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Optimal Tracking Control of Current Profile in Tokamaks

IEEE TRANSACTIONS ON CONTROL systems TECHNOLOGY 2011年第2期19卷 432-441页

作者： Ou, Y. Xu, C. Schuster, E. Luce, T. C. Ferron, J. R. Walker, M. L. Humphreys, D. A. Lehigh Univ Dept Mech Engn & Mech Bethlehem PA 18015 USA Chinese Acad Sci Shenzhen Inst Adv Technol Shenzhen 518055 Guangdong Peoples R China Gen Atom Co DIII D Tokamak San Diego CA 92121 USA

Setting up a suitable current spatial profile in tokamak plasmas has been demonstrated to be a key condition for one possible advanced scenario with improved confinement and possible steady-state operation. Experiments at the DIII-D tokamak focus on creating the desired current profile during the plasma current ramp-up and early flattop phases with the aim of maintaining this target profile during the subsequent phases of the discharge. The evolution in time of the current profile is related to the evolution of the poloidal magnetic flux, which is modeled in normalized cylindrical coordinates using a parabolic partial differential equation usually referred to as the magnetic diffusion equation. We propose a framework to solve a finite-time, optimal tracking control problem for the current profile evolution via diffusivity, interior, and boundary actuation during the ramp-up and early flattop phases of the discharge. The proposed approach is based on reduced order modeling via proper orthogonal decomposition and successive optimal control computation for a bilinear system. Simulation results illustrate the performance of the proposed controller.

关键词： Bilinear optimal tracking control distributed parameter systems proper orthogonal decomposition (POD) tokamak plasma control

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Linear-Quadratic Optimal Actuator Location

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2011年第1期56卷 113-124页

作者： Morris, Kirsten Univ Waterloo Dept Appl Math Waterloo ON N2L 3G1 Canada

In control of vibrations, diffusion and many other problems governed by partial differential equations, there is freedom in the choice of actuator location. The actuator location should be chosen to optimize performance objectives. In this paper, we consider linear quadratic performance. Two types of cost are considered;the choice depends on whether the response to the worst initial condition is to be minimized;or whether the initial condition is regarded as random. In practice, approximations are used in controller design and thus in selection of the actuator locations. The optimal cost and location of the approximating sequence should converge to the exact optimal cost and location. In this work conditions for this convergence are given in the case of linear quadratic control. Examples are provided to illustrate that convergence may fail when these conditions are not satisfied.

关键词： Actuators algebraic Riccati equations convergence of numerical methods distributed parameter systems linear-quadratic control partial differential equations

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Stick-slip Oscillations in Oillwell Drilstrings: distributed parameter and Neutral Type Retarded Model Approaches

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IFAC Proceedings Volumes 2011年第1期44卷 284-289页

作者： Belem Saldivar Sabine Mondié Jean-Jacques Loiseau Vladimir Rasvan Departamento de Control Automático Cinvestav IPN México D.F. Institut de Recherche en Communications et Cybernétique de Nantes Nantes France University of Craiova Craiova Romania

Abstract The drill pipe model is described by the wave equation with mixed boundary conditions in which a sliding velocity is considered at the top end. The proposal of an energy function for the distributed model allows to find a control law that ensures the energy dissipation during the drilling operation. The distributed parameter model is reduced through the d'Alembert transformation to a difference equation model. Torsional drillstring vibrations, also known as “stick-slip” oscillations appearing in oilwell drillstrings are a source of failures which reduce penetration rates and increase drilling operation costs. Some experience-based control strategies are evaluated in order to reduce stick-slip oscillations. The use of the angular velocity at the drillstring upper part, the torque on the bit and the weight on the bit is shown to have a key effect in the reduction of drillstring torsional vibrations.

关键词： Drilling systems stick-slip phenomenon distributed parameter systems time-delay systems model validation

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distributed-parameter second-order sliding-mode control techniques for the uncertain heat and wave equations

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IFAC Proceedings Volumes 2011年第1期44卷 762-767页

作者： Alessandro Pisano Yury Orlov Elio Usai CICESE Research Center Ensenada Mexico Dept. of Electrical and Electronic Engineering (DIEE) Univ. of Cagliari Cagliari Italy

Abstract In the present paper, preliminary results towards the generalization to the infinite-dimensional setting of some finite-dimensional second-order sliding mode control algorithms are illustrated. The main focus of the present paper is on the rejection of non-vanishing external disturbances. The “Twisting” and “SuperTwisting” second-order sliding-mode control algorithms (see (Levant (1993))) are properly generalized to address the state tracking problem for the wave and heat equations. Constructive proofs of stability are developed via Lyapunov functional technique, which leads to simple tuning rules for the controller parameters. Simulation results are discussed to verify the effectiveness of the proposed schemes.

关键词： distributed parameter systems Sliding mode control Uncertain systems

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Optimal boundary control synthesis for a class of distributed parameter systems applying adaptive critics

Optimal boundary control synthesis for a class of distribute...

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Mediterranean Conference on Control and Automation (MED)

作者： Daniela G. Toshkova Petar D. Petrov G. P. Toshkov Technical University of Varna Bulgaria

In the present paper optimal boundary control problem for a class of distributed parameter systems of parabolic type is considered. The simplified adaptive critic methodology is applied for the optimal control synthesis. The methodology requires the distributed parameter system to be reduced to lumped parameter system, as well as to be subsequently discretized. The approximation to finite-dimensional system is realized by using the generalized finite integral transform technique.

