development of efficient modeling and diffusion control approaches of nonlinear spatially distributed processes

Restricted (Penn State Only)
Author:
Yang, Manda
Graduate Program:
Chemical Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
February 19, 2018
Committee Members:
  • Antonios Armaou, Dissertation Advisor
  • Antonios Armaou, Committee Chair
  • Ali Borhan, Committee Member
  • Robert Martin Rioux Jr., Committee Member
  • Constantino Manuel Lagoa, Outside Member
Keywords:
  • distributed parameter system
  • nonlinear control
  • model reduction
Abstract:
The distributed parameter system (DPS) is of significant importance in many chemical and material industry processes. This kind of systems shows spatial variation because of the existence of diffusion, convection and reaction. Due to the motivation to improve product quality and increase economic profit, controlling these processes is significantly important. Examples include plasma enhanced chemical vapor deposition, plasma etching reactors and reaction in porous catalyst particles. A standard way to control these processes is to construct reduced order models (ROMs) via the Galerkin method and then design observers and controllers based on the ROMs, given the fact that the behavior of most of the above chemical and material industry processes can be captured by finite dimensional systems. To improve the accuracy of the ROM and reduce the computational cost, many research studies have been done. The proposed work will relax the assumptions of existing methods. The contribution of this work can be summarized to: (1) proposing an advanced POD method that combines the standard POD method and the analytical approach; (2) combining Adaptive Proper Orthogonal Decomposition (APOD) and Discrete Empirical Interpolation Method (DEIM) to reduce the computational cost of ROMs; (3) proposing Discrete Adaptive Proper Orthogonal Decomposition (DAPOD) to relax the assumptions of APOD and improved its performance; (4) improving the accuracy of ROM for systems with strong convection using DAPOD; (5) proposing an equation-free control method that can control PDE based on model reduction when the governing equation of the system is not available.