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Output feedback boundary control of heterodirectional semilinear hyperbolic systems

AUTOMATICA 2020年 117卷 108990-108990页

作者： Strecker, Timm Aamo, Ole Morten Cantoni, Michael Univ Melbourne Dept Elect & Elect Engn Parkville Vic 3010 Australia Norwegian Univ Sci & Technol NTNU Dept Engn Cybernet N-7491 Trondheim Norway

We solve the problem of stabilizing a general class of 1-d semilinear hyperbolic systems with an arbitrary number of states convecting in each direction and with the actuation and sensing restricted to one boundary. The control design is based on the dynamics on the characteristic lines along which the inputs propagate through the domain and the predictability of states in the interior of the domain up to the time they are affected by the inputs. In the context of broad solutions, the state-feedback controller drives systems with globally Lipschitz nonlinearities from an arbitrary initial condition to the origin in minimum time. Alternatively, it is possible to satisfy a tracking objective at the uncontrolled boundary or, for systems with C-1-coefficients and initial conditions, to design the control inputs to obtain classical C-1-solutions that also reach the origin in finite time. Further, we design an observer that estimates the distributed state from boundary measurements only. The observer combined with the state-feedback controller solves the output-feedback control problem. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Hyperbolic partial differential equations distributed-parameter systems Boundary control Stabilization Estimation

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distributed input observers to integrate satellite data with 3-D atmospheric models

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COMPUTERS & CHEMICAL ENGINEERING 2019年 130卷 106525-000页

作者： McGuffin, Dana L. Ydstie, B. Erik Adams, Peter J. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA Carnegie Mellon Univ Ctr Atmospher Particulate Studies Pittsburgh PA 15213 USA

Chemical transport models (CTMs) simulate the concentration of gas pollutants and particulate matter in the atmosphere. Most CTMs include significant model mismatch from the true atmosphere due to uncertainty in the inputs like meteorology and emission fields, extrapolation and simplification of experimentally-derived relationships for the process dynamics, and possibly un-accounted for atmospheric processes. In this paper we estimate uncertain parameters by utilizing daily satellite measurements of aerosol optical depth, related to particulate matter. A passivity-based input observer (PBIO) projects the high-dimensional CTM to a set of inventory variables. The passive system, in which the input and output is based on the inventories, is stable with proportional feedback. We integrate distributed PBIOs with a 3D CTM to estimate time-varying sea spray emission scaling factors across the Southern Ocean band. We find the measurement error decreases from 305% to 55% by utilizing distributed PBIOs. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Observers parameter estimation Atmospheric model Inverse modeling distributed-parameter systems

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Fault diagnosis for linear heterodirectional hyperbolic ODE-PDE systems using backstepping-based trajectory planning

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AUTOMATICA 2022年 135卷 109952-109952页

作者： Fischer, Ferdinand Deutscher, Joachim Univ Ulm Inst Mess Regel & Mikrotech Albert Einstein Allee 41 D-89081 Ulm Germany

This paper is concerned with the fault diagnosis problem for general linear heterodirectional hyperbolic ODE-PDE systems. A systematic solution is presented for additive time-varying actuator, process and sensor faults in the presence of disturbances. The faults and disturbances are represented by the solutions of finite-dimensional ODEs, which allow to take a large class of signals into account. For disturbances, that are only bounded, a threshold for secured fault diagnosis is derived. By applying integral transformations to the system an algebraic fault detection equation to detect faults in finite time is obtained. The corresponding integral kernels result from the realization of a finite-time transition between a non-equilibrium initial state and a vanishing final state of a hyperbolic ODE-PDE system. For this new challenging problem, a systematic trajectory planning approach is presented. In particular, this problem is facilitated by mapping the kernel equations into backstepping coordinates and tracing the solution of the transition problem back to a simple trajectory planning. The fault diagnosis for a 4 x 4 heterodirectional hyperbolic system coupled with a second order ODE demonstrates the results of the paper. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Hyperbolic systems Fault diagnosis Backstepping Motion planning

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The Modeling and Control of (Renewable) Energy systems by Partial Differential Equations-An Overview

