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Explicit simplicial discretization of distributed-parameter port-Hamiltonian systems

AUTOMATICA 2014年第2期50卷 369-377页

作者： Seslija, Marko Scherpen, Jacquelien M. A. van der Schaft, Arjan Univ Groningen Inst Technol Engn & Management NL-9747 AG Groningen Netherlands Univ Groningen Johann Bernoulli Inst Math & Comp Sci NL-9747 AG Groningen Netherlands

Simplicial Dirac structures as finite analogues of the canonical Stokes Dirac structure, capturing the topological laws of the system, are defined on simplicial manifolds in terms of primal and dual cochains related by the coboundary operators. These finite-dimensional Dirac structures offer a framework for the formulation of standard input output finite-dimensional port-Hamiltonian systems that emulate the behavior of distributed-parameter port-Hamiltonian systems. This paper elaborates on the matrix representations of simplicial Dirac structures and the resulting port-Hamiltonian systems on simplicial manifolds. Employing these representations, we consider the existence of structural invariants and demonstrate how they pertain to the energy shaping of port-Hamiltonian systems on simplicial manifolds. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Port-Hamiltonian systems Dirac structures distributed-parameter systems Structure-preserving discretization Discrete geometry

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Backstepping design of robust state feedback regulators for second order hyperbolic PIDEs

Backstepping design of robust state feedback regulators for ...

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2nd IFAC Workshop on the Control of systems Modeled by Partial Differential Equations (CPDE)

作者： Deutscher, J. Kerschbaum, S. Univ Erlangen Nurnberg Lehrstuhl Regelungstech Cauerstr 7 D-91058 Erlangen Germany

This contribution considers the backstepping design of robust state feedback regulators for second order hyperbolic partial integro-differential equations (PIDEs). To this end, the internal model principle is applied, which amounts to designing a stabilizing backstepping controller for a PIDE-ODE system. By transforming this system into a PDE-ODE cascade a systematic design procedure is presented. Then, robust output regulation is verified for non-destabilizing model uncertainties by means of the extended regulator equations. The results of the article are applied for the robust output regulation of a shear beam with a destabilizing boundary condition. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems hyperbolic systems robust output regulation backstepping state feedback

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Optimal Steady-State Temperature Field in an Experimental Annealing Furnace

Optimal Steady-State Temperature Field in an Experimental An...

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17th IFAC Symposium on Control, Optimization and Automation in Mining, Mineral and Metal Processing (MMM)

作者： Jadachowski, L. Steinboeck, A. Kugi, A. Vienna Univ Technol Automat & Control Inst Christian Doppler Lab Model Based Control Steel I Gusshausstr 27-29 A-1040 Vienna Austria Vienna Univ Technol Automat & Control Inst Gusshausstr 27-29 A-1040 Vienna Austria

The computation of an optimal steady-state operating point in an experimental annealing furnace is considered. In particular, the optimum spatial distribution of electric power supplied to IR-lamps is computed to ensure the temperature uniformity in the specimen fillet. A control-oriented reduced-order model of the steady-state 2D temperature distribution is derived and compared with the full-order model. Saturation functions are used to consider input constraints in a tailored optimization problem. The evaluation of the optimal control input is carried out with the full-order model. Uniqueness of the solution of the optimization problem is investigated numerically. The temperature field in the specimen fillet deviates less than 0.4% of the setpoint value if sufficient heating power is available. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Optimal operating point distributed-parameter systems Elliptic quasilinear PDE Model reduction FE method Non-equidistant grid

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Backstepping observer design for parabolic PDEs with measurement of weighted spatial averages

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AUTOMATICA 2015年 53卷 179-187页

作者： Tsubakino, Daisuke Hara, Shinji Hokkaido Univ Div Syst Sci & Informat Sapporo Hokkaido 0600814 Japan Univ Tokyo Dept Informat Phys & Comp Tokyo 1138656 Japan

This paper is concerned with the observer design for one-dimensional linear parabolic partial differential equations whose output is a weighted spatial average of the state over the entire spatial domain. We focus on the backstepping approach, which provides a systematic procedure to design an observer gain for systems with boundary measurement. If the output is not a boundary value of the state, the backstepping approach is not directly applicable to obtaining an observer gain that stabilizes the error dynamics. Therefore, we attempt to convert the error system into another system to which backstepping is applicable. The conversion is successfully achieved for a class of weighting functions, and the resultant observer realizes exponential convergence of the estimation error with an arbitrary decay rate in terms of the L-2 norm. In addition, an explicit expression of the observer gain is available in a special case. The effectiveness of the proposed observer is also confirmed by numerical simulations. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Observers Backstepping Parabolic partial differential equations Spatial averages

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A backstepping approach to the output regulation of boundary controlled parabolic PDEs

