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A Closed-Form Solution to Estimate Spatially Varying parameters in Heat and Mass Transport

IEEE CONTROL systems LETTERS 2021年第5期5卷 1681-1686页

作者： van Kampen, Ricky J. R. Das, Amritam Weiland, Siep van Berkel, Matthijs DIFFER Dutch Inst Fundamental Energy Res Energy Syst & Control Grp NL-5612 AJ Eindhoven Netherlands Eindhoven Univ Technol Dept Mech Engn NL-5600 MB Eindhoven Netherlands Eindhoven Univ Technol Dept Elect Engn NL-5600 MB Eindhoven Netherlands

This letter presents a closed-form solution to estimate space-dependent transport parameters of a linear one dimensional diffusion-transport-reaction equation. The infinite dimensional problem is approximated by a finite dimensional model by 1) taking a frequency domain approach, 2) linear parameterization of the unknown parameters, and 3) using a semi-discretization. Assuming full state knowledge, the commonly used output error criterion is rewritten as the equation error criterion such that the problem results in linear least squares. The optimum is then given by a closed-form solution, avoiding computational expensive optimization methods. Functioning of the proposed method is illustrated by means of simulation.

关键词： Mathematical model Frequency measurement Closed-form solutions Estimation Boundary conditions Computational modeling Loss measurement Grey-box modeling distributed parameter systems identification inverse problems

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Constructive finite-dimensional boundary control of stochastic 1D parabolic PDEs

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AUTOMATICA 2023年 148卷

作者： Wang, Pengfei Katz, Rami Fridman, Emilia Harbin Inst Technol Sch Math Harbin 150001 Peoples R China Tel Aviv Univ Sch Elect Engn Tel Aviv Israel

Recently, a constructive method for the finite-dimensional observer-based control of deterministic parabolic PDEs was suggested by employing a modal decomposition approach. In this paper, for the first time we extend this method to the stochastic 1D heat equation with nonlinear multiplicative noise. We consider the Neumann actuation and study the observer-based as well as the state-feedback controls via the modal decomposition approach. We employ either trigonometric or polynomial dynamic extension. For observer-based control we consider a noisy boundary measurement. First, we show the well-posedness of strong solutions to the closed-loop systems. Then by suggesting a direct Lyapunov method and employing Ito's formula, we provide mean-square L2 exponential stability analysis of the full-order closed-loop system, leading to linear matrix inequality (LMI) conditions for finding the observer dimension and as large as possible noise intensity bound for the mean-square stabilizability. We prove that the LMIs are always feasible for small enough noise intensity and large enough observer dimension (for observer-based control). We further show that in the case of state -feedback and linear noise, the system is always stabilizable for noise intensities that guarantee the stabilizability of the stochastic finite-dimensional part of the closed-loop system with deterministic measurement. Numerical simulations are carried out to illustrate the efficiency of our method. For both state-feedback and observer-based controls, the trigonometric extension always allows for a larger noise than the polynomial one in the example.(c) 2022 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Stochastic parabolic PDEs Boundary control

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Controllability and Observability Gramians for the Circular Membrane with Radial Symmetry

Controllability and Observability Gramians for the Circular ...

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Automatics and Informatics (ICAI), International Conference

作者： Kamen Perev Systems and Control Department Technical University of Sofia Sofia Bulgaria

ISBN: (数字)9798350353907

ISBN: (纸本)9798350353914

This paper considers the problem of controllability and observability Gramians computation for circular membrane with radial symmetry. The circular membrane is described by second order hyperbolic partial differential equation in polar coordinate system. The derivation of the system Gramians is based on state space formulation of the wave equation in the framework of abstract differential equation. This framework uses the concept of C 0 -strongly continuous semigroup generated by a system operator containing spatial derivatives of the underlying process. The radial symmetry of the membrane simplifies the model description and reduces it to differential equation with simple spatial variable. The time-space separation principle is used to reduce the infinite dimensional problem to simple mathematical calculations. The partial differential equation is solved by using the Fourier – Bessel series expansion. The solution of the wave equation is utilized to derive the Gramians in explicit form.

