0
Technical Briefs

A Note on a Reduced-Order Observer Based Controller for a Class of Lipschitz Nonlinear Systems

[+] Author and Article Information
Mohamadreza Homayounzade

e-mail: m.homayounzade@me.iut.ac.ir

Mehdi Keshmiri

e-mail: mehdik@cc.iut.ac.ir
Department of Mechanical Engineering,
Isfahan University of Technology,
P.O. Box 84156,
Isfahan, Iran

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 22, 2011; final manuscript received May 6, 2012; published online November 7, 2012. Assoc. Editor: Bor-Chin Chang.

J. Dyn. Sys., Meas., Control 135(1), 014505 (Nov 07, 2012) (4 pages) Paper No: DS-11-1126; doi: 10.1115/1.4007235 History: Received April 22, 2011; Revised May 06, 2012

This paper presents a novel reduced-order observer based controller for a class of Lipschitz nonlinear systems, described by a set of second order ordinary differential equations. The control law is designed based on the measured output and estimated states. The main features are: (1) The computation cost is reduced noticeably, since the observer is a reduced-order one; (2) The controller guarantees semi-global exponential stability for both estimation and tracking error; and (3) The proposed method can be used in a large range of applications, especially in mechanical systems. The effectiveness of the proposed method is investigated through the numerical simulation for a two-degrees-of-freedom robot manipulator acting on a horizontal worktable.

FIGURES IN THIS ARTICLE
<>
© 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Misawa, E. A., and Hedrick, J. K., 1989, “Nonlinear Observers—A State-of-the-Art Survey,” ASME J. Dyn. Sys. Meas. Control, 111(3), pp. 344–352. [CrossRef]
Marquez, H. J., 2003, Nonlinear Control Systems, John Wiley, Hoboken, NJ, pp. 50–55.
Karafyllis, I., and Zhong-Ping, J., 2011, Stability and Stabilization of Nonlinear Systems, Springer, New York, pp. 321–322.
Krener, A. J., and Isidori, A., 1983, “Linearization by Output Injection and Nonlinear Observers,” Syst. Control Lett., 3(1), pp. 47–52. [CrossRef]
Rajamani, R., 1998, “Observers for Lipschitz Nonlinear Systems,” IEEE Trans. Autom. Control, 43(3), pp. 397–401. [CrossRef]
Engel, R., 2007, “Nonlinear Observers for Lipschitz Continuous Systems With Inputs,” Int. J. Control, 80(4), pp. 495–508. [CrossRef]
Raghavan, S., 1992, “Observers and Compensators for Nonlinear Systems With Application to Flexible Joint Robots,” Ph.D. dissertation, University of California, Berkeley.
Dawson, D. M., Qu, Z., and Carroll, J. C., 1992, “On State Observation and Output Feedback Problems for Nonlinear Uncertain Dynamic Systems,” Syst. Control Lett., 18(3), pp. 217–222. [CrossRef]
Robenack, K., and Lynch, A. F., 2007, “High Gain Nonlinear Observer Design Using the Observer Canonical Form,” IEE Proc.: Control Theory Appl., 1(6), pp. 1574–1579. [CrossRef]
Zhu, F., and Han, Z., 2002, “A Note on Observers for Lipschitz Nonlinear Systems,” IEEE Trans. Autom. Control, 47(10), pp. 1751–1754. [CrossRef]
Karagiannis, D., Jiang, Z. P., Ortega, R., and Astolfi, A., 2005, “Output-Feedback Stabilization of a Class of Uncertain Non-Minimum-Phase Nonlinear Systems,” Automatica, 41(9), pp. 1609–1615. [CrossRef]
Homayounzade, M. R., and Keshmiri, M., 2011, “Velocity Observer Based Controller Design for Second Order Systems, With Application to Constrained Robotic Systems,” IEEE/ ASME International Conference on Advanced Intelligent Mechatronics. [CrossRef]
Homayounzade, M. R., Keshmiri, M., and Danesh, M., 2010, “An Observer-Based State Feedback Controller Design for Robot Manipulators Considering Actuators' Dynamic,” Conference on Methods and Models in Automation and Robotics, IEEE. [CrossRef]
de Wit, C. C., Fixot, N., and Astrom, K., 1992, “Trajectory Tracking in Robot Manipulators via Nonlinear Estimated State Feedback,” IEEE Trans. Rob. Autom., 8(1), pp. 138–144. [CrossRef]
Pagilla, P. R., and Zhu, Y., 2004, “Controller and Observer Design for Lipschitz Nonlinear Systems,” Proceeding of American Control Conference.
Berghuis, H., and Nijmeijer, H., 1993, “Global Regulation of Robots Using Only Position Meaurement,” Syst. Control Lett., 21(4), pp. 289–293. [CrossRef]
Chen, C. T., 1999, Linear Systems Theory and Design, Oxford University Press, New York, pp. 251–252.
Homayounzade, M. R., and Keshmiri, M., 2011, “On the Robust Tracking Control of Kinematically Constrained Robot Manipulators,” IEEE International Conference on Mechatronics. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Scheme of manipulator constrained to move on a horizontal platform

Grahic Jump Location
Fig. 2

Time history of joint position error

Grahic Jump Location
Fig. 3

Time history of joint velocity error

Grahic Jump Location
Fig. 4

Time history of joint velocity estimation

Grahic Jump Location
Fig. 5

Time history of actuator torque

Grahic Jump Location
Fig. 6

Robustness of joint position error to links mass

Grahic Jump Location
Fig. 7

Robustness of joint position error to links length

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In