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Passive-guaranteed modeling and simulation of a finite element nonlinear string model

IFAC-PapersOnLine 2024年第6期58卷 226-231页

作者： David Roze Mathis Raibaud Thibault Geoffroy Sciences et Technologies de la Musique et du Son IRCAM - CNRS - SU UMR 9912 1 place Igor Stravinsky 75004 Paris France Squarp SAS 12 rue Marceau 93100 Montreuil France

This paper proposes to solve the dynamics of the Kirchhoff-Carrier nonlinear string model using the finite elements method. In order to ensure the power balance of the resulting finite dimensional model it is rewritten in the Port-Hamiltonian System (PHS) formalism. Using a discrete gradient and a quadratization of the Hamiltonian, an explicit power-preserving numerical scheme is proposed. Results of simulation are presented.

关键词： distributed parameter systems Numerical Methods Hamiltonian dynamics Port-Hamiltonian systems Quadratization Nonlinear string model Finite elements method

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Energy Storage in Paraffin: A PDE Backstepping Experiment

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IEEE TRANSACTIONS ON CONTROL systems TECHNOLOGY 2021年第4期29卷 1490-1502页

作者： Koga, Shumon Makihata, Mitsutoshi Chen, Renkun Krstic, Miroslav Pisano, Albert P. Univ Calif San Diego UCSD Dept Mech & Aerosp Engn MAE La Jolla CA 92093 USA Honda Res Inst Inc San Jose CA 95134 USA

This article proposes a novel control algorithm of a thermal phase-change process and shows its experimental verification using paraffin as a phase-change material (PCM). The core problem is to design a boundary feedback control for the "Stefan system" that describes the time evolution of the temperature profile in the liquid phase, which is associated with the time evolution of a position of liquid-solid phase interface, for the sake of stabilizing the interface position at a chosen set point. First, we design the continuous-time full-state feedback control law by means of the PDE backstepping method, which, in the absence of a demand for accelerated convergence, can also be arrived at by the energy-shaping method, and rigorously prove the stability of the closed-loop system under sufficiently small heat loss. Next, the control law is refined via observer-based output feedback under sampled-data measurements of the surface temperature and the phase interface position so that the control algorithm is practically implementable. Then, we conducted an experiment under a constant input to calibrate unknown parameters involved with the heat loss. Finally, the proposed model-based boundary feedback control algorithm is implemented in the experiment of melting paraffin. The experiment was successful: the convergence of the phase interface to the set point was achieved.

关键词： Heating systems Backstepping Phase change materials Mathematical model Observers Liquids Output feedback Backstepping distributed parameter systems moving boundary phase-change material (PCM) Stefan problem

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Reduction and Observer Design for a Grey-Box Model in Continuous Pharmaceutical Manufacturing 4th

Reduction and Observer Design for a Grey-Box Model in Contin...

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4th IFAC Workshop on Control of systems Governed by Partial Differential Equations (CPDE)

作者： Elkhashap, Ahmed Abel, Dirk Rhein Westfal TH Aachen Inst Automat Control Aachen Germany

In this contribution, a novel Reduced Order Model (ROM) formulation of the grey-box model proposed in Elkhashap et al. (2020a) for the pharmaceutical continuous vibrated fluid bed dryer (VFBD) is presented. The ROM exploits the H-2-norm projection-based model order reduction method after a special solution formulation of the model's infinite-dimensional part. This is mainly by introducing a vector field mapping between the model parts casting the semi- discretized PDE into a bilinear form. The ROM produced is then integrated into an nonlinear Kalman Filtering-based observer design also handling the estimation of the model's algebraic variables. Evaluations of the FOM, ROM, ROM-based observer variants, and the FOM-based observer are performed using Monte-Carlo simulations as well as simulations based on experimental data of the real system. It is shown that the ROM could reproduce the FOM states accurately with a relative mean square error below 0.3 % for the experimental data simulation. This is while reaching a computational-time reduction up to a factor of 40. The ROM-based observer with algebraic states correction is shown (using Monte-Carlo simulations) to be able to converge to the true values for all cases regardless of initialization. Moreover, it is also shown that the performance degradation of the observer due to reduction is practically insignificant. This is while the computational speedup of the observer due to reduction reached a factor of more than third order of magnitude. Copyright (C) 2022 The Authors.

