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5th International Conference on Wavelet Analysis and Pattern Recognition

作者： Ding, Dou-Zhang Gu, Xing-Sheng E China Univ Sci & Technol Res Inst Automat Shanghai 200237 Peoples R China

ISBN: (纸本)9781424410651

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： boundary predictive control distributed parameter systems orthogonal wavelets trans formation simulation study

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distributed tracking control of an uncertain heat diffusion process

Distributed tracking control of an uncertain heat diffusion ...

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Mediterranean Conference on Control & Automation

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

ISBN: (纸本)9781467325301

This paper addresses the design of a distributed non smooth tracking controller for a class of uncertain diffusive processes with homogeneous boundary conditions of Neumann type. Uncertainty in the diffusivity parameter, along with the presence of a sufficiently smooth distributed disturbance, characterize the considered class of processes. The paper considers a dynamical controller with a linear PI structure complemented by a certain non-smooth integral term which gives the algorithm its main robustness properties. A constructive Lyapunov-based stability analysis is illustrated which leads to simple tuning conditions for the controller parameters guaranteeing the asympto tic tracking in the space L_2 of sufficiently smooth reference profiles. The main contribution of the present paper over recent related works (cfr. [19], [20]) is the relaxation of a quite restrictive assumption involving the external perturbation and, at the same time, the achievement of the control goal with milder information demand on the system's state. The good performance of the proposed control systems are verified by means of computer simulations.

关键词： distributed parameter systems Diffusion equation distributed control systems Sliding mode control

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Guaranteed Cost distributed Fuzzy Control Design for a Class of Nonlinear First-Order Hyperbolic PDE systems

Guaranteed Cost Distributed Fuzzy Control Design for a Class...

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American Control Conference

作者： Jun-Wei Wang Huai-Ning Wu Science and Technology on Aircraft Control Laboratory School of Automation Science and Electrical Engineering Beihang University (Beijing University of Aeronautics and Astronautics) Beijing 100191 China

ISBN: (纸本)9781457710957

This paper is concerned with the guaranteed cost distributed fuzzy (GCDF) control design problem for a class of nonlinear distributed parameter systems described by first-order hyperbolic partial differential equations (PDEs). Using the Takagi-Sugeno (T-S) fuzzy PDE modeling method, a T-S fuzzy PDE model is initially proposed to accurately represent the nonlinear PDE system. Based on the resulting T-S fuzzy PDE model, a distributed fuzzy state feedback controller is subsequently developed to asymptotically stabilize the PDE system and provide an upper bound of the quadratic cost function. The outcome of GCDF control problem is formulated as a space-dependent linear matrix inequality (SDLMI) optimization problem. Moreover, a suboptimal GCDF controller design is proposed to minimize the upper bound of the cost function. The finite difference method in space and the existing linear matrix inequality (LMI) optimization techniques are employed to approximately solve the SDLMI optimization problem. Finally, the proposed design method is applied to the distributed control of a nonisothermal plug-flow reactor (PFR).

关键词： design control distributed parameter systems Finite difference methods Fuzzy Hyperbolic decentralised control Distribute Fuzzy control linear matrix inequalities nonlinearity Cost functions design approach Upper bound

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Sampled-Data distributed H_∞ Control of a Class of Parabolic systems

Sampled-Data Distributed H_∞ Control of a Class of Paraboli...

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IEEE Annual Conference on Decision and Control

作者： Emilia Fridman Netzer Bar Am School of Electrical Engineering Tel-Aviv University

ISBN: (纸本)9781467320658

We develop, for the first time, sampled-data H_∞ control for a class of parabolic systems. These systems are governed by semilinear transport reaction equations with additive disturbances and with distributed control on a finite interval. We suggest a sampled-data controller design, where the sampling intervals in time and in space are bounded. The network of N stationary sensing devices provide spatially averaged state measurements over the sampling spatial intervals. Our sampled-data static output feedback enters the equation through N shape functions (which are localized in the space) multiplied by the corresponding state measurements. Sufficient conditions for the internal exponential stability and for L_2-gain analysis of the closed-loop system are derived via direct Lyapunov method in terms of Linear Matrix Inequalities (LMIs). By solving these LMIs, upper bounds on the sampling intervals that preserve the internal stability and the resulting L_2-gain can be found. Numerical examples illustrate the efficiency of the method.

