The Control of a Highly Nonlinear Two-wheels Balancing Robot: A Comparative Assessment between LQR and PID-PID Control Schemes
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:64127", author = "A. N. K. Nasir and M. A. Ahmad and R. M. T. Raja Ismail", title = "The Control of a Highly Nonlinear Two-wheels Balancing Robot: A Comparative Assessment between LQR and PID-PID Control Schemes", 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.", volume = "4", number = "10", pages = "1121-6", }