Feedback for physicists: A tutorial essay on control
TL;DR: In this paper, a tutorial essay aims to give enough of the formal elements of control theory to satisfy the experimentalist designing or running a typical physics experiment and enough to satisfy a theorist wishing to understand its broader intellectual context.
Abstract: Feedback and control theory are important ideas that should form part of the education of a physicist but rarely do. This tutorial essay aims to give enough of the formal elements of control theory to satisfy the experimentalist designing or running a typical physics experiment and enough to satisfy the theorist wishing to understand its broader intellectual context. The level is generally simple, although more advanced methods are also introduced. Several types of applications are discussed, as the practical uses of feedback extend far beyond the simple regulation problems where it is most often employed. Sketches are then provided of some of the broader implications and applications of control theory, especially in biology, which are topics of active research.
Citations
More filters
01 Apr 2003
TL;DR: The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it as mentioned in this paper, and also presents new ideas and alternative interpretations which further explain the success of the EnkF.
Abstract: The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.
2,975 citations
Book•
21 Apr 2008
TL;DR: Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems.
Abstract: This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl strm and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. strm and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available. Feedback Systems is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences.Covers the mathematics needed to model, analyze, and design feedback systems Serves as an introductory textbook for students and a self-contained resource for researchers Includes exercises at the end of every chapter Features an electronic solutions manual Offers techniques applicable across a range of disciplines
1,927 citations
Cites background from "Feedback for physicists: A tutorial..."
...The book by Fradkov [77] and the tutorial article by Bechhoefer [25] cover many specific topics of interest to the physics community....
[...]
TL;DR: In this article, the basic principles of modern optical magnetometers, discuss fundamental limitations on their performance, and describe recently explored applications for dynamical measurements of biomagnetic fields, detecting signals in NMR and MRI, inertial rotation sensing, magnetic microscopy with cold atoms, and tests of fundamental symmetries of nature.
Abstract: Some of the most sensitive methods of measuring magnetic fields use interactions of resonant light with atomic vapour. Recent developments in this vibrant field have led to improvements in sensitivity and other characteristics of atomic magnetometers, benefiting their traditional applications for measurements of geomagnetic anomalies and magnetic fields in space, and opening many new areas previously accessible only to magnetometers based on superconducting quantum interference devices. We review basic principles of modern optical magnetometers, discuss fundamental limitations on their performance, and describe recently explored applications for dynamical measurements of biomagnetic fields, detecting signals in NMR and MRI, inertial rotation sensing, magnetic microscopy with cold atoms, and tests of fundamental symmetries of nature.
1,489 citations
Cites background from "Feedback for physicists: A tutorial..."
...However, if the bandwidth is increased by a factor K over the natural bandwidth, the magnetometer output noise also increases by the same factor K [47]....
[...]
TL;DR: In this article, B. Sonnenschein, E.R. dos Santos, P.J. Schultz, C.A. Ha, M.K. Choi and C.P.
683 citations
TL;DR: This work addresses the physically important issue of the energy required for achieving control by deriving and validating scaling laws for the lower and upper energy bounds.
Abstract: The outstanding problem of controlling complex networks is relevant to many areas of science and engineering, and has the potential to generate technological breakthroughs as well. We address the physically important issue of the energy required for achieving control by deriving and validating scaling laws for the lower and upper energy bounds. These bounds represent a reasonable estimate of the energy cost associated with control, and provide a step forward from the current research on controllability toward ultimate control of complex networked dynamical systems.
392 citations
References
More filters
TL;DR: General principles that govern the structure and behaviour of modules may be discovered with help from synthetic sciences such as engineering and computer science, from stronger interactions between experiment and theory in cell biology, and from an appreciation of evolutionary constraints.
Abstract: Cellular functions, such as signal transmission, are carried out by 'modules' made up of many species of interacting molecules Understanding how modules work has depended on combining phenomenological analysis with molecular studies General principles that govern the structure and behaviour of modules may be discovered with help from synthetic sciences such as engineering and computer science, from stronger interactions between experiment and theory in cell biology, and from an appreciation of evolutionary constraints
3,604 citations
01 Jan 2001
3,487 citations
TL;DR: A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias, and an ensemble based optimal interpolation scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications.
Abstract: The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.
3,403 citations
"Feedback for physicists: A tutorial..." refers methods in this paper
...For strong nonlinearities, the analysis is much more difficult, and the search for approximate solution methods is an active area of research (Evensen, 2003; Eyink et al., 2004)....
[...]
Book•
01 Jan 1990
TL;DR: This book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects, covering a wide range of topics written in a standard theorem/proof style and develops the necessary techniques from scratch.
Abstract: Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.
3,353 citations