Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T16:51:19.830Z Has data issue: false hasContentIssue false

A new variable structure controller for robot manipulators with a nonlinear PID sliding surface

Published online by Cambridge University Press:  31 August 2012

Khaled R. Atia*
Affiliation:
Mechanical Design and Production Engineering Department, Faculty of Engineering, Zagazig University, Zagazig, Egypt
*
*Corresponding author. E-mail: [email protected], [email protected]

Summary

In this paper a new sliding mode controller for set-point control of robot manipulators is proposed. The controller does not use any part of the robot dynamics in the control law. Thus, it is structurally simpler than other sliding mode controllers where the control law uses a nominal model of the robot dynamics. The controller uses a new nonlinear Proportional-Integral-Derivative (PID) sliding surface. The stability of the controlled robot dynamics is proved. On applying the boundary-layer approach to remove chattering, a nonlinear PID controller exists inside the boundary layer. This PID controller ensures that the error tend to zero asymptotically if there is no disturbances applied to the robot dynamics.

Type
Articles
Copyright
Copyright © Cambridge University Press 2012 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Stepanenko, Y. and Su, C., “Variable structure control of robot manipulators with nonlinear sliding manifolds,” Int. J. Control 58 (2), 285300 (1993).CrossRefGoogle Scholar
2.Slotine, J. and Sastry, S., “Tracking control of non-linear systems using sliding surfaces, with applications to robot manipulators,” Int. J. Control 38 (2), 465492 (1983).CrossRefGoogle Scholar
3.Muraca, P. and Pugliese, P., “A variable-structure regulator for robotic systems,” Automatica 33 (7), 14231426 (1997).CrossRefGoogle Scholar
4.Kim, N., Lee, C. and Chang, P., “Sliding mode control with perturbation estimation: Application to motion control of parallel manipulator,” Control Eng. Practice 6 (11), 13211330 (1998).CrossRefGoogle Scholar
5.Li, Y., Eriksson, B. and Wikander, J., “Sliding Mode Control of Two-Mass Positioning Systems,” Proceedings of the 14th IFAC Triennial World Congress on Automatic Control, Beijing, China (1999).Google Scholar
6.Stepanenko, Y., Cao, Y. and Su, C., “Variable structure control of robotic manipulator with PID sliding surfaces,” Int. J. Robust Nonlinear Control 8, 7990 (1998).3.0.CO;2-V>CrossRefGoogle Scholar
7.Eker, I., “Sliding mode control with PID sliding surface and experimental application to an electromechanical plant,” ISA Trans. 45 (1), 109118 (2006).CrossRefGoogle Scholar
8.Meza, J., Santibaez, V. and Hernandez, V., “Saturated Nonlinear PID Global Regulator For Robot Manipulators: Passivity Based Analysis,” Proceedings of 16th IFAC World Congress on Automatic Control, Czech Republic (2005).Google Scholar
9.Kasac, J., Novakovic, B., Majetic, D. and Brezak, D., “Performance Optimization of Saturated PID Controller for Robot Manipulators,” In: Proceedings of the 10th IEEE International Conference on Methods and Models in Automation and Robotics (Miedzyzdroje, Poland, 2004) pp. 843848.Google Scholar
10.Kelly, R., “Global positioning of robot manipulators via PD control plus a class of nonlinear integral actions,” IEEE Trans. Autom. Control 43 (7), 934938 (1998).CrossRefGoogle Scholar
11.Kasac, J., Novakovic, B., Majetic, D. and Brezak, D., “Performance Tuning for a New Class of Globally Stable Controllers for Robot Manipulators,” Proceedings of 16th IFAC World Congress on Automatic Control (Czech Republic, 2005).Google Scholar
12.Alvarez-Ramirez, J., Kelly, R. and Cervantes, I., “Semiglobal stability of saturated linear PID control for robot manipulators,” Automatica 39 (4), 989995 (2003).CrossRefGoogle Scholar
13.Cervantes, I. and Alvarez-Ramirez, J., “On the PID tracking control of robot manipulators,” Syst. Control Lett. 42, 3746 (2001).CrossRefGoogle Scholar
14.Loria, A., Lefeber, E. and Nijmeijer, H., “Global asymptotic stability of robot manipulators with linear PID and PI2 D control,” SACTA 3 (2), 138149 (2000).Google Scholar
15.Arimoto, S., Control Theory of Nonlinear Mechanical Systems: A Passivity-Based and Circuit-Theoretic Approach (Oxford University Press, Oxford, UK, 1996).CrossRefGoogle Scholar
16.Ortega, R., Loria, A., Niclasson, P. and Sira-Ramirez, H., Passivity-Based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications (Springer-Verlag, London, 1989).Google Scholar
17.Spong, M. and Vidysagar, M., Robot Dynamics and Control (Wiley, New York, 1998).Google Scholar
18.Yazarel, H., Cheah, C. and Liaw, H., “Adaptive SP-D control of robotic manipulator in the presence of modeling error in a gravity regressor matrix: theory and experiment,” IEEE Trans. Robot. Autom. 18 (3), 373379 (2002).CrossRefGoogle Scholar
19.Kirchoff, S. and Melek, W., “A saturation-type robust controller for modular manipulators arms,” Mechatronics 17, 175190 (2007).CrossRefGoogle Scholar
20.Zeinali, M. and Notash, L., “Adaptive sliding mode control with uncertainty estimator for robot manipulators,” Mech. Mach. Theory 45, 8090 (2010).CrossRefGoogle Scholar
21.Lewis, F., Abdallah, C. and Dawson, D., Control of Robot Manipulators (Maxwell Macmillan, New York, 1993).Google Scholar