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Folding Backstepping Approach to Parabolic PDE Bilateral Boundary Control

IFAC-PapersOnLine 2019年第2期52卷 76-81页

作者： Stephen Chen Rafael Vazquez Miroslav Krstic Department of Mechanical and Aerospace Engineering University of California San Diego La Jolla CA 92093-0411 USA Departmento de Ingeniería Aeroespacial Universidad de Sevilla 41092 Sevilla Spain

We consider the stabilization problem for an unstable 1-D diffusion-reaction partial differential equation using a so-called folding transformation. The diffusion-reaction equation is transformed into a 2 ×2 system of coupled parabolic PDEs with exotic boundary conditions. A first backstepping transformation is designed to map the unstable system into a strict-feedback intermediate target system. A second backstepping transformation is designed to stabilize the intermediate target system. Interestingly, the companion gain kernel PDEs contain the folding boundary condition, exhibiting symmetry with the original system. The kernels posses a cascading structure that allows for sequential solution methods. Finally, the controller derived is shown to be exponentially stabilizing in the L 2 sense.

关键词： Lyapunov-based backstepping techniques distributed parameter systems boundary control

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Model Averaging and Feedforward Temperature Control in an Oscillating Annealing Furnace

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IFAC-PapersOnLine 2018年第21期51卷 163-168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

The impact of an oscillating motion on the temperature uniformity of a specimen in an experimental annealing furnace is analyzed. For the specimen temperature, three feedforward control strategies using dynamic optimization are developed and compared. The controllers provide reference signals to electrically powered infrared lamps to ensure optimal temperature trajectories. In the first controller design, no specimen oscillation is considered. This design uses an amplified adjustment of the steady-state power distribution obtained from static optimization. The second and the third controller are developed for an oscillating specimen. Both these controllers are designed on the basis of a dynamic optimization problem, where in addition to the amplification factor the constant power distribution serves as additional degree of freedom. While the second controller takes into account the oscillating motion directly, the last approach utilizes time averaging of the model equations. An evaluation of all controllers is carried out with an experimentally validated model. This analysis shows that the temperature uniformity can be significantly improved when the specimen oscillates. © 2018

关键词： Controllers Degrees of freedom (mechanics) distributed parameter control systems Evolutionary algorithms Feedforward control Infrared lamps distributed parameter systems FE method Model reduction Optimal feedforward control Oscillating motion Quasi linear Time averaging

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Port-Hamiltonian modeling and reduction of a burning plasma system

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IFAC-PapersOnLine 2018年第3期51卷 68-73页

作者： Vincent, Benjamin Vu, Trang Hudon, Nicolas Lefèvre, Laurent Dochain, Denis ICTEAM Université Catholique de Louvain Bâtiment Euler av. Lemaître 4-6 Louvain-La-NeuveB-1348 Belgium Université Grenoble Alpes LCIS F-26902 France Department of Chemical Engineering Queen's University KingstonONK7L 3N6 Canada

In this contribution, we develop a structured port-Hamiltonian model for a class of irreversible distributed parameter systems and exploit the obtained formulation for model reduction from dimension 3 to dimension 1 in space. The proposed methodology is motivated by the control of burning plasma profiles in Tokamak reactors. The burning plasma is viewed as a multi-physics system built on Maxwell equations and total mass, species, momentum, energies, and entropy balance equations. Moreover, the system presents nonlinear couplings, especially through transport coefficients, and its dynamic evolves over multiple time scales. The main couplings considered here are the Joule effect, the Lorentz forces, and the fusion reaction kinetics. The port-based modeling formulation and reduction rely on the use of the Gibbs relation, Onsager linear transport theory, Stokes–Dirac structures, and energy preserving geometric reduction. © 2018

