The Design and Control for the Balancing Robot with PD and LQR Controller Using Program Simulink

Main Article Content

Kritchanan Charoensuk
Kamolwan Wongwut
Daungkamol Angamnuaysiri
Kanchit Pawananont


In this article, the purpose is to demonstrate PD and LQR balancing robot design principles. In that design, the robot uses the principle of dynamic movement and Newton's laws. The mathematical model of the balancing robot is not linear. Therefore the robot must convert the nonlinear balancing robot mathematical model to a linear one. A mathematical model of the balancing robot is applied to the controller design. In the design of the controller for balancing robots, the researchers chose both controllers because they were easy to adapt to the system of the balancing robot. The Simulink was used to simulate motion and experiment with the controller's logic to stabilize the robot by simulating the system of the robotic balance used in the design of the controller and comparing the efficiency of the robot's angle and balance to maintain stability and eliminate potential interference in the system. The examination results compared the performance index of the balancing robot control system using both controllers. The control of the balancing robot system uses a controller to stabilize the equilibrium robot's angle and balance. The test results showed that stabilizing the balancing robot using the LQR control furnishes better stabilization than the PD controller.


Download data is not yet available.

Article Details

Research Article


F. Grasser, A. D'Arrigo, S. Colombi, and A. C. Rufer, “JOE: A mobile, inverted pendulum,” IEEE Trans. Ind. Electron., vol. 49, no. 1, pp. 107–114, Feb. 2002, doi: 10.1109/41.982254.

S. W. Nawawi, M. N. Ahmad, and J. H. S. Osman, “Development of a two-wheeled inverted pendulum mobile robot,” in Proc. 5th Student Conf. Res. and Develop., Selangor, Malaysia, Dec. 2007, pp. 1–5, doi: 10.1109/SCORED.2007.4451379.

T. Nomura, Y. Kitsuka, H. Suemitsu, and T. Matsuo, “Adaptive backstepping control for a two-wheeled autonomous robot,” in Proc. ICROS-SICE Int. Joint Conf., Fukuoka, Japan, Aug. 2009, pp 4687–4692.

R. M. Brisilla and V. Sankaranarayanan, “Nonlinear control of mobile inverted pendulum,” Robot. Auton. Syst., vol. 70, pp. 145–155, Aug. 2015.

W. An and Y. Li, “Simulation and control of a two-wheeled self-balancing robot,” in Proc. IEEE Int. Conf. Robot. and Biomimetics (ROBIO), Shenzhen, China, Dec. 2013, pp. 456–461.

Y. Takahashi, S. Ogawa, and S. Machida, “Experiments on step climbing and simulations on inverse pendulum control using robotic wheelchair with inverse pendulum control,” Trans. Inst. Meas. Control, vol. 30, no. 1, pp. 47–61, 2008, doi: 10.1177/0142331206075538.

O. Jamil, M. Jamil, Y. Ayaz, and K. Ahmad, “Modeling, control of a two-wheeled self-balancing robot,” in Proc. Int. Conf. Robot. and Emerging Allied Technol. Eng. (iCREATE), Islamabad, Pakistan, Apr. 2014, pp. 191–199.

M. Ahmad and H. Osman, “Real-time control system for a two-wheeled inverted pendulum mobile robot,” in Advanced Knowledge Application in Practice. London, U.K.: IntechOpen, 2010, doi: 10.5772/10362.

G. Sziebig, B. Takarics, and P. Korondi, “Control of an embedded system via internet,” IEEE Trans. Ind. Electron., vol. 57, no. 10, pp. 3324–3333, Oct. 2010, doi: 10.1109/TIE.2010.2041132.

C. U. Maheswararao, Y. S. K. Babu, and K. Amaresh, “Sliding mode speed control of a DC motor,” in Proc. Int. Conf. Commun. Syst. Netw. Technol., Katra, India, Jun. 2011, pp. 387–391.

H. Maghfiroh, O. Wahyunggoro, A. I. Cahyadi, and S. Praptodiyono, “PID-hybrid tuning to improve control performance in speed control f DC motor base on PLC,” in Proc. 3rd Int. Conf. Instrum. Control and Automat. (ICA), Ungasan, Indonesia, Aug. 2013, pp. 233–238.

K. -K. D. Young, “Controller design for a manipulator using theory of variable structure systems,” IEEE Trans. Syst. Man Cybern., vol. 8, no. 2, pp. 101–109, Feb. 1978, doi: 10.1109/TSMC.1978.4309907.

M. A. Imtiaz, M. Naveed, N. Bibi, S. Aziz, and S. Z. H. Naqvi, “Control system design, analysis & implementation of two wheeled self balancing robot (TWSBR),” IEEE 9th Annu. Inf. Technol., Electron. and Mobile Commun. Conf. (IEMCON), Vancouver, Canada, Nov. 2018, pp. 431–437.

A. Y. Zimit, H. J. Yap, M. F. Hamza, I. Siradjuddin, B. Hendrik, and T. Herawan, “Modelling and experimental analysis two-wheeled self balance robot using PID controller,” in Proc. 18th Int. Con. Comput. Sci. and Its Appl., Melbourne, Australia, Jul. 2018, pp. 683–698.

J. Fang, “The LQR controller design of two-wheeled self-balancing robot based on the particle swarm optimization algorithm,” Math. Probl. Eng., vol. 2014, Jun. 2014, Art. No. 729095.

S. I. Han and J. M. Lee, “Balancing and velocity control of a unicycle robot based on the dynamic model,” IEEE Trans. Ind. Electron., vol. 62, no. 1, pp. 405–413, Jan. 2015, doi: 10.1109/TIE.2014.2327562.

H. Jin, J. Hwang, and J. Lee, “A balancing control strategy for a one-wheel pendulum robot based on dynamic model decomposition: Simulations and experiments,” IEEE/ASME Trans. Mechatronics, vol. 16, no. 4, pp. 763–768, Aug. 2011, doi: 10.1109/TMECH.2010.2054102.

D. Buccieri, D. Perritaz, P. Mullhaupt, Z. -P. Jiang, and D. Bonvin, “Velocity-scheduling control for a unicycle mobile robot: Theory and experiments,” IEEE Trans. Robot., vol. 25, no. 2, pp. 451–458, Apr. 2009, doi: 10.1109/TRO.2009.2014494.