(546d) Stochastic Nonlinear Model Predictive Control Applied to an Epitaxial Thin Film Growth Process Under Uncertainty

The design of a nonlinear Model Predictive Controller that regulates the performance of an epitaxial thin film growth process under distributional uncertainty is presented. The epitaxial deposition process has been modeled employing nonlinear partial differential equations (PDEs) coupled with lattice-based kinetic Monte Carlo (KMC) simulations, i.e. a multi-scale model. Since the KMC simulations are computationally prohibitive for online control applications, reduced order models (ROM) are developed in this work based on data-driven simulations of the multiscale system. The key innovative feature in the ROMs is that they explicitly account for distributional uncertainty in the multiscale system’s parameters. Power series expansions are employed in this work for uncertainty propagation. Therefore, the resulting ROMs quantify the key distributional characteristics in the controlled variables due to changes in the key manipulated variables, e.g. substrate temperature, and under distributional uncertainty in the parameters, e.g. the activation energy in the migration process occurring in the thin film’s surface. The ROMs have been validated using open-loop simulations of the multiscale process and have been embedded within a nonlinear model predictive control (NMPC) framework to predict estimates of the control actions that comply with the process control objectives at a user-defined probability of satisfaction, i.e. a stochastic NMPC. The shrinking horizon approach is adopted to minimize the roughness of the thin film while satisfying the constraints on the applied substrate temperature at each time interval and film thickness at the end of the deposition process (at a given probability of occurrence).