关键词： Hamiltonians Couplings distributed computer systems Fusion reactions Magnetoplasma Maxwell equations Models Reaction kinetics Statistical mechanics Thermodynamics Tokamak devices distributed parameter systems Geometric reductions Irreversible thermodynamics Model reduction Multiphysics systems Port Hamiltonian systems Tokamak reactors Transport coefficient

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Modeling and Stabilization of a Rotating Mechanical System with Elastic Plates

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IFAC-PapersOnLine 2018年第2期51卷 493-498页

作者： Zuyev, Alexander Novikova, Julia Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Industrial Institute Donetsk National Technical University Pokrovsk Ukraine

A mechanical system consisting of a rigid body and attached Kirchhoff plates under the action of three independent controls torques is considered. The equations of motion of such model are derived in the form of a system of coupled nonlinear ordinary and partial differential equations. The operator form of this system is represented as an abstract differential equation in a Hilbert space. A feedback control law is constructed such that the corresponding infinitesimal generator is dissipative. © 2018

关键词： distributed parameter control systems Equations of motion Lyapunov methods Mechanics Nonlinear equations Ordinary differential equations Plates (structural components) Abstract differential equations Control design distributed parameter systems Elastic structures Feedback control law Infinitesimal generator Non linear control Ordinary and partial differential equations

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Benchmarking of Industrial Stick-Slip Mitigation Controllers

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IFAC-PapersOnLine 2018年第8期51卷 233-238页

作者： Aarsnes, Ulf Jakob F. di Meglio, Florent Shor, Roman J. Drilling and well centre for improved recovery Oslo Norway and DrillWell Stavanger Norway Centre Automatique et Systmes Mines ParisTech Paris France University of Calgary Department of Chemical and Petroleum Engineering Calgary Canada

The present paper evaluates how three different top-drive feedback controllers influence the occurrence of a stick-slip limit cycle in a rotating drill string. The considered controllers are: 1) The industry standard stiff, high-gain controller, 2) SoftTorque, and, 3) ZTorque. The evaluation is performed as a simulation study on a distributed model of a drill string with a collar section and Coulomb friction as a distributed source term. This model is capable of replicating stick-slip oscillations as caused by the reduction in friction from static to dynamic, and have been shown to yield a good match with field data. The simulation study is summarized as a map for each controller indicating the existence and amplitude of oscillations, parametrized in the key friction parameters. © 2018

关键词： Controllers Automation Closed loop control systems Control system analysis Digital storage distributed parameter control systems Drill collars Drills Infill drilling Slip forming Stick slip Amplitude of oscillation Closed loop control distributed modeling distributed parameter systems Feedback controller Friction parameters Motor control Stick slip oscillation

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Utilizing Industry-oriented Finite Element Codes in the Design of Virtual Steel Mill Concept

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IFAC-PapersOnLine 2018年第21期51卷 313-316页

作者： Ondrejkovi, K. Buek, P. Hulkó, G. eleziarne Podbrezová Research and Development Centre Kolkáre 35 Podbrezová97681 Slovakia Slovak University of Technology in Bratislava Nám. slobody 17 Bratislava81231 Slovakia

Standard industry-oriented finite element codes offer a great degree of versatility and computational efficiency. These software tools in hands of control process engineers help to establish new concepts of control strategies, leading to an effective or autonomous operation. However, their use in continuous casting industry is usually limited to isolated case studies due to missing communication layer interfaces and data processing tools within steel mill infrastructure. Systematic breaking of these barriers would lead to novel concepts of distributed parameter system identification and control system design using off-line or co-simulation control schemes. This marks the way towards virtual technological nodes as a part of a more general concept of virtual steel mill with continuous casting machine at its very heart. © 2018

关键词： Steel castings Computational efficiency Computer aided software engineering Continuous casting Control engineering Data handling Finite element method Solidification Autonomous operations Co simulations Communication layers Continuous casting machines Continuous casting of steels Control strategies distributed parameter systems Finite element codes

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Optimal Actuator Design for Nonlinear Partial Differential Equations

