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Design of Uncertain Nonlinear Feedback systems with Inputs and Outputs Satisfying Bounding Conditions

IFAC Proceedings Volumes 2011年第1期44卷 10970-10975页

作者： Mai Van Sy Suchin Arunsawatwong Eyad H. Abed Department of Electrical Engineering Chulalongkorn University Bangkok 10330 Thailand Department of Electrical and Computer Engineering University of Maryland College Park MD 20742 USA

Abstract This paper develops a computational method for designing a feedback control system where the plant is an uncertain linear time-invariant convolution subsystem with a static memoryless input nonlinearity. The main design objective is to determine a controller ensuring that the error and the controller output are always within respective bounds for all uncertainties and for all inputs having bounded magnitude and slope. First, using Schauder fixed point theorem, we show that (if exists) a design solution for an uncertain linear system obtained by replacing the nonlinearity with a gain and a bounded disturbance is also a solution for the original problem. Then, by extending a known theory and applying it to the so-obtained linear problem, we derive design inequalities that can readily be solved in practice. The usefulness of the developed method is illustrated by a design example of an uncertain heat-conduction process.

关键词： Nonlinear control systems computer-aided control system design robust control uncertain dynamical systems distributed-parameter systems Popov criterion

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Control of the Vertical Gradient Freeze crystal growth process via backstepping

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IFAC-PapersOnLine 2020年第2期53卷 7758-7764页

作者： Stefan Ecklebe Frank Woittennek Jan Winkler

This contribution presents a backstepping-based state feedback design for the tracking control of a two-phase Stefan problem which is encountered in the Vertical Gradient Freeze crystal growth process. A two-phase Stefan problem consists of two coupled free boundary problems and is a vital part of many crystal growth processes due to the time-varying extent of crystal and melt during growth. In addition, a different approach for the numerical approximation of the backstepping transformations kernel is presented.

关键词： Vertical Gradient Freeze two-phase Stefan problem distributed-parameter systems backstepping tracking control numerical methods

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ON REGULATOR DESIGN FOR SPATIAL TEMPERATURE DISTRIBUTION USING FINITE-DIMENSIONAL MODELING OF HEAT EQUATIONS

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IFAC Proceedings Volumes 2005年第1期38卷 119-124页

作者： Jun Imai Yasuaki Ando Masami Konishi Tatsushi Nishi Dept. Electrical and Electronic Eng. Okayama University JAPAN

A regulator problem for a heat conduction system, of which the eigenstructure is just partially known, is formulated to design a stabilizing controller that keeps a performance index less than a prescribed value. The index is made of the spatio integral of the squared deviation from reference temperature distribution. It is shown that through characterizing frequency response from input to temperature at each spatial point, a distributed parameter system with nominal model and additive uncertainty weight, both of which are real rational, is reconstructed using knowledge of the eigenstructure. A main result claims that the formulated problem is reduced to a standard mixed H 2 / H ∞ one for a linear finite dimensional time-invariant system. Numerical study demonstrates feasibility of the proposed design scheme.

关键词： distributed-parameter systems Uncertainty Modeling errors

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Identification of Uncertain, Spatially Varying parameters through Multilevel Sampling

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IFAC Proceedings Volumes 2014年第3期47卷 1778-1783页

作者： Hans-Werner van Wyk Department of Scientific Computing Florida State University FL 32306 USA

While stochastic sampling methods remain widely used to simulate solutions of partial differential equations with random parameters, due to ease of implementation on a parallel computing architecture, they can nevertheless carry a considerable computational cost, especially if reliable statistics are sought at high levels of spatial fidelity. Multilevel sampling methods improve upon the efficiency of traditional sampling schemes without compromising on accuracy and parallelizability, by dynamically incorporating the model's spatial discretization into the sampling procedure. Moreover, the diagnostic estimates that are computed to monitor the solution's convergence behaviour during the course of the algorithm, can be used to inform adaptive spatial refinement strategies. In this paper we leverage these properties to develop an adaptive, multilevel algorithm for identifying the statistical distribution of a spatially varying parameter from the statistical description of a related model output, based on experimental measurements.

关键词： parameter identification uncertainty statistical inference multilevel sampling adaptive algorithm distributed-parameter systems

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Boundary observer design for cascaded ODE - Hyperbolic PDE systems: A matrix inequalities approach

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AUTOMATICA 2020年 119卷 109027-109027页

作者： Ferrante, Francesco Cristofaro, Andrea Prieur, Christophe Univ Grenoble Alpes GIPSA Lab Grenoble INP CNRS F-38000 Grenoble France Sapienza Univ Rome Dept Comp Control & Management Engn I-00185 Rome Italy

Boundary observer design for a system of ODEs in cascade with hyperbolic PDEs is studied. An infinite dimensional observer is used to solve the state estimation problem. The interconnection of the observer and the system is written in estimation error coordinates and analyzed as an abstract dynamical system. The design of the observer is performed to achieve global exponential stability of the estimation error with respect to a suitable norm and with a tunable convergence rate. Sufficient conditions in the form matrix inequalities are given for the design of the observer. The effectiveness of the approach is shown in a numerical example. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Observers Convex optimization Lyapunov methods Computer-aided design

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Bilateral backstepping control of coupled linear parabolic PDEs with spatially varying coefficients

