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

IFAC-PapersOnLine 2015年第13期48卷 1-6页

作者： Krishna Chaitanya Kosaraju Ramkrishna Pasumarthy Dimitri Jeltsema Dept. of Electrical Engineering Indian Institute of Technology Madras India Delft Institute of Applied Mathematics Delft University of Technology The 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.

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

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

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IFAC-PapersOnLine 2015年第13期48卷 194-199页

作者： Paul Kotyczka Antonio Blancato Institute of Automatic Control Technische Universität München 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 be 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 nonminimum-phase systems. The example of the shallow water equations serves to illustrate the design steps and to present simulation results.

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

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distributed Finite Element Kalman Filter

Distributed Finite Element Kalman Filter

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European Control Conference

作者： G. Battistelli L. Chisci N. Forti G. Pelosi S. Selleri Dipartimento di Ingegneria dell'Informazione Universita degli Studi di Firenze

ISBN: (纸本)9781467371605

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 bidimensional heat equation.

关键词： Networked state estimation distributed-parameter systems Finite element method Kalman filtering Consensus

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Hamiltonian perspective on compartmental reaction-diffusion networks

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AUTOMATICA 2014年第3期50卷 737-746页

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

Inspired by the recent developments in modeling and analysis of reaction networks, we provide a geometric formulation of the reversible reaction networks under the influence of diffusion. Using the graph knowledge of the underlying reaction network, the obtained reaction diffusion system is a distributed-parameter port-Hamiltonian system on a compact spatial domain. Motivated by the need for computer-based design, we offer a spatially consistent discretization of the PDE system and, in a systematic manner, recover a compartmental ODE model on a simplicial triangulation of the spatial domain. Exploring the properties of a balanced weighted Laplacian matrix of the reaction network and the Laplacian of the simplicial complex, we characterize the space of equilibrium points and provide a simple stability analysis on the state space modulo the space of equilibrium points. The paper rules out the possibility of the persistence of spatial patterns for the compartmental balanced reaction diffusion networks. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Reaction networks Reaction-diffusion systems distributed-parameter systems Structure-preserving discretization Weighted Laplacian matrix Interconnection Consensus

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Model predictive control of axial dispersion chemical reactor

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JOURNAL OF PROCESS CONTROL 2014年第11期24卷 1671-1690页

作者： Liu, Liu Huang, Biao Dubljevic, Stevan Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2V4 Canada

This paper discusses the development of model predictive control algorithm which accounts for the input and state constraints applied to the parabolic partial differential equations (PDEs) system describing the axial dispersion chemical reactor. Spatially varying terms arising from the nonlinear PDEs model are accounted for in model development. Finite-dimensional modal representation capturing the dominant dynamics of the PDEs system is derived for controller design through Galerkin's method and modal decomposition technique. Tustin's discretization and Cayley transform are used to obtain infinite-dimensional discrete-time dynamic modal representations which are used in subsequent constrained controller design. The proposed discrete-time constrained model predictive control synthesis is constructed in a way that the objective function is only based on the low-order modal representation of the PDEs system, while higher-order modes are utilized only in the constraints of the PDEs state. Finally, the MPC formulations are successfully applied, via simulation results, to the PDEs system with input and state constraints. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Axial dispersion chemical reactor Model predictive control Input/state constraints

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distributed parameter modeling of flexible ball screws using Ritz series discretization

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IFAC Proceedings Volumes 2014年第3期47卷 10132-10137页

作者： B. Henke O. Sawodny R. Neumann Institute for System Dynamics University of Stuttgart Pfaffenwaldring 9 70569 Stuttgart Germany Festo AG & Co. KG Ruiter Straße 82 73734 Esslingen Germany

Ball screw drives are used in automation applications and machine tools to translate rotational motion of an electric motor into translational motion of a slide. Their frequency responses show characteristic torsional and translational resonances. The resonance frequencies vary with the slide position, which is due to the distributed stiffness and inertia of the flexible ball screw. The proposed model treats the ball screw as a flexible element, using Ritz series expansions to obtain a finite approximation of the continuous deformations. The model shows excellent validation results and reproduces the variation of the resonance frequencies with high accuracy.

