In this paper, the vertical carbody dynamics of the railway vehicle excited by random track inputs are investigated. The multi-objective ℋ controllers for carbody weight of the actual, heavy and a mass confined in a polytopic range have been designed with the aim of reducing the wheel forces, heave, pitch and roll body accelerations of the vehicle. Later, the carbody mass is modelled as a free-free Euler Bernoulli beam and the low frequency flexural vibrations of the train body are examined. An omnibus ℋ controller is synthesized to suppress both the rigid and low frequencies flexible modes of the railway vehicle. The performances of the ℋ controllers are verified by using the passive and active suspension responses on the right and left rail track disturbances that are represented by the power spectral density functions authenticated for the stochastic real track data collected from the Qinhuangdao-Shenyang passenger railway line in China. Simulation results showed that all controllers exhibit a very good performance by effectively reducing the car-body accelerations in vicinity of the resonanat frequencies while keeping the wheel-rail forces in the allowable limit.

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