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19th International Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2022

作者： Hernandez-Villa, Luis Melchor-Aguilar, Daniel Silva-Navarro, Gerardo Ipicyt Division of Control and Dynamical Systems San Luis Potosí Mexico Cinvestav Cdmx Mechatronics Section Dept. Electrical Eng. Mexico

ISBN: (数字)9781665455084

ISBN: (纸本)9781665455084

This paper deals with Delayed Resonators (DR) with delayed position and velocity feedback. This special type of DR was recently introduced in the literature and theoretically shown to bring a Single-Degree-of-Freedom (SDOF) system into a resonator. In principle, this induced resonance in an SDOF system can be used as a conventional dynamic vibration absorber, when interconnected to a primary system subject to exogenous vibrations, with capabilities to improve the tuning into better frequency ranges. In the current paper, we propose a design and control implementation in an experimental platform of the DR with delayed position and velocity, including some numerical and experimental validations. © 2022 IEEE.

关键词： Resonators

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On the stability and null-controllability of an infinite system of linear differential equations

arXiv

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arXiv 2021年

作者： Azamov, Abdulla Ibragimov, Gafurjan Mamayusupov, Khudoyor Ruziboev, Marks Section of Dynamical Systems and Their Applications V.I.Romanovskiy Institute of Mathematics Uzbek Academy of Sciences 4 University Street Olmazor100174 Uzbekistan Department of Mathematics Institute for Mathematical Research University Putra Malaysia Malaysia Moscow Institute of Physics and Technology Institutsky Lane 9 Dolgoprudny Moscow Region 141700 Russia The National University of Uzbekistan 4 University Street Tashkent100174 Uzbekistan Faculty of Mathematics University of Vienna Oskar-Morgnstern Platz 1 Austria

In this work, the null controllability problem for a linear system in 2 is considered, where the matrix of a linear operator describing the system is an infinite matrix with λ ∈ R on the main diagonal and 1s above it. We show that the system is asymptotically stable if and only if λ ≤ −1, which shows the fine difference between the finite and the infinite-dimensional systems. When λ ≤ −1 we also show that the system is null controllable in large. We also show a dependence of the stability on the norm i.e. the same system considered in ∞ is not asymptotically stable if λ = −1. © 2021, CC BY.

关键词： Mathematical operators

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Laughlin states change under large geometry deformations and imaginary time Hamiltonian dynamics

arXiv

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arXiv 2021年

作者： Matos, Gabriel Mera, Bruno Mourão, José M. Mourão, Paulo D. Nunes, João P. School of Physics and Astronomy University of Leeds LeedsLS2 9JT United Kingdom Center for Mathematical Analysis Geometry and Dynamical Systems Instituto Superior Técnico Universidade de Lisboa Lisboa1049-001 Portugal Instituto de Telecomunicações Lisboa1049-001 Portugal Department of Mathematics Instituto Superior Técnico Universidade de Lisboa Lisboa1049-001 Portugal Section of Mathematics Université de Genève Switzerland

We study the change of the Laughlin states under large deformations of the geometry of the sphere and the plane, associated with Mabuchi geodesics on the space of metrics with Hamiltonian S1-symmetry. For geodesics associated with the square of the symmetry generator, as the geodesic time goes to infinity, the geometry of the sphere becomes that of a thin cigar collapsing to a line and the Laughlin states become concentrated on a discrete set of S1-orbits, corresponding to Bohr-Sommerfeld orbits of geometric quantization. The lifting of the Mabuchi geodesics to the bundle of quantum states, to which the Laughlin states belong, is achieved via generalized coherent state transforms, which correspond to the KZ parallel transport of Chern-Simons *** Codes 81-10, 81S, 82-10 © 2021, CC BY.

