Abstract
This paper proposes a saturated nonlinear PID regulator for industrial robot manipulators. Our controller considers the natural saturation problem given by the output of the control computer, the saturation phenomena of the internal PI velocity controller in the servo driver, and the actuator torque constraints of the robot manipulator. An approach based on the singular perturbations method is used to analyze the exponential stability of the closed-loop system. Experimental essays show the feasibility of the proposed controller. Furthermore, the theoretical results justify why the classical PID used in industrial robots preserves its exponential stability despite the saturation effects of the electronic control devices and the actuator torque constraints.
Similar content being viewed by others
References
S. Arimoto and F. Miyazaki, “Stability and robustness of PID feedback control for robot manipulators of sensory capability,” in M. Brady and R.P. Paul (Ed.), Robotics Researches: First International Symposium, MIT Press, Cambridge, MA, pp. 783–799, 1984.
S. Arimoto, T. Naniwa, and H. Suzuki, “Asymptotic stability and robustness of PID local feedback for position control of robot manipulators,” Proc. of International Conf. on Automation Robotics and Computer Vision ICARCV’90, Singapore, pp. 382–386, 1990.
R. Kelly, “Regulation of robotic manipulators: stability analysis via the Lyapunov’s first method,” Internal Report, CICESE, Ensenada, B.C., Mexico, 1995.
R. Kelly, “A tuning procedure for stable PID control of robot manipulators,” Robotica, vol. 13, no. 2, pp. 141–148, 1995.
R. Ortega, A. Loria, and R. Kelly, “A semiglobally stable output feedback PI2D regulator for robot manipulators,” IEEE Trans. on Automatic Control, vol. 40, no. 8, pp. 1432–1436, 1995.
J. Alvarez-Ramirez, I. Cervantes, and R. Kelly, “PID regulation of robot manipulators: stability and performance,” Systems and Control Letters, vol. 41, pp. 73–83, 2000.
R. Kelly, V. Santibañez, and A. Loria, Control of Robot Manipulators in Joint Space, Springer-Verlag, London, 2005.
J. L. Meza, V. Santibañez, and R. Campa, “An estimate of the domain of attraction for the PID regulator of manipulators,” Int. Journal of Robotics and Automation, vol. 22, no. 3, pp. 187–195, 2007.
R. Kelly and V. Santibañez, “A class of global regulators with bounded control actions for robot manipulators,” Proc. IEEE Conf. Decision and Control, Kobe, Japan, pp. 3382–3387, 1996.
R. Colbaugh, E. Barany, and K. Glass, “Global regulation of uncertain manipulators using bounded controls,” Proc. IEEE Int. Conf. Robotics and Automation, Albuquerque, NM, USA, pp. 1148–1155, April 1997.
R. Colbaugh, E. Barany, and K. Glass, “Global stabilization of uncertain manipulators using bounded controls,” Proc. IEEE American Control Conf., Albuquerque, NM, USA, pp. 86–91, June 1997.
A. Loria, R. Kelly, R. Ortega, and V. Santibañez, “On global output feedback regulation of Euler-Lagrange systems with bounded inputs” IEEE Trans. Automat. Contr., vol. 42, pp. 1138–1143, 1997.
V. Santibañez and R. Kelly, “On global regulation of robot manipulators: saturated linear state feedback and saturated linear output feedback,” European Journal of Control, vol. 3, pp. 104–113, 1997.
V. Santibañez and R. Kelly, “A new set-point controller with bounded torques for robot manipulators,” IEEE Trans. on Industrial Electronics, vol. 45, pp. 126–133, 1998.
E. Zergeroglu, W. Dixon, A. Behal, and D. Dawson, “Adaptive set-point control of robotic manipulators with amplitude-limited control inputs,” Robotica, vol. 18, pp. 171–181, 2000.
A. Zavala-Rio and V. Santibañez, “Simple extensions of the PD-with-gravity-compensation control law for robot manipulators with bounded inputs,” IEEE Trans. on Control Systems Technology, vol. 14, no. 5, pp. 958–965, 2006.
A. Zavala-Rio and V. Santibañez, “A natural saturating extension of the PD-with-desired-gravity compensation control law for robot manipulators with bounded inputs,” IEEE Trans. on Robotics, vol. 23, no. 2, pp. 386–391, 2007.
W. E. Dixon, “Adaptive regulation of amplitude limited for robot manipulators with uncertain kinematics and dynamics,” IEEE Trans. on Automatic Control, vol. 52, no. 3, pp. 488–493, 2007, also at Proc. of American Control Conf., Boston MA, pp. 3839–3844, 2004.
J. Alvarez-Ramirez, R. Kelly, and I. Cervantes, “Semiglobal stability of saturated linear PID control for robot manipulators,” Automatica, vol. 39, pp. 989–995, 2003.
J. Alvarez-Ramirez, V. Santibáñez, and R. Campa, “Stability of robot manipulators under saturated PID compensation,” IEEE Trans. on Control Systems Technology, vol. 16, no. 6, pp. 1333–1341, 2008.
S. Arimoto, “Fundamental problems of robot control: part I, Innovations in the realm of robot servo-loops,” Robotica, vol. 13, pp. 19–27, 1995.
R. Kelly, “Global positioning of robot manipulators via PD control plus a class of nonlinear integral actions,” IEEE Trans. on Automatic Control, vol. 43, no. 7, pp. 934–938, 1998.
