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

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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Sensitivity Reduction by Strongly Stabilizing Controllers for MIMO distributed parameter systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2012年第8期57卷 2089-2094页

作者： Wakaiki, Masashi Yamamoto, Yutaka Ozbay, Hitay Kyoto Univ Dept Appl Anal & Complex Dynam Syst Grad Sch Informat Kyoto 6068501 Japan Bilkent Univ Dept Elect & Elect Engn TR-06800 Ankara Turkey

This note investigates a sensitivity reduction problem by stable stabilizing controllers for a linear time-invariant multi-input multioutput distributed parameter system. The plant we consider has finitely many unstable zeros, which are simple and blocking, but can possess infinitely many unstable poles. We obtain a necessary condition and a sufficient condition for the solvability of the problem, using the matrix Nevanlinna-Pick interpolation with boundary conditions. We also develop a necessary and sufficient condition for the solvability of the interpolation problem, and show an algorithm to obtain the solutions. Our method to solve the interpolation problem is based on the Schur-Nevanlinna algorithm.

关键词： distributed parameter systems H-infinity-control strong stabilization

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Sensor and Actuator Placement for Proportional Feedback Control in Advection-Diffusion Equations

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IEEE CONTROL systems LETTERS 2020年第1期4卷 193-198页

作者： Veldman, D. W. M. Fey, R. H. B. Zwart, H. J. van de Wal, M. M. J. van den Boom, J. D. B. J. Nijmeijer, H. Eindhoven Univ Technol Dept Mech Engn NL-5600 MB Eindhoven Netherlands Univ Twente Fac Elect Engn Math & Comp Sci Dept Appl Math NL-7500 AE Enschede Netherlands ASML Res NL-5504 DR Veldhoven Netherlands ASML Dev & Engn NL-5504 DR Veldhoven Netherlands

In this letter, advection-diffusion equations with constant coefficients on infinite 1-D and 2-D spatial domains are considered. Suitable sensor and/or actuator locations are determined for which high-gain and low-gain proportional feedback can effectively reduce the influence of a disturbance at a point of interest. These locations are characterized by simple analytic expressions which can be used as guidelines for control system design. The obtained analytic expressions are validated by numerical results.

关键词： distributed parameter systems control system architecture PID control

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Direct Adaptive Control of Non-Minimum Phase Linear distributed parameter Models of Large Flexible Structures 12

Direct Adaptive Control of Non-Minimum Phase Linear Distribu...

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Conference on Active and Passive Smart Structures and Integrated systems XII

作者： Balas, Mark J. Frost, Susan A. Univ Tennessee Inst Space Mech Aerosp & Biomed Engn Dept Tullahoma TN 37388 USA NASA Ames Res Ctr Intelligent Syst Div POB 1M-S 269-3 Moffett Field CA 94035 USA

ISBN: (数字)9781510625907

ISBN: (纸本)9781510625891;9781510625907

Linear distributed parameter systems are governed by partial differential equations. They are linear infinite dimensional systems described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. Using a recently developed normal form for these systems, we have developed the following stability result: an infinite dimensional linear system is Almost Strictly Dissipative (ASD) if and only if its high frequency gain CB is symmetric and positive definite and the open loop system is minimum phase, i.e. its transmission zeros are all exponentially stable. In this paper, we focus on infinite dimensional linear systems that are non-minimum phase because a finite number of transmission zeros are unstable. Several methods to compensate for this issue modify the output of the infinite dimensional plant and then control this modified output rather than the original control output. Here we use a finite dimensional residual mode filter to modify the output to produce a fully minimum phase system. Then direct adaptive control for the infinite dimensional plant can use this modified output rather than the original output, to achieve ASD and produce asymptotically stability of the states on the Hilbert space. These results are illustrated by application to direct adaptive control of general linear systems on a Hilbert space that are described by operators with compact resolvent.

关键词： distributed parameter systems Flexible Mechanical Structures Adaptive Control systems

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Dissipativity for linear neutral distributed parameter systems: LOI approach

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APPLIED MATHEMATICS LETTERS 2012年第2期25卷 115-119页

作者： Tai, Zhixin Lun, Shuxian Bohai Univ Coll Engn Dept Automat Jinzhou 121013 Peoples R China

In this work dissipativity of linear neutral distributed parameter systems has been addressed. Delay-dependent sufficient conditions for the dissipativity with respect to the infinite-dimensional version of energy supply rate (Q(1), S(1), R(1)) characterized exclusively by unbounded operator Q(1) are established in terms of linear operator inequalities (LOIs). Finally, the 3-dimensional heat equation illustrates our result. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Dissipativity distributed parameter systems Heat equation Linear operator inequalities (LOIs)

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Preface: distributed parameter systems in immunology

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Mathematical Modelling of Natural Phenomena 2012年第5期7卷 1-3页

作者： Banks, H.T. Bocharov, G. Grossman, Z. Meyerhans, A. Center for Research in Scientific Computation Center for Quantitative Sciences in Biomedicine N.C. State University Raleigh NC 27695-8212 United States Institute of Numerical Mathematics Russian Academy of Sciences Moscow 119333 Russia Laboratories of Immunology and Cellular and Molecular Immunology National Institute of Allergy and Infectious Diseases National Institutes of Health Bethesda MD 20892 United States Department of Experimental and Health Sciences Universitat Pompeu Fabra Barcelona 08003 Spain Sackler Faculty of Medicine Tel Aviv University Israel

FullText for HTML: https://***/10.1051/mmnp/20127501

关键词： mathematical model distributed parameter systems immunophysiological systems virus infections

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Low-Dimension Robust Computational Algorithm for a Linear distributed parameter Water Hammer Model 23

Low-Dimension Robust Computational Algorithm for a Linear Di...

