Abstract
Based on a continuous piecewise-differentiable increasing functions vector, a class of robust nonlinear PID (RN-PID) controllers is proposed for setpoint control with uncertain Jacobian matrix. Globally asymptotic stability is guaranteed and only position and joint velocity measurements are required. And stability problem arising from integral action and integrator windup, are consequently resolved. Furthermore, RN-PID controllers can be of effective alternative for anti-integrator-wind-up, the control performance would not be very bad in the presence of rough parameter tuning.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Datta, M. T. Ho, S. P. Bhattacharyya, Structure and Synthesis of PID Controllers, Springer-Verlag,London,2000.
K. K. Tan, Q. G. Wang, C. C. Hang, et al, Advances in PID Control, Springer-Verlag, London, 1999.
C. C. Yu, Autotuning of PID Controllers — Relay Feedback Approach, Springer-Verlag, London, 1999.
J. Alvarez-Ramirez, I. Cervantes, R. Kelly, PID regulation of robot manipulators: stability and performance, Systems & Control Letters, Vol. 41, No. 2,pp. 73–83, 2000.
S. Arimoto, Control Theory of Nonlinear Mechanical Systems — A Passivity-based and Circuit-theoretic Approach, Clarendon, Oxford, U.K.,1996.
I. Cervantes, J. Alvarez-Ramirez, On the PID tracking control of robot manipulators, Systems & Control Letters, Vol. 42, No. 1, pp. 37–46, 2001.
R. Gorez, Globally stable PID-like control of mechanical systems. Systems & Control Letters, Vol. 38, No. 1, pp. 61–72,1999.
F. Miyazaki, Y. Masutani, Robustness of sensory feedback control based on imperfect Jacobian. Robotic Research: The 5 th Int. Symposium, H. Miura, S. Arimoto, Edictors. MIT Press, Cambridge, pp. 201–208, 1990.
A.A. Pervozvanski, L. B. Freidovich, Robust stabilization of robotic manipulators by PID controllers, Dynamics and Control, Vol. 9, No. 3, pp. 203–222,1999.
Z. Qu. J. Dorsey, Robust tracking control of robots by linear feedback law, IEEE Trans, on Automatic Control, Vol.36, No. 9,pp. 1081–1084,1991.
C. C. Cheah, S. Kawamura, S. Arimoto, Feedback control for robotic manipulator with uncertain kinematics and dynamics, Proc. IEEE Int. Conf. Robotics and Automation, Belgium,pp. 3607–3612,1998.
C. C. Cheah, S. Kawamura, S. Arimoto, Feedback control for robotic manipulator with an uncertain Jacobian matrix, J. of Robotic Systems, Vol. 16, No. 2,pp. 119–134,1999.
C. C. Cheah, S. Kawamura, S. Arimoto, et al, PID control of robotic manipulator with uncertain Jacobian matrix, Proc. IEEE Int. Conf. Robotics and Automation, Michigan, pp. 494–499,1999.
C. C. Cheah, S. Kawamura, S. Arimoto, et al, H∞ tuning for task-space feedback control of robot with uncertain Jacobian matrix, IEEE Trans, on Automatic Control, Vol.46,pp. 1313–1318,2001.
C.Q. Huang,X.G. Wang, Z. G. Wang, A class of transpose Jacobianbased NPID regulators for robot manipulators with uncertain kinematics, J. of Robotic Systems, Vol. 11, No. 11, pp. 527–539,2002.
de Wit C. Canudas, B. Siciliano, G. Bastin, eds, Theory of Robot Control,2nd ed, Springer-Verlag,London,pp. 61–63,1997.
Author information
Authors and Affiliations
Additional information
This work was supported by the Doctor Foundation of China (No. 2003033306).
Rights and permissions
About this article
Cite this article
Huang, C., Shi, S. Globally robust nonlinear PID controllers for robot manipulators with an uncertain jacobian matrix. J. Control Theory Appl. 2, 105–110 (2004). https://doi.org/10.1007/s11768-004-0052-4
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11768-004-0052-4