关键词： Continuous Pharmaceutical Manufacturing Model Order Reduction Observer Design Early Lumping distributed parameter systems

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Spatio-temporal fault localization for nonlinear spatially distributed processes: A spatial mapping filter-based framework

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2021年第14期31卷 6953-6971页

作者： Feng, Yun Wang, Yaonan Wang, Jun-Wei Li, Han-Xiong Ding, Steven X. Hunan Univ Coll Elect & Informat Engn Changsha 410082 Peoples R China Hunan Univ Natl Engn Lab Robot Visual Percept & Control Tech Changsha Peoples R China Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing Peoples R China City Univ Hong Kong Dept Adv Design & Syst Engn Kowloon Hong Kong Peoples R China Univ Duisburg Essen Inst Automat Control & Complex Syst AKS Duisburg Germany

Compared to the fault detection problem, fault localization for spatially distributed processes is physically intuitive but was seldom studied. The main challenge lies in the contradiction between the spatially distributed nature of the processes and a limited number of sensors that can be placed in the space for applications. In this article, we make the first attempt to systematically study the fault localization problem for a class of nonlinear spatially distributed processes without knowing any prior information of the spatial distribution function of the spatio-temporal fault. The main contribution is that a spatial mapping filter is first designed to generate a distributed residual signal which contains spatial information while using limited sensor measurements. The residual evaluation procedure is also conducted in a distributed manner. With these two parts, a systematic methodology framework is constructed and analyzed rigorously. Finally, the performance of the proposed method is evaluated on a faulty catalytic rod, which widely exists in chemical engineering.

关键词： distributed parameter systems fault detection fault localization spatially distributed processes

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Feedback Stabilization of a Class of Diagonal Infinite-Dimensional systems With Delay Boundary Control

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2021年第1期66卷 105-120页

作者： Lhachemi, Hugo Prieur, Christophe Univ Coll Dublin Sch Elect & Elect Engn Dublin Ireland Univ Grenoble Alpes CNRS Grenoble INP GIPSA Lab F-38000 Grenoble France

This article studies the boundary feedback stabilization of a class of diagonal infinite-dimensional boundary control systems. In the studied setting, the boundary control input is subject to a constant delay while the open-loop system might exhibit a finite number of unstable modes. The proposed control design strategy consists of two main steps. First, a finite-dimensional subsystem is obtained by truncation of the original infinite-dimensional system (IDS) via modal decomposition. It includes the unstable components of the IDS and allows the design of a finite-dimensional delay controller by means of the Artstein transformation and the pole-shifting theorem. Second, it is shown via the selection of an adequate Lyapunov function that: 1) the finite-dimensional delay controller successfully stabilizes the original IDS and 2) the closed-loop system is exponentially input-to-state stable (ISS) with respect to distributed disturbances. Finally, the obtained ISS property is used to derive a small gain condition ensuring the stability of an IDS-ODE interconnection.

关键词： Delays Mathematical model Control design Lyapunov methods Eigenvalues and eigenfunctions Closed loop systems distributed parameter systems delay boundary control Lyapunov function partial differential equation (PDE)-ordinary differential equation (ODE) interconnection

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P-I Boundary Control of Countercurrent Heat Exchanger 1

P-I Boundary Control of Countercurrent Heat Exchanger

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1st IFAC Workshop on Control of Complex systems (COSY)

作者： Kazaku, Jacques Kadima Dochain, Denis Kahilu, Moise Mukepe Kasongo, Jimmy Kalenga Kaunde UCLouvain Dept Math Engn ICTEAM 4-6 Ave G Lemaitre B-1348 Louvain La Neuve Belgium Univ Lubumbashi Dept Electromech & Mine Route Kasapa Lubumbashi 1825 DEM REP CONGO

Heat exchangers are generally described by two coupled partial differential equations (PDEs), and belong to the class of systems of conservation laws. In this paper we propose a result on the regulation of heat exchangers, in which we are choosing a proportional-integral (PI)-controller implemented on an output feedback from a boundary condition. First, a study on the existence and uniqueness of solutions of uncontrolled system is carried out, and we give a condition on the parameters of the system that ensures that the control-observation problem is well-posedness. Secondly we successively study the stability of the system controlled by a proportional and integral action, when the gains are adjusted following respectively a classic Lyapunov approach, and using a recent result that combines Lyapunov's approach and operator perturbation theory. Copyright (c) 2022 The Authors. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0/)

关键词： Well-posedness Boundary control Lyapunov analysis heat exchangers distributed parameter systems PI-control

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Transport Speed Estimation for a 1-D Hyperbolic PDE Based on Output Flow Measurement 10

Transport Speed Estimation for a 1-D Hyperbolic PDE Based on...

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10th International Conference on systems and Control (ICSC)

作者： Paiva, Eduardo B. R. F. Lepreux, Olivier Bresch-Pietri, Delphine IFP Energies Nouvelles F-69360 Solaize France PSL Ctr Automat & Syst MINES Paris Tech 60 Bd St Michel F-75006 Paris France

ISBN: (纸本)9781665465076

We present a method for estimating the transport speed of a class of systems modeled by a 1-D hyperbolic Partial Differential Equation (PDE) where the quantity governed by the PDE is a speed deficit and the measurement fed to the estimator is the transport speed minus this deficit at a given location. Such problem arises when estimating the free flow wind speed using measurements taken inside the wake zone of a wind turbine. We present a simple and easy to implement method and provide sufficient conditions for its convergence.

