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distributed parameter system identification using finite element differential neural networks

APPLIED SOFT COMPUTING 2016年 43卷 633-642页

作者： Aguilar-Leal, O. Fuentes-Aguilar, R. Q. Chairez, I. Garcia-Gonzalez, A. Huegel, J. C. Tecnol Monterrey Monterrey Mexico UPIBI Inst Politecn Nacl Bioproc Dept Mexico City DF Mexico

Most of the previous work on identification involves systems described by ordinary differential equations (ODEs). Many industrial processes and physical phenomena, however, should be modeled using partial differential equations (PDEs) which offer both spatial and temporal distributions that are simply not available with ODE models. systems described by a PDE belong to a class of system called distributed parameter system (DPS). This article presents a method for solving the problem of identification of uncertain DPSs using a differential neural network (DNN). The DPS, assumed to be described by a PDE, is approximated using the finite element method (FEM). The FEM discretizes the domain into a set of distributed and connected nodes, thereby, allowing a representation of the DPS in a finite number of ODEs. The proposed DNN follows the same interconnection structure of the FEM, thus allowing the DNN to identify the FEM approximation of the DPS in both 2D and 3D domains. Lyapunov's second method was used to derive adaptive learning laws for the proposed DNN structure. The identification algorithm, here developed in Nvidia's CUDA/C to reduce the execution time, runs mostly on the graphics processing unit (GPU). A physical experiment served to validate the 2D case. In the experiment, the DNN followed the trajectory of 57 markers that were placed on an undulating square piece of silk. The proposed DNN is compared against a method based on principal component analysis and an artificial neural network trained with group search optimization. In addition to the 2D case, a simulation validated the 3D case, where input data for the DNN was generated by solving a PDE with appropriate initial and boundary conditions over an unitary domain. Results show that the proposed FEM-based DNN approximates the dynamic behavior of both a real 2D and a simulated 3D system. (C) 2016 Elsevier B.V. All rights reserved.

关键词： distributed parameter systems Non-parametric identification Differential neural network Finite element method CUDA/C Parallel numerical solutions

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Admissibility and Exact Observability of Observation Operators for Micro-Beam Model: Time- and Frequency-Domain Approaches

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2017年第12期62卷 6438-6444页

作者： Edalatzadeh, Mohammad S. Alasty, Aria Vatankhah, Ramin Sharif Univ Technol Dept Mech Engn Tehran Iran Sharif Univ Dept Mech Engn Shiraz Iran

This study focuses on the exact observability of a non-classical Euler-Bernoulli micro-beam equation. This non-classical model was derived based on the strain gradient elasticity theory, which is intended to explain the phenomenon of size effect at the micron scale. Spectral properties of the corresponding state operator are studied;an asymptotic expression for eigenvalues is calculated, and eigenfunctions are analyzed in order to check the necessary conditions for the exact observability of the system. By examining the eigenfunctions, it is shown that among non-collocated boundary outputs, only measurement of the non-classical moment at the root of the beam yields an admissible observation operator and also defines an exactly observable system. An alternative proof based on the multiplier method, which is commonly employed in the literature on the observability and controllability of infinite dimensional dynamical systems, is presented to provide a comparison between the time-and frequency-domain approaches.

关键词： distributed parameter systems flexible structures microelectromechanical systems (MEMS) observability

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Backstepping observer using weighted spatial average for 1-dimensional parabolic distributed parameter systems

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IFAC Proceedings Volumes 2011年第1期44卷 13326-13331页

作者： Daisuke Tsubakino Shinji Hara Department of Information Physics and Computing The University of Tokyo Tokyo Japan

Abstract This paper is concerned with designing a backstepping-based observer for a class of 1-dimensional parabolic distributed parameter systems whose output is a weighted spatial average of the state. We first show that an integral transformation converts the original system into another parabolic system with boundary observation if the weighting function satisfies a parameterized ordinary differential equation. Then the backstepping observer for the transformed system is available and an estimate of the original state is obtained through the inverse transformation. We also show that the estimation error exponentially converges to 0 in terms of the L 2 norm with arbitrary decay rate. Furthermore, a closed-form expression of the observer is provided for systems described by linear reaction-diffusion equations.

