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distributed adaptive consensus algorithm for networked Euler-Lagrange systems

IET CONTROL THEORY AND APPLICATIONS 2011年第1期5卷 145-154页

作者： Min, H. Sun, F. Wang, S. Li, H. Tsinghua Univ Dept Comp Sci & Technol Beijing 100084 Peoples R China High Tech Inst Xian Beijing 710025 Peoples R China

Most consensus protocols developed in the past are for linear-integrator systems or deterministic non-linear systems. Here, the authors study the state consensus for non-point, non-linear networked Euler-Lagrange systems with unknown parameters. Specifically, state consensus problems with both coupling time delay and switching topology are investigated. By establishing a unified architecture based on the passivity property, adaptive consensus protocols are developed. It is shown that state consensus is reachable despite the unknown parameters, and the estimation errors of these parameters converge to zero. Furthermore, by introducing the leader-follower architecture, the authors show that each agent will converge its origin. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithms.

关键词： nonlinear systems switching topology Other topics in statistics passivity property adaptive consensus protocols linear integrator system estimation errors state consensus problems time-varying systems Time-varying control systems nonlinear networked Euler-Lagrange systems Nonlinear control systems deterministic nonlinear system leader-follower architecture coupling time delay delays distributed adaptive consensus algorithm distributed parameter systems estimation theory distributed parameter control systems distributed algorithms

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distributed feedback design for systems governed by the wave equation

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INTERNATIONAL JOURNAL OF CONTROL 2011年第8期84卷 1417-1429页

作者： Maidi, Ahmed Corriou, Jean-Pierre Nancy Univ Lab React & Genie Procedes CNRS ENSIC F-54001 Nancy France Univ Mouloud MAMMERI Dept Automat Fac Genie Elect & Informat Tizi Ouzou 15000 Algeria

This article deals with the geometric control of a one-dimensional non-autonomous linear wave equation. The idea consists in reducing the wave equation to a set of first-order linear hyperbolic equations. Then, based on geometric control concepts, a distributed control law that enforces the exponential stability and output tracking in the closed-loop system is designed. The presented control approach is applied to obtain a distributed control law that brings a stretched uniform string, modelled by a wave equation with Dirichlet boundary conditions, to rest in infinite time by considering the displacement of the middle point of the string as the controlled output. The controller performances have been evaluated in simulation by considering both tracking and disturbance rejection problems. The robustness of the controller has also been studied when the string tension is subjected to sudden variations.

关键词： distributed parameter systems partial differential equation wave equation geometric control

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Repetitive Learning Control of a Flexible Whisker in Tip Contact with an Unknown Surface

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JOURNAL OF VIBRATION AND CONTROL 2011年第2期17卷 197-203页

作者： Zhao, Haiyu Rahn, Christopher D. Novellus Syst San Jose CA 95134 USA Penn State Univ Dept Mech & Nucl Engn University Pk PA 16802 USA

Repetitive contact imaging uses a flexible whisker attached to a two-axis robot through a load cell. Assuming small deformations and rotations, the pitch axis decouples from the yaw. The yaw axis, under proportional-integral-derivative control, sweeps periodically back and forth across the object while the pitch axis, under repetitive learning (RL) control, maintains a uniform contact force. Once the RL controller converges, the three-dimensional contact points can be determined using an elastica algorithm. The RL controller is proven stable based on a distributed parameter beam model and is experimentally shown to provide a stable performance with improved moment regulation when compared with under proportional-derivative control.

关键词： Repetitive learning control distributed parameter systems object identification robotics

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distributed Fuzzy Control Design of Nonlinear Hyperbolic PDE systems With Application to Nonisothermal Plug-Flow Reactor

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IEEE TRANSACTIONS ON FUZZY systems 2011年第3期19卷 514-526页

作者： Wang, Jun-Wei Wu, Huai-Ning Li, Han-Xiong Beijing Univ Aeronaut & Astronaut Beihang Univ Sch Automat Sci & Elect Engn Sci & Technol Aircraft Control Lab Beijing 100191 Peoples R China City Univ Hong Kong Dept Mfg Engn & Engn Management Hong Kong Hong Kong Peoples R China

