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Nature of coupling in non-conservative distributed parameter systems attached to external damping sources

MATHEMATICS AND MECHANICS OF SOLIDS 2020年第7期25卷 1367-1383页

作者： Bellos, John Inman, Daniel J. Bakas, Nikolaos Neapolis Univ Pafos Sch Architecture Engn Land & Environm Sci Paphos Cyprus Univ Michigan Dept Aerosp Engn 3064 Francxois Xavier Bagnoud Bldg1320 Beal Ave Ann Arbor MI 48109 USA

Non-conservative distributed parameter systems connected to external damping sources and possessing non-normal modes are analyzed in this work. The mathematical model of such systems is presented and real valued modal analysis is used to obtain the coupled modal equations of motion. A decoupling technique is developed using Fourier expansion, fictitious damping ratios, modal coupling parameters and pseudo forces. The method is applicable to all types of excitation. A normal mode criterion in the form of non-proportionality indices is also provided. The theoretical predictions are verified through application to a non-conservative Euler-Bernoulli beam with non-proportional damping configuration and various types of boundary conditions. Numerical examples emphasize the response errors associated with the proportional damping assumption and reveal the advantages of the proposed approach over the exact method.

关键词： distributed parameter systems non-conservative systems non-proportional damping non-normal modes damping sources

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On SISO and MIMO variable structure control of non linear distributed parameter systems: application to fixed bed reactors

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JOURNAL OF PROCESS CONTROL 2003年第8期13卷 729-737页

作者： Boubaker, O Babary, JP Ctr Urbain Nord Inst Natl Sci Appl & Technol Tunis Tunisia CNRS Lab Anal & Architect Syst Toulouse France

This paper deals with the design of variable structure control of distributed parameter systems. The control problem is discussed in relation to a model consisting of a set of non-linear, time varying partial differential equations of hyperbolic type. A formulation of a Single Input-Single Output (SISO) variable structure controller based on the distributed parameter model (late lumping control) is given. An extension to the Multiple Input-Multiple Output (MIMO) case is derived when the control variables are coupled and located on boundary conditions. A theoretical proof of DPS convergence in sliding mode is given. A fixed bed bioreactor in which drinkable water is treated, was used as a simulated example to prove the effectiveness of the control design. The bioreactor must control the harmful component concentrations in such a way that the quality of water fulfils international standards. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems variable structure control fixed bed bioreactor

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Efficiency improvement in multi-sensor wireless network based estimation algorithms for distributed parameter systems with application at the heat transfer

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EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING 2013年第1期2013卷 1-17页

作者： Volosencu, Constantin Curiac, Daniel-Ioan Politehn Univ Timisoara Dept Automat & Appl Informat Fac Automat & Comp Timisoara 300223 Romania

This paper gives a technical solution to improve the efficiency in multi-sensor wireless network based estimation for distributed parameter systems. A complex structure based on some estimation algorithms, with regression and autoregression, implemented using linear estimators, neural estimators and ANFIS estimators, is developed for this purpose. The three kinds of estimators are working with precision on different parts of the phenomenon characteristic. A comparative study of three methods - linear and nonlinear based on neural networks and adaptive neuro-fuzzy inference system - to implement these algorithms is made. The intelligent wireless sensor networks are taken in consideration as an efficient tool for measurement, data acquisition and communication. They are seen as a "distributed sensor", placed in the desired positions in the measuring field. The algorithms are based on regression using values from adjacent and also on auto-regression using past values from the same sensor. A modelling and simulation for a case study is presented. The quality of estimation is validated using a quadratic criterion. A practical implementation is made using virtual instrumentation. Applications of this complex estimation system are in fault detection and diagnosis of distributed parameter systems and discovery of malicious nodes in wireless sensor networks.

关键词： Intelligent sensor networks distributed parameter systems Estimation techniques System monitoring Virtual instrumentation

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Second-order observers for second-order distributed parameter systems in R²

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systems & CONTROL LETTERS 2008年第10期57卷 787-795页

作者： Nguyen, Tu Duc Norwegian Univ Sci & Technol Fac Informat Technol Math & Elect Engn N-7491 Trondheim Norway

This note addresses observer design for second-order distributed parameter systems in R-2. Particularly, second-order distributed parameter systems without distributed damping are studied. Based on finite number of measurements, exponentially stable observer is designed. The existence, uniqueness and stability of solutions of the observers are based on semigroup theory. (c) 2008 Elsevier B.V. All rights reserved.

