation studies of inverted pendulum based on PID controllers," Elsevier, pp. 440, 441, 2010. [07] M. B. Rhudy, R. A. Salguero and K. Holappa, "A KALMAN FILTERING TUTORIAL FOR UNDERGRADUATE STUDENTS," International Journal of Computer Science & Engineering Survey, vol. 8, no. 1, pp. 1-9, 2017. [08] J. Riggs, Chemical Process Control, Lubbock: Ferret Publishing, 2001. [09] J. Charais, R. Lourens and Microchip Technology Inc., "Software PID Control of an Inverted Pendulum Using the PIC16F684," Microchip Technology Inc., California, 2004. [10] M. Moghaddas, M. RezaDastranj, N. Changizi and N. Khoori, "Design of Optimal PID Controller for Inverted Pendulum," International Journal of Innovation, Management and Technology, vol. 3, pp. 440, 441, 2012. [11] M. Moghavvemi, A. L. Salih, H. A. F. Mohamed and K. S. Gaeid, "Flight PID controller design for a UAV quadrotor," Scientific research and essays, vol. 5, no. 23, p. 3660, 2010. [12] G. Welch and G. Bishop, "An Introduction to the Kalman Filter," 2007. [Online]. Available: http://www.cs.unc.edu/~welch/kalman/kalmanIntro.html. [Accessed 15 April 2017]. [13] D. Simon, "Embedded Systems Programming," 2003. [Online]. Available: http://www.controleng.com/article/CA325983.html. [Accessed 11 April 2017]. [14] T. M. Fowler, LTI System and Control Theory, 2007. [15] Arduino, "Mega 2560 Rev3 - Boards & Modules," [Online]. Available: https://store.arduino.cc/usa/arduino-mega-2560-rev3-956. [Accessed 6 May 2017].