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ENERGIES 2023年第24期16卷 8042页

作者： Radisavljevic-Gajic, Verica Karagiannis, Dimitri Gajic, Zoran Ajman Univ Dept Mech Engn POB 346 Ajman U Arab Emirates Penn State Univ Berks Div Engn Business & Comp Reading PA 19610 USA Rutgers State Univ Dept Elect & Comp Engn 94 Brett Rd Piscataway NJ 08854 USA

Mathematical models of energy systems have been mostly represented by either linear or nonlinear ordinary differential equations. This is consistent with lumped-parameter dynamic system modeling, where dynamics of system state variables can be fully described only in the time domain. However, when dynamic processes of energy systems display both temporal and spatial evolutions (as is the case of distributed-parameter systems), the use of partial differential equations is necessary. distributed-parameter systems, being described by partial differential equations, are mathematically (and computationally) much more difficult for modeling, analysis, simulation, and control. Despite these difficulties in recent years, quite a significant number of papers that use partial differential equations to model and control energy processes and systems have appeared in journal and conference publications and in some books. As a matter of fact, distributed-parameter systems are a modern trend in the areas of control systems engineering and some energy systems. In this overview, we will limit our attention mostly to renewable energy systems, particularly to partial differential equation modeling, simulation, analysis, and control papers published on fuel cells, wind turbines, solar energy, batteries, and wave energy. In addition, we will indicate the state of some papers published on tidal energy systems that can be modelled, analyzed, simulated, and controlled using either lumped or distributed-parameter models. This paper will first of all provide a review of several important research topics and results obtained for several classes of renewable energy systems using partial differential equations. Due to a substantial number of papers published on these topics in the past decade, the time has come for an overview paper that will help researchers in these areas to develop a systematic approach to modeling, analysis, simulation, and control of energy processes and systems whose time

关键词： fuel cells solar cells wind turbines batteries wave energy and tidal energy distributed-parameter systems simulation

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Reduction of Stokes-Dirac structures and gauge symmetry in port-Hamiltonian systems

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IFAC Proceedings Volumes 2012年第19期45卷 114-119页

作者： Marko Seslija Arjan van der Schaft Jacquelien M.A. Scherpen Department of Discrete Technology and Production Automation Faculty of Mathematics and Natural Sciences University of Groningen Nijenborgh 4 9747 AG Groningen The Netherlands Johann Bernoulli Institute for Mathematics and Computer Science University of Groningen Nijenborgh 9 9747 AG Groningen The Netherlands

Stokes-Dirac structures are infinite-dimensional Dirac structures defined in terms of differential forms on a smooth manifold with boundary. These Dirac structures lay down a geometric framework for the formulation of Hamiltonian systems with a nonzero boundary energy flow. Simplicial triangulation of the underlaying manifold leads to the so-called simplicial Dirac structures, discrete analogues of Stokes-Dirac structures, and thus provides a natural framework for deriving finite-dimensional port-Hamiltonian systems that emulate their infinite-dimensional counterparts. The port-Hamiltonian systems defined with respect to Stokes-Dirac and simplicial Dirac structures exhibit gauge and a discrete gauge symmetry, respectively. In this paper, employing Poisson reduction we offer a unified technique for the symmetry reduction of a generalized canonical infinite-dimensional Dirac structure to the Poisson structure associated with Stokes-Dirac structures and of a fine-dimensional Dirac structure to simplicial Dirac structures. We demonstrate this Poisson scheme on a physical example of the vibrating string.

关键词： Port-Hamiltonian systems Poisson structures Dirac structures distributed-parameter systems symmetry reduction

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On distributed port-hamiltonian process systems

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IFAC Proceedings Volumes 2004年第13期37卷 973-978页

作者： Ricardo Lopezlena Jacquelien M.A. Scherpen Instituto Mexicano del Petr6leo (IMP) Eje Central Lázaro Cárdenas 152 Col. San Bartolo Atepehuacan CP 07730 México D.F. México Apdo.Postal 14-805 Tel. +52-9/75-7623 Fax +3/-15-2786679 Delft Center of Systems and Control Delft University of Technology Mekelweg 2 CD Delft The Netherlands Tel. +31-15-278 5489 Fax +3/-15-2786679

In this paper we use the term distributed port-Hamiltonian Process systems (DPHPS) to refer to the result of merging the theory of distributed Port-Hamiltonian systems (DPHS) with the theory of process systems (PS). Such concept is useful for combining the systematic interconnection of PHS with the thermodynamic-passivity properties of PS. Furthermore the systematic methods of control developed for PHS are then expected to be applicable for process systems.

