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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Boscain, U. Pozzoli, E. Sigalotti, M. Univ Paris Sorbonne Univ Lab Jacques Louis Lions CNRSINRIA Paris France INRIA Paris France Univ Paris Sorbonne Univ Lab Jacques Louis Lions CNRS Paris France

In this paper we study the controllability properties of the quantum rotational dynamics of a 3D symmetric molecule, with electric dipole moment not collinear to the symmetry axis of the molecule (that is, an accidentally symmetric-top). We control the dynamics with three orthogonally polarized electric fields. When the dipole has a nonzero component along the symmetry axis, it is known that the dynamics is approximately controllable. We focus here our attention to the case where the dipole moment and the symmetry axis are orthogonal (that is, an orthogonal accidentally symmetric-top), providing a description of the reachable sets. Copyright (C) 2020 The Authors.

关键词： Bilinear control controllability distributed-parameter systems partial differential equations quantum angular momentum reachable states Schrodinger equation

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A Systematic Design of Backstepping-Based State Feedback Controllers for ODE-PDE-ODE systems 24

A Systematic Design of Backstepping-Based State Feedback Con...

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24th International Symposium on Mathematical Theory of Networks and systems (MTNS)

作者： Gehring, N. Johannes Kepler Univ Linz Inst Automat Control & Control Syst Technol A-4040 Linz Austria

The backstepping design of stabilizing state feedback controllers is addressed for bidirectionally coupled ODE-PDE-ODE systems, that naturally arise for infinite-dimensional systems where actuator or sensor dynamics are taken into account. A common framework for both linear parabolic and hyperbolic partial differential equations with spatially varying coefficients is presented, that solely relies on the strict feedback form of these systems. Without imposing any limitation on the dimension of the ODEs and PDEs involved, a multi-step design algorithm is suggested, that makes use of classical concepts (such as integrator backstepping and output zeroing) known for the control of ODE systems. By that, backstepping is brought back to its ODE origins and a systematic design of backstepping controllers for ODE-PDE-ODE systems is offered, with a unified treatise for parabolic and hyperbolic PDEs. Copyright (C) 2021 The Authors.

关键词： backstepping ODE-PDE-ODE systems boundary control distributed-parameter systems state feedback parabolic systems hyperbolic systems

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Backstepping-based tracking control of the vertical gradient freeze crystal growth process 22

Backstepping-based tracking control of the vertical gradient...

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22nd World Congress of the International Federation of Automatic Control (IFAC)

作者： Ecklebe, Stefan Gehring, Nicole Tech Univ Dresden Inst Control Theory Dresden Germany Johannes Kepler Univ Linz Inst Automat Control & Control Syst Technol Linz Austria

ISBN: (纸本)9781713872344

The vertical gradient freeze crystal growth process is the main technique for the production of high quality compound semiconductors that are vital for today's electronic applications. A simplified model of this process consists of two 1D diffusion equations with free boundaries for the temperatures in crystal and melt. Both phases are coupled via an ordinary differential equation that describes the evolution of the moving solid/liquid interface. The control of the resulting two-phase Stefan problem is the focus of this contribution. A flatness-based feedforward design is combined with a multi-step backstepping approach to obtain a controller that tracks a reference trajectory for the position of the phase boundary. Specifically, based on some preliminary transformations to map the model into a time-variant PDE-ODE system, consecutive transformations are shown to yield a stable closed loop. The tracking controller is validated in a simulation that considers the actual growth of a Gallium arsenide single crystal. Copyright (c) 2023 The Authors.

关键词： crystal growth Stefan problem distributed-parameter systems control applications state feedback backstepping

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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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Modulating Function Based Fault Detection for Parabolic systems with Polynomial Faults

Modulating Function Based Fault Detection for Parabolic Syst...

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10th International-Federation-of-Automatic-Control (IFAC) Symposium on Fault Detection, Supervision and Safety for Technical Processes (SAFEPROCESS)

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

This paper presents an algebraic approach to the fault detection for parabolic systems. It is assumed that the unknown time-varying faults are of polynomial type. In addition to the fault, the system is subject to a disturbance that can be separated into a polynomial deterministic part and a remaining bounded part. While the deterministic part is isolated from the fault, the bounded part is taken into account by introducing a threshold. For this setup, the modulating function approach is utilized to determine a directly implementable algebraic equation for the fault detection, which depends only on measurements. The results of the paper are illustrated for a faulty diffusion-reaction system. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems fault detection modulating function set-point change trajectory planning

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Hyperbolicity of the heat equation 3rd

Hyperbolicity of the heat equation

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3rd International-Federation-of-Automatic-Control (IFAC) Workshop on Thermodynamic Foundations for a Mathematical systems Theory (TFMST)

作者： Cassol, Guilherme Ozorio Dubljevic, Stevan Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2V4 Canada

In this manuscript, a comparison between the parabolic and hyperbolic partial differential equations for heat diffusion is studied. First, numerical results and an eigenvalue analysis for these two types of equations are shown, which help to understand the difference in the system dynamics. Then, both equations are also considered in a Stefan problem for the melting of an ice block in a one-dimensional setting. The results show that the hyperbolic partial differential equation shows a finite speed of propagation of heat and can represent the system as properly as the parabolic equation. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Moving boundary conditions Heat flows Linear systems Eigenvalue problems

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Constraints driven optimal actuation policies for diffusion processes with collocated actuators and sensors

Constraints driven optimal actuation policies for diffusion ...

