A vibrating plate system comprises at least two vibrating plates are mechanically coupled to one another via a coupling device and a controlling transmitter for outputting control data to the vibrating plates. Each of the vibrating plates comprises a receiving device for receiving the control data, a drive mechanism for propelling the vibration plate forwardly and rearwardly, and a position determining device for determining the position of the relevant vibrating plate within the group. A rule memory is also provided in which control rules are stored. One control rule defines a correlation between a control measure for controlling the traveling mechanism according to the position of the vibrating plate and an item of control information given by the control data. In each vibrating plate, a single control device selects a suitable control rule according to the position of the vibrating plate and to the control measure.