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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TL;DR: In this article , a high-finesse, micrometer-scale fiber Fabry-Perot cavity, which can be widely tuned using piezoelectric positioners, is used for hybrid optomechanical systems at 4K.
Abstract: We describe an apparatus for the implementation of hybrid optomechanical systems at 4 K. The platform is based on a high-finesse, micrometer-scale fiber Fabry-Perot cavity, which can be widely tuned using piezoelectric positioners. A mechanical resonator can be positioned within the cavity in the object-in-the-middle configuration by a second set of positioners. A high level of stability is achieved without sacrificing either performance or tunability, through the combination of a stiff mechanical design, passive vibration isolation, and an active Pound-Drever-Hall feedback lock incorporating a reconfigurable digital filter. The stability of the cavity length is demonstrated to be better than a few picometers over many hours both at room temperature and at 4 K.
3 citations
01 Jan 2018
TL;DR: Barter et al. as mentioned in this paper investigated the Bose-Hubbard model of interacting bosons on a lattice by experimental investigation of ultracold rubidium atoms in an optical lattice made from laser light.
Abstract: Author(s): Barter, Thomas Hamish | Advisor(s): Stamper-Kurn, Dan M | Abstract: Quantum simulation is the study of one quantum mechanical system via analog with another. In this thesis we explore a simple model of interacting bosons on a lattice, known as the Bose-Hubbard model, by experimental investigation of ultracold rubidium atoms in an optical lattice made from laser light. We describe the construction and stabilization of an optical superlattice with threefold symmetry, and its use in studying the Bose-Hubbard model on triangular and trimerized kagome lattices. We study the short range phase coherence of a Mott insulator on the triangular lattice, and develop a scheme to mitigate out-of-equilibrium effects arising from the state preparation. We show the first experimental realization of an optical trimerized kagome lattice for cold atoms, and discuss experiments characterizing this lattice. Finally, we provide evidence for a Mott insulating state with fractional average particle number per site with measurements of the nearest-neighbor phase coherence of strongly interacting atoms in the trimerized kagome lattice.
3 citations
Cites background or methods from "Feedback for physicists: A tutorial..."
...37) Rules of thumb suggest gain margins of at least 2, and phase margins of at least 45◦ for stable systems [3]....
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...We examine the problem of controlling and stabilizing the relative phase of the two laser beams through the framework of linear time invariant feedback [3]....
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...To avoid this instability, we require that the magnitude of the open loop gain |G(iω)| is less than 1, when the phase argG(iω) reaches 180◦ [3]....
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Dissertation•
15 Oct 2014
Abstract: Portable frequency references are crucial for many practical on-site applications, for example, the Global Position System (GPS) navigation, optical communications, and remote sensing. Fiber laser optical frequency combs are a strong candidate for portable reference systems. However, the conventional way of locking the comb repetition rate, frep, to an RF reference leads to large multiplied RF instabilities in the optical frequency domain. By stabilizing a comb directly to an optical reference, the comb stability can potentially be enhanced by four orders of magnitude. The main goal of this thesis is to develop techniques for directly referencing optical frequency combs to optical references toward an all-fiber geometry. A big challenge for direct fiber comb spectroscopy is the low comb power. With an 89 MHz fiber ring laser, we are able to optically amplify a single comb tooth from nW to mW (by a factor of 10) by building multiple filtering and amplification stages, while preserving the comb signal-to-noise ratio. This amplified comb tooth is directly stabilized to an optical transition of acetylene at ∼ 1539.4 nm via a saturated absorption technique, while the carrier-envelope offset frequency, f0, is locked to an RF reference. The comb stability is studied by comparing to a single wavelength (or CW) reference at 1532.8 nm. Our result shows a short term instability of 6 × 10−12 at 100 ms gate time, which is over an order of magnitude better than that of a GPS-disciplined Rb clock. This implies that our optically-referenced comb is a suitable candidate for a high precision portable reference. In addition, the direct comb spectroscopy technique we have developed opens many new possibilities in precision spectroscopy for low power, low repetition rate fiber lasers. For single tooth isolation, a novel cross-VIPA (cross-virtually imaged phase array) spectrometer is proposed, with a high spectral resolution of 730 MHz based on our simulations. In addition, the noise dynamics for a free space Cr:forsterite-laser-based frequency comb are explored, to explain the significant f0 linewidth narrowing with knife insertion into the intracavity beam. A theoretical model is used to interpret this f0 narrowing phenomenon, but some unanswered questions still remain. DIRECT FIBER LASER FREQUENCY COMB STABILIZATION VIA SINGLE TOOTH SATURATED ABSORPTION SPECTROSCOPY IN HOLLOW-CORE FIBER
3 citations
Cites background from "Feedback for physicists: A tutorial..."
...For stability concerns, it is important to introduce two stability margins [84]....
