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Cross-coupled PID control in position domain for contour tracking

Published online by Cambridge University Press:  01 April 2014

P. R. Ouyang ,
T. Dam  and
V. Pano
P. R. Ouyang*
Affiliation:
Department of Aerospace Engineering, Ryerson University, Toronto, Canada
T. Dam
Affiliation:
Department of Aerospace Engineering, Ryerson University, Toronto, Canada
V. Pano
Affiliation:
Department of Aerospace Engineering, Ryerson University, Toronto, Canada
*
*Corresponding author. E-mail: pouyang@ryerson.ca
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Summary

Accurate contour tracking is one of the main tasks in modern manufacturing processes. By considering coupling effects among multiple axes, this paper proposes a cross-coupled proportional-integral-derivative (PID) control developed in position domain, and the controller is applied to a multi-axis computer numerical control (CNC) machine for contour tracking performance improvement. Stability analysis is conducted for the developed position domain cross-coupled PID control using the Lyapunov method, and guidelines for the selection of control gains are provided. The contour tracking performance are improved compared to an equivalent time domain controller, since the reference axis in position domain control does not contribute any error to the overall contouring error of the system. Simulation results demonstrate the effectiveness of cross-coupled PID position domain control for both linear and circular contour tracking, and prove the robustness of the controller to deal with random disturbances. It also shows that position domain cross-coupled PID control provides better contour tracking performance over position domain PID control and the equivalent time domain PID control.

Keywords

Contour trackingPosition domainPID controlCross-coupled controlCNC machine

Information

Type
Articles
Information
Robotica , Volume 33 , Issue 6 , July 2015 , pp. 1351 - 1374
Copyright
Copyright © Cambridge University Press 2014 

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References

1. Spong, M. W., Hutchinson, S. and Vidyasagar, M., Robot Modeling and Control (John Wiley & Sons, New York, 2006).Google Scholar
2. Craig, J. J., Introduction to Robotics: Mechanics and Control (Addison-Wesley, Massachusetts, 1986).Google Scholar
3. Kelly, P., “PD control with desired gravity compensation of robotic manipulators: A review,” Int. J. Robot. Res. 6 (5), 660–672 (1997).Google Scholar
4. Koren, Y., “Cross-coupled biaxial computer control for manufacturing systems,” ASME J. Dyn. Syst. Meas. Control 102 (4), 265–272 (1980).Google Scholar
5. Koren, Y. and Lo, Ch. Ch., “Variable-gain cross-coupling controller for contouring,” CIRP Ann.-Manuf. Technol. 40 (1), 371–374 (1991).Google Scholar
6. Fang, R.W. and Chen, J. S., “Cross-coupling control for a direct-drive robot,” JSMA, Series C 45 (3), 749–757 (2002).Google Scholar
7. Barton, K. L. and Alleyne, A. G., “A cross-coupled iterative learning control design for precision motion control,” IEEE Control Syst. Technol. 16 (6), 1218–1230 (2008).Google Scholar
8. Årzén, K. E., “A Simple Event-Based PID Controller,” Proceedings of the 14th IFAC World Congress, Beijing, China (1999) pp. 423–428.Google Scholar
9. Åström, K. J., “Event Based Control,” In: Analysis and Design of Nonlinear Control Systems (Astolfi, A. and Marconi, L., eds.) (Springer, 2008) pp. 127–147.Google Scholar
10. Nakano, M., She, J. H., Mastuo, Y. and Hlno, T., “Elimination of position-dependent disturbances in constant-speed-rotation control systems,” Control Eng. Pract. 4 (9), 1241–1248 (1996).Google Scholar
11. Heemels, W., Sandee, J. and Van Den Bosch, P., “Analysis of event-driven controllers for linear systems,” Int. J. Control 81 (4), 571–590 (2008).Google Scholar
12. Ouyang, P. R., Zhang, W. J. and Wu, F. X., “Nonlinear PD Control for Trajectory Tracking with Consideration of the Design for Control Methodology,” Proceedings of 2002 IEEE ICRA, Washington, USA (May 9–11, 2002) pp. 4126–4131.Google Scholar
13. Ouyang, P. R., Dam, T., Huang, J. and Zhang, W.J., “Contour tracking control in position domain,” Mechatronics 22 (7), 934–944 (2012).Google Scholar
14. Ouyang, P. R., Pano, V. and Dam, T., “PID position domain control for contour tracking,” Int. J. Syst. Sci. (2013). http://dx.doi.org/10.1080/00207721.2013.775385.Google Scholar
15. Dam, T. and Ouyang, P. R., “Position Domain Contour Tracking with Cross-coupled Control,” 2012 IEEE 21st International Symposium on Industrial Electronics, Hangzhou, China (May 28–31, 2012) pp. 1303–1308.Google Scholar
16. Slotine, J. J. E. and Li, W. P., Applied Nonlinear Control (Prentice-Hall, Inc., New Jersey, 1991).Google Scholar
17. Khalil, H. K., Nonlinear Systems, 3rd ed. (Prentice Hall, New Jersey, 2002).Google Scholar