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Optimal Sliding Mode Control for a Class of Underactuated Nonlinear Systems

[+] Author Affiliations
Parham Ghorbanian, Sergey G. Nersesov, Hashem Ashrafiuon

Villanova University, Villanova, PA

Paper No. DSCC2011-6057, pp. 629-636; 8 pages
doi:10.1115/DSCC2011-6057
From:
  • 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
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-5475-4
  • Copyright © 2011 by ASME

abstract

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.

Copyright © 2011 by ASME

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