关键词： distributed-parameter systems Process systems Models Energy systems Nonlinear systems

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Port-Hamiltonian Modelling for Buckling Control of a Vertical Flexible Beam with Actuation at the Bottom

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IFAC-PapersOnLine 2015年第13期48卷 31-38页

作者： Megha V. Trivedi Ravi N. Banavar Paul Kotyczka Systems and Control Engineering Indian Institute of Technology Bombay Mumbai 400076 Institute of Automatic Control Technische Universität München 85748 Garching

The use of beams and similar structural elements is finding increasing application in many areas, including micro and nanotechnology devices. For the purpose of buckling analysis and control, it is essential to account for nonlinear terms in the strains while modeling these exible structures. Further, in modeling of micro and nanotechnology devices, the micro length scale parameter effects can be accounted by the use of a 2 dimensional stress-strain relationship. This paper studies the buckling effect for a slender, vertical beam with a tip-mass at one end and fixed on a movable platform at the other. For the purpose of illustration, the movable platform is assumed to be a cart. Accounting for a 2 dimensional stress-strain relationship, nonlinear expressions for strains, and incorporating an inextensibility constraint of the beam, the Hamiltonian equations of motion are obtained. The equations of motion are then cast in a port-Hamiltonian form with appropriately defined flows and efforts. We then carry out a preliminary modal analysis of the system to describe candidate post-buckling configurations and study the stability properties of these equilibria. The vertical configuration of the beam under the action of gravity is without loss of generality, since the objective is to model a potential field that determines the equilibria.

关键词： Nonlinear beam model distributed-parameter systems port-Hamiltonian systems boundary conditions buckling

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Prescribed-Time Stabilization of ODEs with Diffusive Actuator Dynamics

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IFAC-PapersOnLine 2021年第9期54卷 434-439页

作者： Drew Steeves Miroslav Krstic Department of Mechanical & Aerospace Engineering University of California San Diego CA

We study the finite-time stabilization of an ODE plant having diffusive infinite-dimensional actuator dynamics. We follow a predictor-feedback approach relying on time-varying backstepping, where the actuator utilizes time-dependent gains selected to stabilize the actuator dynamics as well as the plant within a finite time which can be prescribed independently of the system’s initial conditions. As the attenuative actuator dynamics cascade into the ODE, the time-varying feedback gains result in cascading backstepping kernel PDEs. We utilize differential flatness of the kernel PDE as well as the method of successive approximations in order to recover these kernels.

关键词： distributed-parameter systems linear systems differential flatness backstepping

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MODEL BASED PREDICTIVE CONTROL OF RIVER RESERVOIRS

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IFAC Proceedings Volumes 2002年第1期35卷 367-372页

作者： Hartmut Linke Eckhard Arnold Technische Universität Ilmenau P. O. Box 100565 D-98684 Ilmenau Germany Fraunhofer Appl. Center for Systems Technology Am Ehrenberg 8 D-98693 Ilmenau Germany

The operational water management of river reservoirs has to consider different and sometimes competitive objectives, e. g. navigation conditions, hydro-power generation, flood protection and environmental aspects. Despite of problem specific extensions to cover the non-linear process behavior the application of local standard (PI) controllers to each reservoir can fulfill only basic management requirements. MBPC algorithms have the capability to give a wide and time proper exploitation of the active storage of the whole cascade. A two-layer control structure, consisting of a predictive controller in the upper layer and local controllers at each barrage, allows to provide the management decisions under real time conditions. Simulation results for three reservoirs of the river Moselle show the aptitude of the proposed approach.

关键词： river reservoir systems model predictive control distributed-parameter systems

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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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