This article considers the problem of achieving a desired supersaturated gas concentration profile inside a polymer part by controlling the gas concentration on the part boundaries at elevated pressure. Such controlled gas concentration can be used to achieve a desired cell-structure inside the polymer when foaming the gas inside as the part is rapidly heat-treated. The goal is to achieve the interior gas concentration at the end of the controllable pressurization, i.e., right before the heat treatment. When the gas diffusion dynamics is Fickian, the main contribution of this article is to show that any specified concentration profile can be achieved provided a sufficiently large relatively-flat offset of the concentration profile is acceptable. This is demonstrated by showing that the interior gas concentration is controllable by changing the gas concentration at the boundary, and the use of an offset ensures that the control input (the outside concentration) remains positive. The controllability, in turn, allows the use of standard optimal control to achieve the state transition to the desired interior gas concentration before the heat treatment. A model-based simulation is used to illustrate the proposed approach.

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