H∞ Optimal Control for Maintaining the R2R Peeling Front

Abstract

Dry transfer using Roll-to-Roll (R2R) mechanical peeling could significantly increase the throughput and efficiency of the production of 2D materials such as graphene and flexible electronics. Currently, such a R2R process does not exist in industry. For this dry transfer R2R process to be practical for industrial applications, the peeling angle between the growth substrate and the functional material needs to be precisely controlled. In this paper, a nonlinear state space representation of the R2R dry peeling process is formulated with the peeling front velocity variation as a disturbance input. This state space model is used to construct a linear parameter varying (LPV) representation of the system, and a methodology on how to bound the LPV representation within a convex polytopic linear differential inclusion (PLDI) set is presented. This PLDI representation is then used in a linear matrix inequality (LMI) optimization framework to design a full state feedback controller that minimizes the H∞ gain of the connection between the adhesion energy variation and the peeling front geometry. Simulation results demonstrate that this controller improves the precision of the R2R peeling angle, and this increase in precision enables higher web speed. Thus, this technique can be an enabling tool for making R2R mechanical peeling dry transfer of 2D materials a reality in industrial settings.