Reduced order based compensator control of thin film growth in a CVD reactor

This paper reports on an interdisciplinary effort, which involves applied mathematicians, material scientists and physicists at North Carolina State University, to integrate new intelligent processing approaches with advanced mathematical modeling, optimization, and control theory to guide the construction and experimental implementation of a series of high pressure (up to 100 atm) organometallic chemical vapor deposition (CVD) reactors. An integral component of this research program is the design of the reactor so that control and sensing are a basic component of the optimal design efforts for the reactor. We report here on the successful use of mathematics in a fundamental role in the development of linear and nonlinear feedback control methods for real-time implementation on the reactor. This is achieved in the required context of gas dynamics coupled with nonlinear surface deposition processes. The problems are optimal tracking problems (for the chemical component fluxes over the substrate) that employ state-dependent Riccati gains with nonlinear observations and the resulting dual state dependent Riccati equations for the compensator gains This control methodology is successfully combined with reduced order model methods based on proper orthogonal decomposition techniques. Computational results to support the efficacy of our approach and methods are also included.