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Mathematical Problems in Engineering
Volume 2016, Article ID 5641478, 11 pages
Research Article

Robust Control of Underactuated Systems: Higher Order Integral Sliding Mode Approach

1Department of Electrical Engineering, Capital University of Science and Technology (CUST), Kahuta Road, Express Highway, Islamabad 44000, Pakistan
2Department of Electrical Engineering, The University of Lahore (UOL), Japan Road, Express Highway, Islamabad 44000, Pakistan
3Department of Mechatronics Engineering, International Islamic University, 50728 Kuala Lumpur, Malaysia
4Center for Advanced Studies in Telecommunications, COMSATS Institute of Information Technology, Islamabad 44000, Pakistan

Received 25 September 2015; Revised 8 January 2016; Accepted 12 January 2016

Academic Editor: Wenguang Yu

Copyright © 2016 Sami ud Din et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a robust control design for the class of underactuated uncertain nonlinear systems. Either the nonlinear model of the underactuated systems is transformed into an input output form and then an integral manifold is devised for the control design purpose or an integral manifold is defined directly for the concerned class. Having defined the integral manifolds discontinuous control laws are designed which are capable of maintaining sliding mode from the very beginning. The closed loop stability of these systems is presented in an impressive way. The effectiveness and demand of the designed control laws are verified via the simulation and experimental results of ball and beam system.