Discrete-time sliding mode control for a class of underactuated mechanical systems with bounded disturbances

Authors

  • That Dinh Nguyen Faculty of Engineering and Information Technology, University of Technology, Sydney, NSW 2007, Australia; Faculty of Marine Electrical and Electronics Engineering, Vietnam Maritime University, Vietnam.

DOI:

https://doi.org/10.15625/1813-9663/30/2/3569

Keywords:

Underactuated mechanical system, sliding mode control, Pendubot, Bounded disturbance, Lyapunov, linear matrix inequalities (LMIs)

Abstract

This article addresses the problem of discrete-time quasi-sliding mode control for a class of underactuated mechanical systems in the presence of bounded external disturbances. Based on the Lyapunov stability method, a sufficient condition for the existence of a stable sliding surface is derived in terms of a linear matrix inequality (LMI). This condition also guarantees that the effects of external disturbances can be suppressed when the system is considered in the sliding mode. Moreover, in the induced sliding dynamics, all the state trajectories are exponentially convergent to a ball whose radius can be minimized. A robust discrete-time quasi-sliding mode controller is then proposed to drive system state trajectories towards the sliding surface infinite time and maintain it thereafter subsequent time. A case study of the Pendubot is provided to illustrate the feasibility of the proposed approach.

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Author Biography

That Dinh Nguyen, Faculty of Engineering and Information Technology, University of Technology, Sydney, NSW 2007, Australia; Faculty of Marine Electrical and Electronics Engineering, Vietnam Maritime University, Vietnam.

Nguyen Dinh That received the B.E.
degree from Hanoi University of
Technology, Vietnam in 2003 and the
M.S. degree from
Vietnam Maritime University,
Vietnam, in 2008, both in Automation
Engineering. He is currently working
towards his PhD degree in automation and control
engineering at the School of Electrical, Mechanical
and Mechatronic Systems, University of Technology,
Sydney, Australia. His research interests include
control and automation and robotics.

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Published

2014-06-10

How to Cite

[1]
T. D. Nguyen, “Discrete-time sliding mode control for a class of underactuated mechanical systems with bounded disturbances”, JCC, vol. 30, no. 2, pp. 93–105, Jun. 2014.

Issue

Section

Cybernetics