ABSTRACT The objective of this paper is to design linear quadratic controllers for a system with an inverted pendulum on a mobile robot. To this goal, it has to be determined which control strategy delivers better performance with respect to pendulum’s angle and the robot’s position. The inverted pendulum represents a challenging control problem, since it continually moves toward an uncontrolled state. Simulation study has been done in MATLAB Simulink environment shows that both LQR and LQG are capable to control this system successfully. The result shows, however, that LQR produced better response compared to a LQG strategy.
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nullR. Eide, P. Egelid, A. Stamsø and H. Karimi, "LQG Control Design for Balancing an Inverted Pendulum Mobile Robot," Intelligent Control and Automation, Vol. 2 No. 2, 2011, pp. 160-166. doi: 10.4236/ica.2011.22019.
 T. Ilic, D. Pavkovic and D. Zorc, “Modeling and Control of a Pneumatically Actuated Inverted Pendulum,” ISA Transactions, Vol. 48, No. 3, 2009, pp. 327-335. doi:10.1016/j.isatra.2009.03.004
 J. Ngamwiwit, N. Komine, S. Nundrakwang and T. Benjanarasuth, “Hybrid Controller for Swinging up Inverted Pendulum System,” Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, Plaza de Espa?a Seville, 12-15 December 2005.
 J. F. Hauser and A. Saccon, “On the Driven Inverted Pendulum,” Proceedings of the 5th International Conference on Information, Communications and Signal Processing, Bangkok, 6-9 December, 2005.
 R. Balan and V. Maties, “A Solution of the Inverse Pendulum on a Cart Problem Using Predictive Control,” Technical University of Cluj-Napoca, Cluj-Napoca, 2005.
 K. Tanaka, T. Ikeda and H. O. Wang, “Fuzzy Regulators and Fuzzy Observers: Relaxed Stability Conditions and Lmibased Designs,” IEEE Transactions on Fuzzy Systems, Vol. 6, No. 2, 1998, pp. 250-265. doi:10.1109/91.669023
 C. Xu and X. Yu, “Mathematical Modeling of Elastic Inverted Pendulum Control System,” Journal of Control Theory and Applications, Vol. 2, No. 3, 2004, pp. 281-282. doi:10.1007/s11768-004-0010-1
 J. Lam, “Control of an Inverted Pendulum,” Georgia Tech College of Computing, Georgia, 2009.
 A. E. Frazhol, “The Control of an Inverted Pendulum,” School of Aeronautics and Astronautics, Purdue University, Indiana, 2007.
 M. Athans, “The Linear Quadratic LQR problem,” Massachusetts Institute of Technology, Massachusetts, 1981.
 R. S. Burns, “Advanced Control Engineering,” Butterworth Heinemann, Oxford, 2001.
 J. Hespanha, “Undergraduate Lecture Notes on LQG/ LQR Controller Design,” 2007.
 G. Welch and G. Bishop, “An Introduction to the Kalman Filter,” University of North Carolina, North Carolina, 2001.
 H. Morimoto, “Adaptive LQG Regulator via the Separation Principle,” IEEE Transactions on Automatic Control, Vol. 35, No. 1, 1991, pp. 85-88. doi:10.1109/9.45150