V. Santibañez and R. Kelly, “A class of nonlinear PID global regulators for robot manipulators,” Proc. of IEEE Int. Conf. on Robotics and Automation, Leuven, Belgium, pp. 3601–3606, 1998.
J. L. Meza and V. Santibáñez, “Analysis via passivity theory of a class of nonlinear PID global regulators for robot manipulators,” Proc. of the IASTED Int. Conf. on Robotics and Applications, Santa Barbara, CA. USA., pp. 288–293, 1999.
D. Sun, S. Hu, X. Shao, and Ch. Liu, “Global stability of a saturated nonlinear PID controller for robot manipulators,” IEEE Trans. on Control Systems Technology, vol. 17, no. 4, pp. 892–899, 2009.
R. Gorez, “Globally stable PID-like control of mechanical systems” Systems and Control Letters, vol. 38, pp. 61–72, 1999.
J. L. Meza, V. Santibañez, and V. Hernandez, “Saturated nonlinear PID global regulator for robot manipulators: passivity based analysis,” Proc. of the 16th IFAC World Congress, Prague, Czech Republic, (2005).
V. Santibanez, R. Kelly, A. Zavala-Rio, and P. Parada, “A new Saturated nonlinear PID global regulator for robot manipulators,” Proc. of the 17th IFAC World Congress, Seoul, Korea, pp. 11690–11695, 2008.
M. Spong, S Hutchinson, and M. Vidyasagar, Robot Modeling and Control, John Wiley and Sons, 2006.
D. Koditschek, “Natural motion for robot arms,” Proc. IEEE Conf. on Decision and Control, Las Vegas, NV, pp. 733–735, 1984.
R. Ortega and M. Spong, “Adaptive motion control of rigid robots: a tutorial,” Automatica, vol. 25, no. 6, pp. 877–888, 1989.
J. J. Craig, Adaptive Control of Mechanical Manipulators, Addison-Wesley, Reading, MA, 1998.
R. Kelly and J. Moreno, “Learning PID structures in an introductory course of automatic control,” IEEE Trans. on Education, vol. 44, no. 4, pp. 373–376, 2001.
H. Khalil, Nonlinear Systems, Prentice Hall, 2002.
J. Moreno-Valenzuela, V. Santibanez, and R. Campa, “On output feedback tracking control of robot manipulators with bounded torque input,” International Journal of Control Automation and Systems, vol. 6, no. 1, pp. 76–85, 2008.
F. Reyes and R. Kelly, “Experimental evaluation of model-based controllers on a direct-drive robot arm,” Mechatronics, vol. 11, no. 3, pp. 267–282, 2001.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Editorial Board member Youngjin Choi under the direction of Editor Jae-Bok Song. This work was supported by CONACYT, SIP-IPN and DGEST.
Victor Santibanez received his B.S. and M.Sc. degrees in Electronics Engineering from the Instituto Tecnologico de La Laguna, Torreon, Mexico, and his Ph.D. degree from CICESE Research Center, Ensenada, Mexico in 1977, 1984 and 1997, respectively. From 1977 to 1981 he worked in the respective Industrial Electronics Departments of the iron and steel industry at Altos Hornos de Mexico and Metalurgica Mexicana Peñoles. From 1989 to 1990 he was with the Instituto de Automatica Industrial (CSIC) in Madrid Spain. He is currently a professor at the Instituto Tecnologico de La Laguna. His research interests are robot control, nonlinear systems control, and fuzzy control.
Karla Camarillo was born in Cd. Juarez, Mexico, in 1979. She received her B.S., M.Sc. and Ph.D. degrees in Electrical and Electronics Engineering from the Instituto Tecnologico de La Laguna in Torreon, Mexico. She is currently a professor at the Instituto Tecnologico de Celaya in Celaya, Mexico. She is active member of IEEE. Recently, she was named vicepresident of the Mexican Association of Robotics (AMRob). Her research interests are robot control, and nonlinear systems control.
Javier Moreno-Valenzuela was born in Culiacán, Mexico, in 1974. He received his B.S. degree in Electronics Engineering from the Instituto Tecnológico de Culiacán, Mexico, in 1997, and his Ph.D. degree in Automatic Control from CICESE Research Center, Ensenada, Mexico, in 2002. He was an Associate Researcher at CITEDI-IPN Research Center, Tijuana, Mexico, from 2002 to 2004 and a Postdoctoral Fellow at the Université de Liège, Belgium, from 2004 to 2005. Currently, he is at CITEDI-IPN Research Center. His main research interests are in control of electro-mechanical systems.
Ricardo Campa was born in Torreón, Mexico, in 1971. He received his M.S. degree in Electrical Engineering from the Instituto Tecnológico de la Laguna, in 1998, and his Ph.D. degree in Electronics and Tele-communications from CICESE Research Center, in 2005. He is currently a professor at the Instituto Tecnológico de la Laguna in Torreon, Mexico. His research interests are robot modeling and control, and real-time control systems.
Rights and permissions
About this article
Cite this article
Santibañez, V., Camarillo, K., Moreno-Valenzuela, J. et al. A practical PID regulator with bounded torques for robot manipulators. Int. J. Control Autom. Syst. 8, 544–555 (2010). https://doi.org/10.1007/s12555-010-0307-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-010-0307-4