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...[84] written by John Bechlhefer is a good tutorial essay that describes feedback control more from a physicist’s point of view....
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TL;DR: In this paper, the authors study the thermodynamic properties induced by non-reciprocally coupled interactions between stochastic degrees of freedom in time and space-continuous systems.
Abstract: We study the thermodynamic properties induced by non-reciprocal interactions between stochastic degrees of freedom in time- and space-continuous systems. We show that, under fairly general conditions, non-reciprocal coupling alone implies a steady energy flow through the system, i.e., non-equilibrium. Projecting out the non-reciprocally coupled degrees of freedom renders non-Markovian, one-variable Langevin descriptions with complex types of memory, for which we find a generalized second law involving information flow. We demonstrate that non-reciprocal linear interactions can be used to engineer non-monotonic memory, which is typical for, e.g., time-delayed feedback control, and is automatically accompanied with a nonzero information flow through the system. Furthermore, already a single non-reciprocally coupled degree of freedom can extract energy from a single heat bath (at isothermal conditions), and can thus be viewed as a minimal version of a time-continuous, autonomous "Maxwell demon". At the same time, the non-reciprocal system has characteristic features of active matter, such as a positive energy input on the level of the flucuating trajectories, without global particle transport.
2 citations
Dissertation•
02 Dec 2015
TL;DR: It is shown that it is possible to detect the force fluctuations that a LifeAct-RFP and non-muscle myosin II-GFP co-transfected cell transmits to two attached beads, and image its acto-myosin cytoskeleton at the same time for up to one hour.
Abstract: Cells are sensitive to mechanical cues from their environment and at the same time generate and transmit forces to their surroundings. In this thesis, we quantitatively measured forces and elastic spring constants of suspended cells. We used a dual optical trap to attach micrometer-sized fibronectin-coated beads to opposite sides of a rounded cell and detected the position fluctuations of the beads with high temporal and spatial resolution. Using a force-feedback mechanism and an acousto-optical deflector we could apply constant or oscillatory external forces to the cell. We found that the elastic response and force generation of cells are strongly governed by their acto-myosin cortex. Cell stiffness decreased substantially with both myosin inhibition by blebbistatin and serum-starvation, but not with microtubule depolymerization by nocodazole. Experiments using giant unilamellar vesicles as a model system showed that the contribution of the lipid envelope to the elastic response of cells is negligible. Force fluctuation experiments showed that cortical forces generated by non-muscle myosin II (NMM II) are present in the range from 0.1 to 10 Hz. While blebbistatin treatment and transfer to serum-free medium strongly reduced the force fluctuations, microtubule depolymerization did not affect them.
To be able to track changes in the acto-myosin cytoskeleton, we built a novel setup incorporating a dual optical trap into a Leica SP5 X confocal microscope. We showed that it is possible to detect the force fluctuations that a LifeAct-RFP and non-muscle myosin II-GFP co-transfected cell transmits to two attached beads, and image its acto-myosin cytoskeleton at the same time for up to one hour. The observed filamentous actin network of fibroblast cells in suspension is highly diverse, ranging from cells with only a flat actin cortex to cells that have actin bundles spanning through their whole interior cytosol. We found that cardiac fibroblasts in control medium have a 40 % thicker actin cortex than cardiac fibroblasts treated with 100 µM blebbistatin.
We further investigated active and passive mechanical properties of cells used in engineered heart muscle. We found that primary fibroblasts originating from heart, skin and gingiva have comparable spring constants. Cardiac fibroblasts proved to have much higher force fluctuations than the other primary fibroblasts. The amplitude of those force fluctuations is even more strongly relying on force generation of myosin II motors compared to NIH 3T3 cells indicated by a roughly fifty-fold reduction after blebbistatin treatment. We could also prove that it is possible to use the dual optical trap setup to measure contraction forces and beating frequency of cardiomyocyte cells.