关键词： Deformation

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Hybrid dynamics in delay-coupled swarms with mothership networks

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Physical Review E 2016年第3期94卷 032306-032306页

作者： Jason Hindes Klementyna Szwaykowska Ira B. Schwartz U.S. Naval Research Laboratory Code 6792 Plasma Physics Division Nonlinear Dynamical Systems Section Washington DC 20375 USA

Swarming behavior continues to be a subject of immense interest because of its centrality in many naturally occurring systems in physics and biology, as well as its importance in applications such as robotics. Here we examine the effects on swarm pattern formation from delayed communication and topological heterogeneity, and in particular, the inclusion of a relatively small number of highly connected nodes, or “motherships,” in a swarm's communication network. We find generalized forms of basic patterns for networks with general degree distributions, and a variety of dynamic behaviors including parameter regions with multistability and hybrid motions in bimodal networks. The latter is an interesting example of how heterogeneous networks can have dynamics that is a mix of different states in homogeneous networks, where high- and low-degree nodes have distinct behavior simultaneously.

关键词： Collective behavior in networks Dynamics of networks Swarming Networks & random structures Nonlinear time-delay systems Chaos & nonlinear dynamics Networks Analysis Tools

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Epidemic Extinction and Control in Heterogeneous Networks

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Physical Review Letters 2016年第2期117卷 028302-028302页

作者： Jason Hindes Ira B. Schwartz U.S. Naval Research Laboratory Code 6792 Plasma Physics Division Nonlinear Dynamical Systems Section Washington D.C. 20375 USA

We consider epidemic extinction in finite networks with a broad variation in local connectivity. Generalizing the theory of large fluctuations to random networks with a given degree distribution, we are able to predict the most probable, or optimal, paths to extinction in various configurations, including truncated power laws. We find that paths for heterogeneous networks follow a limiting form in which infection first decreases in low-degree nodes, which triggers a rapid extinction in high-degree nodes, and finishes with a residual low-degree extinction. The usefulness of our approach is further demonstrated through optimal control strategies that leverage the dependence of finite-size fluctuations on network topology. Interestingly, we find that the optimal control is a mix of treating both high- and low-degree nodes based on theoretical predictions, in contrast to methods that ignore dynamical fluctuations.

关键词： Degree distributions Epidemic Fluctuations & noise Network phase transitions Nonequilibrium & irreversible thermodynamics Nonequilibrium statistical mechanics Population dynamics

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Active Fault Diagnosis in Sampled-data systems

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IFAC-PapersOnLine 2015年第21期48卷 883-888页

作者： Niemann, Henrik Poulsen, Niels Kjolstad Department of Electrical Engineering Automation and Control Technical University of Denmark Building 326 DK-2800 Kgs. Lyngby Denmark Dept. of Applied Mathematics and Computer Science Section for Dynamical Systems Technical University of Denmark DK-2800 Kgs. Lyngby Denmark

The focus in this paper is on active fault diagnosis (AFD) in closed-loop sampleddata systems. Applying the same AFD architecture as for continuous-time systems does not directly result in the same set of closed-loop matrix transfer functions. For continuous-time systems, the LFT (linear fractional transformation) structure in the connection between the parametric faults and the matrix transfer function (also known as the fault signature matrix) applied for AFD is not directly preserved for sampled-data system. As a consequence of this, the AFD methods cannot directly be applied for sampled-data systems. Two methods are considered in this paper to handle the fault signature matrix for sampled-data systems such that standard AFD methods can be applied. The first method is based on a discretization of the system such that the LFT structure is preserved resulting in the same LFT structure in the fault signature matrix as obtained for continuous-time systems. The other method is an approximation method, where the same structure is obtained for small parametric faults. © 2015

关键词： Continuous time systems

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Active fault diagnosis in sampled-data systems 9

Active fault diagnosis in sampled-data systems

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9th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes, SAFEPROCESS 2015

作者： Niemann, Henrik Poulsen, Niels Kjølstad Department of Electrical Engineering Automation and Control Technical University of Denmark Building 326 Kgs. LyngbyDK-2800 Denmark Dept. of Applied Mathematics and Computer Science Section for Dynamical Systems Technical University of Denmark Kgs. LyngbyDK-2800 Denmark

关键词： Continuous time systems

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Characterising the Actual Thermal Performance of Buildings: Current Results of Common Exercises Performed in the Framework of the IEA EBC Annex 58-Project

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Energy Procedia 2015年 78卷 3282-3287页

作者： Staf Roels Peder Bacher Geert Bauwens Henrik Madsen María José Jiménez Building Physics Section KU Leuven University of Leuven Kasteelpark Arenberg 40 box 02447 3001 Heverlee Belgium DTU Compute Dynamical Systems Technical University of Denmark Denmark Energy Efficiency in Buildings R&D Unit CIEMAT Spain

