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A major challenge of the large-scale application of two-dimensional (2D) materials is the scaling up of the process for its growth and transfer. Mechanical peeling has been demonstrated to be a promising method for transferring graphene in a fast and environmentally friendly manner. However, efforts in scaling up the process have been lacking. Performing mechanical peeling using a roll-to-roll (R2R) system could significantly increase the throughput of graphene transfer. Such a R2R process does not exist in industry. In this paper a novel R2R mechanical peeling system that has both speed and tension control capabilities is presented. Controllers that control the peeling tensions on both sides of the peeling front are developed based on a tension dynamics model. Both controllers contain a feedback and a feedforward term to account for large steady-state error. The control performance is validated using both experiments and simulation, demonstrating that the R2R mechanical peeling technique can be a viable method for dry transfer of 2D materials in a high-throughput industrial setting.