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A tuning procedure for stable PID control of robot manipulators*

Published online by Cambridge University Press:  09 March 2009

Rafael Kelly
Rafael Kelly
Affiliation:
División de Fisica Aplicada, CICESE, Carretera Tijuana-Ensenada Km. 107, Apdo. Postal 2732, Ensenada, B.C., 22800 (Mexico)
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Summary

In this paper we propose some simple rules for PID tuning of robot manipulators. The procedure suggested requires the knowledge of the structure of the inertia matrix and the gravitational torque vector of the robot dynamics, but only upper bounds on the dynamics parameters are needed. This tuning procedure is extracted from the stability analysis by using a suitable Lyapunov function together with the LaSalle invariance principle. We show that with this guideline, the overall closed-loop system is asymptotically stable. This procedure is illustrated for a two degrees-of-freedom robot

Keywords

PID controlSet-point controlStabilityRobots
Type
Articles
Information
Robotica , Volume 13 , Issue 2 , March 1995 , pp. 141 - 148
Copyright
Copyright © Cambridge University Press 1995

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References

1.Craig, J. J., Introduction to Robotics: Mechanics and control (Addison-Wesley, Reading, MA., 1989).Google Scholar
2.Takegaki, M. and Arimoto, S., “A new feedback method for dynamic control of manipulators” Trans. ASME Journal of Dynamic Systems, Measurement, and Control 103, 119–125 (06 1981).CrossRefGoogle Scholar
3.Wang, W. S. and Liu, C.H., “Controller design and implementation for industrial robots with flexible joints” IEEE Trans, on Industrial Electronics 39, No. 5, 379–391 (10, 1992).CrossRefGoogle Scholar
4.Arimoto, S. and Miyazaki, F., “Stability and robustness of PID feedback control for robot manipulators of sensory capability” (Brady, M. & Paul, R.P., eds.), Robotics Research: First International Symposium (The MIT Press, Cambridge, Mass., 1984) pp. 783–799.Google Scholar
5.Kawamura, S., Miyazaki, F. and Arimoto, S., “Is a local linear PD feedback control law effective for trajectory tracking of robot motion?” Proceedings of the 1988 IEEE International Conference on Robotics and Automation,Philadelphia, PA(April, 1988) pp. 1335–1340.Google Scholar
6.Kelly, R., Carelli, R., Ortega, R. and Kuchen, B., “PD and PID Control: Application to DC motors and robotic joints” (In Spanish), DEPFI Report (Universidad National Autónoma de México, 04, 1989).Google ScholarPubMed
7.Wen, J. T., “PID control of robot manipulators” Tech. Report (Rensselaer Polytechnic Institute, 06, 1989).Google Scholar
8.Wen, J. T. and Murphy, S., “PID control for robot manipulators”, CIRSSE Document #54 (Rensselaer Polytechnic Institute, 05, 1990).Google Scholar
9.Qu, Z. and Dorsey, J., “Robust PID control of robots” Int. J. Robotics and Automation 6, No. 4, 228–235 (1991).Google Scholar
10.Spong, M. and Vidyasagar, M., Robot Dynamics and Control (John Wiley & Sons, New York, 1989).Google Scholar
11.Vidyasagar, M., Nonlinear Systems Analysis (Prentice Hall, Englewood Cliffs, New Jersey, 1993).Google Scholar
12.Arimoto, S. and Miyazaki, F., “Stability and robustness of PD feedback control with gravity compensation for robot manipulators” In: (Paul, F.W. and Youcef-Toumi, D., eds.). Robotics: Theory and Applications DSC Vol. 3 (1986) pp. 67–72.Google Scholar
13.Ortega, R. and Kelly, R., “PID self-tuners: Some theoretical and practical aspects” IEEE Trans, on Industrial Electronics IE-31, No. 4, 332–338 (11, 1984).CrossRefGoogle Scholar
14.Ozaki, T., Suzuki, T., Furuhashi, T., Okuma, S. and Uchikawa, Y., “Trajectory control of robotic manipulators using neural networks”, IEEE Transactions on Industrial Electronics 38, No. 3, 195–202 (06, 1991).CrossRefGoogle Scholar
15.Horn, R. A. and Johnson, C. R., Matrix Analysis (Cambridge University Press, Cambridge, 1985).CrossRefGoogle Scholar
16.Åström, K. J. and Wittenmark, B., Adaptive Control (Addison-Wesley, Wokingham UK, 1989).Google Scholar