Journal Article10.1002/AIC.11511
Model predictive control of nonlinear stochastic partial differential equations with application to a sputtering process
TL;DR: In this paper, a method for model predictive control of nonlinear stochastic partial differential equations (PDEs) to regulate the state variance, which physically represents the roughness of a surface in a thin film growth process, to a desired level was developed.
read more
Abstract: A method is developed for model predictive control of nonlinear stochastic partial differential equations (PDEs) to regulate the state variance, which physically represents the roughness of a surface in a thin film growth process, to a desired level. Initially a nonlinear stochastic PDE is formulated into a system of infinite nonlinear stochastic ordinary differential equations by using Galerkin's method. A finite-dimensional approximation is then derived that captures the dominant mode contribution to the state variance. A model predictive control problem is formulated, based on the finite-dimensional approximation, so that the future state variance can be predicted in a computationally efficient way. To demonstrate the method, the model predictive controller is applied to the stochastic Kuramoto-Sivashinsky equation, and the kinetic Monte Carlo model of a sputtering process to regulate the surface roughness at a desired level. © 2008 American Institute of Chemical Engineers AIChE J, 2008
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Considerations on nonlinear model predictive control techniques
TL;DR: The idea is to give the NMPC the possibility to automatically select the best combination of algorithms (differential solvers and optimizers) in accordance with the specific problem to be solved, which could be easily extended to many scientific fields traditionally far from process systems and computer-aided process engineering.
82
Regulation of film thickness, surface roughness and porosity in thin film growth using deposition rate
TL;DR: In this article, the authors focus on distributed control of film thickness, surface roughness and porosity in a porous thin film deposition process using the deposition rate as the manipulated input.
54
Modeling and control of film porosity in thin film deposition
TL;DR: In this article, the authors developed a methodologies for modeling and control of film porosity in thin film deposition via kinetic Monte Carlo (kMC) simulation on a triangular lattice, where microscopic events involve atom adsorption and migration and allow for vacancies and overhangs to develop.
44
Robust stabilization design of nonlinear stochastic partial differential systems: Fuzzy approach
TL;DR: A robust fuzzy estimator-based stabilization controller to stabilize the NSPDSs is proposed and robust stochastic H ∞ stabilization design is suggested to attenuate the effects of random external disturbances and measurement noise in the spatio-temporal domain from the area energy point of view.
34
Stochastic Modeling and Simultaneous Regulation of Surface Roughness and Porosity in Thin Film Deposition
TL;DR: In this article, the authors focus on stochastic modeling and simultaneous regulation of surface roughness and porosity for a porous thin film deposition process modeled via kinetic Monte Carlo (kMC) simulation on a triangular lattice.
References
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
TL;DR: This paper presents convergence properties of the Nelder--Mead algorithm applied to strictly convex functions in dimensions 1 and 2, and proves convergence to a minimizer for dimension 1, and various limited convergence results for dimension 2.
Dynamic Scaling of Growing Interfaces
TL;DR: A model is proposed for the evolution of the profile of a growing interface that exhibits nontrivial relaxation patterns, and the exact dynamic scaling form obtained for a one-dimensional interface is in excellent agreement with previous numerical simulations.
Model predictive control: theory and practice—a survey
TL;DR: The flexible constraint handling capabilities of MPC are shown to be a significant advantage in the context of the overall operating objectives of the process industries and the 1-, 2-, and ∞-norm formulations of the performance objective are discussed.
5.6K
•Book
Algorithms for Minimization Without Derivatives
Richard P. Brent
- 01 Jan 1972
TL;DR: In this paper, a monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions, and some of these methods can be used to find approximate minima as well.