Optimal configurations to minimize disturbance propagation in manufacturing networks

In this paper, we consider the problem of determining optimal configurations of Roll-to-Roll (R2R) process machines which consist of many interconnected dynamic elements to transport flexible materials (webs) on rollers. The problem is to optimally locate the controlled dynamic elements within the R2R machine so as to minimize the effect of disturbances propagated by the transported web. Typical disturbances on R2R machines include misalignment and out-of-roundness of rollers which cause web wrinkles and registration errors if unattenuated. The central contribution of this paper is to pose the combinatorial problem of determining the optimal configuration for a R2R machine as a Mixed-Integer Semi-Definite Program (MISDP) and provide an algorithm to efficiently compute feasible configurations and bounds on their sub-optimality. The proposed algorithm is based on tools such as McCormick relaxations, outer-approximation via eigenvalue cuts, and bound tightening procedures. We provide numerical results for representative R2R systems to show the efficiency of the proposed algorithm.