Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-23T17:51:45.041Z Has data issue: false hasContentIssue false
  • English
  • Français

Sampled data output regulation of n-link robotic manipulator using a realizable reconstruction filter

Published online by Cambridge University Press:  13 August 2014

Muwahida Liaquat  and
Mohammad Bilal Malik
Muwahida Liaquat*
Affiliation:
Department of Electrical Engineering, College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Islamabad, Pakistan
Mohammad Bilal Malik
Affiliation:
Department of Electrical Engineering, College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Islamabad, Pakistan
*
*Corresponding author. E-mail: muwahida@ee.ceme.edu.pk
Get access Rights & Permissions [Opens in a new window]

Summary

This paper proposes a solution to the sampled-data regulation problem for feedback linearizable n-link robotic manipulators. The prime focus is on the development and stability analysis of the proposed control scheme in the presence of model uncertainties and external disturbances. A major constraint is the availability of sampled measurements of output signal. This leads to designing an impulsive observer for feedback linearization. The discrete-time control input is mapped into its continuous-time counterpart using a realizable reconstruction filter (RRF). The underlying control scheme relies on the sampled-data regulator theory based on the discrete-time equivalence of the plant and RRF modeled as impulsive system. This method leads to controller/observer design in discrete time. The working of the entire scheme is dependent on the stability of impulsive observer; hence a Lyapunov-based stability analysis is also included to ensure the stability of a closed-loop system. The working of the proposed scheme along with a comparison with conventional solution is presented, when applied to the control of a 3-degree-of-freedom PUMA 560 robot.

Keywords

Robotic manipulatorsSampled-data controlMIMO systemsOutput regulationImpulsive systems
Type
Articles
Information
Robotica , Volume 34 , Issue 4 , April 2016 , pp. 900 - 912
Copyright
Copyright © Cambridge University Press 2014 

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.Lee, K. W. and Khalil, H., “Adaptive output feedback control of robotic manipulators using high gain observers,” Int. J. Controls 67 (6), 869–886 (1997).Google Scholar
2.Atashzar, S. F., Shahbazi, M., Talebi, H. A. and Towhidkhah, F. “A force observation method for tracking control of flexible link manipulators,” Robotica 31 (4), 589–598 (2012). doi:10.1017/S0263574712000689.Google Scholar
3.Korayem, M. H., Irani, M., Charesaz, A., Korayem, A. H. and Hashemi, A., “Trajectory planning of mobile manipulators using dynamic programming approach,” Robotica 31 (4), 643–656 (2012) doi:10.1017/S0263574712000628.Google Scholar
4.Dabroom, M. and Khalil, H. K., “Output feedback sampled data control of nonlinear systems using high-gain observers,” IEEE Trans. Automatic Control 46 (11), 1712–1725 (2001).Google Scholar
5.Oppenheim, A. V., Schafer, R. W. and Buck, J. R., Discrete Signal Processing, 2nd ed. (Pearson Education, Upper Saddle River, NJ, 1999).Google Scholar
6.Liaquat, M. and Malik, M. B., “A Realizable Reconstruction Filter for Sampled Data Systems,” Proceedings of the IEEE 9th International Conference on ASIC, China (2011) pp. 973–976.Google Scholar
7.Malik, M. B., “State-space recursive least-squares: Part I,” Signal Process. 84, 1709–1728 (2004).CrossRefGoogle Scholar
8.Haykin, S., Adaptive Filter Theory, 4th ed. (Prentice Hall, Upper Saddle River, NJ, 2001).Google Scholar
9.Malik, M. B. and Munawar, K., “Robust control of an n-link robotic manipulator using high-gain observer,” Proceedings of the 12th Mediterranean Conference on Control and Automation (2004).Google Scholar
10.Medina, E. A. and Lawrence, D. A., “State Estimation for Linear Impulsive Systems,” Proceedings of the American Control Conference (2009) pp. 1183–1188.Google Scholar
11.Zang, G., Orlov, Y., Perruquetti, W. and Richard, J.-P., “Finite time observer-based control of linear impulsive systems with persistently acting impact,” Proceedings of the 18th IFAC World Congress (2011) pp. 2442–2557.Google Scholar
12.Aghdam, A. G. and Davison, E. J., “Decentralized switching control for hierarchical systems,” Automatica 43 (6), 1092–1100 (Jun. 2007).CrossRefGoogle Scholar
13.Momeni, A. and Aghdam, A. G., “An adaptive tracking problem for a family of retarded time-delay plants,” Int. J. Adapt. Control Signal Process. 21, 885–910 (2007).Google Scholar
14.Khalil, H. K., Non-Linear Systems, 3rd ed. (Prentice Hall, 2002).Google Scholar
15.Liaquat, M., Malik, M. B. and Malik, F. M., “Output regulation of sampled data systems using a realizable reconstruction filter,” Arab. J. Sci. Eng. 39 (5), 3895–3905 (2014).Google Scholar
16.Liaquat, M. and Malik, M. B., “On sampled data output regulation of feedback linearizable systems uising a realizable reconstruction filter,” Int. J. Control. Autom. Syst. 11 (6), 1162–1169 (2013).Google Scholar
17.Dabroom, M. and Khalil, H. K., “Output feedback sampled-data control of nonlinear systems using high-gain observer,” IEEE Trans. Automatic Control, 46, 1712–1725 (2001).CrossRefGoogle Scholar
18.Kabamba, P. T., “Control of linear systems using generalized sampled data hold functions,” IEEE Trans. Autom. Control 32, 772–783 (1987).Google Scholar
19.Rugh, W. J., Linear Systems Theory, 2nd ed. (Prentice Hall, 1996).Google Scholar
20.Maroni, M., Bolzern, P., De Nicolao, R., Shaked, U.et al., “Existence and convergence of solutions to the H∞ sampled-data estimation problem,” Int. J. Control 73 (15), 1382–1391 (2000).Google Scholar
21.Sun, W., Nagpal, K. M. and Khargonekar, P. P., “H∞ control and filtering for sampled-data systems,” IEEE Trans. Autom. Control 38 (8), 1162–1175 (1993).CrossRefGoogle Scholar
22.De Nicolao, R. and Strada, S., “Kalman filtering with mixed discrete continuous observations,” Int. J. Control 70 (1), 71–84 (1998).Google Scholar
23.Liaquat, M., “Sampled-Data Based Regulation Based on Realizable Reconstruction Filter,” PhD Dissertation (National University of Sciences and Technology, Islamabad, Pakistan, 2013).Google Scholar