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Tracking control for boundary controlled parabolic PDEs with varying parameters: Combining backstepping and differential flatness

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AUTOMATICA 2009年第5期45卷 1182-1194页

作者： Meurer, Thomas Kugi, Andreas Vienna Univ Technol Automat & Control Inst Complex Dynam Syst Grp A-1040 Vienna Austria

The combination of backstepping-based state-feedback control and flatness-based trajectory planning and feedforward control is considered for the design of an exponentially stabilizing tracking controller for a linear diffusion-convection-reaction system with spatially and temporally varying parameters and nonlinear boundary input. For this, in a first step the backstepping transformation is utilized to determine a state-feedback controller, which transforms the original distributed-parameter system into an appropriately chosen exponentially stable distributed-parameter target system of a significantly simpler structure. In a second step, the flatness property of the target system is exploited in order to determine the feedforward controller, which allows us to realize the tracking of suitably prescribed trajectories for the system output. This results in a systematic procedure for the design of an exponentially stabilizing tracking controller for the considered general linear diffusion-convection-reaction system with varying parameters, whose applicability and tracking performance is evaluated in simulation studies. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Tracking control distributed-parameter systems Diffusion-convection-reaction systems Backstepping Stabilization Differential flatness Trajectory planning

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LAGRANGIAN AND HAMILTONIAN FORMULATION OF TRANSMISSION LINE systems WITH BOUNDARY ENERGY FLOW

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REPORTS ON MATHEMATICAL PHYSICS 2009年第1期63卷 55-74页

作者： Jeltsema, Dimitri van der Schaft, Arjan J. Delft Univ Technol Delft Inst Appl Math NL-2628 CD Delft Netherlands Univ Groningen Inst Math & Comp Sci NL-9700 AV Groningen Netherlands

The classical Lagrangian and Hamiltonian formulation of an electrical transmission line is reviewed and extended to allow for varying boundary conditions, The method is based on the definition of an infinite-dimensional analogue of the affine Lagrangian and Hamiltonian input-output systems formulation. The boundary energy flow is then captured in an interaction Lagrangian. This leaves the associated Hamiltonian equations of motion symplectic in form, while the internal Hamiltonian still coincides with the total stored energy in the transmission line. The framework is, however, limited to a line that is terminated on both ends by independent voltage sources. This stems from the fact that the classical formulation captures only one wave equation for a lossless transmission line in terms of an integrated charge density. Additionally, the inclusion of the usual line resistance and shunt conductance via a Rayleigh dissipation function(al) is nontrivial. To circumvent these problems, a family of alternative Lagrangian functionals is proposed. The method is inspired by a (not so well-known) concept from network theory called 'the traditor'.

关键词： Lagrangian equations Hamiltonian equations transmission line boundary conditions distributed-parameter systems

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Optimal Boundary Control of Kuramoto-Sivashinsky Equation

Optimal Boundary Control of Kuramoto-Sivashinsky Equation

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American Control Conference 2009

作者： Dubljevic, Stevan Univ Calif Los Angeles Dept Chem & Biomol Engn Los Angeles CA 90095 USA

ISBN: (纸本)9781424445233

This work focuses on optimal boundary control of highly dissipative Kuramoto-Sivashinsky equation (KSE) which describes the long-wave motions of a thin film over vertical plane. A standard transformation is initially used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation (PDE) in an appropriate functional space setting. Low dimensional representation of the KSE is used in the synthesis of a finite dimensional linear quadratic regulator (LQR) in the full-state feedback control realization and in a compensator design with a Luenberger-type observer. The proposed control problem formulation and the performance and robustness of the closed-loop system in the full state-feedback, output-feedback and in the output-feedback with the presence of noise controller realization have been evaluated through simulations.

关键词： distributed-parameter systems Kuramoto-Sivashinsky Equation Boundary control LQR State/Output Feedback Control

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Boundary Model Predictive Control of Kuramoto-Sivashinsky Equation with Input and Point State Constraints

Boundary Model Predictive Control of Kuramoto-Sivashinsky Eq...

