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Simulation, Stability and Blow-Up of a Non-Linear Heat Process

IFAC Proceedings Volumes 2012年第2期45卷 1271-1276页

作者： M. Vajta Department of Applied Mathematics University of Twente P.O.Box 217 7500 AE Enschede The Netherlands (Tel: 31-53-489-3372)

Abstract We consider a one-dimensional heat process with exponential internal heat source described by a second order, non-linear, parabolic partial differential equation. The model can describe various physical processes from electric space charge problem, diffusion-reaction processes, some nuclear process or explosion. Due to the exponential heat source, stability is of prime interest. We investigate under which conditions (i.e. boundary conditions, parameters etc.) the process remains stable and provide the stability region for different boundary conditions. Another important question concerns what happens if the source gain exceeds the stability limit. Then, inevitably, a blow-up (explosion) happens, that is, given sufficient time, the temperature will grow unbounded. In this case it is important to estimate the time until blow-up. Based on reasonable assumptions we provide a good estimate for the blow-up time. Computer simulations verified the results.

关键词： distributed parameter systems partial differential equations stability domains blow-up

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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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Application of Proper Orthogonal Decomposition to Particulate Processes

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IFAC Proceedings Volumes 2012年第2期45卷 728-733页

作者： Michael Mangold Mykhaylo Krasnyk Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg Germany (Tel: +49-391-6110361) Donetsk National Technical University Faculty of Computer Science and Technology Donetsk Ukraine

Abstract Particulate processes like industrial crystallisation or granulation are often described by population balances. This leads to mathematical models containing partial integro differential equations. In many cases, the flow conditions of the fluid phase have a strong impact on the particle formation. To describe this properly, Navier Stokes equations have to be solved in addition. The resulting model equation system is too complicated to apply them to typical process control tasks. Reduced models are desirable. In this contribution, the use of proper orthogonal decomposition is suggested as a powerful reduction method. The usefulness of the approach is illustrated by two application examples: a granulation process with particle aggregation and a crystallisation process with particle growth and complex fluid dynamics.

关键词： particulate processing distributed parameter systems nonlinear systems model reduction population balance system proper orthogonal decomposition crystallisation granulation

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Output Regulation for General Infinite-Dimensional Exosystems

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IFAC Proceedings Volumes 2012年第13期45卷 168-173页

作者： L. Paunonen S. Pohjolainen Department of Mathematics Tampere University of Technology PO. Box 553 33101 Tampere Finland

In this paper we study output regulation of distributed parameter systems with infinite-dimensional exosystems. The purpose of the paper is to find simple and minimal conditions on the signal generator under which the solvability of the output regulation problem can be characterized by the solvability of the regulator equations. We also study the properties of the dynamic steady state of the closed-loop system and the uniqueness of the solution of Sylvester operator equations. The presented results have applications in robust regulation of infinite-dimensional systems.

关键词： Robust output regulation distributed parameter systems infinite-dimensional exosystems

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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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Model reduction of a batch drum granulator by proper orthogonal decomposition

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IFAC Proceedings Volumes 2012年第15期45卷 856-861页

作者： Michael Mangold Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg Germany (Tel: +49-391-6110361)

Particle processes with agglomeration or breakage are often described by population balances. This leads to mathematical models containing partial integro differential equations. It is quite challenging to solve such equations numerically and to apply them to process control tasks. Reduced models for agglomeration and breakage processes are desirable. In this contribution, the use of proper orthogonal decomposition is suggested as a method to derive such reduced models. The reduction method is applied to a batch granulator. A low order model is formulated and found to be in good agreement with the reference model. The usefulness of the low order model is demonstrated by applying it to an optimal control problem.

关键词： particulate processing distributed parameter systems nonlinear systems model reduction optimal control population balance system proper orthogonal decomposition granulation

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Advanced State Estimation Techniques for Packed Bed Reactors

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IFAC Proceedings Volumes 2012年第15期45卷 519-524页

作者： Sreenivasa Rao Pacharu Ravindra Gudi Sachin Patwardhan Deapartment of chemical engineering IIT Bombay Powai Mumbai-400076 INDIA

This work focuses on the evaluation of some of the advanced recursive state estimation techniques applied to packed bed reactors. Tubular, packed or fixed bed reactors are typically modeled as infinite dimensional partial differential equations, also called distributed parameter systems (DPS). Discretization methods such as orthogonal collocation or any other polynomial approximation can be used to convert these DPS into a set of Ordinary Differential Equations (ODE) or Differential Algebraic Equations (DAE), that are more suitable for application of the estimation algorithms. Here we demonstrate the superior performance of the Ensemble Kalman Filter over its other variants (EKF and UKF) for a tubular reactor model. This work also includes the evaluation of the constrained forms of these algorithms for the same tubular reactor model and the results show that the Constrained EnKF which is a nondeterministic approach is able to estimate the states accurately and is less susceptible to numerical errors unlike the Constrained UKF and Constrained EKF which encounter the problem of the covariance matrix becoming negative definite.

