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: The phase diagram of the bistable lactose utilization network of Escherichia coli is presented, coupled with a mathematical model of the network, to quantitatively investigate processes such as sugar uptake and transcriptional regulation in vivo and shows how the hysteretic response of the wild-type system can be converted to an ultrasensitive graded response.
Abstract: Multistability, the capacity to achieve multiple internal states in response to a single set of external inputs, is the defining characteristic of a switch. Biological switches are essential for the determination of cell fate in multicellular organisms1, the regulation of cell-cycle oscillations during mitosis2,3 and the maintenance of epigenetic traits in microbes4. The multistability of several natural1,2,3,4,5,6 and synthetic7,8,9 systems has been attributed to positive feedback loops in their regulatory networks10. However, feedback alone does not guarantee multistability. The phase diagram of a multistable system, a concise description of internal states as key parameters are varied, reveals the conditions required to produce a functional switch11,12. Here we present the phase diagram of the bistable lactose utilization network of Escherichia coli13. We use this phase diagram, coupled with a mathematical model of the network, to quantitatively investigate processes such as sugar uptake and transcriptional regulation in vivo. We then show how the hysteretic response of the wild-type system can be converted to an ultrasensitive graded response14,15. The phase diagram thus serves as a sensitive probe of molecular interactions and as a powerful tool for rational network design.
1,059 citations
TL;DR: Using techniques from control and dynamical systems theory, it is demonstrated that integral control is structurally inherent in the Barkai-Leibler model and identified and characterize the key assumptions of the model.
Abstract: ‡Integral feedback control is a basic engineering strategy for ensuring that the output of a system robustly tracks its desired value independent of noise or variations in system parameters. In biological systems, it is common for the response to an extracellular stimulus to return to its prestimulus value even in the continued presence of the signal—a process termed adaptation or desensitization. Barkai, Alon, Surette, and Leibler have provided both theoretical and experimental evidence that the precision of adaptation in bacterial chemotaxis is robust to dramatic changes in the levels and kinetic rate constants of the constituent proteins in this signaling network [Alon, U., Surette, M. G., Barkai, N. & Leibler, S. (1998) Nature (London) 397, 168 ‐171]. Here we propose that the robustness of perfect adaptation is the result of this system possessing the property of integral feedback control. Using techniques from control and dynamical systems theory, we demonstrate that integral control is structurally inherent in the Barkai‐ Leibler model and identify and characterize the key assumptions of the model. Most importantly, we argue that integral control in some form is necessary for a robust implementation of perfect adaptation. More generally, integral control may underlie the robustness of many homeostatic mechanisms.
1,058 citations
1,019 citations
"Feedback for physicists: A tutorial..." refers background in this paper
...The heavy (red) curve shows an example trajectory (Pontryagin et al., 1964)....
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...These types of problems led Pontryagin and collaborators to generalize the treatment of optimizations, as expressed in the famous “minimum principle” Pontryagin et al., 1964 .21 The main result is that if the control variables u t are required to lie within some closed and bounded set in the…...
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...showed that if an nth-order, linear system is controllable and if all eigenvalues of its system matrix A are real, then the optimum control will have at most n − 1 jump discontinuities (Pontryagin et al., 1964)....
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...The curve AOB is thus known as the “switching curve” Pontryagin et al., 1964 ....
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...Pontryagin et al. showed that if an nth-order, linear system is controllable and if all eigenvalues of its system matrix A are real, then the optimum control will have at most n−1 jump discontinuities Pontryagin et al., 1964 ....
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TL;DR: It is concluded that magnetic tweezers represent a low-cost and biocompatible setup that could become a suitable alternative to the other available micromanipulators.
952 citations
Book•
02 Feb 2000
TL;DR: In this paper, the authors present an approach for detecting models and controllers from data using a multilayer perceptron (MLP) model and a linear model of the control system.