This paper considers the problem of fuzzy control design for a class of nonlinear distributed parameter systems that is described by first-order hyperbolic partial differential equations (PDEs), where the control actuators are continuously distributed in space. The goal of this paper is to develop a fuzzy state-feedback control design methodology for these systems by employing a combination of PDE theory and concepts from Takagi-Sugeno (T-S) fuzzy control. First, the T-S fuzzy hyperbolic PDE model is proposed to accurately represent the nonlinear first-order hyperbolic PDE system. Subsequently, based on the T-S fuzzy-PDE model, a Lyapunov technique is used to analyze the closed-loop exponential stability with a given decay rate. Then, a fuzzy state-feedback control design procedure is developed in terms of a set of spatial differential linear matrix inequalities (SDLMIs) from the resulting stability conditions. Furthermore, utilizing the finite-difference approximation method (with a backward difference for the spatial derivative), a recursive algorithm is presented to solve the SDLMIs via the existing LMI optimization techniques. Finally, the developed design methodology is successfully applied to the control of a nonisothermal plug-flow reactor.

关键词： distributed parameter systems exponential stability fuzzy control linear matrix inequalities (LMIs) Takagi-Sugeno (T-S) fuzzy model

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BOUNDARY CONTROLLERS AND OBSERVERS FOR THE LINEARIZED SCHRODINGER EQUATION

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2011年第4期49卷 1479-1497页

作者： Krstic, Miroslav Guo, Bao-Zhu Smyshlyaev, Andrey Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA Acad Sinica Acad Math & Syst Sci Beijing 100190 Peoples R China Shanxi Univ Sch Math Sci Taiyuan 030006 Peoples R China Univ Witwatersrand Sch Computat & Appl Math ZA-2050 Johannesburg Johannesburg South Africa

We consider a problem of stabilization of the linearized Schrodinger equation using boundary actuation and measurements. We propose two different control designs. First, a simple proportional collocated boundary controller is shown to exponentially stabilize the system. However, the decay rate of the closed-loop system cannot be prescribed. The second, full-state feedback boundary control design, achieves an arbitrary decay rate. We formally view the Schrodinger equation as a heat equation in complex variables and apply the backstepping method recently developed for boundary control of reaction-advection-diffusion equations. The resulting controller is then supplied with the backstepping observer to obtain an output-feedback compensator. The designs are illustrated with simulations.

关键词： distributed parameter systems backstepping stabilization

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Dynamics and control of aggregate thin film surface morphology for improved light trapping: Implementation on a large-lattice kinetic Monte Carlo model

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CHEMICAL ENGINEERING SCIENCE 2011年第23期66卷 5955-5967页

作者： Huang, Jianqiao Zhang, Xinyu Orkoulas, Gerassimos Christofides, Panagiotis D. Univ Calif Los Angeles Dept Chem & Biomol Engn Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90095 USA

This work demonstrates the use of feedback control, coupled with a suitable actuator design, in manufacturing thin films whose surface morphology is characterized by a desired visible light reflectance/ transmittance level. The problem is particularly important in the context of thin film manufacturing for thin film solar cells where it is desirable to produce thin films with precisely tailored light trapping characteristics. Initially, a thin film deposition process involving atom adsorption and surface migration is considered and is modeled using a large-lattice (lattice size=40,000) kinetic Monte Carlo simulation. Subsequently, thin film surface morphology characteristics like roughness and slope are computed with respect to different characteristic length scales ranging from atomic to the ones corresponding to visible light wavelength and it is found that a patterned actuator design is needed to induce thin film surface roughness and slope at visible light wavelength spatial scales, which lead to desired thin film reflectance and transmittance levels. Then, an Edwards-Wilkinson-type equation (a second-order stochastic partial differential equation) is used to model the surface evolution at the visible light wavelength spatial scale and form the basis for the design of a feedback controller whose objective is to manipulate the deposition rate across the spatial domain of the process. The model parameters of the Edwards-Wilkinson equation are estimated from kinetic Monte Carlo simulations and their dependence on the deposition rate is used in the formulation of the predictive controller to predict the influence of the control action on the surface roughness and slope throughout the thin film growth process. Analytical solutions of the expected surface roughness and surface slope at the visible light wavelength spatial scale are obtained by solving the Edwards-Wilkinson equation and are used in the control action calculation. The cost function of the controller inv

关键词： Surface morphology Light trapping optimization Model predictive control distributed parameter systems Thin film growth Thin film solar cells

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Sliding mode boundary control of a parabolic PDE system with parameter variations and boundary uncertainties

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AUTOMATICA 2011年第2期47卷 381-387页

作者： Cheng, Meng-Bi Radisavljevic, Verica Su, Wu-Chung Natl Chung Hsing Univ Dept Elect Engn Taichung 402 Taiwan Calif State Univ Los Angeles Dept Mech Engn Los Angeles CA 90032 USA Amer Univ Sharjah Dept Mech Engn Sharjah U Arab Emirates

