While railway vehicles are moving, a sudden change of superstructure stiffness in crossings at the starting and ending points of tunnels or bridges leads to undesired vibrations both on the track structure and in the vehicle. In this paper, simulations are performed by using a one-dimensional train-track coupled dynamic model under the condition of a light rail vehicle passed through a slab superstructure line with different stiffness values as a transition zone of the railway. The actual conditions used in Istanbul transportation are taken into account in the modelling of the track and the light metro vehicle. The model of the track consists of an Euler-Bernoulli beam resting on discrete supported rail pads, which are connected as a viscoelastic foundation to a rigid ground. The vertical vibrations are analyzed by a model in which track and 16 DOF semi-vehicle models are combined, including a dynamic wheel-rail contact. Two different controllers are designed in parallel with secondary suspensions in order to suppress vertical vibrations of the light rail vehicle resulting from the change in the dynamic conditions of the superstructure and the rail irregularity in the transition zone to increase the comfort of the passengers. For many simulation scenarios, including unloaded and fully loaded vehicle conditions at the average and maximum operational speeds, with and without track irregularities, the superiority of the fuzzy logic controller over the commonly used PID controller is shown in the time and frequency domain.