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FREE BEAM VIBRATION ANALYSIS BASED ON THE METHOD OF INTEGRODIFFERENTIAL RELATIONS

IFAC Proceedings Volumes 2007年第14期40卷 115-119页

作者： V.V. Saurin G.V. Kostin Institute for Problems in Mechanics of the Russian Academy of Sciences

Equations describing small free oscillations of a rectilinear elastic beam with a rectangular cross section have been obtained within the framework of the linear theory of elasticity and solved using the method of integrodifferential relations (IDR). The influence of geometry and elastic characteristics on the frequencies and shapes of free beam oscillations is studied. It is shown that the longitudinal motions admit two types of displacement and internal stress fields. The lateral oscillations obtained are specified by two frequency bands, which correspond to different types of the characteristic equation roots. Numerical examples of free beam oscillations are presented and discussed. Copyright © 2002 IFAC

关键词： distributed-parameter systems Eigenvalue problems Frequency characteristics Verification

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Predictive output feedback control of parabolic partial differential equations (PDEs)

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INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2006年第25期45卷 8421-8429页

作者： Dubljevic, Stevan Christofides, Panagiotis D. Univ Calif Los Angeles Dept Chem & Biomol Engn Los Angeles CA 90095 USA

This work focuses on predictive output feedback control of linear parabolic partial differential equation (PDE) systems with state and control constraints. Under the assumption that a finite, yet sufficiently large, number of output measurements is available, two predictive output feedback controllers are constructed and sufficient conditions are derived under which these controllers enforce stability and constraint satisfaction in the infinite-dimensional closed-loop system, respectively. The controllers are applied to an example of a linear parabolic PDE with Dirichlet boundary conditions subject to state and control constraints, and the numerical simulations demonstrate their ability to enforce closed-loop system stability and constraint satisfaction.

关键词： distributed-parameter systems TRANSPORT-REACTION PROCESSES OPTIMAL ACTUATOR/SENSOR PLACEMENT DIFFUSION-PROCESSES INERTIAL MANIFOLDS MODEL-REDUCTION ROBUST-CONTROL STATE OPTIMIZATION CONSTRAINTS constraint satisfaction problems Predictive Diffusion processes enforcement System stability Partial differential equations Closed loop systems Reduced order model distributed parameter systems Constraint Output Feedback Control Controllers Robust control

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Hamiltonian formulation of distributed-parameter systems with boundary energy flow

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JOURNAL OF GEOMETRY AND PHYSICS 2002年第1-2期42卷 166-194页

作者： van der Schaft, AJ Maschke, BM Univ Twente Fac Math Sci NL-7500 AE Enschede Netherlands Univ Lyon 1 Lab Automat & Genie Procedes F-69622 Villeurbanne France

A Hamiltonian formulation of classes of distributed-parameter systems is presented, which incorporates the energy flow through the boundary of the spatial domain of the system, and which allows to represent the system as a boundary control Hamiltonian system. The system is Hamiltonian with respect to an infinite-dimensional Dirac structure associated with the exterior derivative and based on Stokes' theorem. The theory is applied to the telegraph equations for an ideal transmission line, Maxwell's equations on a bounded domain with non-zero Poynting vector at its boundary, and a vibrating string with traction forces at its ends. Furthermore, the framework is extended to cover Euler's equations for an ideal fluid on a domain with permeable boundary. Finally, some properties of the Stokes-Dirac structure are investigated, including the analysis of conservation laws. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： distributed-parameter systems Hamiltonian systems boundary variables Dirac structures Stokes' theorem conservation laws

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IDENTIFICATION OF FINITE-DIMENSIONAL MODELS FOR distributed-parameter systems

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IFAC Proceedings Volumes 2002年第1期35卷 301-306页

作者： Daniel Coca Stephen A. Billings Department of Automatic Control & Systems Engineering University of Sheffield Mappin Street Sheffield S1 3JD UK

This paper addresses the problem of obtaining finite dimensional models of distributed-parameter systems from measurement data using system identification. The data are used to construct approximations of the solution and the forcing function in a finite dimensional space, which are expressed in terms of a finite element basis. A discrete time model is then identified based on the resulting finite dimensional coordinate vector. The existence and convergence of such a representation is established for a class of abstract first order systems. The proposed approach is illustrated in practice using simulated noise contaminated data.

关键词： distributed-parameter systems Finite Element Solutions Identification Algorithms Interpolation Approximation System Identification

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DYNAMIC PROCESS MODELING USING FUZZY SUBMODELS

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IFAC Proceedings Volumes 2005年第1期38卷 221-226页

作者： Ben H.L. Betlem Pascal F. van Lith Brian Roffel Faculty for Science and Technology University of Twente P.O.Box 217 7500 AE Enschede The Netherlands

This article discusses a new modular design approach for hybrid models consisting of a dynamic framework augmented with static fuzzy sub-models. As the framework is physically based, the models have a dynamic behaviour that corresponds well with the original process. Their fit to process data assures good steady state behaviour and corrects the dynamic behaviour for assumptions and simplifications. The hybrid model design is illustrated for three dynamically different processes: an ideally mixed, a distributed and a chained process.

