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.
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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....
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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]....
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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
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TL;DR: In this article, the increasing ability to coherently control quantum systems, designer Hamiltonians can be created to explore new physics and to yield a better understanding of complex phenomena, and they can be used to create new physics models.
Abstract: Thanks to the increasing ability to coherently control quantum systems, designer Hamiltonians can be created to explore new physics and to yield a better understanding of complex phenomena.
411 citations
TL;DR: In this paper, the authors proposed an alternative method for quantum feedback control, in which the sensors, controller, and actuators are quantum systems that interact coherently with the system to be controlled.
Abstract: In the conventional picture of quantum feedback control, sensors perform measurements on the system, a classical controller processes the results of the measurements, and actuators supply semiclassical potentials to alter the behavior of the quantum system. In this picture, the sensors tend to destroy coherence in the process of making measurements, and although the controller can use the actuators to act coherently on the quantum system, it is processing and feeding back classical information. This paper proposes an alternative method for quantum feedback control, in which the sensors, controller, and actuators are quantum systems that interact coherently with the system to be controlled. In this picture, the controller gets, processes, and feeds back quantum information. Controllers that operate using such quantum feedback loops can perform tasks such as entanglement transfer that are not possible using classical feedback. Necessary and sufficient conditions are presented for Hamiltonian quantum systems to be controllable and observable using both classical and quantum feedback.
371 citations
"Feedback for physicists: A tutorial..." refers background in this paper
...Lloyd has emphasized that one can imagine a fully quantum feedback scheme wherein one adds an element to the quantum system that interacts (without making a measurement) with it in such a way that the dynamics are altered in a desired way (Lloyd, 2000)....
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Book•
01 Mar 1992
367 citations
"Feedback for physicists: A tutorial..." refers background or methods in this paper
...The output-feedback approach is more direct—when it works Lewis, 1992 ....
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...One can also show that a similar test exists for observability and, indeed, that controllability and observability are dual properties corresponding to how one gets information into and out of the dynamical system and that any property pertaining to one has a counterpart Lewis, 1992 ....
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...In the latter case, high-frequency components of f will mix down into the spectrum of fs Lewis, 1992 ....
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...5.24 corresponds to using the rectangular rule Lewis, 1992, Chap....
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...The reader is cautioned, however, to consult a more detailed reference such as Lewis 1992 before actually implementing a digital control loop in an experiment....
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Abstract: We have learned much about the workings of natural sinks like the oceans and terrestrial plants, but are just beginning to understand how their behavior might change as atmospheric CO2 concentrations rise.
356 citations
"Feedback for physicists: A tutorial..." refers background in this paper
...There is a tremendous flux of carbon between the atmosphere and various “sinks,” such as the oceans and forests, and the dependence of these fluxes on greenhouse gasses must be evaluated accurately to know the cumulative effect on climate (Sarmiento and Gruber, 2002)....
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TL;DR: Quantitative analysis shows that the existence of two stable steady states depends on the details of the system, and that functions describing positive cooperativity of binding, non-additive effects of multiple operator sites, or depletion of free repressor can lead to working switches.
328 citations
"Feedback for physicists: A tutorial..." refers background in this paper
...[The specific value n = 2 is not important, but at least one of the exponents needs to be larger than one to have a switch of the kind discussed below (Cherry and Adler, 2000)....
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