关键词： Propagation Partial differential equations Force Aerospace electronics Controllability Harmonic analysis Mathematical models Observability Informatics distributed parameter systems

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Mutual Impedance-Based Force/Velocity Transmission Improvement for Bilateral Teleoperation

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IFAC-PapersOnLine 2023年第2期56卷 9992-9997页

作者： Kosuke Shikata Seiichiro Katsura Department of System Design Engineering Keio University Yokohama 223-8522 Japan

Tackling communication delays attracts interest in improving the stability and transparency of bilateral teleoperation. This study presents a novel concept; mutual impedance. Under the delays, this impedance is intrinsic in four-channel acceleration-based bilateral control (4ch ABC). In 4ch ABC, wave propagations can characterize the transmissions of force and velocity, which are described in distributed-parameter systems. The delays induce interference between applied force and velocity response and decrease transparency. The mutual relationship between force and position controllers can explain the interference. The proposed mutual impedance is the indicator of the impact of the relationship. This study notes that the impedance comprises a ratio of force and position controllers. Thus, a force proportional-integral (PI) controller with a gain constraint between the position controller is introduced. One-degree-of-freedom (1-DOF) motion experiments compare the proposed method with conventional methods in superiority. The applicability of the proposed approach to delay fluctuations and multi-DOF motion is verified through 3-DOF manipulators.

关键词： Motion control systems Telepresence Networked robotic system modeling and control distributed parameter systems Time-delay systems

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Thermal Diffusivity Identification of distributed parameter systems to Sea Ice

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JOURNAL OF APPLIED MATHEMATICS 2013年第SI17期000卷 1-8页

作者： Shi, Liqiong Li, Zhijun Feng, Enmin Bai, Yila Yang, Yu Dalian Univ Technol State Key Lab Coastal & Offshore Engn Dalian 116024 Peoples R China Dalian Univ Technol Sch Math Sci Dalian 116024 Peoples R China Bohai Univ Math & Phys Dept Jinzhou 121000 Peoples R China

A method of optimal control is presented as a numerical tool for solving the sea ice heat transfer problem governed by a parabolic partial differential equation. Taken the deviation between the calculated ice temperature and the measurements as the performance criterion, an optimal control model of distributed parameter systems with specific constraints of thermal properties of sea ice was proposed to determine the thermal diffusivity of sea ice. Based on sea ice physical processes, the parameterization of the thermal diffusivity was derived through field data. The simulation results illustrated that the identified parameterization of the thermal diffusivity is reasonably effective in sea ice thermodynamics. The direct relation between the thermal diffusivity of sea ice and ice porosity is physically significant and can considerably reduce the computational errors. The successful application of this method also explained that the optimal control model of distributed parameter systems in conjunction with the engineering background has great potential in dealing with practical problems.

关键词： THERMAL diffusivity IDENTIFICATION (Statistics) distributed parameter systems SEA ice OPTIMAL control theory HEAT transfer

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Data-Driven Modelling and Robust Control of a Semiconductor Manufacturing Process

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IFAC-PapersOnLine 2023年第2期56卷 4234-4239页

作者： Paul Mayr Martin Kleindienst Stefan Koch Markus Reichhartinger Martin Horn Christian Doppler Laboratory for Model-Based Control of Complex Test Bed Systems Institute of Automation and Control Graz University of Technology Graz Austria Lam Research AG Villach Austria Institute of Automation and Control Graz University of Technology Graz Austria

The paper presents a model-based controller design technique for a thermal process in silicon wafer manufacturing. The underlying model is obtained by dynamic mode decomposition which is a purely data-driven approach. The control scheme consists of a state feedback controller in combination with a disturbance observer, which allows robust tracking of feasible reference temperature profiles. The approach is validated using a laboratory setup.

关键词： Data-driven control distributed parameter systems Model order reduction

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Observability and observer design for a class of hyperbolic PDEs with van de Pol type boundary conditions

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2023年 127卷

作者： Xiang, Qiaomin Wu, Ze-Hao Deng, Feiqi Wu, Chufen Foshan Univ Dept Math & Big Data Foshan 528000 Peoples R China South China Univ Technol Syst Engn Inst Guangzhou 510640 Peoples R China

This paper focuses on observability and observer design for nonlinear complex dynamical systems described by a class of hyperbolic partial differential equations (PDEs) with nonlinear van de Pol type boundary conditions. The systems exhibit complex dynamics due to its imbalance of energy flows. Both the exact observability and approximate observability of the systems with different boundary output measurements are shown by using methods of characteristics and boundary nonlinear reflections. Motivated by the approximate observability of the systems, a PDE state observer by using the boundary displacement measurement only is designed, and a sufficient condition to guarantee the estimation error systems to be exponentially stable is given. Theoretical results are proved rigorously, with some numerical simulations performed to validate the effect of the proposed observer. (c) 2023 Elsevier B.V. All rights reserved.

