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Coupled Systems Mechanics
  Volume 7, Number 6, December 2018 , pages 707-729
DOI: https://doi.org/10.12989/csm.2018.7.6.707
 

Semi-active bounded optimal control of uncertain nonlinear coupling vehicle system with rotatable inclined supports and MR damper under random road excitation
Z. G. Ying, G. F. Yan and Y. Q. Ni

 
Abstract
    The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.
 
Key Words
    stochastic nonlinear vibration; semi-active bounded optimal control; coupling vehicle system; uncertainty; random road excitation; MR damper; stochastic dynamical programming; minimax strategy
 
Address
Z. G. Ying and G. F. Yan: Department of Mechanics, School of Aeronautics and Astronautics, Zhejiang University,
Hangzhou 310027, P.R. China
Y. Q. Ni: Department of Civil and Environmental Engineering, National Rail Transit Electrification and Automation Engineering Technology Research Centre (Hong Kong Branch), The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
 

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