An adaptive robust quadratic stabilization tracking controller with hybrid scheme is proposed for robotic system with uncertainties and external disturbances. The hybrid scheme combines computed torque controller (CTC) with an adaptive robust compensator, in which variable structure control (VSC) and optimal control approaches are adopted. The uncertain robot manipulator is mainly controlled by CTC, the VSC is used to eliminate the effect of the uncertainties and ensure global stability, and approach is designed to achieve a certain tracking performance of closed-loop system. A quadratic stability approach, which allows separate treatment of parametric uncertainties, is used to reduce the conservatism of the conventional robust control approach. It can be also guaranteed that all signals in closed-loop system are bounded. The validity of the proposed control scheme is shown by computer simulation of a two-link robotic manipulator. 1. Introduction Due to the uncertainties, disturbance, and nonlinear system dynamics, tracking control for robot manipulator always is a challenging problem [1, 2]. Therefore, in the past decades, many control approaches have been proposed and applied on controlling the robot manipulator, such as PID control [3], computed torque control method (CTC) [4–6], adaptive control [7, 8], variable structure control (VSC) [9, 10], robust control [11–16], fuzzy control [17–19], and neural networks control [20–24]. Varieties of hybrid control systems have been designed for controlling the complex robotic systems. Chang [25] and Wai [26] utilized neural networks to entirely approximate the equivalent control of VSC and then applied the technique to achieve a certain tracking performance. In these controllers, the robotic system nominal model is not included. Actually, the robotic nominal model could be known provided that the uncertainties are all considered to be reasonably modeled. For this reason, CTC could not be neglected in designing controller for complex robotic system due to its good performances [5], even though uncertainties exist in robotic system which would degrade the tracking performance. In order to eliminate the effect of the uncertainties, Song et al. [5] proposed an approach of CTC plus fuzzy compensator, the nominal system was controlled by using CTC method and for uncertain system, and a fuzzy controller acts as compensator. In [6], CTC plus a neural network compensator was proposed and simulations were conducted on a two-link robotic manipulator; furthermore, an experimental example was tested on PUMA560. However,
References
[1]
W. J. Book, “Modeling, design, and control of flexible manipulator arms: a tutorial review,” in Proceedings of the 29th IEEE Conference on Decision and Control, pp. 500–506, IEEE Press, San Francisco, Calif, USA, December 1990.
[2]
F. L. Lewis, S. Jagannathan, and A. Yesildirek, Neural Network Control of Robot Manipulators and Nonlinear Systems, Philadelphia, Pa, USA, SIAM Press, 2002.
[3]
J. Y. S. Luh, “Conventional controller design for industrial robots—a tutorial,” IEEE Transactions on Systems, Man and Cybernetics, vol. 13, no. 3, pp. 298–316, 1983.
[4]
R. H. Middleton and G. C. Goodwin, “Adaptive computed torque control for rigid link manipulations,” Systems & Control Letters, vol. 10, no. 1, pp. 9–16, 1988.
[5]
Z. Song, J. Yi, D. Zhao, and X. Li, “A computed torque controller for uncertain robotic manipulator systems: fuzzy approach,” Fuzzy Sets and Systems, vol. 154, no. 2, pp. 208–226, 2005.
[6]
Y. Zuo, Y. Wang, X. Liu et al., “Neural network robust tracking control strategy for robot manipulators,” Applied Mathematical Modelling, vol. 34, no. 7, pp. 1823–1838, 2010.
[7]
R. Ortega and M. W. Spong, “Adaptive motion control of rigid robots: a tutorial,” Automatica, vol. 25, no. 6, pp. 877–888, 1989.
[8]
S. Battilotti and L. Lanari, “Adaptive disturbance attenuation with global stability for rigid and elastic joint robots,” Automatica, vol. 33, no. 2, pp. 239–243, 1997.
[9]
O. Kaynak, K. Erbatur, and M. Ertugrul, “The fusion of computationally intelligent methodologies and sliding-mode control—a survey,” IEEE Transactions on Industrial Electronics, vol. 48, no. 1, pp. 4–17, 2001.
[10]
K. S. Yeung and Y. P. Chen, “A new controller design for manipulators using the theory of variable structure systems,” IEEE Transactions on Automatic Control, vol. 33, no. 2, pp. 200–206, 1988.