关键词： distributed parameter systems Sampled-data control H_∞ control Lyapunov method LMIs distributed parameter systems Data sampling Lyapunov methods Standing Orders sampled-data controller internal stability Time intervals shape functions data control exponential stability. decentralised control

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distributed parameter Bioprocess Plant Identification and I-Term Control Using Centralized Recurrent Neural Network Models

Distributed Parameter Bioprocess Plant Identification and I-...

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International Joint Conference on Neural Networks (IJCNN)

作者： Baruch, Ieroham S. Saldierna, Eloy E. Castillo, Oscar CINVESTAV IPN Dept Automat Control Mexico City 07360 DF Mexico Inst Technol Grad Div Comp Sci Tijuana BC Mexico

ISBN: (纸本)9781424496365

In the paper, it is proposed to use a recurrent neural network model, and a real-time Levenberg-Marquardt algorithm of its learning for centralized data-based modeling, identification and control of an anaerobic digestion bioprocess, carried out in a fixed bed and a recirculation tank of a wastewater treatment system. The analytical model of the digestion bioprocess, used as process data generator, represented a distributed parameter system, which is reduced to a lumped system using the orthogonal collocation method, applied in four collocation points plus one- in the recirculation tank. The paper proposed to use three types of I-term adaptive control: direct adaptive integral plus states neural control, indirect adaptive I-term sliding mode control and real-time I-term optimal control. The comparative graphical simulation results of the digestion wastewater treatment system control, exhibited a good convergence and precise reference tracking, giving slight priority to the direct control with respect to the other methods of control applied.

关键词： Adaptation models Artificial neural networks Biological system modeling Equations Mathematical model Optimal control Topology adaptive control anaerobic digestion bioprocess biotechnology centralised control centralized data-based modeling centralized recurrent neural network models comparative graphical simulation digestion wastewater treatment system control direct adaptive integral plus states neural control distributed parameter bioprocess plant identification distributed parameter systems fixed bed tank indirect adaptive I-term sliding mode control lumped system neurocontrollers orthogonal collocation method process data generator real-time I-distributed term optimal control real-time Levenberg-Marquardt algorithm recirculation tank recurrent neural nets variable structure systems wastewater treatment

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Computation of empirical eigenfunctions of parabolic PDEs with time-varying domain

Computation of empirical eigenfunctions of parabolic PDEs wi...

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American Control Conference

作者： Mojtaba Izadi Stevan Dubljevic Department of Chemical & Materials Engineering University of Alberta Canada T6G 2V4

ISBN: (纸本)9781457710957

In this work, we explore a methodology to compute the empirical eigenfunctions for the order-reduction of nonlinear parabolic partial differential equations (PDEs) system with time-varying domain. The idea behind this method is to obtain the mapping functional, which relates the time-evolution scalar physical property solution ensemble of the nonlinear parabolic PDE with the time-varying domain to a fixed reference domain, while preserving space invariant properties of the raw solution ensemble. Subsequently, the Karhunen-Loeve decomposition is applied to the solution ensemble with fixed spatial domain resulting in a set of optimal eigenfunctions that capture the most energy of data. Further, the low dimensional set of empirical eigenfunctions is mapped ("pushed-back") on the time-varying domain by an appropriate mapping resulting in the basis for the construction of the reduced-order model of the parabolic PDEs with time-varying domain. Finally, this methodology is applied in the representative cases of calculation of empirical eigenfunctions in the case of one and two dimensional model of nonlinear reaction-diffusion parabolic PDE systems with analytically defined domain evolutions. In particular, the design of both mappings which relate the raw data and function spaces transformations from the time-varying to time-invariant domain are designed to preserve dynamic features of the scalar physical property and we provide comparisons among reduced and high order fidelity models.

