Recently, the class of spatially invariant systems was introduced with motivating examples of partial differential equations on an infinite domain. For these it was shown that by taking Fourier transforms, one obtains...
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Recently, the class of spatially invariant systems was introduced with motivating examples of partial differential equations on an infinite domain. For these it was shown that by taking Fourier transforms, one obtains infinitely many finite-dimensional systems with a scalar parameter. The idea is that, for the LQR controller design for these systems, one can solve the parameterized LQR-Riccati equation pointwise. While for simple first order systems like the heat equations this approach works, for second order systems like wave or beam equations it is easy to construct examples for which this approach fails. Here we give a correct formulation for second order partial differential systems including wave and beam type equations. (C) 2011 Elsevier Ltd. All rights reserved.
This work focuses on modeling and control of aggregate thin film surface morphology for improved light trapping using a patterned deposition rate profile. The dynamics of the evolution of the thin film surface height ...
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This work focuses on modeling and control of aggregate thin film surface morphology for improved light trapping using a patterned deposition rate profile. The dynamics of the evolution of the thin film surface height profile are modeled by an Edwards-Wilkinson-type equation (a second-order stochastic partial differential equation) in two spatial dimensions. The thin film surface morphology is characterized in terms of aggregate surface roughness and surface slope. These variables are computed with respect to appropriate visible light-relevant characteristic length scales and defined as the root-mean-squares of height deviation and slope of aggregate surface height profiles, respectively. Analytical solutions of the expected aggregate surface roughness and surface slope are obtained by solving the Edwards-Wilkinson equation and are used in the controller design. The model parameters of the Edwards-Wilkinson equation are estimated from kinetic Monte-Carlo simulations using a novel parameter estimation procedure. This parameter dependence on the deposition rate is used in the formulation of the predictive controller to predict the influence of the control action on the surface roughness and slope at the end of the growth process. The cost function of the controller involves penalties on both aggregate surface roughness and mean slope from set-point values as well as constraints on the magnitude and rate of change of the control action. The controller is applied to the two-dimensional Edwards-Wilkinson equation. Simulation results show that the proposed controller successfully regulates aggregate surface roughness and slope to set-point values at the end of the deposition that yield desired levels of thin film reflectance and transmittance. (C) 2011 Elsevier Ltd. All rights reserved.
Polymeric gels that undergo deformation upon appropriate changes in pH or temperature have considerable promise as drug delivery vehicles. Uptake of drug macromolecules into swelling and nonswelling gel spheres and re...
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Polymeric gels that undergo deformation upon appropriate changes in pH or temperature have considerable promise as drug delivery vehicles. Uptake of drug macromolecules into swelling and nonswelling gel spheres and release of drug macromolecules from deswelling and nondeforming gel spheres into a target fluid are investigated here. A mathematical model for gel-solution composite, a composite of a distributedparameter system (gel spheres) and a lumped parameter system (surrounding solution), is developed. The polymer network displacement in swelling/deswelling gels is described by a stress diffusion coupling model. The analytical solution for network displacement is used to predict solvent intake by swelling gels, solvent efflux from deswelling gels, and changes in pressure, porosity, and effective drug diffusivity resulting from network displacement. These in turn influence drug uptake during and after gel swelling and drug release from gel during and after gel deswelling. Numerical results illustrate benefits of gel swelling for drug loading and merits of different modes of drug release. Comparisons are made, as concerns drug uptake and drug release, with gels not subject to deformation.
Polymer flooding is one of the most important technologies for enhanced oil recovery (EOR). In this paper, an optimal control model of distributed parameter systems (DPSs) for polymer injection strategies is establish...
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Polymer flooding is one of the most important technologies for enhanced oil recovery (EOR). In this paper, an optimal control model of distributed parameter systems (DPSs) for polymer injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding, and some inequality constraints as polymer concentration and injection amount limitation. The optimal control model is discretized by full implicit finite-difference method. To cope with the discrete optimal control problem (OCP), the necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagin's discrete maximum principle. A modified gradient method with new adjoint construction is proposed for the computation of optimal injection strategies. The numerical results of an example illustrate the effectiveness of the proposed method.
