Optimization and control of multiscale process systems using model reduction: Application to thin-film growth

Multiscale modeling has emerged as a powerful modeling tool for processes where product quality specifications range from macroscopic length scales to microscopic length scales. These multiscale models typically couple continuum macroscopic descriptions obtained from conservation laws with discrete atomistic descriptions obtained from microscopic simulations to obtain a unified description of the process which is capable of predicting phenomena at all range of length scales involved. With the increase in global competition and decrease in profit margins, efforts are being made to incorporate multiscale process models into process optimization and control frameworks. However, extensive computational requirements and the unavailability of microscopic models in closed-form present key challenges for the above task. This thesis outlines a series of methodologies developed in order to address the above problems. Initially, a framework aimed at efficient solution of dynamic process optimization problems constrained by partial differential equation (PDE) constraints is developed by combining nonlinear order reduction techniques for dissipative PDEs with the control vector parameterization (CVP) approach. Subsequently, the above approach is augmented to account for multiscale process models which also include microscopic simulations coupled to PDE based macroscopic description. Similarly to the previous case, the central idea is to develop a reduced order multiscale model which is computationally efficient but simultaneously preserves the accuracy of the original full-order model. This is achieved by combined nonlinear order reduction for dissipative PDEs with in situ adaptive tabulation of microscopic simulation data.; The problem of feedback control of microscopic processes is also considered. The issue of non-availability of closed-form dynamic models is circumvented by deriving low-order state-space models that approximate the detailed microscopic simulations. A system identification algorithm based on Carleman linearization and subspace identification is developed for the above task. Applications of the above approach for surface roughness control during thin-film growth are presented.