关键词： Packed Bed Reactors distributed parameter systems State Estimation Kalman Filters Constrained State Estimation

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Electrodeposition Process Filtering and Boundary Control

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IFAC Proceedings Volumes 2012年第25期45卷 206-211页

作者： R. Tenno Aalto University School of Electrical Engineering P.O. Box 15500 Aalto Finland

Electrodeposition process filtering and boundary control problem is solved in this paper based on a stochastic model that depends on a finite number of Wiener processes. The problem is 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 in an interval with the Dirichlet data on one end (bulk solution) and Neumann data on the other end (cathode surface). Since the concentration of oxidizing species is unattainable for observations the flux on the boundary is measured with a sensor noise. The total flux of the main reaction and side reactions is controlled by the electric current measurements on the cathode while the disturbing effect of the side reactions is considered 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 PDE in dependence on the covariance kernel. A relatively good quality of estimation and control is demonstrated in 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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An Integrodifferential Approach to Adaptive Control Design for Heat Transfer systems with Uncertainties

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IFAC Proceedings Volumes 2012年第2期45卷 520-525页

作者： Vasily Saurin Georgy Kostin Andreas Rauh Luise Senkel Harald Aschemann Institute for Problems in Mechanics of the Russian Academy of Sciences Moscow Russia Chair of Mechatronics University of Rostock Rostock Germany

Abstract Open-loop and closed-loop control problems for distributed parameter systems, described by parabolic partial differential equations, are considered in this contribution. The goal of the study is the development of strategies for control and estimation of states, disturbances, and parameters. These strategies are based on the method of integrodifferential relations, a projection approach, and a suitable finite element technique. A real-time applicable control algorithm is proposed and its specific features are discussed. A verification of the control laws derived in this contribution is performed taking into account explicit error estimates resulting directly from the integrodifferential approach. The parameters, geometry, and actuation principles of a heat transfer system available at the Chair of Mechatronics, University of Rostock, are used for the numerical simulation and experimental validation. The test setup consists of a metallic rod equipped with a finite number of Peltier elements which are used as distributed control inputs allowing for active cooling and heating.

关键词： Heat transfer adaptive control optimal control distributed parameter systems

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MODELLING, IDENTIFICATION AND SIMULATION OF A DOUBLE CLOSED-LOOP INDUSTRIAL WET GRINDING CIRCUIT

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IFAC Proceedings Volumes 2012年第23期45卷 72-77页

作者： Moïse Mukepe Kahilu Michel Kinnaert Pierre Kalenga Ngoy Jean-Marie Moanda Ndeko Department of Automatic Control and Systems Analysis Université Libre de Bruxelles (ULB) 50 Av F.D. Roosevelt 1050 Brussels e-mail:{mmukepek michel.kinnaert}@ulb.ac.be Polytechnic Faculty Université de Lubumbashi (UNILU) DR Congo e-mail:kalenga.ngoy@unilu.ac.cd Polytechnic Faculty Université de Kinshasa (UNIKIN) DR Congo e-mail: jmariemoanda@unikin.cd

In this paper, a comprehensive approach for modelling, parameter estimation and global simulation of the grinding circuit of the Kolwezi Concentrator is presented. This process can be described by a nonlinear distributed parameter system. To differentiate between wet and dry grinding, the derived model takes into account the increase of the specific rate of breakage in the wet grinding process. In order to determine material transport dynamics within the mills, a new experimental method has been developed. Due to the lack of a colorant or a radioactive sensor, this procedure is based on the use of the G41 foaming as tracer. Both steady-state and dynamic simulation results are discussed and are shown to be in agreement with the experimental data.

关键词： Concentrators distributed parameter systems dynamic modelling multi-input/multi-output systems nonlinear models process parameter estimation process simulators

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