In this paper, a general framework that provides sufficient conditions for asymptotic stabilization of underactuated nonlinear systems using an optimal sliding mode control in the presence of system uncertainties is presented. A performance objective is used to optimally select the parameters of the sliding mode control surfaces subject to state and input constraints. It is shown that the closed-loop system trajectories reach the optimal sliding surfaces in finite time and a constructive methodology to determine exponential stability of the closed-loop system on the sliding surfaces is developed which ensures asymptotic stability of the overall closed-loop system. The framework further provides the basis to determine an estimate of the domain of attraction for the closed-loop system with uncertainties. The results developed in this work are experimentally validated using a linear inverted pendulum testbed which show a good match between the actual domain of attraction of the upward equilibrium state and its analytical estimate.
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ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control
October 31–November 2, 2011
Arlington, Virginia, USA
Conference Sponsors:
- Dynamic Systems and Control Division
ISBN:
978-0-7918-5475-4
PROCEEDINGS PAPER
Optimal Sliding Mode Control for a Class of Underactuated Nonlinear Systems
Parham Ghorbanian,
Parham Ghorbanian
Villanova University, Villanova, PA
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Sergey G. Nersesov,
Sergey G. Nersesov
Villanova University, Villanova, PA
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Hashem Ashrafiuon
Hashem Ashrafiuon
Villanova University, Villanova, PA
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Parham Ghorbanian
Villanova University, Villanova, PA
Sergey G. Nersesov
Villanova University, Villanova, PA
Hashem Ashrafiuon
Villanova University, Villanova, PA
Paper No:
DSCC2011-6057, pp. 629-636; 8 pages
Published Online:
May 5, 2012
Citation
Ghorbanian, P, Nersesov, SG, & Ashrafiuon, H. "Optimal Sliding Mode Control for a Class of Underactuated Nonlinear Systems." Proceedings of the ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control. ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 1. Arlington, Virginia, USA. October 31–November 2, 2011. pp. 629-636. ASME. https://doi.org/10.1115/DSCC2011-6057
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