关键词： distributed parameter systems Observability Observer design Nonlinear van de Pol type boundary conditions

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Minimal Differential Difference Realizations of Delay Differential, Differential Difference, and Neutral Delay systems

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IEEE CONTROL systems LETTERS 2021年第4期5卷 1471-1476页

作者： Peet, Matthew M. Arizona State Univ Sch Engn Matter Transport & Energy Tempe AZ 85298 USA

Delay-Differential Equations (DDEs) are often used to represent control of and over large networks. However, the presence of delay makes the problems of analysis and control of such networks challenging. Recently, Differential Difference Equations (DDFs) have been proposed as a modelling framework which allows us to more efficiently represent the low-dimensional nature of delayed channels in a network or large-scale delayed system. Unfortunately, however, the standard conversion formulae from DDE to DDF do not account for this low-dimensional structure - hence any efficient DDF representation of a large delayed network or system must be hand-crafted. In this letter, we propose an algorithm for constructing DDF realizations of both DDE and DDF systems wherein the dimension of the delayed channels has been minimized. Furthermore, we provide a convenient PIETOOLS implementation of these algorithms and show that the algorithm significantly reduces the complexity of the model for several illustrative examples, including Neutral Delay systems (NDSs).

关键词： Delay systems Difference equations Computational modeling Integral equations Delays Mathematical model Standards Computational methods delay systems distributed parameter systems modeling network analysis and control

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parameter Estimation of Hyperbolic Model of Counterflow Heat Exchanger

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IFAC-PapersOnLine 2023年第2期56卷 3235-3240页

作者： Jacques Kadima Kazaku Denis Dochain Moïse Mukepe Kahilu Jimmy Kalenga Kaunde Kasongo Department of Mathematical Engineering ICTEAM UCLouvain 4-6 avenue G. Lemaître B-1348 Louvain-La-Neuve Belgium Department of Electromechanics and Mine Université de Lubumbashi route Kasapa 1825 D.R. Congo

The aim of this paper is to estimate the parameters of a counterflow heat exchanger in the case where the dynamics are described by a system of two hyperbolic partial differential equations (PDEs). This study is performed using data collected on a laboratory test bench. First we study the practical identifiability of the system, the objective of which is to verify the possibility of determining the parameters of the system in a unique way from the available data. Next the parameter estimation is performed by a nonlinear optimization method, typically by the Levenberg-Marquardt algorithm on a set of ordinary differential equations obtained from the reduction of the original PDEs by the method of lines. Since the Levenberg-Marquardt algorithm may only converge with a reasonable estimate of the parameters, we first consider a least squares parameter estimation approach based on the global difference model. Finally, the results of this Identification are validated by using laboratory data, and by verifying some statistical properties.

关键词： Identifiability system Identification parameter estimation heat exchangers distributed parameter systems

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DMD-Based Model Predictive Control for a Coupled PDE-ODE System

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IFAC-PapersOnLine 2023年第2期56卷 4258-4263页

作者： Dirk Wolfram Thomas Meurer Chair of Automation and Control Faculty of Engineering Kiel University 24143 Kiel Germany Digital Process Engineering Group Institute for Mechanical Process Engineering and Mechanics Karlsruhe Institute of Technology (KIT) 76187 Karlsruhe Germany

Models resulting from the application of the finite element method (FEM) are usually high dimensional, thus in general preventing the application of optimal control concepts under real-time conditions. In this work a system consisting of the heat equation defined on a 3-dimensional domain with local in-domain thermal actuators is considered, whose modeling results in a coupled PDE-ODE description. Based on simulation data, a data driven reduced order model is determined using the Dynamic Mode Decomposition with control (DMDc). Based on the DMDc model a model predictive control (MPC) approach with state estimator is developed to realize a desired temperture profile on the given domain. The concept is evaluated involving the high-dimensional finite element model as plant model.

关键词： distributed parameter systems Reduced order model Data-driven control Model predictive control Heat conduction

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