关键词： Hyperbolic systems parameter estimation time-delay systems distributed parameter systems wind speed estimation

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Explicit model predictive control for PDEs: The case of a heat equation 25th

Explicit model predictive control for PDEs: The case of a he...

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25th International Symposium on Mathematical Theory of Networks and systems (MTNS)

作者： Dubljevic, Stevan Humaloja, Jukka-Pekka Kurula, Mikael Univ Alberta Edmonton AB Canada Abo Akad Univ Turku Finland

Explicit model predictive control design is carefully developed for discrete-time linear plants on Hilbert spaces, and we highlight the role of the so-called Slater condition in the reliable explicit solution of the MPC optimization. We then proceed to present an explicit MPC algorithm that accounts for the stabilization and input constraints satisfaction. We do structure preserving temporal discretization of the infinite-dimensional parabolic PDE system by application of the Cayley transformation. The salient feature of explicit MPC design is the realization of the region-free approach in explicit MPC design with identification of active constraint sets to realize optimal stabilization and constraints satisfaction. Finally, the resulting design is illustrated by the application to the PDE model given by an unstable heat equation with boundary actuation and Neumann boundary conditions. The example demonstrates simultaneous stabilization and input constraints satisfaction on the one hand, and on the ability to deal with a relatively high plant dimension and a long optimization horizon on the other hand. Copyright (C) 2022 The Authors.

关键词： Explicit MPC distributed parameter systems Heat Equation Boundary Control

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Discrete-time model-based output regulation of fluid flow systems

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EUROPEAN JOURNAL OF CONTROL 2021年 57卷 1-13页

作者： Xie, Junyao Koch, Charles Robert Dubljevic, Stevan Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2V4 Canada Univ Alberta Dept Mech Engn Edmonton AB T6G 2V4 Canada

Model-based discrete-time output regulator design is proposed for fluid flow systems using a geometric approach. More specifically, a class of vortex shedding and falling thin film phenomena modelled by complex Ginzburg-Landau equation (CGLE) and Kuramoto-Sivashinsky equation (KSE) are considered. Differently from a traditional continuous-time controller design, a novel discrete-time modelling technique is proposed in a general infinite-dimensional state-space setting, which does not pertain any spatial approximation or model reduction, and preserves model intrinsic properties (such as stability, controllability and observability). Based on the time discretized plant model (CGLE and KSE systems) by the Cayley-Tustin method, discrete regulator regulation equations are established and facilitated for an output regulator design to achieve fluid flow control and manipulation. To address model instability, a spectrum analysis is utilized in stabilizing continuous-time CGLE and KSE systems, and a link between discrete- and continuous-time closed-loop system stabilizing gains is established. Finally, the proposed methodology is demonstrated through a set of simulation cases, by which the output tracking, disturbance rejection, and model stabilization are achieved for the considered CGLE and KSE systems. (C) 2020 European Control Association. Published by Elsevier Ltd. All rights reserved.

关键词： Flow control and manipulation distributed parameter systems Ginzburg-Landau equation Kuramoto-Sivashinsky equation Output regulation

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Iterative Learning Control for a Class of Multivariable distributed systems With Experimental Validation

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IEEE TRANSACTIONS ON CONTROL systems TECHNOLOGY 2021年第3期29卷 949-960页

作者： Mandra, Slawomir Galkowski, Krzysztof Rauh, Andreas Aschemann, Harald Rogers, Eric Nicolaus Copernicus Univ Fac Phys Astron & Informat Dept Automat & Measurement Syst PL-87100 Torun Poland Univ Zielona Gora Inst Control & Computat Engn PL-65516 Zielona Gora Poland Univ Rostock Chair Mechatron D-18059 Rostock Germany Univ Southampton Sch Elect & Comp Sci Southampton SO17 1BJ Hants England

This article develops an iterative learning control (ILC) design for a class of multiple-input-multiple-output systems where a distributed heating system is used as a particular example to experimentally validate the design. The class of systems considered is described by a parabolic partial differential equation, which, for control design, is approximated by a finite-dimensional state-space model obtained by applying the method of integro-differential relations combined with a projection approach. In some cases, including the distributed heating system, this approximation may result in a nonminimum phase system and, hence, pose an additional design challenge. In this work, the ILC law is computed in the frequency domain by solving a convex optimization problem, and its performance is evaluated in both simulation and experiment.

关键词： Heating systems Mathematical model MIMO communication State-space methods distributed parameter systems Trajectory Actuators distributed parameter system feedback control iterative learning control (ILC) multivariable system nonminimum phase system

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