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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Book•
01 Sep 2000
TL;DR: A key aspect of the book is the frequent use of real world design examples drawn directly from the authors' industrial experience, represented by over 15 substantial case studies ranging from distillation columns to satellite tracking.
Abstract: From the Publisher:
A key aspect of the book is the frequent use of real world design examples drawn directly from the authors' industrial experience. These are represented by over 15 substantial case studies ranging from distillation columns to satellite tracking. The book is also liberally supported by modern teaching aids available on both an accompanying CD-ROM and Companion Website. Resources to be found there include MATLAB® routines for all examples; extensive PowerPoint lecture notes based on the book; and a totally unique Java Applet-driven "virtual laboratory" that allows readers to interact with the real-world case studies.
1,701 citations
Book•
01 Jan 1999
1,700 citations
TL;DR: In this paper, the problem of controlling a fixed nonlinear plant in order to have its output track (or reject) a family of reference (or disturbance) signal produced by some external generator is discussed.
Abstract: The problem of controlling a fixed nonlinear plant in order to have its output track (or reject) a family of reference (or disturbance) signal produced by some external generator is discussed. It is shown that, under standard assumptions, this problem is solvable if and only if a certain nonlinear partial differential equation is solvable. Once a solution of this equation is available, a feedback law which solves the problem can easily be constructed. The theory developed incorporates previously published results established for linear systems. >
1,639 citations
TL;DR: It is argued that the key properties of biochemical networks should be robust in order to ensure their proper functioning, and it is shown that this applies in particular to bacterial chemotaxis.
Abstract: 1 are responsible for many important cellular processes, including cell-cycle regulation and signal transduction. Here we address the issue of the sensitivity of the networks to variations in their biochemical parameters. We propose a mechanism for robust adaptation in simple signal transduction networks. We show that this mechanism applies in particular to bacterial chemotaxis 2-7 . This is demonstrated within a quantitative model which explains, in a unified way, many aspects of chemotaxis, including proper responses to chemical gradients 8-12 . The adaptation property 10,13-16 is a consequence of the network's connectivity and does not require the 'fine-tuning' of parameters. We argue that the key properties of biochemical networks should be robust in order to ensure their proper functioning. Cellular biochemical networks are highly interconnected: a per- turbation in reaction rates or molecular concentrations may affect numerous cellular processes. The complexity of biochemical net- works raises the question of the stability of their functioning. One possibility is that to achieve an appropriate function, the reaction rate constants and the enzymatic concentrations of a network need to be chosen in a very precise manner, and any deviation from the 'fine-tuned' values will ruin the network's performance. Another possibility is that the key properties of biochemical networks are robust; that is, they are relatively insensitive to the precise values of biochemical parameters. Here we explore the issue of robustness of one of the simplest and best-known signal transduction networks: a biochemical network responsible for bacterial chemotaxis. Bacteria such as Escherichia coli are able to sense (temporal) gradients of chemical ligands in their vicinity 2 . The movement of a swimming bacterium is composed of a series of 'smooth runs', interrupted by events of 'tumbling', in which a new direction for the next run is chosen randomly. By modifying the tumbling frequency, a bac- terium is able to direct its motion either towards attractants or away from repellents. A well established feature of chemoxis is its property of adaptation 10,13-16 : the steady-state tumbling frequency in a homogeneous ligand environment is insensitive to the value of ligand concentration. This property allows bacteria to maintain their sensitivity to chemical gradients over a wide range of attractant or repellent concentrations. The different proteins that are involved in chemotactic response have been characterized in great detail, and much is known about the interactions between them (Fig. 1a). In particular, the receptors that sense chemotactic ligands are reversibly methylated. Biochem- ical data indicate that methylation is responsible for the adaptation property: changes in methylation of the receptor can compensate for the effect of ligand on tumbling frequency. Theoretical models proposed in the past assumed that the biochemical parameters are fine-tuned to preserve the same steady-state behaviour at different ligand concentrations 17,18 . We present an alternative picture in which adaptation is a robust property of the chemotaxis network and does not rely on the fine-tuning of parameters. We have analysed a simple two-state model of the chemotaxis network closely related to the one proposed previously 2,19 . The two- state model assumes that the receptor complex has two functional states: active and inactive. The active receptor complex shows a kinase activity: it phosphorylates the response regulator molecules,
1,567 citations
"Feedback for physicists: A tutorial..." refers background in this paper
...coli and shown, both in a model (Barkai and Leibler, 1997) and in experiment (Alon et al....
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TL;DR: Simple gene circuits consisting of a regulator and transcriptional repressor modules in Escherichia coli are designed and constructed and the gain of stability produced by negative feedback is shown.
Abstract: The genetic and biochemical networks which underlie such things as homeostasis in metabolism and the developmental programs of living cells, must withstand considerable variations and random perturbations of biochemical parameters These occur as transient changes in, for example, transcription, translation, and RNA and protein degradation The intensity and duration of these perturbations differ between cells in a population The unique state of cells, and thus the diversity in a population, is owing to the different environmental stimuli the individual cells experience and the inherent stochastic nature of biochemical processes (for example, refs 5 and 6) It has been proposed, but not demonstrated, that autoregulatory, negative feedback loops in gene circuits provide stability, thereby limiting the range over which the concentrations of network components fluctuate Here we have designed and constructed simple gene circuits consisting of a regulator and transcriptional repressor modules in Escherichia coli and we show the gain of stability produced by negative feedback
1,551 citations