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Boundary control of coupled reaction-advection-diffusion equations having the same diffusivity parameter. The research leading to these results has received funding from the research project “Modeling, control and experimentation of innovative thermal storage systems”, funded by Sardinia regional government under grant agreement n. CRP-60193

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IFAC-PapersOnLine 2016年第8期49卷 86-91页

作者： Pisano, Alessandro Baccoli, Antonello Orlov, Yury Usai, Elio Department of Electrical and Electronic Engineering University of Cagliari Cagliari Italy CICESE Research Center Ensenada Mexico

We consider the problem of boundary stabilization for a system of n coupled parabolic linear PDEs of the reaction-diffusion-advection type. Particularly, we design a state-feedback law with Dirichlet-type actuation on only one end of the domain and prove exponential stability of the closed-loop system with an arbitrarily fast convergence rate. The backstepping method is used for controller design, and the transformation kernel matrix is derived by using the method of successive approximations to solve the corresponding PDE. Simulation results support the effectiveness of the suggested design. © 2016

关键词： distributed parameter control systems Advection Backstepping Closed loop systems Controllers Diffusion Heat storage Linear transformations Partial differential equations State feedback Back stepping method Boundary controls Boundary stabilization distributed parameter systems Fast convergence rate Method of successive approximations Reaction advection diffusion equations Thermal storage system

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CFD modeling and control of a steam methane reforming reactor

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CHEMICAL ENGINEERING SCIENCE 2016年 148卷 78-92页

作者： Lao, Liangfeng Aguirre, Andres Tran, Anh Wu, Zhe Durand, Helen 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 initially focuses on developing a computational fluid dynamics (CFD) model of an industrial scale steam methane reforming reactor (reforming tube) used to produce hydrogen. Subsequently, we design and evaluate three different feedback control schemes to drive the area-weighted average hydrogen mole fraction measured at the reforming tube outlet ((x) over bar (outlet)(H2)) to a desired set-point value ((x) over bar (set)(H2)) under the influence of a tube-side feed disturbance. Specifically, a CFD model of an industrial-scale reforming tube is developed in ANSYS Fluent with realistic geometry characteristics to simulate the transport and chemical reaction phenomena with approximate representation of the catalyst packing. Then, to realize the real-time regulation of the hydrogen production, the manipulated input and controlled output are chosen to be the outer reforming tube wall temperature profile and (x) over bar (outlet)(H2) respectively. On the problem of feedback control, a proportional (P) control scheme, a proportional-integral (PI) control scheme and a control scheme combining dynamic optimization and integral feedback control to generate the outer reforming tube wall temperature profile based on (x) over bar (set)(H2) are designed and integrated into real-time CFD simulation of the reforming tube to track (x) over bar (set)(H2). The CFD simulation results demonstrated that feedback control schemes can drive the value of (x) over bar (outlet)(H2) toward (x) over bar (set)(H2) in the presence of a tube side feed disturbance and can significantly improve the process dynamics compared to the dynamics under open-loop control. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Steam methane reforming CFD modeling Process dynamics Process identification Process control distributed parameter systems

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Stabilization of Reaction Diffusion Equations With State Delay Using Boundary Control Input

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2016年第12期61卷 4041-4047页

作者： Hashimoto, Tomoaki Krstic, Miroslav Osaka Inst Technol Dept Mech Engn Asahi Ku Osaka Osaka 5358585 Japan Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA

This study analyses a stabilization method for reaction-diffusion equations with state delay using boundary control input. The proposed control strategy is based on the back-stepping method, wherein the controlled system is transformed into a target system. The objective of this study is to show that the conventional transformation, which was proposed for undelayed reaction-diffusion equations, can still provide a stabilizing boundary controller for a special class of delayed equations.