关键词： Eigenvalues and eigenfunctions Moment methods Time varying systems Reduced order systems distributed parameter systems Jacobian matrices Chemicals

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A NOTE ON THE MODEL REFERENCE ADAPTIVE CONTROL OF LINEAR PARABOLIC systems WITH CONSTANT COEFFICIENTS

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Journal of systems Science & Complexity 2011年第6期24卷 1110-1117页

作者： Chaohua JIA School of Mathematics and Systems Science Beihang University Beijing 100191 China LMIB of the Ministry of Education Beijing 100191 China

The problem of constructing a model reference adaptive control law for an uncertain 1- dimensional parabolic system with one constant coefficient is considered in this paper. Adaptive control law are obtained by Lyapunov redesign method. The energy method for parabolic systems and the Agmon＇s inequality are applied in the analysis, which leads to a stronger result than that of Hong and Bentsman （Automatica, 1994）.

关键词： Adaptive law distributed parameter systems model reference adaptive control parabolic system.

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On exponential stability of linear retarded distributed parameter systems

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IFAC Proceedings Volumes 2007年第23期40卷 59-64页

作者： Yury Orlov Emilia Fridman CICESE Research Center Km.107 Carretera Tijuana-Ensenada Ensenada B.C. 22 860 Mexico Department of Electrical Engineering-Systems Tel-Aviv University Tel-Aviv 69978 Israel

Exponential stability analysis via Lyapunov-Krasovskii method is extended to linear time-delay systems in a Hilbert space. The operator acting on the delayed state is supposed to be bounded. The system delay is admitted to be unknown and time-varying with an a priori given upper bound on the delay derivative. Sufficient exponential stability conditions are derived in the form of Linear Operator Inequalities (LOIs), where the decision variables are operators in the Hilbert space. Being applied to a heat equation, these conditions are represented in terms of standard Linear Matrix Inequalities (LMIs). The proposed method is expected to provide effective tools for robust control of distributed parameter systems with time-delay.

关键词： distributed parameter systems time-varying delay stability Lyapunov functional LMI

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Lyapunov Stability of Linear Predictor Feedback for distributed Input Delays

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2011年第3期56卷 655-660页

作者： Bekiaris-Liberis, Nikolaos Krstic, Miroslav Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA

Compensation of distributed delays in MIMO, LTI systems is achieved using Artstein's reduction method. In this technical note, we construct a Lyapunov functional for the resulting closed-loop system and establish exponential stability. The key element in our work is the introduction of an infinite-dimensional forwarding-backstepping transformation of the infinite-dimensional actuator states. We illustrate the construction of the Lyapunov functional with a detailed example of a single-input system, in which the input is entering through two individual channels with different delays. Finally, we develop an observer equivalent to the predictor feedback design, for the case of distributed sensor delays and prove exponential convergence of the estimation error.

关键词： Delays distributed parameter systems linear systems

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FEEDFORWARD BOUNDARY CONTROL OF LINEAR distributed parameter systems USING A NUMERICAL INVERSE LAPLACE TRANSFORM

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IFAC Proceedings Volumes 2007年第20期40卷 673-678页

作者： Tobias Kreuzinger Frank A. King Matthias Bitzer Wolfgang Marquardt Mechatronic Engineering Group Corporate Sector Research and Advance Engineering Robert Bosch GmbH 71701 Schwieberdingen Germany Department of Process Systems Engineering RWTH Aachen University 52056 Aachen Germany

The feedforward boundary control design and disturbance compensation for a class of linear distributed parameter systems with fiat and non-fiat outputs is presented based on the analytical derivation of a control law in the Laplace domain and the use of a numerical inverse Laplace transformation. Control laws are derived for a conduction system, a conduction-convection system with source term, and two different types of counter-current heat exchanger systems. For the calculation of the inverse Laplace transform, a variant of the Weeks algorithm with automatic parameter tuning is employed. Simulation results show that the algorithm converges for different desired output trajectories and a wide range of parameter configurations.

关键词： distributed parameter systems Laplace Transform Numerical Inverse Laplace Transform Feedforward Boundary Control Heat Exchanger

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