关键词： dynamic modelling fuzzy modelling distributed-parameter systems lumped parameter systems polymer reactor pulp digester batch distillation column

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BOUNDARY CONTROL systems AND THE SYSTEM NODE

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IFAC Proceedings Volumes 2005年第1期38卷 308-313页

作者： J.A. Villegas Y. Le Gorrec H. Zwart A.J. van der Schaft University of Twente Department of Applied Mathematics PO Box 217 7500 AE Enschede The Netherlands LAGEP UCB Lyon 1 – UMR CNRS 5007 Bât. 308 G 43 Bd du 11 nov. 1918 69622 Villeurbanne cedex France

In this paper we show how to formulate a boundary control system in terms of the system node, that is, as an operator where X is the state space and Y is the output space. Here we give results which show how to find the top part of this operator and its domain in an easy way. For a class of boundary control systems, associated with a skew-symmetric differential operator, we completely identify the system node. Some results about stability and approximate observability are presented for this class of systems.

关键词： Boundary value problem distributed-parameter systems controllability stability

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ON REGULATOR DESIGN FOR SPATIAL TEMPERATURE DISTRIBUTION USING FINITE-DIMENSIONAL MODELING OF HEAT EQUATIONS

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IFAC Proceedings Volumes 2005年第1期38卷 119-124页

作者： Jun Imai Yasuaki Ando Masami Konishi Tatsushi Nishi Dept. Electrical and Electronic Eng. Okayama University JAPAN

A regulator problem for a heat conduction system, of which the eigenstructure is just partially known, is formulated to design a stabilizing controller that keeps a performance index less than a prescribed value. The index is made of the spatio integral of the squared deviation from reference temperature distribution. It is shown that through characterizing frequency response from input to temperature at each spatial point, a distributed parameter system with nominal model and additive uncertainty weight, both of which are real rational, is reconstructed using knowledge of the eigenstructure. A main result claims that the formulated problem is reduced to a standard mixed H 2 / H ∞ one for a linear finite dimensional time-invariant system. Numerical study demonstrates feasibility of the proposed design scheme.

关键词： distributed-parameter systems Uncertainty Modeling errors

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OPTIMAL OPERATION OF THIN FILM GROWTH WITH MULTISCALE PROCESS OBJECTIVES

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IFAC Proceedings Volumes 2005年第1期38卷 315-320页

作者： Amit Varshney Antonios Armaou Department of Chemical Engineering The Pennsylvania State University University Park PA-16802 USA

The issue of optimal time-varying operation for transport-reaction processes is considered, when the cost functional and/or equality constraints necessitate the consideration of phenomena that occur over disparate length scales. Multiscale process models are initially developed, linking continuum conservation laws with microscopic scale simulators. Subsequently, order reduction techniques for dissipative partial-differential equations are combined with adaptive tabulation methods for microscopic simulators to reduce the computational requirements of the optimization problem, which is then solved using standard search algorithms. The method is demonstrated on a thin film deposition process, where optimal surface temperature profiles and inlet switching times that simultaneously maximize thickness uniformity and minimize surface roughness across the film surface are computed.

关键词： optimization distributed-parameter systems order reduction process control complex systems

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SOLVING OPTIMAL FEEDBACK CONTROL OF CHINESE POPULATION DYNAMICS BY VISCOSITY SOLUTION APPROACH

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IFAC Proceedings Volumes 2005年第1期38卷 489-494页

作者： Bing Sun Bao-Zhu Guo Institute of Systems Science Academy of Mathematics and System Sciences Academia Sinica Beijing 100080 China

In this paper, the optimal birth feedback control of a McKendrick type age-structured population dynamic system based on the Chinese population dynamics is considered. Adopt the dynamic programming approach, to obtain the Hamilton-Jacobi-Bellman equation and prove that the value function is its viscosity solution. By the derived classical verification theorem, the optimal birth feedback control is found explicitly. A finite dierence scheme is designed to solving numerically the optimal birth feedback control. Under the same constraint, by comparing with dierent controls, the validity of the optimality of the obtained control is verified numerically.

关键词： Numerical solutions Finite dierence Optimal control Feedback control Dynamic programming distributed-parameter systems Optimality

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OPTIMAL CONTROL OF DISPERSIVE TUBULAR CHEMICAL REACTORS: PART I

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IFAC Proceedings Volumes 2005年第1期38卷 621-626页

作者： F. Logist I.Y. Smets J.F. Van Impe Bio TeC Department of Chemical Engineering Katholieke Universiteit Leuven W. de Croylaan 46 B-3001 Leuven Belgium

This paper, the first of a series of two, deals with the determination of optimal steady-state jacket fluid temperature profiles for dispersive tubular chemical reactors, ranging from plug flow to perfectly mixed reactors. According to Pontryagin's minimum principle, the optimal control is of the bang-bang type for the proposed terminal cost criterion. The bang-bang switching position is numerically optimised, by means of a weighted shooting-type procedure for the determination of the reactor profiles, ensuring the Danckwerts boundary conditions are satisfied. Following this procedure the impact of dispersion on the optimised profiles is illustrated. In the second paper, the performance of the obtained optimal control laws will be compared with that of practically more feasible controls. Furthermore, the transient behaviour will be assessed.

关键词： chemical industry distributed-parameter systems model-based control optimal control reactor control second-order systems

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