A Modeling Framework and Flux Controller for Free Molecular Flow Deposition Processes

In this paper, we introduce a modeling framework for free molecular flow (FMF) processes (such as, deposition processes under an ultra-high vacuum condition) that is suitable for model-based control design. The generic dynamical model is comprised of four important elements present in such processes: (i) particle transfer, which is modeled based on the wellknown Knudsen cosine law; (ii) particle leakage; (iii) adsorption and desorption described by a (nonlinear) sticking function; and (iv) control input particle flux. As a starting point for obtaining accurate control on the deposition process in FMF regime, we propose a control design method for stabilization with guaranteed transient behavior for fluxes. It is based on a point-wise min-norm control approach, employing both control Lyapunov and control barrier functions. Lastly, we validate our model, applied to a cylindrical geometry, with existing results in the literature and evaluate the effectiveness of the proposed control method for controlling the fluxes.