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Joint 48th IEEE Conference on Decision and Control (CDC) / 28th Chinese Control Conference (CCC)

作者： Dubljevic, Stevan Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2V4 Canada

ISBN: (纸本)9781424438723

In this work an infinite dimensional system representation of a highly dissipative Kuramoto-Sivashinsky equation (KSE) is been utilized in the model modal predictive control (MMPC) synthesis framework to achieve asymptotic stabilization of an unstable KS equation in the presence of input and point exerted state constraints. The KS equation is initially defined in an appropriate functional space setting and an exact transformation is used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation (PDE). An appropriate discrete infinite dimensional representation of the abstract boundary control problem is used for synthesis of low dimensional model modal predictive controller (MMPC) incorporating both the pointwise enforced KSE state constraints and input constraints. The proposed control problem formulation and the performance of the closed-loop system in the full state-feedback controller realization have been evaluated through simulations.

关键词： distributed-parameter systems Kuramoto-Sivashinsky Equation Boundary Control Model Predictive Control (MPC) Input/State Constraints

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Model-based Control Design of a Diesel Oxidation Catalyst

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IFAC Proceedings Volumes 2009年第11期42卷 279-284页

作者： Olivier Lepreux Yann Creff Nicolas Petit IFP Lyon Technology Computer Science and Applied Mathematics Division BP 3 69360 Solaize France Centre Automatique et Systèmes Mathématiques et Systèmes MINES ParisTech 60 bd. Saint-Michel 75272 Paris Cedex 06 France

Abstract This paper proposes a control strategy for a Diesel Oxidation Catalyst (DOC) which is grounded on a one-dimensional distributed parameter model. This first principles model for the propagation of the temperature variations accounts for spatially distributed heat generation (due to oxidation of reductants). As is discussed, heat generation can be regarded as equivalent inlet temperature variations. This fact is supported by experimental results. By nature, DOC outlet temperature response includes long and time-varying delays. An approximation of the proposed model allows to derive delays analytically, and can be used to schedule control parameters. As a consequence, it is easy to design several standard controllers for the DOC outlet temperature which account for the effects of the inlet temperature (disturbance) and the reductant (control). In this paper, simulation results are presented for a PI, a PID, and a Smith predictor. Interestingly, the three controllers use solely parameters determined from the previous analysis and do not need any extra tuning parameter. The strategies are tested on a standard NEDC driving cycle in simulation. It appears that, among these standard strategies, the DOC partial derivative equations can be efficiently controlled using the presented Smith predictor.

关键词： Automotive exhaust aftertreatment systems Diesel oxidation catalyst distributed-parameter systems Boundary control Control applications

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Log-Normal Merging for distributed System Identification

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IFAC Proceedings Volumes 2009年第10期42卷 551-556页

作者： Václav Ŝmídl Miroslav Kárný Institute of Information Theory and Automation Prague Czech Republic

Growing interest in applications of distributed systems, such as multi-agent systems, increases demands on identification of distributed systems from partial information sources collected by local agents. We are concerned with fully distributed scenario where system is identified by multiple agents, which do not estimate state of the whole system but only its local ‘state'. The resulting estimate is obtained by merging of marginal and conditional posterior probability density functions (pdf) on such local states. We investigate the use of recently proposed non-parametric log-normal merging of such ‘fragmental’ pdfs for this task. We derive a projection of the optimal merger to the class of weighted empirical pdfs and mixtures of Gaussian pdfs. We illustrate the use of this technique on distributed identification of a controlled autoregressive model.

