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Transfer functions of distributed parameter systems: A tutorial

AUTOMATICA 2009年第5期45卷 1101-1116页

作者： Curtain, Ruth Morris, Kirsten Univ Waterloo Dept Appl Math Waterloo ON N2L 3G1 Canada Univ Groningen Dept Math NL-9700 AV Groningen Netherlands

In this tutorial article the rich variety of transfer functions for systems described by partial-differential equations is illustrated by means of several examples under various boundary conditions. An important feature is the strong influence of the choice of boundary conditions on the dynamics and on system theoretic properties such as pole and zero locations, properness, relative degree and minimum phase. It is sometimes possible to design a controller using the irrational transfer function, and several such techniques are outlined. More often, the irrational transfer function is approximated by a rational one for the purpose of controller design. Various approximation techniques and their underlying theory are briefly discussed. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Infinite-dimensional systems Partial-differential equations Control theory distributed parameter systems Relative degree Minimum phase

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An account of chronological developments in control of distributed parameter systems

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ANNUAL REVIEWS IN CONTROL 2009年第1期33卷 59-68页

作者： Padhi, Radhakant Ali, Sk. Faruque Indian Inst Sci Dept Aerosp Engn Bangalore 560012 Karnataka India Indian Inst Sci Dept Civil Engn Bangalore 560012 Karnataka India

Control systems arising in many engineering fields are often of distributed parameter type, which are modeled by partial differential equations. Decades of research have lead to a great deal of literature on distributed parameter systems scattered in a wide spectrum. Extensions of popular finite-dimensional techniques to infinite-dimensional systems as well as innovative infinite-dimensional specific control design approaches have been proposed. A comprehensive account of all the developments would probably require several volumes and is perhaps a very difficult task. In this paper, however, an attempt has been made to give a brief yet reasonably representative account of many of these developments in a chronological order. To make it accessible to a wide audience, mathematical descriptions have been completely avoided with the assumption that an interested reader can always find the mathematical details in the relevant references. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Partial differential equations distributed parameter systems Review Control Infinite dimensional systems

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Adaptive Neural Control Design for Nonlinear distributed parameter systems With Persistent Bounded Disturbances

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IEEE TRANSACTIONS ON NEURAL NETWORKS 2009年第10期20卷 1630-1644页

作者： Wu, Huai-Ning Li, Han-Xiong Beihang Univ Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China City Univ Hong Kong Dept Mfg Engn & Engn Management Hong Kong Hong Kong Peoples R China

In this paper, an adaptive neural network (NN) control with a guaranteed L-infinity-gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system to derive a low-order ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, based on the low-order slow model and the Lyapunov technique, an adaptive modal feedback controller is developed such that the closed-loop slow system is semiglobally input-to-state practically stable (ISpS) with an L-infinity-gain performance. In the proposed control scheme, a radial basis function (RBF) NN is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown system nonlinearities. The outcome of the adaptive L-infinity-gain control problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L-infinity-gain, while control constraints are respected. Furthermore, it is shown that the proposed controller can ensure the semiglobal input-to-state practical stability and L-infinity-gain performance of the closed-loop PDE system. Finally, by applying the developed design method to the temperature profile control of a catalytic rod, the achieved simulation results show the effectiveness of the proposed controller.

关键词： adaptive control distributed parameter systems input-to-state stability (ISS) linear matrix inequality (LMI) L-infinity-gain control neural network (NN)

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distributed Control of Spatially-Interconnected parameter-Invariant and LPV Models for Actuated Beams

Distributed Control of Spatially-Interconnected Parameter-In...

