By Panagiotis D. Christofides, Antonios Armaou, Yiming Lou, Amit Varshney
Interest within the keep watch over and optimization of multiscale strategy platforms has been prompted by means of the necessity to in attaining tight suggestions keep an eye on and optimum operation of advanced procedures, corresponding to deposition and sputtering of skinny motion pictures in semiconductor production, that are characterised through hugely coupled macroscopic and microscopic phenomena. Drawing from contemporary advances within the dynamics and regulate of allotted parameter methods for which continuum legislation are appropriate in addition to stochastic modeling of phenomena at mesoscopic/microscopic size scales, regulate and optimization of multiscale technique platforms has developed right into a very lively examine quarter of structures and keep an eye on engineering.
This book—the first of its kind—presents basic equipment for suggestions controller synthesis and optimization of multiscale structures, illustrating their software to thin-film progress, sputtering methods, and catalytic platforms of commercial curiosity. starting with an creation to basic matters on keep watch over and optimization of multiscale platforms and a evaluation of prior paintings during this zone, the ebook discusses precise modeling ways for multiscale strategies with emphasis at the idea and implementation of kinetic Monte Carlo simulation, equipment for suggestions keep an eye on utilizing kinetic Monte Carlo versions, stochastic version development and parameter estimation, predictive and covariance keep watch over utilizing stochastic partial differential equation versions, and either steady-state and dynamic optimization algorithms that successfully tackle coupled macroscopic and microscopic goals.
Key positive aspects of the paintings:
* Demonstrates some great benefits of the tools awarded for keep an eye on and optimization via vast simulations.
* contains new concepts for suggestions controller layout and optimization of multiscale method structures that aren't integrated in different books.
* Illustrates the appliance of controller layout and optimization ways to advanced multiscale methods of commercial interest.
* incorporates a wealthy choice of new learn subject matters and references to major fresh work.
The e-book calls for simple wisdom of differential equations, likelihood thought, and keep watch over idea, and is meant for researchers, graduate scholars, and approach keep watch over engineers. in the course of the booklet, sensible implementation concerns are addressed to assist researchers and engineers comprehend the improvement and alertness of the tools awarded in higher depth.
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Additional info for Control and Optimization of Multiscale Process Systems
Solve the fixed short-horizon optimization problem of minimizing the difference between the instantaneous surface roughness and the reference value with a single decision variable. Therefore, the computation time of each optimization is greatly reduced, since the kMC simulation duration is reduced from the scale of the total deposition time to the controller turnover time. This is very important since kMC simulation is relatively time-consuming and large-scale numerical optimization using kMC models is almost impossible to solve in real time.
Various definitions of surface roughness can be found in the literature. Note that estimation and control of surface roughness using different surface roughness definitions can be readily studied within the framework presented in this chapter, which consides the surface roughness represented by the number of broken bonds on the surface and the surface roughness represented by the standard deviation of the surface from its average height . When the surface roughness is represented by the number of broken bonds on the surface, it is computed as follows: (|hi+1,j − hi,j | + |hi−1,j − hi,j | + |hi,j+1 − hi,j | + |hi,j−1 − hi,j |) + 1.
Diagram of the estimator/controller structure using a kinetic Monte Carlo simulator based on multiple small lattice models. controlled variable (surface roughness or growth rate) in a time scale comparable to the real-time evolution of the process. The estimates are used in the controller to determine the control action. MIMO Control We now turn our attention to the design and evaluation of a multivariable feedback control structure, based on kinetic Monte Carlo models, used to control the surface roughness and thin-film growth rate by manipulating the substrate temperature and inlet precursor concentration.