By Panagiotis D. Christofides, Antonios Armaou, Yiming Lou, Amit Varshney
Interest within the keep watch over and optimization of multiscale technique structures has been prompted by way of the necessity to in achieving tight suggestions keep an eye on and optimum operation of advanced procedures, corresponding to deposition and sputtering of skinny movies in semiconductor production, that are characterised by way of hugely coupled macroscopic and microscopic phenomena. Drawing from fresh advances within the dynamics and keep watch over of disbursed parameter strategies for which continuum legislation are appropriate in addition to stochastic modeling of phenomena at mesoscopic/microscopic size scales, regulate and optimization of multiscale approach structures has advanced right into a very energetic examine quarter of structures and keep watch over engineering.
This book—the first of its kind—presents common tools for suggestions controller synthesis and optimization of multiscale platforms, illustrating their program to thin-film development, sputtering strategies, and catalytic structures of business curiosity. starting with an creation to common matters on regulate and optimization of multiscale platforms and a assessment of prior paintings during this quarter, the ebook discusses particular modeling ways for multiscale techniques with emphasis at the idea and implementation of kinetic Monte Carlo simulation, tools for suggestions keep watch over utilizing kinetic Monte Carlo types, 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 handle coupled macroscopic and microscopic ambitions.
Key positive aspects of the paintings:
* Demonstrates some great benefits of the equipment awarded for regulate and optimization via wide simulations.
* contains new strategies for suggestions controller layout and optimization of multiscale procedure platforms that aren't integrated in different books.
* Illustrates the applying of controller layout and optimization easy methods to advanced multiscale strategies of business interest.
* includes a wealthy number of new learn themes and references to major contemporary work.
The publication calls for uncomplicated wisdom of differential equations, likelihood concept, and regulate idea, and is meant for researchers, graduate scholars, and method regulate engineers. in the course of the e-book, useful implementation matters are addressed to assist researchers and engineers comprehend the advance and alertness of the equipment provided in higher depth.
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Extra info for Control and Optimization of Multiscale Process Systems
2. Comparison of the surface roughness profiles from three independent kinetic Monte Carlo simulations that utilize a 20 × 20 lattice. 20 18 16 Roughness 14 12 10 8 6 4 2 0 0 2 4 6 8 10 τ 12 14 16 18 20 Fig. 3. Comparison of the surface roughness profiles from three independent kinetic Monte Carlo simulations that utilize a 50 × 50 lattice. , cluster formation). 2 Real-Time Estimation 31 estimates of the desired properties to be controlled. For example, in the case of surface roughness, this quantity is defined as the average number of broken bonds for every surface atom and the microscopic unit involved is an individual atom.
However, when the property of interest is, for example, step density, a larger lattice is needed to obtain a convergent average value from the kinetic Monte Carlo simulation. At this point, it is important to note that the proposed reduction of lattice size can be viewed as an alternative (and quite intuitive) way to perform order reduction of the master equation . The fluctuations of the roughness value obtained by using a small lattice Monte Carlo model can be reduced by independently running several Monte Carlo simulations using a small lattice with the same parameters and averaging the roughness values obtained from the different runs.
There is also model inaccuracy when the outputs of kinetic Monte Carlo simulators that use multiple small lattices and a high-order lattice are compared. This can be corrected by using a measurement error compensator that uses the available roughness measurements obtained from a kinetic Monte Carlo simulator that uses the high-order lattice model (or directly from experiments at discrete time instants) to produce an improved roughness estimate. The state-space representation of the measurement error compensator is K(τ ) = K0 de = Ke (yh (τmi ) − yˆ(τmi )), dτ τmi < τ ≤ τmi+1 , i = 1, 2, .