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American Control Conference

作者： Liu, Qin Gonzalez, Antonio Mendez Werner, Herbert Hamburg Univ Technol Inst Control Syst D-21073 Hamburg Germany

ISBN: (纸本)9781479932740

This paper presents a case study on distributed controller design for spatially-invariant and linear parameter-varying (LPV) models. To apply recently proposed state-space-based synthesis conditions, the experimentally identified input/output models are realized in terms of multidimensional state space representations, both for spatially-invariant and LPV models. Inheriting the interconnected structure of the plant, a spatially-invariant distributed controller is synthesized for a spatially-invariant model, and a spatial LPV controller for a spatially-varying model using constant Lyapunov functions. Considered here is vibration control of an actuated beam, equipped with an array of collocated piezo actuators and sensors. Experimental results show that vibrations at the dominant modes are effectively attenuated for both cases.

关键词： Actuators Aerospace electronics Interconnected systems Lyapunov methods Resonant frequency Sensors Uncertainty distributed parameter systems Flexible structures Linear parameter-varying systems

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Boundary output feedback of second-order distributed parameter systems

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systems & CONTROL LETTERS 2009年第7期58卷 519-528页

作者： Nguyen, Tu Duc Norwegian Univ Sci & Technol NTNU Fac Informat Technol Math & Elect Engn N-74910 Trondheim Norway

Boundary output feedback of a class of second order distributed parameter systems is addressed. In particular, second order distributed parameter systems without distributed damping are studied. First, a uniformly exponentially stable observer is designed. Then, exponentially stabilizing control laws are proposed. The existence, uniqueness and stability of solutions of the observer and the closed loop system are based on semigroup theory. (C) 2009 Elsevier B.V. All rights reserved.

关键词： distributed parameter systems Boundary output feedback Semigroup

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Optimal control of switched distributed parameter systems with spatially scheduled actuators

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AUTOMATICA 2009年第2期45卷 312-323页

作者： Iftime, Orest V. Demetriou, Michael A. Univ Groningen Fac Econ Dept Econometr NL-9700 AV Groningen Netherlands Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA

In many areas of control there are gaps between the existing theory and applications. This is more so in hybrid infinite dimensional systems and in particular hybrid systems in which both the actuator and the controller are switched. The main objective of this paper is to start filling in one of these gaps. We present a theoretical formulation and provide methodologies for implementing optimal and switching policies of spatially scheduled actuators for a class of distributed parameter systems (DPS). The optimization method employed is based on finite horizon LQR optimal control. Well posedness and optimality, pertaining to the switching policies of spatially scheduled actuators. are presented and proven. Tutorial examples motivated by thermal manufacturing applications along with extensive simulation results of the proposed actuator-plus-controller switching scheme are presented. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Scheduled actuator Optimal control Hybrid systems Switched systems Switched controllers

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Anthropomorphic finger antagonistically actuated by SMA plates

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BIOINSPIRATION & BIOMIMETICS 2015年第5期10卷 056002-056002页

作者： Engeberg, Erik D. Dilibal, Savas Vatani, Morteza Choi, Jae-Won Lavery, John Florida Atlantic Univ Ocean & Mech Engn Dept Boca Raton FL 33431 USA Univ Akron Dept Mech Engn ASEC Akron OH 44325 USA Gedik Univ Dept Mech Engn Istanbul Turkey

Most robotic applications that contain shape memory alloy (SMA) actuators use the SMA in a linear or spring shape. In contrast, a novel robotic finger was designed in this paper using SMA plates that were thermomechanically trained to take the shape of a flexed human finger when Joule heated. This flexor actuator was placed in parallel with an extensor actuator that was designed to straighten when Joule heated. Thus, alternately heating and cooling the flexor and extensor actuators caused the finger to flex and extend. Three different NiTi based SMA plates were evaluated for their ability to apply forces to a rigid and compliant object. The best of these three SMAs was able to apply a maximum fingertip force of 9.01N on average. A 3D CAD model of a human finger was used to create a solid model for the mold of the finger covering skin. Using a 3D printer, inner and outer molds were fabricated to house the actuators and a position sensor, which were assembled using a multi-stage casting process. Next, a nonlinear antagonistic controller was developed using an outer position control loop with two inner MOSFET current control loops. Sine and square wave tracking experiments demonstrated minimal errors within the operational bounds of the finger. The ability of the finger to recover from unexpected disturbances was also shown along with the frequency response up to 7 rad s(-1). The closed loop bandwidth of the system was 6.4 rad s(-1) when operated intermittently and 1.8 rad s(-1) when operated continuously.

