The possibilities of controlling the time of damping of Zitterbewegung oscillations in graphene and graphene superlattice have been investigated. The decay time of Zitterbewegung oscillations in graphene in the presence of high-frequency radiation has been calculated. An increase in the duration of the Zitterbewegung with the inclusion of an alternating field has been explicitly demonstrated. The decay time of the Zitterbewegung for a graphene superlattice has been shown to be controlled by changing the ratio between the period of the superlattice and the width of the electron wave packet.