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Output regulation for general linear heterodirectional hyperbolic systems with spatially-varying coefficients

AUTOMATICA 2017年 85卷 34-42页

作者： Deutscher, Joachim Univ Erlangen Nurnberg Lehrstuhl Regelungstech Cauerstr 7 D-91058 Erlangen Germany

This article presents a backstepping solution to the output regulation problem for general linear heterodirectional hyperbolic systems with spatially-varying coefficients. The disturbances can act at both boundaries, distributed in-domain or at the output to be controlled. The latter is defined at a boundary, distributed or pointwise in-domain and has not to be available for measurement. By utilizing backstepping coordinates it is shown that all design equations are explicitly solvable. This allows a simple determination of a state feedback regulator, that is implemented by a reference and a disturbance observer. Furthermore, an easy evaluation of the existence conditions for the resulting output feedback regulator is possible in terms of the plant transfer behaviour. In order to facilitate the parameterization of the regulator, the resulting closed-loop dynamics is directly related to the design parameters. The proposed backstepping-based design of the output feedback regulator is demonstrated for an unstable heterodirectional 4 x 4 hyperbolic system. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Hyperbolic systems Output regulation Backstepping Boundary control Observer

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PID-deadtime control of distributed processes

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CONTROL ENGINEERING PRACTICE 2001年第11期9卷 1177-1183页

作者： Shinskey, FG Process Control Consultant 260 Whiteface Rd. North Sandwich NH 03259 USA

While model-based controllers have been used successfully to control paper machines and other processes dominated by time delay, matching the model to the process gives poor load regulation over lag-dominant processes. An important class of lag-dominant processes including heat exchangers and distillation columns consists of distributed tags. A PID controller having time-delay compensation, while functionally similar to a model-based controller, is a much better load regulator, and twice as effective as a conventional PID controller on these processes. It is applied in this paper to regulate steam superheat temperature. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： adaptive control distillation columns distributed-parameter systems heat exchangers load regulation model-based control PID control steam plant temperature control time delay

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A simplified lumped parameter model for pneumatic tubes

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MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL systems 2017年第5期23卷 523-535页

作者： Kaminski, Zbigniew Bialystok Tech Univ Fac Mech Engn Wiejska 45C PL-15351 Bialystok Poland

Tubes are commonly used in pneumatic systems for transferring energy and control signals. Using the control volume method, a mathematical tube model has been developed, which takes into account the effect of resistance, capacitance and inertance on the dynamic properties of control and supply circuits of pneumatic systems. The adequacy of the computer model developed in Matlab/Simulink was verified by comparing the results of simulation studies with the results of experimental tests of airflow through tubes of varying diameter and length. The advantage of the computer model is the capability to model pneumatic systems under varying conditions of heat exchange with the environment by changing the coefficient of the polytropic process coefficient.

关键词： Compressible fluid flow computer simulation pneumatic systems distributed-parameter systems

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Model based feedforward control of an industrial glass feeder

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CONTROL ENGINEERING PRACTICE 2012年第1期20卷 62-68页

作者： Malchow, F. Sawodny, O. Univ Stuttgart Inst Syst Dynam D-70569 Stuttgart Germany

This article presents the automation of set point changes of an industrial glass feeder in container glass production. A model is proposed consisting of multiple first order partial differential equations (PDEs). Based on the derived model a feedforward control approach is presented. The approach allows for the calculation of control inputs out of reference trajectories of the system outputs and is used to perform automated set point changes with short transition time. Finally, the approach is implemented at an industrial glass feeder. Measurement results from the Thuringer Behalterglas GmbH (Schleusingen, Germany) are included. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Feedforward control Model-based control Process control

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IDENTIFICATION MODELS OF A ONE-DIMENSIONAL SPACE- TIME PROCESS

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CYBERNETICS AND systems ANALYSIS 2007年第5期43卷 704-718页

作者： Skopetskii, V. V. Stoyan, V. A. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine Taras Shevehenko Natl Univ Kiev Ukraine

Problems of constructing linear and polynomially nonlinear mathematical models are solved for distributed space-time processes with discretely-continuously observable states under distributed space-time perturbations that create such states. The cases of exact and optimal (with respect to the mean-square criterion) identification of kernels of such models are considered. The identifiability conditions are specified for the process and accuracy conditions are established for its mathematical models.