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AUTOMATICA 2022年 135卷 109923-109923页

作者： Kerschbaum, Simon Deutscher, Joachim Univ Erlangen Nurnberg Lehrstuhl Regelungstech Cauerstr 7 D-91058 Erlangen Germany Univ Ulm Inst Mess Regel & Mikrotech Albert Einstein Allee 41 D-89081 Ulm Germany

This paper considers the backstepping state feedback control of coupled linear parabolic PDEs with spatially varying coefficients and bilateral actuation. By making use of the folding technique, a system representation with unilateral actuation is obtained, allowing to apply the standard backstepping transformation. To ensure the regularity of the solution, the folded system is subject to unusual folding boundary conditions, which lead to additional boundary couplings between the PDEs. Therefore, the solution of the corresponding kernel equations determining the transformations is a very challenging problem. A systematic approach to derive the corresponding integral equations is proposed, allowing to solve them with the method of successive approximations. By making use of a Volterra and a Volterra-Fredholm transformation, the closed-loop system is mapped into a cascade of stable parabolic systems. This allows a simple proof of exponential stability in the L-2-norm with the decay rate as design parameter. The bilateral state feedback stabilization of an unstable system of two coupled parabolic PDEs and the comparison to the application of an unilateral controller demonstrates the results of the paper. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Parabolic systems Bilateral control Backstepping Boundary control

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Closed-form H-infinity optimal control for a class of infinite-dimensional systems

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AUTOMATICA 2020年 117卷 108916-108916页

作者： Bergeling, Carolina Morris, Kirsten A. Rantzer, Anders Lund Univ Dept Automat Control Box 118 SE-22100 Lund Sweden Univ Waterloo Dept Appl Math Waterloo ON N2L 3G1 Canada

H infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given. Unlike traditional methods for H-infinity synthesis, no iteration is needed to obtain the optimal solution. Moreover, the optimal performance for both the state feedback and state estimation problems are explicitly calculated. This is shown to be useful for problems of H-infinity optimal actuator and sensor location. Furthermore, the results can be used in testing and bench-marking of general purpose algorithms for H-infinity synthesis. The results also apply to finite-dimensional systems. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： H-infinity control Linear systems distributed-parameter systems Optimal control Optimal estimation

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Predictive feedback boundary control of semilinear and quasilinear 2 x 2 hyperbolic PDE-ODE systems

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AUTOMATICA 2022年 140卷

作者： Strecker, Timm Aamo, Ole Morten Cantoni, Michael Univ Melbourne Dept Elect & Elect Engn Parkville Vic 3010 Australia Norwegian Univ Sci & Technol NTNU Dept Engn Cybernet Trondheim Norway

We present a control design for semilinear and quasilinear 2 x 2 hyperbolic partial differential equations with the control input at one boundary and a nonlinear ordinary differential equation coupled to the other. The controller can be designed to asymptotically stabilize the system at an equilibrium or relative to a reference signal. Two related but different controllers for semilinear and general quasilinear systems are presented and the additional challenges in quasilinear systems are discussed. Moreover, we present an observer that estimates the distributed PDE state and the unmeasured ODE state from measurements at the actuated boundary only, which can be used to also solve the output feedback control problem.

关键词： Available online xxxx Hyperbolic PDE-ODE systems distributed-parameter systems Boundary control Stabilization Estimation

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Adaptive set-point regulation of linear 2 x 2 hyperbolic systems with application to the kick and loss problem in drilling

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AUTOMATICA 2020年 119卷 109078-109078页

作者： Holta, Haavard Anfinsen, Henrik Aamo, Ole Morten Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway

We study the kick and loss detection and attenuation problem in managed pressure drilling by modeling the well as a distributed parameter system. Two cases are considered, distinguished by whether down-hole pressure measurements are available or not. The main contribution of the paper is a theoretical result on adaptive stabilization and set-point regulation by boundary control for a general 2 x 2 linear hyperbolic system in the case of measurements taken at both boundaries, with stability proven in the L-2-sense. The design is applied to the drilling system and shown to solve the kick and loss problem with sensing at both boundaries. An earlier result on adaptive set-point regulation for 2 x 2 hyperbolic systems is also applied to the drilling system and shown to solve a kick and loss problem with sensing restricted to the actuated boundary only. The two designs are compared in a simulation of a loss incident, showing a significant reduction in convergence time and total accumulated loss for the design with sensing allowed at both boundaries. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Adaptive control parameter estimation Managed pressure drilling Kick and loss detection

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A Decoupling Approach to the Control of Large Spaceborne Antenna systems

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IFAC Proceedings Volumes 1983年第10期16卷 139-146页

作者： P.K.C. Wang Department of System Science University of California Los Angeles California USA

A simple practical method for designing antenna-feed positioning control systems for large deployable spaceborne antenna systems with flexible booms is proposed. The approach is based on the mechanical decoupling of the antenna-feed from the boom so that the positioning control system can be designed without taking boom dynamics into consideration, thus avoiding a complex infinite dimensional control problem. The basic idea is illustrated by a simple angular positional control system attached to a flexible boom restricted to torsional motion only. The application of this approach to more complex situations is discussed briefly.

关键词： Large space structures distributed-parameter systems decoupling feedback control stability antenna control systems

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