This paper considers the stabilization problem of a one-dimensional unstable heat conduction system (rod) modeled by a parabolic partial differential equation (PDE), powered with a Dirichlet type actuator from one of the boundaries. By applying the Volterra integral transformation, a stabilizing boundary control law is obtained to achieve exponential stability in the ideal situation when there are no system uncertainties. The associated Lyapunov function is used for designing an infinite-dimensional sliding manifold, on which the system exhibits the same type of stability and robustness against certain types of parameter variations and boundary disturbances. It is observed that the relative degree of the chosen sliding function with respect to the boundary control input is zero. A continuous control law satisfying the reaching condition is obtained by passing a discontinuous (signum) signal through an integrator. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Sliding mode control distributed parameter systems Boundary control Chattering reduction Lyapunov function

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A Self-Tuning Robust Regulator for Infinite-Dimensional systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2011年第9期56卷 2116-2127页

作者： Hamalainen, Timo Pohjolainen, Seppo Tampere Univ Technol Dept Math FIN-33101 Tampere Finland

In this paper, we consider the problem of designing a robust controller for an unknown, infinite-dimensional, exponentially stable, linear time-invariant plant. The controller should be able to asymptotically track and reject reference and disturbance signals which are finite linear combinations of constants and sinusoids of known frequencies, in such a way that the plant and controller states remain bounded. A self-tuning controller is proposed, which generalizes to infinite-dimensional systems and sinusoidal reference and disturbance signals the controller given by Miller and Davison in 1989 for finite-dimensional systems and constant reference and disturbance signals. The only information needed of the plant is the values of its transfer function P (i omega(k)) at the reference and disturbance frequencies. Since the values P (i omega(k)) can be measured from the open loop plant with frequency response measurements, no plant model is needed. As far as the authors know, the results given in this paper are new even for finite-dimensional systems.

关键词： Adaptive control distributed parameter systems regulation robust control tracking

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Instabilities and multiplicities in non-isothermal blown film extrusion including the effects of crystallization

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JOURNAL OF PROCESS CONTROL 2011年第3期21卷 405-414页

作者： Pirkle, J. Carl, Jr. Braatz, Richard D. MIT Dept Chem Engn Cambridge MA 02139 USA Univ Illinois Urbana IL 61801 USA

Stable operating regions for blown film extrusion are mapped using a dynamic model that includes the effect of crystallization on the rheological properties of the polymer. In the computations, the bubble air mass and take-up ratio were held constant, and the machine tension and bubble inflation pressure were treated as dependent variables. For a given bubble air mass, the take-up ratio was used as the continuation parameter for mapping steady-state solutions. The take-up ratio varies smoothly, but not necessarily monotonically, with the machine tension. Curves of either blow-up ratio or thickness reduction versus take-up ratio reveal that there are take-up ratios where no, one, or multiple solutions exist. The heat transfer coefficient from the polymer film to the external air and surroundings has a marked influence on the qualitative and quantitative features of the blow-up ratio versus thickness reduction curves. Generalized eigenvalue analysis of the linearized blown film equations indicates that increasing the heat transfer rate increases the stability of operations. A corresponding decline occurs, however, in the thickness reduction of the blown film for a given blow-up ratio. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Differential-algebraic equations Nonlinear dynamics Stability analysis Polymer processes Polymer film extrusion

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Feedback Stabilization of Infinite-Dimensional Linear systems with Constraints on Control and its Rate

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EUROPEAN JOURNAL OF CONTROL 2011年第2期17卷 183-190页

作者： Abouzaid, Bouchra Achhab, M. Elarbi Wertz, Vincent Univ Chouaib Doukkali Dept Math & Informat Lab Ingn Math El Jadida Morocco Univ Cadi Ayyad Ecole Super Technol Safi Safi 46000 Morocco Catholic Univ Louvain CESAME B-1348 Louvain Belgium

The feedback stabilization problem in the presence of non-symmetrical constraints on both control and its rate is addressed for a class of distributed parameter systems. Necessary and sufficient conditions are established, under which the constraints are satisfied for autonomous infinite-dimensional systems. The approach is developed using the semigroup formulation and the positive invariance concept. The main result allows us to determine some suitable positively invariant sets of admissible initial states, in which the constraints are satisfied, with respect to the asymptotically stable closed-loop system.

关键词： distributed parameter systems constrained control increment or rate constraints positive invariance

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