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Mathematical Problems in Engineering
Volume 2013, Article ID 523251, 7 pages
Research Article

Study on the Nonsingular Problem of Fractional-Order Terminal Sliding Mode Control

State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China

Received 9 June 2013; Accepted 7 July 2013

Academic Editor: G. Rega

Copyright © 2013 Kening Li 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.


An improved type of control strategy combining the fractional calculus with nonsingular terminal sliding mode control named non-singular fractional terminal sliding mode control (NFOTSM) is proposed for the nonlinear tire-road friction control system of vehicle in this paper. A fractional-order switching manifold is proposed, and the corresponding control law is formulated based on the Lyapunov stability theory to guarantee the sliding condition. The proposed controller ensures the finite time stability of the closed-loop system. Then, a terminal attractor is introduced to solve the singularity problem of fractional terminal sliding mode control (FOTSM). Finally, the performance of the NFOTSM is fully investigated compared with other related algorithms to find the effectiveness for the tire-road friction system. The results show that the NFOTSM has better performance than other related algorithms.