关键词： distributed parameter systems observers second-order systems semigroup

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Improving control and estimation for distributed parameter systems utilizing mobile actuator-sensor network

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ISA TRANSACTIONS 2014年第4期53卷 1087-1095页

作者： Mu, Wenying Cui, Baotong Li, Wen Jiang, Zhengxian Jiangnan Univ Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Peoples R China

This paper proposes a scheme for non-collocated moving actuating and sensing devices which is unitized for improving performance in distributed parameter systems. By Lyapunov stability theorem, each moving actuator/sensor agent velocity is obtained. To enhance state estimation of a spatially distributes process, two kinds of filters with consensus terms which penalize the disagreement of the estimates are considered. Both filters can result in the well-posedness of the collective dynamics of state errors and can converge to the plant state. Numerical simulations demonstrate that the effectiveness of such a moving actuator sensor network in enhancing system performance and the consensus filters converge faster to the plant state when consensus terms are included. (C) 2014 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Moving actuator sensor network distributed parameter systems Spatial distribution Consensus filter Disagreement penalty term

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Empirical Gramian-based spatial basis functions for model reduction of nonlinear distributed parameter systems

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MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL systems 2018年第3期24卷 258-274页

作者： Jiang, Mian Wu, Jigang Zhang, Wenan Li, Xuejun Hunan Univ Sci & Technol Hunan Prov Key Lab Hlth Maintenance Mech Equipmen Xiangtan 411201 Peoples R China Hunan Univ Sci & Technol Engn Res Cent Adv Min Equipment Minist Educ Xiangtan Peoples R China

Correct selection of spatial basis functions is crucial for model reduction for nonlinear distributed parameter systems in engineering applications. To construct appropriate reduced models, modelling accuracy and computational costs must be balanced. In this paper, empirical Gramian-based spatial basis functions were proposed for model reduction of nonlinear distributed parameter systems. Empirical Gramians can be computed by generalizing linear Gramians onto nonlinear systems, which results in calculations that only require standard matrix operations. Associated model reduction is described under the framework of Galerkin projection. In this study, two numerical examples were used to evaluate the efficacy of the proposed approach. Lower-order reduced models were achieved with the required modelling accuracy compared to linear Gramian-based combined spatial basis function- and spectral eigenfunction-based methods.

关键词： distributed parameter systems model reduction spatial basis functions empirical balanced truncation

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Variable selection methods as a tool to find sensor locations for distributed parameter systems

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INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2008年第4期47卷 1184-1191页

作者： Stanimirovic, Olja Hoefsloot, Huub C. J. De Bokx, Pieter K. Smilde, Age K. Univ Amsterdam Swammerdam Inst Life Sci Biosyst Data Anal Grp NL-1018 WV Amsterdam Netherlands Philips Res Mat Anal Proc Anal NL-5656 AA Eindhoven Netherlands

The problem of finding suitable sensor locations for distributed parameter systems (DPS) is tackled as a variable selection problem. Two existing variable selection methods are used: one is based on principal component analysis (PCA) and the other on the principal variable (PV) method. A new PCA-based variable selection method, called "orthogonal variables in loading space" (OVL) is introduced. The best sensor location for DPS is dependent on sensor characteristics and also on the time interval of interest. This is illustrated in a case study where the best point in time to replace a packed bed filter is studied. Sensor positions are determined for different time intervals and different types of measurement errors. The resulting sensor positions characterize the overall time behavior of the DPS in the selected time interval. As a test, the specific problem of predicting the exit concentration of the packed bed filter is considered. Lagged PLS models are built and a full search is done to determine the best possible sensor locations. These "benchmark" sensor positions are compared to the sensor locations found by the variable selection methods. The OVL method and the PV method both perform well, but the OVL method is additionally computationally less demanding.