关键词： ball screw drive mechanical systems distributed-parameter systems modelling

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Identification of Uncertain, Spatially Varying parameters through Multilevel Sampling

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IFAC Proceedings Volumes 2014年第3期47卷 1778-1783页

作者： Hans-Werner van Wyk Department of Scientific Computing Florida State University FL 32306 USA

While stochastic sampling methods remain widely used to simulate solutions of partial differential equations with random parameters, due to ease of implementation on a parallel computing architecture, they can nevertheless carry a considerable computational cost, especially if reliable statistics are sought at high levels of spatial fidelity. Multilevel sampling methods improve upon the efficiency of traditional sampling schemes without compromising on accuracy and parallelizability, by dynamically incorporating the model's spatial discretization into the sampling procedure. Moreover, the diagnostic estimates that are computed to monitor the solution's convergence behaviour during the course of the algorithm, can be used to inform adaptive spatial refinement strategies. In this paper we leverage these properties to develop an adaptive, multilevel algorithm for identifying the statistical distribution of a spatially varying parameter from the statistical description of a related model output, based on experimental measurements.

关键词： parameter identification uncertainty statistical inference multilevel sampling adaptive algorithm distributed-parameter systems

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A Low Cost Filter Design for State and parameter Estimation in very High Dimensional systems

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IFAC Proceedings Volumes 2014年第3期47卷 3256-3261页

作者： Hong Son Hoang Remy Baraille SHOM/HOM/REC 42 av Gaspard Coriolis 31057 TOULOUSE FRANCE (Tel: 33 (0)5 67 76 68 23 SHOM/HOM/REC 42 av Gaspard Coriolis 31057 TOULOUSE FRANCE (Tel: 33 (0)5 67 76 68 44

In this paper we consider the filter design problem for very high dimensional systems. Assuming the hypothesis on separability of the vertical and horizontal structure for the error covariance, the number of unknown elements in the error covariance is reduced drastically and are estimated from generated error samples. A low-cost filtering algorithm is thus determined and parameterized up to some pertinent gain coefficients to be tuned to optimize the filter performance. Results from the experiment on assimilation of the sea surface height (SSH) into an oceanic numerical model demonstrate the high effectiveness of the proposed filtering approach.

关键词： Filtering problems Adaptation Error estimation distributed-parameter systems Environmental engineering

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Trajectory Planning For a Deep Drawing Tool

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IFAC Proceedings Volumes 2014年第3期47卷 665-670页

作者： Timo Böhm Thomas Meurer Group Tool Shops Volkswagen AG 38436 Wolfsburg Germany Chair of Automatic Control Christian-Albrechts-University Kiel 24143 Kiel Germany

Model-based trajectory planning is addressed for the realization of desired temperature trajectories for a deep drawing tool. Based on the distributed-parameter system description of the tool a finite element approximation is deduced which serves as basis for a systematic flatness-based design of a feedforward control. Trajectory assignment is considered by taking into account the minimization of a process-related objective function. Simulation and experimental data obtained from a fully equipped forming tool are presented for pure feedforward control and a two-degree-of-freedom control concept amending the feedforward part by an output error feedback controller. These confirm the applicability of the design technique and the tracking performance.

关键词： deep drawing distributed-parameter systems trajectory planning flatness temperature control experiments

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Simultaneous Boundary and distributed Feedback Control of the Current Profile in H-mode Discharges on DIII-D

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IFAC Proceedings Volumes 2014年第3期47卷 1568-1573页

作者： Mark D. Boyer Justin Barton Wenyu Shi William Wehner Eugenio Schuster John Ferron Mike Walker Dave Humphreys Francesca Turco Tim Luce Robert Johnson Benjamin Penaflor Lehigh University Bethlehem PA 18015 USA General Atomics San Diego CA 92121 USA Columbia University New York NY 10027 USA

Control of the current profile in tokamak plasmas has been shown to play an important role in achieving advanced scenarios that could enable steady-state operation. The nonlinearity and spatially distributed nature of the current profile dynamics motivate the use of model-based control designs. In this work, we consider a control-oriented model of the current profile evolution in DIII-D high-confinement (H-mode) discharges, and the problem of regulating the current profile around a desired trajectory. The PDE model is discretized in space with a finite difference method and a backstepping design is applied to obtain a transformation from the original system into a particular target system with desirable properties. The resulting boundary condition control law is complemented with control laws for the available distributed actuators. The combined control strategy uses nonlinear combinations of the total plasma current, total power, and line averaged density as actuators. Simulation and experimental results show the ability of the controller to track desired targets and to reject input disturbances.

关键词： Energy Control Nuclear Reactors Nonlinear Control distributed-parameter systems Lyapunov Stability

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