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Riccati equations for second order spatially invariant partial differential systems

AUTOMATICA 2012年第1期48卷 139-144页

作者： Curtain, Ruth F. Univ Groningen Dept Math NL-9700 AV Groningen Netherlands

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.

关键词： distributed parameter systems Riccati equations Spatially invariant systems

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Controlling aggregate thin film surface morphology for improved light trapping using a patterned deposition rate profile

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CHEMICAL ENGINEERING SCIENCE 2012年第1期67卷 101-110页

作者： Zhang, Xinyu Huang, Jianqiao Hu, Gangshi Orkoulas, Gerassimos Christofides, Panagiotis D. Univ Calif Los Angeles Dept Chem & Biomol Engn Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90095 USA

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.

关键词： Surface mean slope Surface roughness Light trapping optimization Model predictive control distributed parameter systems Thin film growth

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Drug Delivery Using Stimuli-Responsive Polymer Gel Spheres

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INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2012年第4期51卷 1741-1755页

作者： Ninawe, Pravin R. Parulekar, Satish J. IIT Dept Chem & Biol Engn Chicago IL 60616 USA

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 distributed parameter 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.

关键词： POLYMER colloids DEFORMATIONS (Mechanics) MACROMOLECULES MATHEMATICAL models DRUG delivery systems distributed parameter systems LUMPED parameter systems PHARMACEUTICAL chemistry

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Dynamic Optimization of a Polymer Flooding Process Based on Implicit Discrete Maximum Principle

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MATHEMATICAL PROBLEMS IN ENGINEERING 2012年第1期2012卷 1-23页

作者： Lei, Yang Li, Shurong Zhang, Xiaodong Zhang, Qiang Guo, Lanlei China Univ Petr Coll Informat & Control Engn Qingdao 266580 Peoples R China Sinopec Shengli Oilfield Co Res Inst Geol Sci Dongying 257015 Peoples R China

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.

关键词： ENHANCED oil recovery OPTIMAL control theory distributed parameter systems POLYMERS MAXIMUM principles (Mathematics)

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A stochastic model for electrodeposition process with applications in filtering and boundary control

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INTERNATIONAL JOURNAL OF CONTROL 2012年第12期85卷 1807-1826页

作者： Tenno, R. Aalto Univ Sch Elect Engn Aalto Finland

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.

关键词： stochastic process distributed parameter systems filtering boundary control

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Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2012年第2期57卷 291-301页

作者： Amin, Saurabh Hante, Falk M. Bayen, Alexandre M. MIT Dept Civil & Environm Engn Cambridge MA 02139 USA Heidelberg Univ Interdisciplinary Ctr Sci Comp IWR D-69120 Heidelberg Germany Univ Calif Berkeley Dept Civil & Environm Engn Berkeley CA 94704 USA

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.

关键词： distributed parameter systems stability of hybrid systems switched systems

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Comments on 'Numerical approach to the non-linear diofantic equations with applications to the controllability of infinite dimensional dynamical systems', International Journal of Control, 78 (13), (2005), pp. 1017-1030

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INTERNATIONAL JOURNAL OF CONTROL 2012年第11期85卷 1802-1805页

作者： Respondek, Jerzy Stefan Silesian Tech Univ Inst Comp Sci Fac Automat Control Elect & Comp Sci PL-44100 Gliwice Poland Higher Sch Finance & Law Bielsko Biala PL-43382 Bielsko Biala Poland

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.

关键词： controllability distributed parameter systems partial differential equations

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LQ-boundary control of a diffusion-convection-reaction system

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INTERNATIONAL JOURNAL OF CONTROL 2012年第2期85卷 171-181页

作者： Mohammadi, L. Aksikas, I. Dubljevic, S. Forbes, J. F. Univ Alberta Dept Chem & Mat Engn Edmonton AB Canada King Abdulaziz Univ Dept Math Jeddah 21413 Saudi Arabia

In this work, the boundary control of a distributed parameter 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.

关键词： distributed parameter systems parabolic PDEs LQ controller boundary control

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Thermoelectric figure of merit for bulk nanostructured composites with distributed parameters

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SEMICONDUCTORS 2012年第5期46卷 659-665页

作者： Snarskii, A. A. Sarychev, A. K. Bezsudnov, I. V. Lagarkov, A. N. Natl Tech Univ Kyiv Polytech Inst UA-03056 Kiev Ukraine Russian Acad Sci Inst Theoret & Appl Electromagnet Moscow 125412 Russia Nauka Serv Sci & Prod Co Moscow 103473 Russia

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.

关键词： THERMOELECTRICITY distributed parameter systems NANOCOMPOSITE materials THERMAL conductivity ELECTRIC conductivity TEMPERATURE SEMICONDUCTORS

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Problems with a robust mixed control for the linearized Boussinesq equation

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DIFFERENTIAL EQUATIONS 2012年第4期48卷 574-585页

作者： Plekhanova, M. V. Islamova, A. F. Chelyabinsk State Univ Chelyabinsk Russia

We consider optimal control problems for distributed systems unsolved for the time derivative whose performance functional does not depend on the control functions explicitly. We simultaneously use distributed and ini... 详细信息

关键词： CONTROL theory (Mathematics) distributed parameter systems BOUNDARY value problems DIFFERENTIAL equations MATHEMATICAL analysis

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