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AUTOMATICA 2015年 57卷 56-64页

作者： Deutscher, Joachim Univ Erlangen Nurnberg Lehrstuhl Regelungstech D-91058 Erlangen Germany

In this article the output regulation problem for boundary controlled parabolic systems with spatially varying coefficients is solved by applying the backstepping approach. Thereby, the outputs to be controlled are not required to be measurable and can be pointwise, distributed or boundary quantities, whereas the measurement is located at the boundary. By solving the state feedback regulator problem in the backstepping coordinates regulator equations with a simple structure result, so that their analysis and solution is facilitated. The output feedback regulator design is completed by determining a finite-dimensional reference observer and an infinite-dimensional disturbance observer. For the latter a backstepping approach is presented that consists of a triangular decoupling in the backstepping coordinates. This allows a systematic design and the explicit derivation of directly verifiable existence conditions for the disturbance observer. It is shown that for the resulting compensator the separation principle holds implying output regulation for the exponentially stable closed-loop system with a prescribed stability margin. The output regulation results of the article are illustrated by means of a parabolic system with an in-domain pointwise controlled output. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Output regulation Backstepping Boundary control Observer

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Feedforward control of a channel flow based on a discretized port-Hamiltonian model 5

Feedforward control of a channel flow based on a discretized...

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5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control

作者： Kotyczka, Paul Blancato, Antonio Tech Univ Munich Inst Automat Control D-85748 Garching Germany

systems of conservation laws can be modeled (including dissipation) in an elegant, physically insightful way within the port-Hamiltonian framework. A structure-preserving discretization renders the partial differential equations ordinary ones. In this paper, we show how the structure of the lumped-parameter state representation for two conservation laws On a One-dimensional. spatial domain can he exploited to easily formulate different (inverse) models. Based thereon, a simple modular procedure for feedforward controller design is developed, using known results from the dynamic inversion of nonminimilm-phase systems. The example of the shallow water equations serves to illustrate the design steps and to present simulation results. (C) 2015, ILAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems conservation laws port-Hamiltonian systems discretization feedforward control stable dynamic inversion

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Port-Hamiltonian Modelling for Buckling Control of a Vertical Flexible Beam with Actuation at the Bottom 5

Port-Hamiltonian Modelling for Buckling Control of a Vertica...

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5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control

作者： Trivedi, Megha V. Banavar, Ravi N. Kotyczka, Paul Indian Inst Technol Syst & Control Engn Bombay 400076 Maharashtra India Tech Univ Munich Inst Automat Control D-85748 Garching Germany

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 let in the strains while modeling these flexible 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. (C) 2015, ILAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

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

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distributed Finite Element Kalman Filter

Distributed Finite Element Kalman Filter

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European Control Conference (ECC)

作者： Battistelli, G. Chisci, L. Forti, N. Pelosi, G. Selleri, S. Univ Florence Dipartimento Ingn Informaz Via Santa Marta 3 I-50139 Florence Italy

ISBN: (纸本)9783952426937

This paper addresses state estimation for spatially distributed systems governed by linear partial differential equations from discrete in-space-and-time noisy measurements provided by sensors deployed over the spatial domain of interest. A decentralised and scalable approach is undertaken by decomposing the domain into overlapping subdomains assigned to different processing nodes interconnected to form a network. Each node runs a local finite-dimensional Kalman filter which exploits the finite element approach for spatial discretisation and the parallel Schwarz method to iteratively enforce consensus on the estimates and covariances over the boundaries of adjacent subdomains. The effectiveness of the proposed distributed consensus-based finite element Kalman filter is demonstrated via simulation experiments concerning a temperature estimation problem modelled by the bi-dimensional heat equation.

关键词： networked state estimation distributed-parameter systems finite element method Kalman filtering consensus

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Alternative Passive Maps for Infinite-Dimensional systems Using Mixed-Potential Functions 5

Alternative Passive Maps for Infinite-Dimensional Systems Us...

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5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control

作者： Kosaraju, Krishna Chaitanya Pasumarthy, Ramkrishna Jeltsema, Dimitri Indian Inst Technol Dept Elect Engn Madras 600036 Tamil Nadu India Delft Univ Technol Delft Inst Appl Math NL-2600 AA Delft Netherlands

This paper aims at developing a Brayton-Moser analogue of an infinite-dimensional system in the port-Hamiltonian framework, defined with respect to a Stokes-Dirac structure. It is shown that such a formulation leads to defining alternative passive maps, which differ from those in the port-Hamiltonian framework via a "power-like" function called the mixed-potential function. This mixed-potential function can also be used for stability analysis. We present our results for a general port-Hamiltonian system, with Maxwell's equations and the transmission line, with nonzero boundary conditions, as examples. (C) 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems infinite-dimensional systems Brayton-Moser equations gradient systems passivity port-Hamiltonian 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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