Abstract: 1. Introduction.- 1.1 Background.- 1.1.1 Inferring Models and Controllers from Data.- 1.1.2 Why Use Neural Networks?.- 1.2 Introduction to Multilayer Perceptron Networks.- 1.2.1 The Neuron.- 1.2.2 The Multilayer Perceptron.- 1.2.3 Choice of Neural Network Architecture.- 1.2.4 Models of Dynamic Systems.- 1.2.5 Recurrent Networks.- 1.2.6 Other Neural Network Architectures.- 2. System Identification with Neural Networks.- 2.1 Introduction to System Identification.- 2.1.1 The Procedure.- 2.2 Model Structure Selection.- 2.2.1 Some Linear Model Structures.- 2.2.2 Nonlinear Model Structures Based on Neural Networks.- 2.2.3 A Few Remarks on Stability.- 2.2.4 Terminology.- 2.2.5 Selecting the Lag Space.- 2.2.6 Section Summary.- 2.3 Experiment.- 2.3.1 When is a Linear Model Insufficient?.- 2.3.2 Issues in Experiment Design.- 2.3.3 Preparing the Data for Modelling.- 2.3.4 Section Summary.- 2.4 Determination of the Weights.- 2.4.1 The Prediction Error Method.- 2.4.2 Regularization and the Concept of Generalization.- 2.4.3 Remarks on Implementation.- 2.4.4 Section Summary.- 2.5 Validation.- 2.5.1 Looking for Correlations.- 2.5.2 Estimation of the Average Generalization Error.- 2.5.3 Visualization of the Predictions.- 2.5.4 Section Summary.- 2.6 Going Backwards in the Procedure.- 2.6.1 Training the Network Again.- 2.6.2 Finding the Optimal Network Architecture.- 2.6.3 Redoing the Experiment.- 2.6.4 Section Summary.- 2.7 Recapitulation of System Identification.- 3. Control with Neural Networks.- 3.1 Introduction to Neural-Network-based Control.- 3.1.1 The Benchmark System.- 3.2 Direct Inverse Control.- 3.2.1 General Training.- 3.2.2 Direct Inverse Control of the Benchmark System.- 3.2.3 Specialized Training.- 3.2.4 Specialized Training and Direct Inverse Control of the Benchmark System.- 3.2.5 Section Summary.- 3.3 Internal Model Control (IMC).- 3.3.1 Internal Model Control with Neural Networks.- 3.3.2 Section Summary.- 3.4 Feedback Linearization.- 3.4.1 The Basic Principle of Feedback Linearization.- 3.4.2 Feedback Linearization Using Neural Network Models..- 3.4.3 Feedback Linearization of the Benchmark System.- 3.4.4 Section Summary.- 3.5 Feedforward Control.- 3.5.1 Feedforward for Optimizing an Existing Control System.- 3.5.2 Feedforward Control of the Benchmark System.- 3.5.3 Section Summary.- 3.6 Optimal Control.- 3.6.1 Training of an Optimal Controller.- 3.6.2 Optimal Control of the Benchmark System.- 3.6.3 Section Summary.- 3.7 Controllers Based on Instantaneous Linearization.- 3.7.1 Instantaneous Linearization.- 3.7.2 Applying Instantaneous Linearization to Control.- 3.7.3 Approximate Pole Placement Design.- 3.7.4 Pole Placement Control of the Benchmark System.- 3.7.5 Approximate Minimum Variance Design.- 3.7.6 Section Summary.- 3.8 Predictive Control.- 3.8.1 Nonlinear Predictive Control (NPC).- 3.8.2 NPC Applied to the Benchmark System.- 3.8.3 Approximate Predictive Control (APC).- 3.8.4 APC applied to the Benchmark System.- 3.8.5 Extensions to the Predictive Controller.- 3.8.6 Section Summary.- 3.9 Recapitulation of Control Design Methods.- 4. Case Studies.- 4.1 The Sunspot Benchmark.- 4.1.1 Modelling with a Fully Connected Network.- 4.1.2 Pruning of the Network Architecture.- 4.1.3 Section Summary.- 4.2 Modelling of a Hydraulic Actuator.- 4.2.1 Estimation of a Linear Model.- 4.2.2 Neural Network Modelling of the Actuator.- 4.2.3 Section Summary.- 4.3 Pneumatic Servomechanism.- 4.3.1 Identification of the Pneumatic Servomechanism.- 4.3.2 Nonlinear Predictive Control of the Servo.- 4.3.3 Approximate Predictive Control of the Servo.- 4.3.4 Section Summary.- 4.4 Control of Water Level in a Conic Tank.- 4.4.1 Linear Analysis and Control.- 4.4.2 Direct Inverse Control of the Water Level.- 4.4.3 Section Summary.- References.
923 citations