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: Only within the past decade have researchers warmed to the possibility of abrupt shifts in Earth's climate as mentioned in this paper, and it takes a while to see what one is not prepared to look for.
Abstract: Only within the past decade have researchers warmed to the possibility of abrupt shifts in Earth’s climate. Sometimes, it takes a while to see what one is not prepared to look for.
36 citations
"Feedback for physicists: A tutorial..." refers background in this paper
...Models of thermohaline circulation in the oceans show bistable behavior analogous to the genetic switch discussed above, where positive feedback effects can toggle the climate between warm and icy states (Weart, 2003)....
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TL;DR: In this paper, a theoretical analysis of the feedback system in the scanning tunneling microscope (STM) is presented, which includes all the elements involved in the STM loop and the mathematical models for each element of the loop has been used and the problem has been solved using control theory.
Abstract: A theoretical analysis of the feedback system in the scanning tunneling microscope (STM) is presented. The proposed model includes all the elements involved in the STM loop. The knowledge of its behavior allow one to accurately determine the region where the unstable STM operation could affect the measurements, and also to set the optimal working parameters. Each element of the feedback circuitry is analyzed and discussed as well as their mutual interactions. Thus the stability region of a STM has been obtained analytically, using all the possible elements in the feedback loop and without using simplifications or rare models for the system. The mathematical models for each element of the loop has been used and the problem has been solved using control theory. Different working conditions are simulated and analyzed. Some relations for stability conditions, considering the value of each component involved in the feedback loop, are proposed and analyzed. The good agreement between theory and experimentation ...
35 citations
"Feedback for physicists: A tutorial..." refers methods in this paper
...) Another widely used application of feedback to linearize a signal, mentioned briefly above in our discussion of feedforward techniques is the scanning tunneling microscope (STM), where the exponential dependence of tunneling current on the distance between conductors is linearized by feedback (Oliva et al., 1995)....
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...…used application of feedback to linearize a signal, mentioned briefly above in our discussion of feedforward techniques is the scanning tunneling microscope STM , where the exponential dependence of tunneling current on the distance between conductors is linearized by feedback Oliva et al., 1995 ....
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TL;DR: In this article, the authors outline the derivation of the Kalman filter and give three examples of its use: (a) in estimating the value of a constant, with both system and measurement noise, (b) in numerical differentiation of noisy data, and (c) in optimally estimating the amplitude of a signal with arbitrary but known time dependence superimposed on a noisy background.
Abstract: The Kalman filter, a powerful and useful optimal estimation technique, does not seem to be widely known among physicists. Here we outline the derivation of the algorithm, and give three examples of its use: (a) in estimating the value of a constant, with both system and measurement noise, (b) in numerical differentiation of noisy data, and (c) in optimally estimating the amplitude of a signal with arbitrary but known time dependence superimposed on a noisy background.
31 citations
TL;DR: In this article, the actuator dynamics are modeled and iteratively inverted to find the input that compensates for the induced mechanical vibrations, and the inversion-base is used to determine the displacement of a mass by utilizing stick-slip phenomena between the mass and the device's actuators.
Abstract: Inertial reaction devices (also referred to as impact drive, or slip-stick devices) enable nano/micro resolution positioning over macroscopic ranges. Such positioning devices are characterized by the displacement of a mass by utilizing stick-slip phenomena between the mass and the device’s actuators. The displacement of the actuator (i.e., the driving wave form) is chosen such that the mass sticks to the actuator and is displaced with the actuator during the first tracking phase, and the mass slips with respect to the actuator during the second retrace phase during which the actuator’s position is reset. However, as the driving wave form’s frequency is increased to operate an inertial-reaction device at high speed, induced mechanical vibrations prevent accurate actuator positioning and thereby, limit the maximum achievable operating speed. In this article, the actuator dynamics is modeled and iteratively inverted to find the input that compensates for the induced mechanical vibrations. This inversion-base...
30 citations
"Feedback for physicists: A tutorial..." refers background in this paper
...Adding a feedforward element allows one to “shape” the input so that resonances are not excited; the actual response can then be closer to the desired step than it would be were the “naive” input used instead Singhose, 1997; Croft and Devasia, 1999; Schitter and Stemmer, 2004; Zou et al., 2005 ....
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01 Jan 1972
TL;DR: “But let your communication be Yea, yea; Nay, nay; for whatsoever is more than these cometh of evil,” says Matthew 5:37.
Abstract: “But let your communication be Yea, yea; Nay, nay; for whatsoever is more than these cometh of evil.”
MATTHEW 5:37
30 citations