Several studies have shown that actual thermal performance of buildings after construction may deviate significantly from that anticipated at design stage. As a result, there is growing interest in full scale testing of components and whole buildings. The IEA EBC Annex 58-project ‘Reliable Building Energy Performance Characterisation Based on Full Scale Dynamic Measurements’ is developing the necessary knowledge and tools to achieve reliable in-situ dynamic testing and data analysis methods that can be used to characterise the actual thermal performance and energy efficiency of building components and whole buildings. The research within this project is driven by case studies. As a first simple case, an experiment on testing and data analysis is performed on a round robin test box. This test box can be seen as a scale model of a building, built by one of the participants, with fabric properties unknown to all other participants. Full scale measurements have been performed on the test box in different countries under real climatic conditions. The obtained dynamic data are distributed to all participants who have to try to characterise the thermal performance of the test box's fabric based on the provided data. This paper presents the first results obtained on the round robin exper ment. It is shown how different techniques can be used to characterise the thermal performance of the test box, ranging from a simple stationary analysis to advanced dynamic data analysis methods.

关键词： Integrated building simulation mono-simulation co-simulation efficiency

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Adaptive Backstepping Control of Lightweight Tower Wind Turbine

Adaptive Backstepping Control of Lightweight Tower Wind Turb...

引用

American Control Conference

作者： Roberto Galeazzi Kasper T. Borup Henrik Niemann Niels K. Poulsen Fabio Caponetti Automation and Control Group DTU Electrical Engineering Technical University of Denmark Kgs. Lyngby Denmark Centre for Autonomous Marine Operations and Systems Norwegian University of Science and Technology Trondheim Norway Section of Dynamical Systems DTU Compute Technical University of Denmark Kgs. Lyngby Denmark Vestas Wind Systems Aarhus Denmark

ISBN: (纸本)9781479917730

This paper investigates the feasibility of operating a wind turbine with lightweight tower in the full load region exploiting an adaptive nonlinear controller that allows the turbine to dynamically lean against the wind while maintaining nominal power output. The use of lightweight structures for towers and foundations would greatly reduce the construction cost of the wind turbine, however extra features ought be included in the control system architecture to avoid tower collapse. An adaptive backstepping collective pitch controller is proposed for tower point tracking control, i.e. to modify the angular deflection of the tower with respect to the vertical axis in response to variations in wind speed. The controller is shown to guarantee asymptotic tracking of the reference trajectory. The performance of the control system is evaluated through deterministic and stochastic simulations including an extreme wind gust event, and the feasibility of stabilizing the tower position while maintaining the rated power output is shown.

关键词： Poles and towers Wind turbines Rotors Aerodynamics Torque Wind speed Generators

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Stochastic switching in slow-fast systems: A large-fluctuation approach

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Physical Review E 2014年第2期89卷 022919-022919页

作者： Christoffer R. Heckman Ira B. Schwartz []U.S. Naval Research Laboratory Code 6792 Plasma Physics Division Nonlinear Dynamical Systems Section Washington DC 20375 USA

In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we model rare event occurrences due to large fluctuations probabilistically and employ a WKB ansatz to approximate their rate of occurrence. This results in the generation of a two-point boundary value problem that models the interaction of the state variables and the most likely noise force required to induce a rare event. The resulting equations of motion of describing the phenomenon are shown to be singularly perturbed. Vastly different time scales among the variables are leveraged to reduce the dimension and predict the dynamics on the slow manifold in a deterministic setting. The resulting constrained equations of motion may be used to directly compute an exponent that determines the probability of rare events. To verify the theory, a stochastic damped Duffing oscillator with three equilibrium points (two sinks separated by a saddle) is analyzed. The predicted switching time between states is computed using the optimal path that resides in an expanded phase space. We show that the exponential scaling of the switching rate as a function of system parameters agrees well with numerical simulations. Moreover, the dynamics of the original system and the reduced system via center manifolds are shown to agree in an exponentially scaling sense.

关键词： STOCHASTIC analysis PERTURBATION (Mathematics) PROBABILITY density function FLUCTUATIONS (Physics) EQUILIBRIUM

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