(581c) Nonlinear Predictive Control Of Thin Film Microstructure Using A Stochastic Pde Model
This work focuses on the parameter identification of a two-dimensional (2D) nonlinear stochastic partial differential equation (SPDE) model for a thin film growth process, and the design of a model predictive controller based on the identified SPDE model to control thin film surface roughness. The thin film growth process considered in this work includes three microscopic processes, adsorption, desorption and surface migration. The evolution of thesurface height profile of the process can be modelled by a highly nonlinear 2D stochastic diffusion-reaction type PDE. The parameters of the SPDE model is initially identified by following a systematic parameter identification procedure that we recently proposed based on data obtained by a kinetic Monte-Carlo simulator of the process. Specifically, the nonlinear SPDE is initially reformulated into a system of infinite nonlinear stochastic ordinary differential equations (ODEs). Then, kinetic Monte-Carlo simulations of the thin film growth process are performed to generate surface snapshots to determine the state covariance of the stochastic ODE system. The correlations between model parameters and the state covariance are established and the parameters of the nonlinear SPDE model are subsequently computed so that the evolution of the surface roughness computed from the SPDE model is consistent to that computed from kinetic Monte-Carlo simulations.
After the identification of model parameters, a finite-dimensional approximation of the identified nonlinear SPDE model is derived that captures the dominant mode contribution to the surface roughness. An output feedback model predictive controller is designed based on the finite-dimensional model to control the surface roughness. In the predictive control formulation, the finite-dimensional model is used to predict the surface roughness and the control action is computed by minimizing an objective function including the distance between the predicted surface roughness and a reference trajectory and a terminal penalty. A state observer is designed so that the states of the finite-dimensional model can be estimated based on the output measurements of the process. The design of the output feedback predictive controller is completed by combining the predictive control law and the state observer. The model predictive controller is applied to the kinetic Monte-Carlo simulation of the deposition process to control the surface roughness in the presence of parameter uncertainties and external disturbances. Closed-loop simulation results demonstrate that the identified model is adequately accurate and that the model predictive controller is effective.