关键词： distributed parameter systems PRINCIPAL components analysis CONTROL theory (Mathematics) SYSTEM analysis

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An adaptive nonmonotone truncated Newton method for optimal control of a class of parabolic distributed parameter systems

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ENGINEERING WITH COMPUTERS 2020年第2期36卷 689-702页

作者： Nosratipour, Hadi Sarani, Farhad Fard, Omid Solaymani Borzabadi, Akbar Hashemi Razi Univ Dept Math Fac Sci Kermanshah Iran Univ Damghan Sch Math & Comp Sci Dept Appl Math Damghan Iran Ferdowsi Univ Mashhad Fac Math Sci Dept Appl Math Mashhad Razavi Khorasan Iran Univ Sci & Technol Mazandran Dept Appl Math Behshahr Iran

A black-box method using the finite elements, the Crank-Nicolson and a nonmonotone truncated Newton (TN) method is presented for solving optimal control problems (OCPs) governed by partial differential equations (PDEs). The proposed method finds the optimal control of a class of linear and nonlinear parabolic distributed parameter systems with a quadratic cost functional. To this end, the piecewise linear finite elements method and the well-known Crank-Nicolson method are used for discretizing in space and in time, respectively. Afterwards, regarding the implicit function theorem (IFT), the optimal control problem is transformed into an unconstrained nonlinear optimization problem. Considering that in a gradient-based method for solving optimal control problems, the evaluations of gradients and Hessians of the cost functional is important, hence, an adjoint technique is used to evaluate them effectively. In addition, to make a globalization strategy, we first introduce an adaptive nonmonotone strategy which properly controls the degree of nonmonotonicity and then incorporate it into an inexact Armijo-type line search approach to construct a more relaxed line search procedure. Finally, the obtained unconstrained nonlinear optimization problem is solved by utilizing the proposed nonmonotone truncated Newton method. Results gained from the new offered method compared with existing methods show that the new method is promising.

关键词： Optimal control distributed parameter systems Finite elements method Crank-Nicolson method Nonmonotone truncated Newton method

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Active fault-tolerant control of sampled-data nonlinear distributed parameter systems

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2012年第1期22卷 24-42页

作者： Ghantasala, Sathyendra El-Farra, Nael H. Univ Calif Davis Dept Chem Engn & Mat Sci Davis CA 95616 USA

This work presents an integrated fault detection and fault-tolerant control architecture for spatially distributed systems described by highly dissipative systems of nonlinear partial differential equations with actuator faults and sampled measurements. The architecture consists of a family of nonlinear feedback controllers, observer-based fault detection filters that account for the discrete measurement sampling, and a switching law that reconfigures the control actuators following fault detection. An approximate finite-dimensional model that captures the dominant dynamics of the infinite-dimensional system is embedded in the control system to provide the controller and fault detection filter with estimates of the measured output between sampling instances. The model state is then updated using the actual measurements whenever they become available from the sensors. By analyzing the behavior of the estimation error between sampling times and exploiting the stability properties of the compensated model, a sufficient condition for the stability of the sampled-data nonlinear closed-loop system is derived in terms of the sampling rate, the model accuracy, the controller design parameters, and the spatial placement of the control actuators. This characterization is used as the basis for deriving appropriate rules for fault detection and actuator reconfiguration. Singular perturbation techniques are used to analyze the implementation of the developed architecture on the infinite-dimensional system. The results are demonstrated through an application to the problem of stabilizing the zero solution of the KuramotoSivashinsky equation. Copyright (C) 2011 John Wiley & Sons, Ltd.

关键词： fault detection actuator reconfiguration sampled-data control distributed parameter systems wave suppression

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Nonlinear Frequency Response Analysis of distributed parameter systems with One Spatial Coordinate

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CHEMIE INGENIEUR TECHNIK 2024年第12期96卷 1604-1612页

作者： Zivkovic, Luka Petkovska, Menka Max Planck Inst Dynam Complex Tech Syst Sandtorstr 1 D-39106 Magdeburg Germany Univ Belgrade Fac Technol & Met Karnegijeva 4 Belgrade 11000 Serbia

The objective of this paper is to investigate possible strategies for applying nonlinear frequency response (NFR) analysis based on the concept of higher-order frequency response functions to distributed parameter systems. Three approaches are presented and compared: one based on applying the existing procedure directly to the partial differential model, and two based on approximation of the distributed parameter system with a series of lumped parameter segments. One of them treats the complete series of segments integrally, while the other treats it segment by segment, so it uses only the model of a single segment. A simple example, an isothermal plug-flow reactor with a simple reaction mechanism, is used as a case study. Pros and cons for all three approaches are given. The application of the nonlinear frequency response analysis based on the concept of higher-order frequency response functions to distributed parameter systems is evaluated systematically. In order to facilitate the understanding of the presented concepts, only single-input-single-output distributed parameter systems with one spatial coordinate are considered. image

关键词： distributed parameter systems Frequency response functions Lumped parameter systems Nonlinear frequency response analysis Segmentation

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