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: In this article, the authors identify the dynamics of an atomic force microscope (AFM) in order to design a feedback controller that enables faster image acquisition at reduced imaging error compared to the now generally employed proportional integral differential (PID) controllers.
Abstract: We identify the dynamics of an atomic force microscope (AFM) in order to design a feedback controller that enables faster image acquisition at reduced imaging error compared to the now generally employed proportional integral differential (PID) controllers. First, a force model for the tip–sample interaction in an AFM is used to show that the dynamic behavior of the cantilever working in contact mode can be neglected for control purposes due to the relatively small oscillation amplitude of the cantilever in response to a defined topography step. Consequently, the dynamic behavior of the AFM system can be reduced to the behavior of the piezoelectric scanner making the design of a model based controller for the AFM possible. Second, a black box identification of the scanner of a commercial AFM (Nanoscope IIIa, Digital Instruments) is performed using subspace methods. Identification yields a mathematical model of the scanner which allows us to design a new controller utilizing H∞ theory. Finally, this contro...
279 citations
"Feedback for physicists: A tutorial..." refers background in this paper
...In the physics literature, robust controller design has seldom been used, but two recent examples both concern the control of a positioner for an atomic force microscope head (Salapaka et al., 2002; Schitter et al., 2001)....
[...]
01 Jan 2001
TL;DR: In this paper, the theory of the feedback principle and its application in a carrier-in-cable system were described and explained. And the results of this trial were highly satisfactory and demonstrated conclusively the correctness of the theory and the practicability of its commercial application.
Abstract: This paper describes and explains the theory of the feedback principle and then demonstrates how stability of amplification and reduction of modulation products, as well as certain other advantages, follow when stabilized feedback is applied to an amplifier. The underlying principle of design by means of which singing ia avoided is next set forth. The paper concludes with some examples of results obtained on amplifiers which have been built employing this new principle. The carrier-in-cable system dealt with in a companion paper1 involves many amplifiers in tandem with many telephone channels passing through each amplifier and constitutes, therefore, an ideal field for application of this feedback principle. A field trial of this system was made at Morristown, New Jersey, in which seventy of these amplifiers were operated in tandem. The results of this trial were highly satisfactory and demonstrated conclusively the correctness of the theory and the practicability of its commercial application.
279 citations
TL;DR: A modified feedforward input is proposed that only uses the model information in frequency regions where plant uncertainty is sufficiently small and results in improvement of the output tracking performance, when compared to the use of the feedback alone.
Abstract: Bounds on the size of the plant uncertainties are found such that the use of the inversion-based feedforward input improves the output-tracking performance when compared to the use of feedback alone. The output-tracking error is normalized by the size of the desired output and used as a measure of the output tracking performance. The worst-case performance is compared for two cases: (1) with the use of feedback alone and (2) with the addition of the feedforward input. It is shown that inversion-based feedforward controllers can lead to performance improvements at frequencies w where the uncertainty /spl Delta/ (jw) in the nominal plant is smaller than the size of the nominal plant G/sub 0/(jw) divided by its condition number K/sub G0/ (jw), i.e., /spl par//spl Delta/(jw)/spl par//sub 2/ < /spl par/G/sub 0/(jw) /spl par//sub 2//k/sub G0/ (jw). A modified feedforward input is proposed that only uses the model information in frequency regions where plant uncertainty is sufficiently small. The use of this modified inverse with (any) feedback results in improvement of the output tracking performance, when compared to the use of the feedback alone.
272 citations
Additional excerpts
...See Devasia 2002 and Sec....
[...]
TL;DR: In this paper, the theory of the feedback principle and the underlying principle of design by means of which singing is avoided is described and some examples of results obtained on amplifiers which have been built employing this new principle.
Abstract: This paper describes and explains the theory of the feedback principle and then demonstrates how stability of amplification and reduction of modulation products, as well as certain other advantages, follow when stabilized feedback is applied to an amplifier. The underlying principle of design by means of which singing is avoided is next set forth. The paper concludes with some examples of results obtained on amplifiers which have been built employing this new principle.
257 citations
TL;DR: The Taylor Instrument Company introduced a completely redesigned version of its Fulscope pneumatic controller in 1939 as mentioned in this paper, which provided an action which the Taylor Instrument Companies called pre-act.
Abstract: In 1939, the Taylor Instrument Companies introduced a completely redesigned version of its Fulscope pneumatic controller. In addition to proportional and reset control actions, this new instrument provided an action which the Taylor Instrument Companies called pre-act. In the same year the Foxboro Instrument Company added Hyper-reset to the proportional and reset control actions provided by their Stabilog pneumatic controller. The pre-act and Hyper-reset actions each provide a control action proportional to the derivative of the error signal. Reset provides a control action proportional to the integral of the error signal and hence both controllers offered PID control. The historical development of these controllers is discussed. >
256 citations