Skip to main content
×
Home
    • Aa
    • Aa

Alternative proofs of four stability properties of rigid-link manipulators under PID position control

  • Ryo Kikuuwe (a1)
Summary
SUMMARY

This paper presents new proofs of four stability properties (semiglobal strict passivity, semiglobal asymptotic stability, semiglobal input-to-state stability, and semiglobal uniform ultimate boundedness with an arbitrarily reducible ultimate bound) of a rigid-link manipulator under proportional-integral-derivative (PID) position control. The proofs employ a strict Lyapunov function and a novel parameterization to provide four inequality conditions for the stability properties. In those inequalities, arithmetic operations on physical quantities are physically consistent if the joints are all revolute or all prismatic. A gain selection procedure is presented by which the ultimate bounds of velocity error, position error, and its integral can be independently designed.

Copyright
Corresponding author
*Corresponding author. E-mail: kikuuwe@mech.kyushu-u.ac.jp
References
Hide All
1. J. Alvarez-Ramirez , R. Kelly and I. Cervantes , “Semiglobal stability of saturated linear PID control for robot manipulators,” Automatica 39 (6), 989995 (2003).

2. J. Alvarez-Ramirez , V. Santibáñez and R. Campa , “Stability of robot manipulators under saturated PID compensation,” IEEE Trans. Control Syst. Technol. 16 (6), 13331341 (2008).

5. I. Cervantes and J. Alvarez-Ramirez , “On the PID tracking control of robot manipulators,” Syst. Control Lett. 42, 3746 (2001).

6. A. Chaillet , A. Loria and R. Kelly , “Robustness of PID-controlled manipulators vis á vis actuator dynamics and external disturbances,” Eur. J. Control 13 (6), 563576 (2007).

7. Y. Choi and W. K. Chung , PID Trajectory Tracking Control for Mechanical Systems (Springer, Berlin, 2004).

8. V. M. Hernández-Guzmán , V. Santibáñez and R. Silva-Ortigoza , “A new tuning procedure for PID control of rigid robots,” Adv. Robot. 22 (9), 10071023 (2008).

14. J. I. Mulero-Martínez , “Uniform bounds of the Coriolis/centripetal matrix of serial robot manipulators,” IEEE Trans. Robot. 23 (5), 10831089 (2007).

15. A. A. Pervozvanski and L. B. Freidovich , “Robust stabilization of robotic manipulators by PID controllers,” Dyn. Control 9 (3), 203222 (1999).

16. R. Ortega , A. Loria and R. Kelly , “A semiglobally stable output feedback PI2D regulator for robot manipulators,” IEEE Trans. Autom. Control 40 (8), 14321436 (1995).

18. P. Rocco , “Stability of PID control for industrial robot arms,” IEEE Trans. Robot. Autom. 12 (4), 606614 (1996).

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Robotica
  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 4 *
Loading metrics...

Abstract views

Total abstract views: 117 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 26th September 2017. This data will be updated every 24 hours.