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On General Properties of Eigenvalues and Eigenfunctions of a Sturm-Liouville Operator: Comments on "ISS With Respect to Boundary Disturbances for 1-D Parabolic PDEs"

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2017年第11期62卷 5970-5973页

作者： Orlov, Yury CICESE Res Ctr Dept Elect & Telecommun Ensenada 22860 Baja California Mexico

In the paper "ISS with respect to boundary disturbances for 1-D parabolic PDEs" (IEEE Transactions on Automatic Control, vol. 61, pp. 3712-3724, 2016), input-to-state stability properties are established for 1-D spatially varying parabolic partial differential equations (PDEs) under certain assumptions, imposed on eigenvalues and eigenfunctions of an associated Sturm-Liouville operator. A key assumption on the absolute convergence of an associated Fourier series, composed of the normalized eigenfunctions and inverse eigenvalues of the Sturm-Liouville operator, is analyzed in the present note. General properties of the Sturm-Liouville operator are carried out to demonstrate that such a key assumption becomes redundant for the underlying PDEs with signdefinite sufficiently smooth coefficients.

关键词： Autonomous systems distributed parameter systems linear systems Sturm-Liouville problem

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MATHEMATICAL MODELS OF STATIONARY AND DYNAMIC PROCESSES IN TUBULAR FURNACES

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CHEMICAL AND PETROLEUM ENGINEERING 2017年第1-2期53卷 78-83页

作者： Demidenko, N. D. Kulagina, L. V. Russian Acad Sci Siberian Branch Inst Computat Technol Nauka Special Designing & Technol Bur Krasnoyarsk Russia Siberian Fed Univ Krasnoyarsk Russia

Mathematical models are proposed for stationary and dynamic processes of technological furnaces as objects with distributed parameters based on the laws of conservation of energy, mass and momentum. Computational investigation of the stationary modes of tubular furnaces was conducted. The boundary-value problem was formulated for the calculations of the concentration of combustible substance, density, velocity, temperatures of the flue gas and the heated raw materials headed for separation in the rectification column. Results of calculations of the technological parameters are presented. The proposed method can be used for automating rectification units in petroleum-refining and petrochemical industry.

关键词： mathematical modeling distributed parameter systems heat and mass exchange numerical method

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Boundary control of delayed ODE-heat cascade under actuator saturation

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AUTOMATICA 2017年 83卷 252-261页

作者： Kang, Wen Fridman, Emilia Tel Aviv Univ Sch Elect Engn Tel Aviv Israel

In this paper, we consider boundary stabilization for a cascade of ODE-heat system with a time-varying state delay under actuator saturation. To stabilize the system, we design a state feedback controller via the backstepping method and find a bound on the domain of attraction. The latter bound is based on Lyapunov method, whereas the exponential stability conditions for the delayed cascaded system are derived by using Halanay's inequality. Numerical examples illustrate the efficiency of the method. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Backstepping transformation Actuator saturation Time-delay Lyapunov method

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Rise-Time Improvement in Bipolar Pulse Solid-State Marx Modulators

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IEEE TRANSACTIONS ON PLASMA SCIENCE 2017年第10期45卷 2656-2660页

作者： Canacsinh, Hiren Fernando Silva, J. Redondo, L. M. INESC ID P-1000029 Lisbon Portugal Inst Super Engn Lisboa Inst Politecn Lisboa P-1959007 Lisbon Portugal Univ Lisbon Inst Super Tecn P-1959007 Lisbon Portugal Inst Politecn Lisboa ISEL GIAAPP P-1959007 Lisbon Portugal

This paper presents the effect of stray capacitances in bipolar (negative and/or positive) pulses generated by the two different topologies of the solid-state Marx modulators. According to the analysis, the stray capacitances influence the energy transfer from the Marx modulator capacitors to the load affecting the bipolar (negative and/or positive) pulse rise time. This paper deals with the structure design to reduce the influence of the stray capacitance and to improve the pulse rise time of these bipolar solid-state Marx modulators. A four-stage laboratory prototype of the two topologies has been assembled using 1200-V insulated gate bipolar transistors and diodes, operating with 1000-V dc input voltage and 1-kHz frequency, producing 4-kV bipolar pulses, with 5-mu s pulse duration and 120-ns rise time, into a resistive load.

