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Journal of Sensors
Volume 2017 (2017), Article ID 8419295, 11 pages
Research Article

Online Estimation of the Adhesion Coefficient and Its Derivative Based on the Cascading SMC Observer

1Hunan University of Technology, Zhuzhou 412007, China
2National University of Defense Technology, Changsha 410073, China

Correspondence should be addressed to Jing He

Received 17 September 2016; Revised 14 November 2016; Accepted 27 November 2016; Published 3 January 2017

Academic Editor: Rene Romero-Troncoso

Copyright © 2017 Changfan Zhang 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.


The adhesion coefficient of wheel-rail surface cannot be directly measured, so a cascaded sliding-mode observer is proposed to observe adhesion coefficient and its derivative. A kinetic model for running heavy-duty locomotive is also established. The state equation of wheel adhesion control system is derived from the equation of traction motor torque balance, and adhesion coefficient is proposed to be calculated by load torque. Then, the cascaded sliding-mode observer is designed, and its stability is justified by Lyapunov stability. Based on the equivalence control principle for sliding-mode variable structure, an algorithm to estimate adhesion coefficient and its derivative is established. The simulation and experimental results are used to verify the effectiveness of the observer with load variations or wheel-rail status changes.