关键词： distributed parameter systems Partial differential equations Observers Average values

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Software sensor as distributed parameter system for the control of secondary cooling in the continuous casting of steel

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IFAC-PapersOnLine 2016年第20期49卷 49-54页

作者： Hulkó, G. Ondrejkovi, K. Buek, P. Bartko, M. Institute of Automation Measurement and Applied Informatics FME STU in Bratislava Nám. slobody 17 Bratislava812 31 Slovakia P VVC s.r.o. Kolkáre 35 Podbrezová976 81 Slovakia

Sophisticated numerical models are created nowadays for the continuous casting of steel, partly thanks to the rapid development of information technology. These models are based on the numerical solutions of nonlinear partial differential equations describing the dynamics of modelled phenomena. Such distributed parameter numerical models used as “software sensors” offer the possibility to control the secondary cooling process. However, in current engineering practice the control synthesis is solved by lumped parameter systems approach. This paper shows how to solve the control synthesis problem based on distributed parameter system approach, using widely available software products for numerical modelling of continuous casting of steel combined with algorithms for control of lumped and distributed parameter systems. © 2016

关键词： distributed parameter control systems Continuous casting Control system synthesis Intelligent control Model predictive control Nonlinear equations Numerical models Partial differential equations Steel castings Approximation problems Constrained model predictive control Continuous casting of steels Control design distributed parameter systems Software sensor

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A STABILIZATION OF FIXED GAIN CONTROLLED INFINITE DIMENSIONAL systems BY AUGMENTATION WITH DIRECT ADAPTIVE CONTROL

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ASME Conference on Smart Materials, Adaptive Structures and Intelligent systems (SMASIS 2017)

作者： Balas, Mark J. Frost, Susan A. Embry Riddle Aeronaut Univ Daytona Beach FL 32504 USA NASA Ames Res Ctr Moffett Field CA 94035 USA

ISBN: (纸本)9780791858264

Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. We have developed the following stability result: an infinite dimensional linear system is Almost Strictly Dissipative (ASD) if and only if its high frequency gain CB is symmetric and positive definite and the open loop system is minimum phase, i.e. its transmission zeros are all exponentially stable. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. It is usually true that fixed gain controllers are designed for particular applications but these controllers may not be able to stabilize the plant under all variations in the operating domain. Therefore we propose to augment this fixed gain controller with a relatively simple direct adaptive controller that will maintain stability of the full closed loop system over a much larger domain of operation. This can ensure that a flexible structure controller based on a reduced order model will still maintain closed-loop stability in the presence of unmodeled system dynamics. The augmentation approach is also valuable to reduce risk in loss of control situations. First we show that the transmission zeros of the augmented infinite dimensional system are the open loop plant transmission zeros and the eigenvalues (or poles) of the fixed gain controller. So when the open-loop plant transmission zeros are exponentially stable, the addition of any stable fixed gain controller does not alter the stability of the transmission zeros. Therefore the combined plant plus control

关键词： Adaptive control distributed parameter systems

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Deadzone compensation based boundary control of a flexible aerial refueling hose with output constraint

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IFAC-PapersOnLine 2017年第1期50卷 645-650页

作者： Liu Z. Liu J. He W. School of Automation Science and Electrical Engineering Beihang University Beijing 100191 China School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing 100083 China

In this paper, boundary control schemes are designed for a flexible aerial refueling hose subject to input deadzone, output constraint and external disturbances, based on partial differential equations (PDEs). Firstly, a basic boundary control scheme, based on the backstepping method, is proposed to regulate the hose's vibration. A radial basis function (RBF) neural network is used to handle the effect of the input deadzone. Then we propose a new controller based on a barrier Lyapunov function to prevent constraint violation. It is shown that the states of the system are proven to converge to a small neighborhood of zero, and the output constraint is not violated in the presence of the input deadzone and external distrubances. Finally, simulation results are demonstrated for control performance verification. © 2017

关键词： boundary control deadzone compensation distributed parameter systems output constraint

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Boundary Actuation in Galerkin-Models of Linear distributed parameter systems

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IFAC Proceedings Volumes 2011年第1期44卷 7541-7546页