关键词： Backstepping control delays distributed parameter systems Lyapunov-Razumikhin functions nonnegative semigroups

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Design of a Nonlinear, Dynamic Feedforward Part for the Evaporator Control of an Organic Rankine Cycle in Heavy Duty Vehicles

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IFAC-PapersOnLine 2016年第11期49卷 625-632页

作者： Seitz, D. Gehring, O. Bunz, C. Brunschier, M. Sawodny, O. Institute for System Dynamics University of Stuttgart Stuttgart70511 Germany Daimler AG Stuttgart70546 Germany

A model-based two degree of freedom (2DOF) controller for the evaporator outlet condition in an organic Rankine cycle (ORC) system is presented. The ORC is used in a heavy duty vehicle to convert exhaust gas heat into mechanical power which increases the fuel efficiency The evaporator outlet condition of the working fluid is a crucial variable for the ORC efficiency which thus has to be controlled very accurately However, the exhaust gas thermal energy which serves as heat source to the evaporator, is highly transient depending on the actual engine load. Therefore, excellent disturbance rejection is required with help of an efficient feedforward part. Its novel derivation is based on an exact inversion of a nonlinear, dynamic evaporator model, obtained by the finite volume method that is reduced subsequently. The resulting feedforward controller is therefore very close to the exact inverse dynamic model. Furthermore, online parameter adaption enhances the steady state accuracy of the feedforward part and compensates for model uncertainties. The improvements by the feedforward controller are shown in simulations and its applicability on the vehicle control unit is demonstrated by measurements on a Daimler prototype truck under real traffic conditions. © 2016

关键词： Rankine cycle Control system synthesis Controllers Degrees of freedom (mechanics) Disturbance rejection Evaporators Feedforward control Finite volume method Fluid dynamics Gases Inverse problems Uncertainty analysis Vehicles 2DOF distributed parameter systems Feed forward controllers Inverse dynamic model Organic Rankine Cycle(ORC) Organic Rankine cycles Real traffic conditions Steady state accuracy

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Effect of Sensor Noise on Estimation of Diffusion. The financial support of the National Science and Engineering Research Council of Canada Discovery Grant program for the research discussed in this article is gratefully acknowledged.

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IFAC-PapersOnLine 2016年第8期49卷 60-65页

作者： Zhang, Minxin Morris, Kirsten Dept. of Applied Mathematics Univ. of Waterloo Waterloo Canada

A Kalman filter is commonly used for state estimation. It is optimal in that the variance of the error is minimized by the estimator. In this paper the problem of optimal sensor location is combined with estimator design to obtain a sensor placement that minimizes the error variance. The question of whether of a larger number of inaccurate sensors, that is those with large noise variance, can provide as good an estimate as a single highly accurate (but probably more expensive) sensor. This question can be investigated with the assumption that all the selected sensors are placed optimally. Estimation of the state of a one-dimensional diffusion equation with three different disturbances is examined in this context. Despite the difference among disturbances, similar proportional relations between the sensor noise variance and the estimation error are observed in numerical simulations. Furthermore, it appears that multiple low quality sensors can lead to better estimation than a single high quality sensor, provided that enough sensors are used. © 2016

关键词： Kalman filters Errors Estimation Partial differential equations Riccati equations Spurious signal noise Algebraic Riccati equations distributed parameter systems Optimal sensor locations Sensor noise Sensor selection

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distributed identification and control of spatially interconnected systems with application to an actuated beam

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CONTROL ENGINEERING PRACTICE 2016年 54卷 104-116页

作者： Liu, Qin Werner, Herbert Univ Georgia Complex Syst Control Lab Athens GA 30602 USA Hamburg Univ Technol Inst Control Syst D-21073 Hamburg Germany

This paper presents a case study on modelling and control of spatially interconnected systems. Considered is a vibration control problem, with experimental results on a flexible beam that is equipped with an array of piezo sensors and actuators. The sensor actuator array induces a spatial discretization of the beam into an array of interconnected subsystems. Models are experimentally identified that have the structure of spatially interconnected systems. Based on the identified models, distributed control schemes are designed by solving a linear matrix inequality (LMI) problem that has the size of a single subsystem. Modelling and control is considered for both spatially invariant and spatially varying systems;in the latter case the system is represented as linear parameter-varying (LPV) system that is scheduled not over time but over space. Simulation and experimental closed-loop results demonstrate the practicality and efficiency of the underlying framework. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Spatially interconnected systems Linear parameter-varying systems distributed control distributed identification distributed parameter systems

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Trajectory planning for quasilinear parabolic distributed parameter systems based on finite-difference semi-discretisations

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INTERNATIONAL JOURNAL OF CONTROL 2010年第6期83卷 1093-1106页

作者： Utz, T. Meurer, T. Kugi, A. Vienna Univ Technol Automat & Control Inst A-1040 Vienna Austria

In this contribution, a flatness-based approach is considered for the solution of the trajectory planning problem for quasilinear parabolic distributed parameter systems (DPS) by making use of finite-difference semi-discretisations. It is shown that the method yields solutions which are equivalent to results known from the infinite-dimensional trajectory planning for a certain class of quasi-linear parabolic DPS. Furthermore, the methodology being proposed can also be applied to systems with general analytic nonlinearities. As analytical convergence results are not available in this case, a numerical test criterion for the convergence behaviour is suggested.