关键词： distributed-parameter systems dynamics simulation identification the Green function

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ACTIVE CONTROL OF FLEXIBLE systems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1978年第3期25卷 415-436页

作者： BALAS, MJ CHARLES STARK DRAPER LAB INC CAMBRIDGEMA

Since mechanically flexible systems are distributed-parameter systems, they are infinite-dimensional in theory and, in practice, must be modelled by large-dimensional systems. The fundamental problem of actively controlling very flexible systems is to control a large-dimensional system with a much smaller dimensional controller. For example, a large number of elastic modes may be needed to describe the behavior of a flexible satellite; however, active control of all these modes would be out of the question due to onboard computer limitations and modelling error. Consequently, active control must be restricted to a few critical modes. The effect of the residual (uncontrolled) modes on the closed-loop system is often *** this paper, we consider the class of flexible systems that can be described by a generalized wave equation,utt+Au=F, which relates the displacementu(x,t) of a body Θ inn-dimensional space to the applied force distributionF(x,t). The operatorA is a time-invariant symmetric differential operator with a discrete, semibounded spectrum. This class of distributed parameter systems includes vibrating strings, membranes, thin beams, and thin *** control force distribution$$F(x,t) = \sum\limits_{i = 1}^M { \delta (x - x_i )f_i (t)} $$ is provided byM point force actuators located at pointsxi on the body. The displacements (or their velocities) are measured byP point sensorsyi(t)=u(zj,t), orut(zj,t),j=1, 2, ...,P, located at various pointszj along the *** obtain feedback control ofN modes of the flexible system and display the controllability and observability conditions required for successful operation. We examine the control and observation spillover due to the residual modes and show that the combined effect of spillover can lead to instabilities in the closed-loop system. We suggest some remedies for spillover, including a straightforward phase-locked loop prefilter, to remove the instability *** illustrate the concepts of this p

关键词： distributed-parameter systems flexible systems partial differential equations

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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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Backstepping Design of Dynamic Observers for Hyperbolic systems

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IEEE CONTROL systems LETTERS 2024年 8卷 3452-3457页

作者： Gehring, Nicole Deutscher, Joachim Irscheid, Abdurrahman Otto von Guericke Univ Chair Syst Theory & Control Engn D-39106 Magdeburg Germany Ulm Univ Inst Measurement Control & Microtechnol D-89081 Ulm Germany Saarland Univ Chair Syst Theory & Control Engn D-66123 Saarbrucken Germany

This letter considers the backstepping design of dynamically extended observers, or dynamic observers for short, for systems described by heterodirectional hyperbolic partial differential equations based on a collocated boundary measurement. In contrast to classical Luenberger-type observers, which usually consist of a copy of the system dynamics with appropriate injections of the measurement error, the dynamic observer incorporates an additional dynamics. The latter is chosen so that the extended observer error dynamics admits homogenized transport velocities on the unit spatial interval. With the added flexibility of the dynamic observer, using backstepping, it is possible to obtain a desired stable extended observer error dynamics with arbitrary in-domain couplings. An example illustrates the new dynamic observer design.

关键词： Observers Backstepping Couplings State feedback Kernel Measurement errors Finite element analysis Vectors System dynamics Servers distributed-parameter systems dynamic observers hyperbolic systems observer design

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Optimizing geometrical control of surface distributions in rapid prototyping deposition

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EUROPEAN JOURNAL OF CONTROL 2000年第3期6卷 279-289页

作者： Doumanidis, H Skordeli, E Tufts Univ Dept Mech Engn Medford MA 02155 USA

Rapid prototyping techniques employing thermal material deposition are intended for direct layered fabrication of functional products. This article introduces an analytical geometric model of such material transfer processes, using superposition of unit deposition distributions, composed of elementary ellipsoidal primitives. The real-time surface geometry model, with its deposition features identified by in-process height measurements, is used for Smith-prediction of the material shape in the deposition region that is inaccessible to sensing. Thus, a distributed-parameter geometry control scheme is established to obtain a desired surface topology, by modulating the feed and motion of a moving mass source. This is obtained by dynamic surface shaping based on minimization of the geometric error-distribution by robust real-time optimization techniques.,A moving constrained polytope and a simulated annealing method at random sampled Surface locations are employed for this purpose. These methodologies are compared experimentally in geometric command following a robotic fused wire deposition plasma-arc welding station, using laser profilometric scanner sensing.

关键词： distributed-parameter systems optimizing control rapid prototyping surface geometry

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Stabilization of Unstable distributed Port-Hamiltonian systems in Scattering Form

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IEEE CONTROL systems LETTERS 2022年 6卷 3116-3121页

作者： Macchelli, Alessandro Le Gorrec, Yann Ramirez, Hector Univ Bologna Dept Elect Elect & Informat Engn I-40136 Bologna Italy Univ Bourgogne Franche Comte CNRS AS2M Dept FEMTO ST Inst F-25000 Besancon France Univ Tecn Federico Santa Maria Dept Elect Valparaiso 2390382 Chile

In this letter, we consider the exponential stabilization of a distributed parameter port-Hamiltonian system interconnected with an unstable finite-dimensional linear system at its free end and control input at the opposite one. The infinite-dimensional system can also have in-domain anti-damping. The control design passes through the definition of a finite-dimensional linear system that "embeds" the response of the distributed parameter model, and that can be stabilized by acting on the available control input. The conditions that link the exponential stability of the latter system with the exponential stability of the original one are obtained thanks to a Lyapunov analysis. Simulations are presented to show the pros and cons of the proposed synthesis methodology.

关键词： Linear systems Stability analysis Control design Mathematical models Delays Control theory Scattering distributed-parameter systems Lyapunov methods port-Hamiltonian systems

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