The Control of a Highly Nonlinear Two-wheels Balancing Robot: A Comparative Assessment between LQR and PID-PID Control Schemes

Authors: A. N. K. Nasir, M. A. Ahmad, R. M. T. Raja Ismail

Abstract:

The research on two-wheels balancing robot has gained momentum due to their functionality and reliability when completing certain tasks. This paper presents investigations into the performance comparison of Linear Quadratic Regulator (LQR) and PID-PID controllers for a highly nonlinear 2–wheels balancing robot. The mathematical model of 2-wheels balancing robot that is highly nonlinear is derived. The final model is then represented in statespace form and the system suffers from mismatched condition. Two system responses namely the robot position and robot angular position are obtained. The performances of the LQR and PID-PID controllers are examined in terms of input tracking and disturbances rejection capability. Simulation results of the responses of the nonlinear 2–wheels balancing robot are presented in time domain. A comparative assessment of both control schemes to the system performance is presented and discussed.

Keywords: PID, LQR, Two-wheels balancing robot.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1084448

References:

[1] A. Isidori, L. Marconi, A. Serrani, Robust Autonomous Guidance: An Internal Model Approach. New York: Springer Verlag, 2003.
[2] Y.-S. Ha and S. Yuta, "Trajectory tracking control for navigation of the inverse pendulum type self-contained mobile robot," J. Robotics and Autonomous System, vol. 17(1-2), pp. 65-80, Apr. 1996.
[3] F. Grasser, A. Arrigo, S. Colombi and A. C. Rufer, "JOE: a mobile inverted pendulum," IEEE Trans. Industrial Electronics, vol. 49(1), pp. 107-114, Feb. 2002.
[4] A. Salerno and J. Angeles, "On the nonlinear controllability of a quasiholonomic mobile robot," Proc. of IEEE Int.. Conf. on Robotics and Automation, vol. 3, pp. 3379-3384, Sept. 2003.
[5] A. Salerno and J. Angeles, "The control of semi-autonomous twowheeled robots undergoing large payload-variations," Proc. of IEEE Int. Conf. on Robotics and Automation, vol. 2, pp. 1740-1745, Apr. 2004.
[6] A. Blankespoor and R. Roemer, "Experimental verification of the dynamic model for a quarter size self-balancing wheelchair," Proc. of American Control Conf., pp. 488-492, 2004.
[7] S. S. Ge and C. Wang, "Adaptive neural control of uncertain MIMO nonlinear systems," IEEE Trans. Neural Networks, vol. 15(3), pp. 674- 692, 2004.
[8] K. Pathak, J. Franch and S. K. Agrawal, "Velocity and position control of a wheeled inverted pendulum by partial feedback linearization," IEEE Trans. Robotics, vol. 21(3), pp. 505-513, 2005.
[9] D. S. Nasrallah, H. Michalska and J. Angeles, "Controllability and posture control of a wheeled pendulum moving on an inclined plane," IEEE Trans. Robotics, vol. 23(3), pp. 564-577, 2007.
[10] R. C. Ooi, "Balancing a Two-Wheeled Autonomous Robot." B.Sc. Final Year Project, University of Western Australia School of Mechanical Engineering, 2003.