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A practical PID regulator with bounded torques for robot manipulators

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.

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References

  1. 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.

    Google Scholar 

  2. 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.

  3. R. Kelly, “Regulation of robotic manipulators: stability analysis via the Lyapunov’s first method,” Internal Report, CICESE, Ensenada, B.C., Mexico, 1995.

    Google Scholar 

  4. R. Kelly, “A tuning procedure for stable PID control of robot manipulators,” Robotica, vol. 13, no. 2, pp. 141–148, 1995.

    Article  Google Scholar 

  5. 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.

    MATH  Article  MathSciNet  Google Scholar 

  6. 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.

    MATH  Article  MathSciNet  Google Scholar 

  7. R. Kelly, V. Santibañez, and A. Loria, Control of Robot Manipulators in Joint Space, Springer-Verlag, London, 2005.

    Google Scholar 

  8. 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.

    Google Scholar 

  9. 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.

  10. 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.

  11. 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.

  12. 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.

    MATH  Article  Google Scholar 

  13. 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.

    MATH  Google Scholar 

  14. 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.

    Article  Google Scholar 

  15. 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.

    Article  Google Scholar 

  16. 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.

    Article  Google Scholar 

  17. 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.

    Article  Google Scholar 

  18. 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.

    Article  Google Scholar 

  19. 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.

    MATH  Article  MathSciNet  Google Scholar 

  20. 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.

    Article  Google Scholar 

  21. S. Arimoto, “Fundamental problems of robot control: part I, Innovations in the realm of robot servo-loops,” Robotica, vol. 13, pp. 19–27, 1995.

    Article  Google Scholar 

  22. 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.

    MATH  Article  Google Scholar 

  23. 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.

  24. 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.

  25. 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.

    Article  Google Scholar 

  26. R. Gorez, “Globally stable PID-like control of mechanical systems” Systems and Control Letters, vol. 38, pp. 61–72, 1999.

    MATH  Article  MathSciNet  Google Scholar 

  27. 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).

  28. 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.

  29. M. Spong, S Hutchinson, and M. Vidyasagar, Robot Modeling and Control, John Wiley and Sons, 2006.

  30. D. Koditschek, “Natural motion for robot arms,” Proc. IEEE Conf. on Decision and Control, Las Vegas, NV, pp. 733–735, 1984.

  31. R. Ortega and M. Spong, “Adaptive motion control of rigid robots: a tutorial,” Automatica, vol. 25, no. 6, pp. 877–888, 1989.

    MATH  Article  MathSciNet  Google Scholar 

  32. J. J. Craig, Adaptive Control of Mechanical Manipulators, Addison-Wesley, Reading, MA, 1998.

    Google Scholar 

  33. 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.

    Article  Google Scholar 

  34. H. Khalil, Nonlinear Systems, Prentice Hall, 2002.

  35. 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.

    Google Scholar 

  36. 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.

    Article  Google Scholar 

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Correspondence to Victor Santibañez.

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.

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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

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  • DOI: https://doi.org/10.1007/s12555-010-0307-4

Keywords

  • Bounded torques
  • PID control
  • singular perturbations
  • stability analysis