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23rd International Conference on System Theory, Control and Computing (ICSTCC)

作者： Danciu, Daniela Stinga, Florin Univ Craiova Dept Automat Control & Elect Craiova Romania

ISBN: (纸本)9781728106991

Water hammer is a hydraulic phenomenon occurring in cases of sudden load drop e.g. hydraulic turbine shutdown. These undesirable events lead to fast transients processes which require taking into account the distributed parameters. As a system with distributed parameters, the most realistic mathematical model of the water hammer phenomenon is that described by hyperbolic Partial Differential Equations. The qualitative evaluation of this phenomenon is performed by means of its computational model obtained by using a loworder robust computational algorithm previously introduced. Simulated experiments are discussed from the points of view of the engineering problem as well as of the numerical approach.

关键词： distributed parameter systems Hyperbolic Partial Differential Equations Water hammer Computational procedure

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D-Type Iterative Learning Control for Open Container Motion System With Sloshing Constraints

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IEEE ACCESS 2021年 9卷 136666-136673页

作者： Li, Guang Hou, Li Lu, Yong Guangdong Polytech Sci & Trade Sch Informat & Automat Guangzhou 510430 Peoples R China Guangdong Construct Polytech Sch Mech & Elect Engn Guangzhou 510440 Peoples R China South China Univ Technol Sch Automat Sci & Engn Guangzhou 510641 Peoples R China

In this paper, the iterative learning control (ILC) problem is investigated for the motion system of an open container with sloshing constraints in industrial fluid packaging. Initially, a broader class of second-order in space and first-order in time linear time-invariant singular distributed parameter system is decomposed by analyzing the motion system of an open container with sloshing constraints. Meanwhile, to eliminate the influence of singular terms on the system, a closed-loop D-type ILC algorithm is designed, and the corresponding convergence conditions are manifested. Then the convergence of the control algorithm is proved strictly. The resulting tracking error of systems can converge to any small tracking accuracy. Finally, a numerical example is given to verify the convergence and effectiveness of the closed-loop D-type ILC algorithm.

关键词： Liquids Containers Symmetric matrices distributed parameter systems Iterative learning control Convergence Packaging Sloshing constraints iterative learning control singular distributed parameter systems convergence analysis

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Towards implementation of PDE control for Stefan system: Input-to-state stability and sampled-data design

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AUTOMATICA 2021年 127卷 109538-109538页

作者： Koga, Shumon Karafyllis, Iasson Krstic, Miroslav Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA Natl Tech Univ Athens Dept Math Athens 15780 Greece Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA

The Stefan system is a representative model for a liquid-solid phase change which describes the dynamics of a material's temperature profile and the liquid-solid interface position. Our previous work designed a boundary feedback control to stabilize the phase interface position modeled by the Stefan system. This paper resolves two issues our previous work did not study, that are, the robustness analysis under the unknown heat loss and the digital control action. First, we introduce the one-phase Stefan problem with a heat loss by modeling a 1-D diffusion Partial Differential Equation (PDE) dynamics of the liquid temperature and the interface position governed by an Ordinary Differential Equation (ODE) with a time-varying disturbance. We focus on the closed-loop system under the control law proposed in our previous work, and show an estimate of L2 norm in a sense of Input-to-State Stability (ISS) with respect to the unknown heat loss. Second, we consider the sampled-data control of the one-phase Stefan problem without the heat loss, by applying Zero-Order-Hold (ZOH) to the control law in our previous work. We prove that the closed-loop system under the sampled-data control law satisfies the global exponential stability in the spatial L2 norm. Analogous ISS result for the two-phase Stefan problem which incorporates the dynamics of the solid phase is also obtained. Numerical simulation verifies our theoretical results for showing the robust performance under the heat loss and the digital control implemented to vary at each sampling time. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Input-to-state stability (ISS) Sampled-data system Stefan problem distributed parameter systems Nonlinear stabilization

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Network-based deployment of nonlinear multi agents over open curves: A PDE approach

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AUTOMATICA 2021年 129卷 109697-109697页

作者： Terushkin, Maria Fridman, Emilia Tel Aviv Univ Sch Elect Engn Tel Aviv Israel

Deployment of the first-order and second-order nonlinear multi agent systems over desired open (and, as a particular case, closed) smooth curves in 2D or 3D space is considered. The considered nonlinearities are globally Lipschitz. We assume that the agents have access to the local information of the desired curve and to their positions with respect to their closest neighbors (as well as to their velocities for the second-order systems), whereas in addition a leader agent is able to measure its absolute position. We assume that a small number of leaders (distributed in the spatial domain) transmit their measurements to other agents through a communication network. We take into account the following network imperfections: variable sampling, transmission delay and quantization. We propose a static output-feedback controller and model the resulting closed-loop system as a disturbed (due to quantization) nonlinear heat equation (for the first-order systems) or damped wave equation (for the second-order systems) with delayed point state measurements, where the state is the relative position of the agents with respect to the desired curve. In order to cope with the open curve we consider Neumann boundary conditions that ensure mobility of the boundary agents. We derive linear matrix inequalities (LMIs) that guarantee the input-to-state stability (ISS) of the system. The advantage of our approach is in the simplicity of the control law and the conditions. Numerical examples illustrate the efficiency of the method. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Multi-agent systems Network-based control Time-delay

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