关键词： system identification distributed-parameter systems distributed artificial intelligence decentralized systems

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OPTIMAL ACTIVATION STRATEGY OF DISCRETE SCANNING SENSORS FOR FAULT DETECTION IN distributed-parameter systems

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IFAC Proceedings Volumes 2005年第1期38卷 209-214页

作者： Maciej Patan Dariusz Uciński Institute of Control and Computation Engineering University of Zielona Góra ul. Podgórna 50 65-246 Zielona Góra

The problem under consideration is to determine an activation policy of discrete scanning sensors in such a way as to maximize the power of a simple parametric hypothesis test, which verifies the nominal state of the considered distributed system specified over a given multi-dimensional spatial domain. The optimal locations of sensors are determined based on the D s -optimality criterion defined on the respective Fisher Information Matrix. The proposed approach exploits the notion of directly constrained design measures recently introduced in modern optimum experimental design theory which leads to an extremely fast iterative procedure of exchange type. In this work, a general scheme of such an approach leading to maximization of the fault detection efficiency in distributed-parameter systems is delineated and tested via computer simulations regarding an advection-diffusion problem.

关键词： distributed-parameter systems fault detection hypothesis testing scanning observations

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Optimal Boundary Control of Kuramoto-Sivashinsky Equation

Optimal Boundary Control of Kuramoto-Sivashinsky Equation

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2009 American Control Conference (ACC 2009)

作者： Stevan Dubljevic Department of Chemical and Biomolecular Engineering University of California Los Angeles CA 90095

ISBN: (纸本)9781424445233

关键词： distributed-parameter systems Kuramoto-Sivashinsky Equation Boundary control LQR State/Output Feedback Control

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Boundary Model Predictive Control of Kuramoto-Sivashinsky Equation with Input and Point State Constraints

Boundary Model Predictive Control of Kuramoto-Sivashinsky Eq...

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Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference

作者： Stevan Dubljevic Department of Chemical and Materials Engineering University of Alberta

In this work an infinite dimensional system representation of a highly dissipative Kuramoto-Sivashinsky equation(KSE) is been utilized in the model modal predictive control(MMPC) synthesis framework to achieve asymptotic stabilization of an unstable KS equation in the presence of input and point exerted state *** KS equation is initially defined in an appropriate functional space setting and an exact transformation is used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation(PDE).An appropriate discrete infinite dimensional representation of the abstract boundary control problem is used for synthesis of low dimensional model modal predictive controller(MMPC) incorporating both the pointwise enforced KSE state constraints and input *** proposed control problem formulation and the performance of the closed-loop system in the full statefeedback controller realization have been evaluated through simulations.

关键词： distributed-parameter systems Kuramoto Sivashinsky Equation Boundary Control Model Predictive Control(MPC) Input/State Constraints

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Sliding Mode Boundary Control of Unstable Parabolic PDE systems with parameter Variations and Matched Disturbances

Sliding Mode Boundary Control of Unstable Parabolic PDE Syst...

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2009 American Control Conference (ACC 2009)

作者： Meng-Bi Cheng Verica Radisavljevic Wu-Chung Su Electrical Engineering Department at National Chung Hsing University Taiwan Electrical and Computer Engineering Department at Rutgers State University of New Jersey

ISBN: (纸本)9781424445233

This paper considers the stabilization problem of a one-dimensional unstable heat conduction system subject to parametric variations and boundary uncertainties. This system is modeled as a parabolic partial differential equation (PDE) and is only powered from one boundary with a Dirichlet type of actuator. By taking the Volterra integral transformation, we obtain a nominal PDE with asymptotic stability characteristics in the new coordinates when an appropriate boundary control input is applied. The associated Lyapunov function can then be used for designing an infinite-dimensional sliding surface, on which the system exhibits exponential stability, invariant of the bounded matched disturbance, and is robust against certain types of parameter variations. A continuous variable structure boundary control law is employed to attain the sliding mode on the sliding surface. The proposed method can be extended to other parabolic PDE systems such as diffusion-advection system. Simulation results are demonstrated and compared with the other outstanding back-stepping control schemes.

关键词： Boundary control chattering distributed-parameter systems sliding surface Lyapunov methods parameter variation Sliding mode Boundary boundary layer Liapunov function Slip surfaces Unstable actuators heat conduction system

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