关键词： trajectory planning differential flatness distributed parameter systems finite-difference semi-discretisation diffusion-convection-reaction systems

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Estimation of process parameters on a moving horizon for a class of distributed parameter systems

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JOURNAL OF PROCESS CONTROL 2010年第2期20卷 58-62页

作者： Studener, Stephan Habaieb, Khaled Lohmann, Boris Wolf, Roland Tech Univ Munich Inst Automat Control Fac Mech Engn D-85748 Munich Germany OCE Printing Syst GmbH D-85586 Poing Germany

In this contribution we address the issue of estimating parameters of a process, which is described by a set of first order, quasi-linear partial differential equations (PDEs) from a set of measurements. The parameters are found by minimizing the sum of the square of the errors over a finite set of measurement data. The errors are defined as the differences between the model Outputs and corresponding measurements. Since the assumption of constant model parameters may not be realistic in many practical applications, the estimation is carried out using a moving and fixed-size window of data. When a new measurement becomes available, the oldest measurement is discarded and the new one is added. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Nonlinear parameter estimation Moving horizon estimation

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Guidance of Mobile Actuator-Plus-Sensor Networks for Improved Control and Estimation of distributed parameter systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2010年第7期55卷 1570-1584页

作者： Demetriou, Michael A. Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA

This paper presents an abstract framework for the optimization of actuating and sensing devices in distributed parameter systems. The optimization is performed on the repositioning of these devices throughout the spatial domain. It is assumed that a network of mobile sensing and actuating devices is available to obtain measurements from the spatially distributed process and dispense control signals to the spatially distributed process. By taking advantage of the properties that the spatial operator that governs the process dynamics possesses, namely symmetry, coercivity and boundedness, a scheme for the guidance of a mobile actuator-plus-sensor network is developed and used for the performance enhancement of the spatial process. The class of systems is governed by diffusion PDEs equipped with actuators having a boxcar spatial distribution and a collocated sensing device that provides the spatially averaged state measurement over the range of the actuating device. Using Lyapunov stability arguments, a stable guidance scheme is provided for each of the mobile agents. Due to the specific structure of the closed loop system operator with time-varying input and output operators, the same guidance schemes are applicable to the dual problem of mobile sensors employed for enhancing the state estimation problem. Both a centralized state estimator with mobile sensors and a network of consensus distributed estimators are considered, since both filters can be shown to result in the specific algebraic structure of a symmetric spatial operator with collocated input and output operators. Extensive numerical simulations for a 1-D diffusion equation with two actuator/sensor agents, a 2-D diffusion equation with one collocated actuator/sensor agent plus a centralized filter for a 1-D diffusion equation are included to verify the effectiveness of a such a mobile actuator-plus-sensor network in suppressing the effects of spatially varying disturbances and enhancing the system's perform

关键词： Centralized filters distributed consensus filters distributed parameter systems mobile actuators mobile sensors

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Dissipativity-based observer design for a class of coupled 1-D semi-linear parabolic PDE systems

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IFAC-PapersOnLine 2016年第8期49卷 98-103页

作者： Schaum, A. Moreno, J.A. Meurer, T. Chair of Automatic Control Christian–Albrechts–University Kiel Germany Instituto de Ingenieria Universidad Nacional Autonoma de Mexico D.F. Mexico

In the present paper the dissipativity-based observer design approach is extended to a class of 1-D semi-linear parabolic PDE systems with pointwise in-domain measurement. On the basis of a modal innovation over the set of slow eigenvalues of the linear operator and the consideration of a dissipativity (sector) condition for the nonlinearity an exponential convergence condition for the estimation error is derived in form of a linear operator inequality, which is solved on the basis of an eigenfunction expansion of the linear operator. The approach is illustrated by numerical simulations for a coupled two-state semi-linear PDE system. © 2016

关键词： Mathematical operators Eigenvalues and eigenfunctions distributed parameter systems Domain measurements Eigenfunction expansions Estimation errors Exponential convergence Linear operators Observer Semi linear parabolic PDE

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