Electrodeposition is a complex partially observed mass-transfer process driven by several surface reactions without exact model. In this article, the process uncertainties are described by a finite number of Wiener pr...
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Electrodeposition is a complex partially observed mass-transfer process driven by several surface reactions without exact model. In this article, the process uncertainties are described by a finite number of Wiener processes in a stochastic model applied in the filtering and control problems. These problems are solved as a boundary observation-control problem based on a finite diffusion model with uncertainties in the domain interior and on the boundaries. A mixed boundary problem is considered on an interval with the Dirichlet data on one end (bulk solution) and Neumann data on the other end (cathode surface). The concentration of oxidising species in the domain interior is unattainable for observations but the flux on the boundary (electric current) can be measured with a limited accuracy (sensor error). The total flux for the main and side reactions is controlled by the current density on the cathode surface. The disturbing effect of the side reactions is modelled as a noise. The concentration of species is stabilised at the desired level near to the cathode surface with a relatively simple feedback control. The concentration on the boundary and in the domain is estimated as a conditionally Gaussian process in the course of filtering. The estimated conditional mean of concentration is solved from a stochastic partial differential equation in dependence on the covariance kernel. A relatively good quality of estimation and control is demonstrated in the process of simulation in the realistic conditions for a copper deposition process.
We consider the initial-boundary value problem governed by systems of linear hyperbolic partial differential equations in the canonical diagonal form and study conditions for exponential stability when the system disc...
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We consider the initial-boundary value problem governed by systems of linear hyperbolic partial differential equations in the canonical diagonal form and study conditions for exponential stability when the system discontinuously switches between a finite set of modes. The switching system is fairly general in that the system matrix functions as well as the boundary conditions may switch in time. We show how the stability mechanism developed for classical solutions of hyperbolic initial boundary value problems can be generalized to the case in which weaker solutions become necessary due to arbitrary switching. We also provide an explicit dwell-time bound for guaranteeing exponential stability of the switching system when, for each mode, the system is exponentially stable. Our stability conditions only depend on the system parameters and boundary data. These conditions easily generalize to switching systems in the nondiagonal form under a simple commutativity assumption. We present tutorial examples to illustrate the instabilities that can result from switching.
In this article, we give some comments on the article 'Numerical approach to the non-linear diofantic equations with applications to the controllability of infinite dimensional dynamical systems'. The article ...
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In this article, we give some comments on the article 'Numerical approach to the non-linear diofantic equations with applications to the controllability of infinite dimensional dynamical systems'. The article gives an algorithm for the controllability analysis of the parabolic dynamical system defined in the n-D rectangular prism. The severe drawback of that algorithm is multiple nested, time-consuming loops which are necessary to perform. In the comments, we propose how to avoid performing sophisticated algorithms in that problem thanks to involving new advanced results of the number theory.
In this work, the boundary control of a distributedparameter system modelled by linear parabolic partial differential equations (PDEs) with spatially varying coefficients is studied. An infinite-dimensional state spa...
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In this work, the boundary control of a distributedparameter system modelled by linear parabolic partial differential equations (PDEs) with spatially varying coefficients is studied. An infinite-dimensional state space setting is considered and an exact transformation of the boundary actuation is realised to obtain an evolutionary model. The evolutionary model which incorporates the spatially varying coefficients of the underlying set of the PDEs is used for subsequent linear quadratic regulator synthesis. The formulated linear quadratic-state feedback controller is applied to a nonlinear model of the reactor and its performance is studied.
The effective properties of composites whose structure includes nanocontacts between bulk-phase macrocrystallites are considered. A model for such a nanostructured composite is constructed. Effective values of the the...
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The effective properties of composites whose structure includes nanocontacts between bulk-phase macrocrystallites are considered. A model for such a nanostructured composite is constructed. Effective values of the thermoelectric power, thermal and electrical conductivities, and thermoelectric figure of merit are calculated in the mean-field approximation.
We consider optimal control problems for distributedsystems unsolved for the time derivative whose performance functional does not depend on the control functions explicitly. We simultaneously use distributed and ini...
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We consider optimal control problems for distributedsystems unsolved for the time derivative whose performance functional does not depend on the control functions explicitly. We simultaneously use distributed and initial-time controls.
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