关键词： Optimal control Control system synthesis distributed parameter systems Adaptive systems Programmable control Adaptive control Neural networks Boundary conditions Integral equations Partial differential equations

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Boundary predictive control of first-order linear modulus-varying distributed parameter systems based on wavelets transformation

Boundary predictive control of first-order linear modulus-va...

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International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)

作者： Dou-Zhang Ding Xing-Sheng Gu Research Institute of Automation East China University of Science and Technology Shanghai China Electrical Engineering Department Shanghai Dianji University Shanghai China

A new idea to control of distributed parameter systems is to induct the boundary control idea into predictive control of distributed parameter systems. Because of complexity of distributed parameter systems, control system design is the difficulty of control theory. In this paper, discrete-time boundary predictive control algorithm of first-order linear modulus-varying distributed parameter systems based on orthogonal wavelets transformation is proposed. First-order linear modulus-varying distributed parameter systems in boundary control is approximated in Haar wavelets transformation. So the predictive control proposition of distributed parameter systems has been transformed into the predictive control issue of lumped parameter systems. The boundary predictive controller is designed for the input sequence returning to the boundary predictive control rule of the original system. Simulation studies of the proposed algorithm, as well as the system robustness under uncertainty such as the parameters perturbations, and a disturb occurring to the system output are showed. The results have verified the control effectiveness of the proposed algorithm.

关键词： Predictive control distributed parameter systems Control systems Wavelet analysis distributed control Predictive models Prediction algorithms Discrete wavelet transforms Robustness Pattern analysis

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Flatness-based Deformation Control of a 1-Dimensional Microbeam with In-domain Actuation

Flatness-based Deformation Control of a 1-Dimensional Microb...

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Annual Conference on IEEE Industrial Electronics Society

作者： Amir Badkoubeh Guchuan Zhu Department of Electrical Engineering Ecole Polytechnique de Montreal

ISBN: (纸本)9781467324199

This paper addresses the problem of asymptotic tracking control of a micro-beam described by Euler-Bernoulli equation actuated by a one-dimensional array of micro-actuators. This system represents a one-dimensional model of deformable mirrors widely used in wavefront control and optical aberration correction in adaptive optics systems. The proposed control that allows steering the mirror along smooth reference trajectories consists in first mapping the nonhomogeneous partial differential equation model of the system into a standard boundary control form. Then, a combination of the methods of energy multiplier and flatness-based motion planning is used so that the closed-loop system is stabilized around reference trajectories. The viability and the applicability of the developed scheme is demonstrated through numerical simulations.

关键词： Microelectromechanical systems distributed parameter systems Tracking control Flat systems

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On the Exact Observability of distributed parameter systems

On the Exact Observability of Distributed Parameter Systems

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Proceedings of the 46th IEEE Conference on Decision and Control, Pages 1839-2300

作者： Karl Rieger Kurt Schlacher Institute of Automatic Control and Control Systems Technology Johannes Kepler University Linz Linz Austria

ISBN: (纸本)9781424414970;1424414970

This contribution is devoted to the observability analysis of distributed parameter systems derived on the basis of the Calculus of Variations. A system theoretical analysis is motivated by the utilization of a differential geometric framework, which allows a covariant description of infinite dimensional systems. In particular, the (exact) observability along a trajectory of dynamic systems is discussed in general and it is shown that by means of the obtained formal approach (local) observability criteria can be provided.

关键词： distributed parameter systems Observability Multidimensional systems Calculus of variation Dynamic systems Exact trajectory

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Observer Design for Second-Order distributed parameter systems in ℝ2

Observer Design for Second-Order Distributed Parameter Syste...

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IEEE Conference on Decision and Control

作者： Tu Duc Nguyen Faculty of Information Technology Mathematics and Electrical Engineering Norwegian University of Science and Technology Trondheim Norway

Observer design for second-order distributed parameter systems in R 2 is addressed. Particularly, second order distributed parameter systems without distributed damping are studied. Based on finite number of measurements, exponentially stable observer is designed. The existence, uniqueness and stability of solutions of the observer are based on semigroup theory.

关键词： distributed parameter systems Damping Observers Control systems State estimation Flexible structures Stability Differential equations Partial differential equations Finite element methods

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Model Reference Adaptive H_(infinity) Control for distributed parameter systems of Hyperbolic Type by Finite Dimensional Controllers - Construction with Unbounded Observation Operator

Model Reference Adaptive H_(infinity) Control for Distribute...

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Proceedings of the 46th IEEE Conference on Decision and Control, Pages 1-459

作者： Yoshihiko Miyasato Department of Mathematical Analysis and Statistical Inference Institute for Statistical Mathematics Tokyo Japan

The problem of constructing model reference adaptive H_(infinity) control for distributed parameters systems of hyperbolic type is considered in this paper. The proposed control strategy is composed of finite dimensional compensators, and is derived as a solution of certain H_(infinity) control problem where spillovers are regarded as external disturbance. Contrary to our previous research, we consider the case where the observation operator is unbounded in the present paper.

关键词： Adaptive control Programmable control Optimal control Control systems distributed control distributed parameter systems Eigenvalues and eigenfunctions USA Councils Partial differential equations Hilbert space

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