作者： Mathias Hakenberg Günter C. Keßler Kristina Schindelar Dirk Abel Institute of Automatic Control (IRT) RWTH Aachen University D-52056 Aachen Germany Siemens AG D-81739 München Germany

Abstract Proper orthogonal decomposition and subsequent Galerkin-projection is a common technique to obtain low-dimensional models for distributed parameter systems. In this paper a transformation of boundary conditions into equivalent source terms for linear partial differential equations is used to set up such reduced-order models. This approach provides the means to consider boundary actuation in Galerkin-models, which is essential for the design of feedback controllers. Using the example of a one-dimensional convection-diffusion equation, the transient dynamics between the non-actuated and actuated steady state are described with such a reduced-order-model. Dynamic range and model accuracy are investigated in connection with the employed number of POD modes and the dynamics of actuation.

关键词： distributed parameter systems reduced-order-models proper orthogonal decomposition

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Boundary Control of Nonlinear distributed parameter systems by Input-Output Linearization

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IFAC Proceedings Volumes 2011年第1期44卷 10910-10915页

作者： Ahmed MAIDI Jean Pierre CORRIOU Université Mouloud MAMMERI Faculté de Génie Electrique et d'Informatique Département Automatique Tizi-Ouzou Algérie Laboratoire Réactions et Génie des Procédés (LRGP) CNRS-ENSIC 1 Rue Grandville BP 20451 54001 Nancy Cedex France

Abstract The present study focuses on boundary control of nonlinear distributed parameter systems and deals with Dirichlet actuation. Thus, a design approach of a geometric control law that enforces stability and output tracking of a given punctual output is developed based on the notion of the characteristic index. The control performance of the proposed strategy is evaluated through numerical simulation by considering two control problems. The former concerns the control of the temperature of a thin metal rod modelled by a heat equation with a nonlinear source, and the later concerns the control of concentration of a dye in liquid medium modeled by Fick law with nonconstant diffusivity.

关键词： distributed parameter systems nonlinear partial differential equation geometric control input-output linearization

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Dynamic Pollutant Plume Front Tracking and Monitoring by a Single Mobile Robot

Dynamic Pollutant Plume Front Tracking and Monitoring by a S...

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Chinese Automation Congress (CAC)

作者： Wang, Jun-Wei Guo, Yi Zhang, Lan Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing Peoples R China Stevens Inst Technol Dept Elect & Comp Engn Hoboken NJ 07030 USA

ISBN: (纸本)9781538635247

This paper presents an observer-based motion control scheme for a single mobile robot to track and monitor a dynamic pollutant plume propagation in m-dimensional space. The spatiotemporal dynamics of the pollutant plume is modeled by an advection-diffusion partial differential equation (PDE), and the plume front is described by a level set with a pre-specified threshold value. In the suggested control scheme, a Luenberger-type PDE observer using the local area concentration measurement taken from the onboard concentration sensor is first constructed to derive the concentration field knowledge over the entire spatial domain. Then, a motion control law is constructed based on the observer equation to drive the robot to track and patrol on the plume front. Rigorous convergence analysis of the suggested control algorithm is provided by the set stability concept and Lyapunov's direct method. Numerical simulations of planar pollutant plume front tracking and monitoring are demonstrated for the effectiveness of the proposed control scheme.

关键词： Monitoring dynamic plume field mobile robot Luenberger observer distributed parameter systems

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Time delay and wave propagation in controlling systems of conservation laws 21

Time delay and wave propagation in controlling systems of co...

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21st International Conference on System Theory, Control and Computing (ICSTCC)

作者： Rasvan, Vladimir Danciu, Daniela Popesar, Dan Univ Craiova Dept Automat Elect & Mechatron RO-200585 Craiova Romania

ISBN: (纸本)9781538638422

In this paper there are considered some applications arising from power engineering and involving hyperbolic equations of conservation laws. Focusing on the control of the flow in open channels, there is considered the linearized model and a Lyapunov functional is associated. A linear multivariable controller with saturation is synthesized to make the Lyapunov functional exponentially decreasing along the solutions of the closed loop system. By integrating the Riemann invariants along the characteristics there is associated a linear system of difference equations. On this system the basic theory is constructed and the stability verified. Finally a research program for analyzing nonlinear cases is sketched.

关键词： control design distributed parameter systems delay systems

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