关键词： shape memory alloy NiTi robotic finger grasp distributed parameter systems

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A Parallel Algorithm for Optimum Monitoring Network Design in parameter Estimation of distributed systems

A Parallel Algorithm for Optimum Monitoring Network Design i...

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European Control Conference (ECC)

作者： Ucinski, Dariusz Baranowski, Przemyslaw Univ Zielona Gora Inst Control & Computat Engn Ul Podgorna 50 PL-65246 Zielona Gora Poland Univ Zielona Gora Ctr Comp Zielona Gora Poland

ISBN: (纸本)9783033039629

The design of a network of observation nodes in a spatial domain is addressed. The observations are to be used to estimate unknown parameters of a distributed parameter system. Given a finite number of possible sites at which to locate a sensor, the problem is formulated as the selection of the gauged sites so as to minimize a convex criterion defined on the Fisher information matrix associated with the estimated parameters. The search for an optimal solution to this binary optimization problem is performed through solving a relaxed problem in which a constrained discrete probability distribution on the set of all allowable sites is sought. The main contribution here consists in properly parallelizing this solution using the parallel variable distribution approach. As a result, each processor minimizes a convex function subject to linear constraints through the use of a simplicial decomposition algorithm. The resulting individual solutions are then synchronized by finding their optimal convex combination.

关键词： Parallel algorithms Probability distribution distributed systems parameter estimation Network design Convex function monitoring network distributed parameter systems spatial domain Unknown parameter optimal solution PROCESSOR Convexity information matrix

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Variable structure sliding mode control for a class of uncertain distributed parameter systems with time-varying delays

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INTERNATIONAL JOURNAL OF CONTROL 2009年第2期82卷 287-297页

作者： Xing, Hailong Gao, Cunchen Tang, Gongyou Li, Donghai Tsinghua Univ Dept Thermal Engn Beijing 100084 Peoples R China Ocean Univ China Coll Math Qingdao 266071 Peoples R China Ocean Univ China Coll Informat Sci & Engn Qingdao 266071 Peoples R China

This article considers sliding mode control of a class of parabolic linear uncertain distributed parameter systems with time-varying delays. The sliding mode controller design does not contain time delay terms and drives the state trajectory of the system to the sliding manifold in finite time. A sufficient condition of asymptotic stability for the sliding motion is derived. A simulation example is presented to illustrate effectiveness of the proposed method.

关键词： distributed parameter systems uncertain sliding mode control time-varying delays

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Modal Reduction Based Tracking Control for Installation of Subsea Equipments ∗

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IFAC-PapersOnLine 2015年第6期48卷 15-20页

作者： Fabricio Rodrigues Monteiro Jose Oniram de Aquino Limaverde Filho Eugenio Fortaleza GRACO - Grupo de Automagao e Controle Universidade de Brasilia Brasilia Brazil

This paper proposes a control strategy for the deep sea installation of wellhead equipments hanged by flow line structures, named risers. A fundamental step of this operation is the positioning of the equipment over the wellhead, which can be costly, time-consuming, and unfeasible in bad weather conditions. The approach taken considers the riser structure an Euler-Bernoulli beam submerged in a fluid, whose top end is fixed in the offshore platform and the bottom end attached to a payload. A dynamic analysis is carried to identify the structure's most significant modes of vibration and create a reduced-order model. Then, a flatness-based approach is used for trajectory planning and tracking, resulting in a low complexity control structure. Numerical simulations are presented to validate the proposed controller and to analyse its performance in the presence of external perturbations.

关键词： Offshore Structures distributed parameter systems Modal Reduction Trajectory Tracking

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