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Technical Brief

Nonlinear Robust Output Stabilization for Mechanical Systems Based on Luenberger-Like Controller/Observer

[+] Author and Article Information
Patricio Ordaz

Research Center on Technology of Information and Systems (CITIS),
Autonomous University of Hidalgo State (UAEH),
Hidalgo 42039, Mexico;
Engineer School,
LaSalle-Pachuca University,
Hidalgo 42160, Mexico
e-mail: jesus_ordaz@uaeh.edu.mx

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 26, 2015; final manuscript received January 11, 2017; published online June 5, 2017. Assoc. Editor: Srinivasa M. Salapaka.

J. Dyn. Sys., Meas., Control 139(8), 084501 (Jun 05, 2017) (6 pages) Paper No: DS-15-1536; doi: 10.1115/1.4036227 History: Received October 26, 2015; Revised January 11, 2017

This paper addresses to demonstrate the uniform-ultimately bounded stability (uniformly-ultimately-bounded (UUB)-stability) of the proportional derivative (PD+) compensator where, the joint velocity is not available to be measured but rather it is estimated. The proposed stabilization control strategy is developed for a “n” degrees-of-freedom (DOF) robotic manipulator process, where the joint speed is not available to be measured; furthermore, the external disturbances and/or uncertain dynamics are considered in the system dynamics. To conclude the closed-loop robust stabilization, the proposed feedback strategy is based on the nonlinear state estimation with a Luenberger-like observer and the classical PD+ used in robot manipulators.

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References

Lewis, F. , Dawson, M. , and Abdallah, T. , 2003, Robot Manipulator Control: Theory and Practice, CRC Press, Boca Raton, FL.
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Ordaz, P. , Espinoza, E. , and Munoz, F. , 2014, “ Global Stability of PD+ Controller With Velocity Estimation,” 53rd IEEE Conference on Decision and Control (CDC), Los Angeles, CA, Dec. 15–17, pp. 2580–2585.
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Poznyak, A. , Polyakov, A. , and Azhmyakov, V. , 2014, Attractive Ellipsoids in Robust Control, Springer International Publishing, Urbana, IL.
Haddad, W. M. , and Chellaboina, V. , 2008, Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach, Princeton University Press, Princeton, NJ.
Poznyak, A. , 2009, Advanced Mathematical Tools for Automatic Control Engineers, Vol. 2, Elsevier, Oxford, UK.

Figures

Grahic Jump Location
Fig. 1

Robot 2R manipulator system

Grahic Jump Location
Fig. 2

Robot trajectory on work-space

Grahic Jump Location
Fig. 3

Links speed and its estimated speed

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