关键词： distributed parameter systems pulsed power systems solid-state unipolar/bipolar Marx modulators stray capacitances

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Boundary control of reaction-diffusion equation with state-delay in the presence of saturation*

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IFAC-PapersOnLine 2017年第1期50卷 12002-12007页

作者： Kang, Wen Fridman, Emilia Department of Electrical Engineering Tel Aviv University Israel Department of Mathematics Harbin Institute of Technology China Department of Electrical Engineering Tel Aviv University Israel

The boundary stabilization for reaction-diffusion equation with state delay in the presence of actuator saturation is concerned. The state feedback is designed by using the backstepping method. We find a bound on the domain of attraction. The latter bound is based on Lyapunov method, whereas the exponential stability is proved by using Halanay's inequality. A numerical example validates the efficiency of the method. © 2017

关键词： Equations of state Actuators Diffusion in liquids Linear equations Lyapunov methods Numerical methods Partial differential equations State feedback Time delay Actuator saturations Back stepping method Boundary controls Boundary stabilization distributed parameter systems Domain of attraction Reaction diffusion equations State delay

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Feedforward Control of the Temperature Field in an Experimental Annealing Furnace

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IFAC-PapersOnLine 2017年第1期50卷 13790-13795页

作者： Jadachowski, L. Steinboeck, A. Kugi, A. Christian Doppler Laboratory for Model-Based Control in the Steel Industry Automation and Control Institute Vienna University of Technology Gußhausstraße 27-29 Vienna1040 Austria Automation and Control Institute Vienna University of Technology Gußhausstraße 27-29 Vienna1040 Austria

Two feedforward control strategies for an experimental annealing furnace equipped with electrically powered infrared (IR) lamps are developed and compared. For the first controller, the optimal time evolution of the electric power supplied to IR-lamps is computed from a dynamic optimization problem. This ensures optimal temperature trajectories and temperature uniformity in the specimen fillet. The second controller is based on an amplified adjustment of the steady-state power distribution obtained from static optimization at an operating point. Here, the temperature uniformity during transients is traded-off against the computing time while still ensuring the best temperature uniformity at the final temperature level. For both strategies, a tailored control-oriented reduced-order model of the 2D spatial-temporal temperature evolution is used. The evaluation of the feedforward controllers is carried out with an experimentally validated simulation model. The temperature non-uniformity during transients is less than 0.9 % and reduces to 0.3 % of the setpoint value at the steady state. © 2017

关键词： Feedforward control Computer aided software engineering Controllers distributed parameter control systems Evolutionary algorithms Infrared lamps distributed parameter systems FE method Model reduction Optimal feedforward control Optimal operating point Quasi linear

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Optimal Control of Linear Transport systems with distributed Control Input

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IFAC-PapersOnLine 2017年第1期50卷 13306-13311页

作者： Schaut, Stefan Alt, Simon Schmidt, Kevin Sawodny, Oliver Institute for System Dynamics University of Stuttgart StuttgartD-70569 Germany

The transport systems considered in this paper are conveyor belts or conduit systems, which are mainly used for two operational tasks. The first objective is the transportation of goods between subsequent process stages, the second one is the conditioning of the transported goods by a spatially acting control input along the transportation path. The control task under consideration is defined by a setpoint change of the subsequent process stage by a constrained control input. To obtain the desired properties of the goods at the end of the transportation path, an optimal feedforward control approach is developed. © 2017

关键词： Feedforward control Belt conveyors distributed parameter control systems Freight transportation Constrained controls Delay compensation distributed control distributed parameter systems Optimal controls Optimal feedforward control Transport delay Transportation of goods

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A systemic viewpoint on the approximation of a power transmission line model

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IFAC-PapersOnLine 2017年第1期50卷 14818-14823页