[11]
S. Lin and A. A. Goldenberg, “Robust damping control of mobile manipulators,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 32, no. 1, pp. 126–132, 2002.
[12]
F. Alonge, F. d'Ippolito, and F. M. Raimondi, “Globally convergent adaptive and robust control of robotic manipulators for trajectory tracking,” Control Engineering Practice, vol. 12, no. 9, pp. 1091–1100, 2004.
[13]
Y. Wang, J. Peng, W. Sun, H. Yu, and H. Zhang, “Robust adaptive tracking control of robotic systems with uncertainties,” Journal of Control Theory and Applications, vol. 6, no. 3, pp. 281–286, 2008.
[14]
J. J. Rubio, Z. Zamudio, J. Pacheco, and D. M. Vargas, “Proportional derivative control with inverse dead-zone for pendulum systems,” Mathematical Problems in Engineering, vol. 2013, Article ID 173051, 9 pages, 2013.
[15]
C. Torres, J. J. Rubio, C. Aguilar-Ibá？ez, and J. H. Pérez-Cruz, “Stable optimal control applied to a cylindrical robotic arm,” Neural Computing and Applications, vol. 24, no. 3-4, pp. 937–944, 2014.
[16]
S. Galvan, M. A. Moreno-Armendariz, J. J. Rubio, F. I. Rodriguez, W. Yu, and C. F. A. Ibá？ez, “Dual PD control regulation with nonlinear compensation for a ball and plate system,” Mathematical Problems in Engineering. In press.
[17]
Y. C. Hsu, G. Chen, and H. X. Li, “A fuzzy adaptive variable structure controller with applications to robot manipulators,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 31, no. 3, pp. 331–340, 2001.
[18]
H. Hu and P.-Y. Woo, “Fuzzy supervisory sliding-mode and neural-network control for robotic manipulators,” IEEE Transactions on Industrial Electronics, vol. 53, no. 3, pp. 929–940, 2006.
[19]
F. C. Sun, Z. Q. Sun, and G. Feng, “An adaptive fuzzy controller based on sliding mode for robot manipulators,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 29, no. 5, pp. 661–667, 1999.
[20]
F. L. Lewis, K. Liu, and A. Yesildirek, “Neural net robot controller with guaranteed tracking performance,” IEEE Transactions on Neural Networks, vol. 6, no. 3, pp. 703–715, 1995.
[21]
Z. Liu and C. Li, “Fuzzy neural networks quadratic stabilization output feedback control for biped robots via approach,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 33, no. 1, pp. 67–84, 2003.
[22]
J. Peng, J. Wang, and Y. Wang, “Neural network based robust hybrid control for robotic system: an approach,” Nonlinear Dynamics, vol. 65, no. 4, pp. 421–431, 2011.
[23]
F. Sun, Z. Sun, and P.-Y. Woo, “Neural network-based adaptive controller design of robotic manipulators with an observer,” IEEE Transactions on Neural Networks, vol. 12, no. 1, pp. 54–67, 2001.
[24]
J. J. Rubio, “Modified optimal control with a backpropagation network for robotic arms,” IET Control Theory & Applications, vol. 6, no. 14, pp. 2216–2225, 2012.
[25]
Y. C. Chang, “Neural network-based tracking control for robotic systems,” IEE Proceedings—Control Theory and Applications, vol. 147, no. 3, pp. 303–311, 2000.
[26]
R.-J. Wai, “Tracking control based on neural network strategy for robot manipulator,” Neurocomputing, vol. 51, pp. 425–445, 2003.
[27]
J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, NJ, USA, 1991.
[28]
C. Aguilar-Ibá？ez, J. A. Mendoza-Mendoza, M. Suarez-Casta？on, and J. Davila, “A nonlinear robust PI controller for an uncertain system,” International Journal of Control, 2014.
[29]
J. J. Rubio, G. Gutierrez, J. Pacheco, and H. Pérez-Cruz, “Comparison of three proposed controls to accelerate the growth of the crop,” International Journal of Innovative Computing, Information and Control, vol. 7, no. 7, pp. 4097–4114, 2011.
[30]
J. J. Rubio, L. A. Soriano, and W. Yu, “Dynamic model of a wind turbine for the electric energy generation,” Mathematical Problems in Engineering, vol. 2014, Article ID 409268, 8 pages, 2014.
