An Account of Chronological Developments in Control of Distributed Parameter Systems (original) (raw)

Control of Distributed Parameter Systems

Distributed parameter systems (DPS) is an established area of research in control which can trace its roots back to the sixties. While the general aims are the same as for lumped parameter systems, to adequately describe the distributed nature of the system one needs to use partial differential equation (PDE) models. The modelling issue is in itself nontrivial, especially when there is boundary control action and sensing on the boundary. Controllability and observability concepts are subtle and investigating these for a single PDE example leads to a sophisticated mathematical problem. The action of controlling the system introduces feedback into the PDE model which results in a more complicated mathematical model; the resulting closed-loop system may not be well-posed and this issue has only quite recently become well understood. At this stage, the mathematical machinery for formulating the basic control problems is available (although not so well known), and this has led to a wealth of new system theoretic results for DPS.

Control of Distributed Parameter Systems : a Practical Approach

2009

Control on finite and infinite horizons as well as state and parameter estimation of distributed parameter systems are dealt with in the paper. If the target output is a particular point of the distributed parameter plant, control may be achieved through a discretized lumped parameter model. Several target outputs may be handled through model change, averaging or multivariable control. Once a discretized model is obtained, design methods developed for control of lumped parameter systems may be applied, including methods for adaptive control. State and parameter estimation may be achieved, too, similarly to the lumped parameter case through dynamic optimization on a finite horizon.

Computational methods for the control of distributed parameter systems

Proceedings of the IEEE Conference on Decision and Control

Finite dimensional approximation schemes that work well for distributed parameter systems are often not suitable for the analysis and implementation of feedback control systems. The relationship between approximation schemes for distributed parameter systems and their application to optimal control problems is discussed. A numerical example is given.

On the control of distributed parameter systems using a multidimensional systems setting

Mechanical Systems and Signal Processing, 2008

The unique characteristic of a repetitive process is a series of sweeps, termed passes, through a set of dynamics defined over a finite duration with resetting before the start of the each new one. On each pass an output, termed the pass profile is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This leads to the possibility that the output, i.e. the sequence of pass profiles, will contain oscillations which increase in amplitude in the pass-to-pass direction. Such behavior cannot be controlled by standard linear systems approach and instead they must be treated as a multidimensional system, i.e. information propagation in more than one independent direction. Physical examples of such processes include long-wall coal cutting and metal rolling. In this paper, stability analysis and control systems design algorithms are developed for a model where a plane, or rectangle, of information is propagated in the passto-pass direction. The possible use of these in the control of distributed parameter systems is then described using a fourthorder wavefront equation. r

Control of distributed-parameter systems using normal forms: an introduction

at - Automatisierungstechnik

This paper gives an overview of the control of distributed-parameter systems using normal forms. Considering linear controllable PDE-ODE systems of hyperbolic type, two methods derive tracking controllers by mapping the system into a form that is advantageous for the control design, analogous to the finite-dimensional case. A flatness-based controller makes use of the hyperbolic controller canonical form that follows from a parametrization of the system’s solutions. A backstepping design exploits the strict-feedback form of the system to recursively stabilize and transform the subsystems.

Control and Optimal Design of Distributed Parameter Systems

The IMA Volumes in Mathematics and its Applications, 1995

Library of Congress Cataloging-in-Publication Data Control and optimal design of distributed parameter systems I John E. Lagnese, David L. Russell, Luther W. White, editors. p. cm.-(The IMA volumes in mathematics and its applications; v. 70) Papers based on the proceedings of a 1992 workshop. Includes bibliographical references.

Finite dimensional modeling and control of distributed parameter systems

Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002

Developing low-order models of high fidelity is important if the objective is accurate control of the DPS. This work presents a novel method to develop a loworder models when there is no available exact model of the system. The foundations for this method, SVD-KL, are singular value decomposition (SVD) theory and the Karhunen-Loève (KL) expansion. It is shown that satisfactory closed-loop performance of the nonlinear DPS can be obtained using a Dynamic Matrix Controller designed using the finite order model.