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26th American Control Conference

作者： Dubljevic, Stevan Univ Calif Los Angeles David Geffen Sch Med Los Angeles CA 90095 USA

ISBN: (纸本)9781424409884

This work introduces modal model predictive control (MMPC) design methodology in the framework of optimal actuation policies which arise due to the presence of input and state constraints for a class of distributed parameter systems modeled by parabolic PDEs. The predictive control law accounts for input and state constraints and with respect to actuator/sensor position placement it generates an optimal actuation policy that switches applied control action among available pre-specified actuator locations. The proposed constrained predictive control law utilizes a low order modal representation in the optimization functional while higher modes are included only in the PDE state constraints. Accordingly, the proposed control law is formulated by the minimization algorithm whereby optimization is performed over all available preset collocated actuator/sensor positions. In this sense, the minimizing algorithm provides a control law that chooses among best collocated actuator/sensor positions available with respect to the lowest optimal cost among these positions. An example of a diffusion-reaction process, with spatially-uniform unstable steady state, subject to flux boundary conditions is considered.

关键词： distributed-parameter systems model predictive control input/state constraints optimal actuator switching

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Adaptive set-point regulation of linear n+1 hyperbolic systems with uncertain affine boundary condition using collocated sensing and control

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systems & CONTROL LETTERS 2020年 145卷 104777-104777页

作者： Holta, Haavard Aamo, Ole Morten Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway

We solve an adaptive control problem for n + 1 hyperbolic systems using collocated sensing and control, extending recent results for adaptive control of 2 x 2 systems and systems with non-collocated sensing and control. The boundary condition has an affine form with both unknown reflective and additive parameters and can be used to model well-reservoir interactions in oil and gas drilling where properties of the reservoir are unknown. Boundedness of the system states in the L-2-norm, and convergence to a steady state profile satisfying a control objective relevant to the drilling application, are proved. The state estimation error is shown to converge to zero in the L-2-norm and one of the boundary parameter estimates (modelling the reservoir pressure in the drilling application) is shown to converge to the true parameter value. The design is illustrated in a simulation example. (C) 2020 The Author(s). Published by Elsevier B.V.

关键词： distributed-parameter systems Adaptive control parameter estimation

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Output regulation for general heterodirectional linear hyperbolic PDEs coupled with nonlinear ODEs

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AUTOMATICA 2023年 148卷

作者： Irscheid, Abdurrahman Deutscher, Joachim Gehring, Nicole Rudolph, Joachim Saarland Univ Chair Syst Theory & Control Engn Saarbrucken Germany Ulm Univ Inst Measurement Control & Microtechnol Ulm Germany Johannes Kepler Univ Linz Inst Automat Control & Control Syst Technol Linz Austria

This paper considers general heterodirectional linear hyperbolic PDEs with boundary actuation and collocated measurement, that are bidirectionally coupled with nonlinear ODEs at the unactuated boundary. An output feedback regulator is designed to have the control output track a reference in the presence of disturbances, with a nonlinear signal model generating the reference and the disturbances. This leads to new challenges for both the observer and controller design. The regulator design makes use of results from output regulation theory for nonlinear lumped-parameter and distributed-parameter systems. The derivation of the state feedback regulator requires solving a new type of regulator equations, which consist of a Cauchy problem for linear and semilinear hyperbolic PDEs. A key component of the novel observer design is a nonlinear retarded observer for a finite -dimensional subsystem. Both the controller and the observer design are systematic in nature and derived in several successive steps, that include backstepping transformations and, most notably, predictions of PDE and ODE states. The latter are shown to be the unique solution of general nonlinear Volterra integro-differential equations. Combining the observer with the state feedback regulator is proven to achieve output regulation for the closed-loop system. A numerical example illustrates and confirms the theoretical results.(c) 2022 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Hyperbolic systems Nonlinear PDE-ODE systems Output regulation Prediction Observer design Output feedback Backstepping

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A backstepping approach to output regulation for coupled linear wave-ODE systems

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AUTOMATICA 2021年 123卷 109338-109338页

作者： Deutscher, Joachim Gabriel, Jakob Univ Ulm Inst Mess Regel & Mikrotech Albert Einstein Allee 41 D-89081 Ulm Germany

This paper is concerned with the output regulation problem for coupled wave-ODE systems subject to spatially-varying coefficients. This problem is traced back to the regulator design for a coupled 2 x 2 hyperbolic PIDE-ODE system, for which a new and systematic backstepping design procedure is presented. The related state and disturbance estimation problem are solved by determining a natural disturbance observer of second order. The corresponding observer design relies on the backstepping stabilization of a coupled 2 x 2 hyperbolic ODE-PIDE-ODE system by dynamic output injection control. With this, a constructive solution of the output regulation problem is presented for coupled wave-ODE systems with disturbances acting in-domain, at a boundary or at the ODE. The output to be controlled can depend both on the distributed and lumped states, while in the former case in-domain and boundary outputs are allowed. A large class of exogenous signals is taken into account by considering a non-diagonalizable signal model. The new regulator design method is illustrated for a heavy chain system with a load of forth order. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Hyperbolic systems wave-ODE systems Output regulation Backstepping

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