作者： Belhocine, M. Marinescu, B. Ecole Centrale Nantes-LS2N 1 rue de la Noë Nantes44300 France

This paper explains, from a systemic viewpoint, the importance to take into account the dynamic structure of the whole system in order to simplify the distributed parameters model of the transmission lines. Usually, the latter is approximated without considering its connection with the rest of the system, by comparing only its input-output behaviour with the one of the simplified model. Here, it is shown that this way to do can lead to biased results. More precisely, it is shown that the short-lines hypothesis leads to a reduction link with the π-model but does not indicate clearly which dynamics have to be kept in the simplified model as well as their number. This is illustrated by considering the voltage collapse phenomenon. From this analysis, a more systemic approximation way is proposed to reduce subsystems of a general complex system. In power systems field, all these investigations can help to improve the models used for simulation and control synthesis. Especially, to better connect the models to the specific phenomena which have to be reproduced in simulation. © 2017

关键词： Electric lines Electric power systems Electric power transmission Spectrum analysis Transmission line theory Control synthesis distributed parameter systems distributed parameters models Dynamic structure Input output Model reduction Pi models Voltage collapse

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Explicit Boundary Controls for Finite Diffusion Process

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IFAC-PapersOnLine 2017年第1期50卷 15337-15342页

作者： Tenno, R. Aalto University School of Electrical Engineering PO Box 15500 Aalto Finland

Three types of boundary controls are considered: proportional control, feed-forward control and integrated-by-past-values control. They stabilise the diffusion process exponentially at the desired reference on the controlled boundary. The process is actuated through the Neumann boundary while on other boundaries it is given with the Dirichlet data and, in higher dimensions, also with the homogeneous Neumann boundary condition. Two systems, deterministic and stochastic are compared as an ideal and real description of a physical system. Disturbance in the stochastic system is originated by a white noise on the controlled boundary. Physically this noise represents different types of uncertainties like a side-reaction mass-flux and other uncertainties that are not part of a deterministic model. At first the proportional control is analysed on the deterministic system and then it is represented in the feedback integrated past controls form, and lastly the developed controls are modified as a version of stochastic control that applied on the stochastic system, which boundary is disturbed with an unmeasured noise. The regulation error that emerges in the stochastic system control is analysed and proved to be a zero-mean, bounded-variance Gaussian variable that is correlated spatially and temporarily. The process control is demonstrated on an electrodeposition process example. © 2017

关键词： Process control Boundary conditions Random processes Stochastic control systems Stochastic systems White noise Boundary controls Deterministic modeling Deterministic systems distributed parameter systems Electrodeposition process Gaussian variables Neumann boundary condition Proportional control

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Establishing Traveling Wave in Bistable Reaction-Diffusion System by Feedback

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IEEE CONTROL systems LETTERS 2017年第1期1卷 62-67页

作者： Bliman, Pierre-Alexandre Vauchelet, Nicolas UPMC Univ Paris 06 Sorbonne Univ INRIA Lab JL Lions UMR CNRS 7598 Paris France Fundacao Getulio Vargas Escola Matemat Aplicada BR-22250900 Rio De Janeiro Brazil Univ Paris 13 Inst Galilee LAGA UMR 7539 F-93430 Villetaneuse France

Several stains of the intracellular parasitic bacterium Wolbachia limit severely the competence of the mosquitoes Aedes aegypti as a vector of dengue fever and possibly other arboviroses. For this reason, the release of mosquitoes infected by this bacterium in natural populations is presently considered a promising tool in the control of these diseases. Following works by Barton and Turelli and subsequently Strugarek et al., we consider a simple scalar reaction-diffusion model describing the evolution of the proportion of infected mosquitoes, sufficient to reveal the bistable nature of the Wolbachia dynamics. A simple distributed feedback law is proposed, whose application on a compact domain during finite time is shown to be sufficient to invade the whole space. The corresponding stabilization result is established for any space dimension.

关键词： Biological systems distributed parameter systems distributed control

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