By Panagiotis D. Christofides, Antonios Armaou, Yiming Lou, Amit Varshney
Interest within the regulate and optimization of multiscale technique structures has been caused by means of the necessity to in achieving tight suggestions keep watch over and optimum operation of advanced methods, corresponding to deposition and sputtering of skinny motion pictures in semiconductor production, that are characterised via hugely coupled macroscopic and microscopic phenomena. Drawing from fresh advances within the dynamics and regulate of allotted parameter strategies for which continuum legislation are appropriate in addition to stochastic modeling of phenomena at mesoscopic/microscopic size scales, keep an eye on and optimization of multiscale strategy platforms has advanced right into a very energetic learn region of platforms and regulate engineering.
This book—the first of its kind—presents normal equipment for suggestions controller synthesis and optimization of multiscale structures, illustrating their program to thin-film development, sputtering procedures, and catalytic structures of commercial curiosity. starting with an creation to basic matters on regulate and optimization of multiscale structures and a assessment of past paintings during this region, the publication discusses distinct modeling methods for multiscale tactics with emphasis at the conception and implementation of kinetic Monte Carlo simulation, tools for suggestions keep watch over utilizing kinetic Monte Carlo versions, stochastic version building and parameter estimation, predictive and covariance regulate utilizing stochastic partial differential equation versions, and either steady-state and dynamic optimization algorithms that successfully deal with coupled macroscopic and microscopic goals.
Key positive factors of the paintings:
* Demonstrates some great benefits of the equipment awarded for keep watch over and optimization via vast simulations.
* comprises new innovations for suggestions controller layout and optimization of multiscale approach platforms that aren't incorporated in different books.
* Illustrates the appliance of controller layout and optimization easy methods to complicated multiscale approaches of commercial interest.
* includes a wealthy selection of new examine issues and references to major contemporary work.
The booklet calls for easy wisdom of differential equations, chance thought, and keep an eye on conception, and is meant for researchers, graduate scholars, and procedure regulate engineers. in the course of the booklet, useful implementation matters are addressed to assist researchers and engineers comprehend the improvement and alertness of the tools provided in larger depth.
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Extra resources for Control and Optimization of Multiscale Process Systems
A diagram of the multivariable control system using the estimator/controller structure with interaction compensation is shown in Fig. 7. G1 (s) is the transfer function between the substrate temperature and the growth rate and G2 (s) is the transfer function between the inlet precursor mole fraction and the growth rate. Step tests are used to identify the expression and parameters of G1 (s) and G2 (s). 2 Model-Predictive Control In order to achieve a robust closed-loop operation in certain highly complex deposition processes, a kinetic Monte Carlo model-based predictive control scheme is developed.
Since a cubic lattice is used, the surface atom could hop to, four nearest neighbors, which are (10, 2), (2, 2), (1, 1), and (1, 3). Note that since the site (1, 2) is on the boundary of the 10×10 simulation lattice, its nearest neighbor on the left is outside of the simulation lattice. Periodic boundary conditions are applied and its nearest neighbor on the left becomes (10, 2). To randomly select one nearest neighbor among the four nearest neighbors, the four nearest neighbors are indexed from 1 to 4 and a random number, ζ2 , following the uniform distribution in the (0, 1) interval is generated to pick a nearest neighbor to which the surface atom hops.
8413 for the selection of the next Monte Carlo event. Since ζ satisfies Wa /(Wa + Wd + Wm ) < ζ < (Wa + Wd )/(Wa + Wd + Wm ), a desorption event is selected. Then, Wdi is computed by multiplying the desorption rate for a surface atom with i nearest neighbors by the total number of this type of surface atom, Mi . 06/s and there are M0 = 8 surface atoms that have zero side neighbors. 48/s. 28 × 10−15 /s. Based on these rates, the zeroth class, which contains all surface atoms having no nearest neighbors, is selected because ζ satisfies Wa /(Wa + Wd + Wm ) < ζ < (Wa + Wd0 )/(Wa + Wd + Wm ).
Control and Optimization of Multiscale Process Systems by Panagiotis D. Christofides, Antonios Armaou, Yiming Lou, Amit Varshney