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IFAC-PapersOnLine 2019年第2期52卷 128-131页

作者： M. Sajjad Edalatzadeh Kirsten A. Morris University of Waterloo Waterloo ON Canada

For systems modeled by partial differential equations, the location and shape of the actuators can be regarded as a design variable and included as part of the controller synthesis procedure. Optimal actuator location is a special case of optimal design. For linear partial differential equations (PDEs), the existence of an optimal actuator location for a number of cost functions has been established. However, many dynamics are affected by nonlinearities and linearization of the PDE can neglect some important aspects of the model. This paper describes recent results establishing conditions for existence of optimal actuator design and control for important classes of nonlinear PDEs.

关键词： Optimal control Nonlinear systems distributed parameter systems Actuators Partial differential equations

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Hierarchical sliding mode observers for distributed parameter systems

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JOURNAL OF VIBRATION AND CONTROL 2011年第10期17卷 1441-1453页

作者： Drakunov, Sergey V. Reyhanoglu, Mahmut Embry Riddle Aeronaut Univ Dept Phys Sci Daytona Beach FL USA

In this work we suggest hierarchical sliding mode observers for complex systems which include distributed parameter systems and combinations of distributed parameter and lumped parameter systems, modeling, for example, an actuator dynamics. The main idea is based on the observer suggested previously for general nonlinear lumped parameter systems that is using the equivalent values of the discontinuous function to obtain additional information about the system state. Such observers can be written directly into system's original variables without requiring the state transformation. In this paper, using a modal representation of the distributed system and the hierarchy of sliding modes, we develop a structure of such an observer for a wide class of systems described by partial differential equations or combinations of ordinary and partial differential equations. An example is presented which illustrates the proposed method.

关键词： Sliding mode observer distributed parameter systems

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Slow gas flow passing a solid is a convection/diffusion equation

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IFAC-PapersOnLine 2019年第1期52卷 341-345页

作者： Delphine Bresch-Pietri Nicolas Petit MINES ParisTech PSL Research University CAS - Centre Automatique et Systèmes 60 bd St Michel 75006 Paris FRANCE

This paper exposes a formal result showing that a set of two coupled hyperbolic equations governing the thermal exchanges between a gas passing by a solid is actually close, in a detailed mathematical sense, to a single convection/diffusion equation. Exhaust gas passing by a solid catalyst is a typical example of such a situation. This result, the key derivation steps of which are given here, bridges the gap between the two formulations, which have received distinct types of contributions by the control community in the recent years.

关键词： distributed parameter systems reduction method convection diffusion thermal exchanges

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Comparision of approximation methods for weakly damped waves Discussion paper

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IFAC-PapersOnLine 2018年第3期51卷 97-100页

作者： Morris, Kirsten Dept. of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada

A number of applications involving wave propagation are asymptotically stable, but the decay rate of the mode does not increase with increasing wave number. Applications include electrical transmission, acoustic waves and water waves. There are many different approximation methods for these systems that are fine for simulation. But the qualitative behaviour of the approximated eigenvalues can be quite different. Controller and estimator design with different approximations can yield different results. A number of partial differential equations (PDEs) are derived using Hamilton's principle. This provides information about the energy of the system that can be a guideline in establishing well-posedness on an appropriate state space. Recent work on a port-Hamiltonian approach to approximation shows promise in obtaining finite-dimensional approximations that are useful for control and estimation. A key feature of the port-Hamiltonian approach is careful attention to how the energy in the system is modelled and approximated. How does this approach compare to more traditional approaches to scientific computation? In particular, what are the similarities and what are the differences? These questions will be examined in the talk, and in discussion, through several relatively simple examples. © 2018

关键词： Hamiltonians Approximation theory Decay (organic) Eigenvalues and eigenfunctions Water waves Wave propagation approximation Controller designs Discretizations distributed parameter systems energy Infinite dimensional system Port hamiltonians

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