Enhanced Sliding Mode Control and Online Estimation of Optimal Slip Ratio for Railway Vehicle Braking Systems

  • Jianfeng Liu
  • Qing Peng
  • Zhiwu Huang
  • Weirong Liu
  • Heng Li
Regular Paper


This paper proposes an optimal anti-locking control scheme so as to improve the braking performance of railway vehicles. The controlling effect of sliding mode control is improved, and the optimal slip ratio is achieved by extreme seeking algorithm. Firstly, a substitute function for the conventional sign function is proposed. Secondly, a closed loop observer for braking systems is used to enhance the estimation value of adhesion force, which can also be used for calculating reference speed. Finally Sliding Mode Controlbased controller needs to be entered a reference slip ratio called optimal slip ratio, which is searched by extreme seeking algorithm from the functional relationship between slip ratio and friction coefficient. Thus, the maximum adhesion is achieved despite wheel/ rail surface changes. The simulation result demonstrates the effect of real-time adjustment for braking torque, which guarantees the braking performance.


Railway vehicles Enhanced sliding mode control Observer Extreme seeking algorithm Optimal slip ratio 



i th group adhesion torque


i th group braking force torque


i th group interference torque


i th group adhesion force


radius of wheel


moment of inertia of wheel-set


adhesion coefficient


i th group angular velocity of wheel


pressure by wheel on track


initial velocity at the moment of starting braking


reference velocity for railway vehicles

\(\hat v\)

estimation of railway vehicles velocity


actual slip/slide velocity


reference slip/slide velocity

\(\dot \lambda \)

derivative of slip/skid ratio


i th group actual slip/skid ratio


optimal slip/skid ratio


reference slip/skid ratio


high-pass filter’s cut-off frequency


actual but unknown extremum value


unknown constant by extremum seeking

\(\hat \theta \)

estimation for θ*


small positive constant


barrier Lyapunov function


pressure by the i th group wheel on the tread


quality of railway vehicle

\({\Omega _\lambda }^{creep}\)

creep region

\({\Omega _\lambda }^{slide}\)

slide region


positive constant


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Copyright information

© Korean Society for Precision Engineering and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of information Science and EngineeringCentral South UniversityChangshaChina

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