2 citations
References
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Book•
01 Jan 1991TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Abstract: Preface to the Second Edition. Preface to the First Edition. Acknowledgments for the Second Edition. Acknowledgments for the First Edition. 1. Introduction and Preview. 1.1 Preview of the Book. 2. Entropy, Relative Entropy, and Mutual Information. 2.1 Entropy. 2.2 Joint Entropy and Conditional Entropy. 2.3 Relative Entropy and Mutual Information. 2.4 Relationship Between Entropy and Mutual Information. 2.5 Chain Rules for Entropy, Relative Entropy, and Mutual Information. 2.6 Jensen's Inequality and Its Consequences. 2.7 Log Sum Inequality and Its Applications. 2.8 Data-Processing Inequality. 2.9 Sufficient Statistics. 2.10 Fano's Inequality. Summary. Problems. Historical Notes. 3. Asymptotic Equipartition Property. 3.1 Asymptotic Equipartition Property Theorem. 3.2 Consequences of the AEP: Data Compression. 3.3 High-Probability Sets and the Typical Set. Summary. Problems. Historical Notes. 4. Entropy Rates of a Stochastic Process. 4.1 Markov Chains. 4.2 Entropy Rate. 4.3 Example: Entropy Rate of a Random Walk on a Weighted Graph. 4.4 Second Law of Thermodynamics. 4.5 Functions of Markov Chains. Summary. Problems. Historical Notes. 5. Data Compression. 5.1 Examples of Codes. 5.2 Kraft Inequality. 5.3 Optimal Codes. 5.4 Bounds on the Optimal Code Length. 5.5 Kraft Inequality for Uniquely Decodable Codes. 5.6 Huffman Codes. 5.7 Some Comments on Huffman Codes. 5.8 Optimality of Huffman Codes. 5.9 Shannon-Fano-Elias Coding. 5.10 Competitive Optimality of the Shannon Code. 5.11 Generation of Discrete Distributions from Fair Coins. Summary. Problems. Historical Notes. 6. Gambling and Data Compression. 6.1 The Horse Race. 6.2 Gambling and Side Information. 6.3 Dependent Horse Races and Entropy Rate. 6.4 The Entropy of English. 6.5 Data Compression and Gambling. 6.6 Gambling Estimate of the Entropy of English. Summary. Problems. Historical Notes. 7. Channel Capacity. 7.1 Examples of Channel Capacity. 7.2 Symmetric Channels. 7.3 Properties of Channel Capacity. 7.4 Preview of the Channel Coding Theorem. 7.5 Definitions. 7.6 Jointly Typical Sequences. 7.7 Channel Coding Theorem. 7.8 Zero-Error Codes. 7.9 Fano's Inequality and the Converse to the Coding Theorem. 7.10 Equality in the Converse to the Channel Coding Theorem. 7.11 Hamming Codes. 7.12 Feedback Capacity. 7.13 Source-Channel Separation Theorem. Summary. Problems. Historical Notes. 8. Differential Entropy. 8.1 Definitions. 8.2 AEP for Continuous Random Variables. 8.3 Relation of Differential Entropy to Discrete Entropy. 8.4 Joint and Conditional Differential Entropy. 8.5 Relative Entropy and Mutual Information. 8.6 Properties of Differential Entropy, Relative Entropy, and Mutual Information. Summary. Problems. Historical Notes. 9. Gaussian Channel. 9.1 Gaussian Channel: Definitions. 9.2 Converse to the Coding Theorem for Gaussian Channels. 9.3 Bandlimited Channels. 9.4 Parallel Gaussian Channels. 9.5 Channels with Colored Gaussian Noise. 9.6 Gaussian Channels with Feedback. Summary. Problems. Historical Notes. 10. Rate Distortion Theory. 10.1 Quantization. 10.2 Definitions. 10.3 Calculation of the Rate Distortion Function. 10.4 Converse to the Rate Distortion Theorem. 10.5 Achievability of the Rate Distortion Function. 10.6 Strongly Typical Sequences and Rate Distortion. 10.7 Characterization of the Rate Distortion Function. 10.8 Computation of Channel Capacity and the Rate Distortion Function. Summary. Problems. Historical Notes. 11. Information Theory and Statistics. 11.1 Method of Types. 11.2 Law of Large Numbers. 11.3 Universal Source Coding. 11.4 Large Deviation Theory. 11.5 Examples of Sanov's Theorem. 11.6 Conditional Limit Theorem. 11.7 Hypothesis Testing. 11.8 Chernoff-Stein Lemma. 11.9 Chernoff Information. 11.10 Fisher Information and the Cram-er-Rao Inequality. Summary. Problems. Historical Notes. 12. Maximum Entropy. 12.1 Maximum Entropy Distributions. 12.2 Examples. 12.3 Anomalous Maximum Entropy Problem. 12.4 Spectrum Estimation. 12.5 Entropy Rates of a Gaussian Process. 12.6 Burg's Maximum Entropy Theorem. Summary. Problems. Historical Notes. 13. Universal Source Coding. 13.1 Universal Codes and Channel Capacity. 13.2 Universal Coding for Binary Sequences. 13.3 Arithmetic Coding. 13.4 Lempel-Ziv Coding. 13.5 Optimality of Lempel-Ziv Algorithms. Compression. Summary. Problems. Historical Notes. 14. Kolmogorov Complexity. 14.1 Models of Computation. 14.2 Kolmogorov Complexity: Definitions and Examples. 14.3 Kolmogorov Complexity and Entropy. 14.4 Kolmogorov Complexity of Integers. 14.5 Algorithmically Random and Incompressible Sequences. 14.6 Universal Probability. 14.7 Kolmogorov complexity. 14.9 Universal Gambling. 14.10 Occam's Razor. 14.11 Kolmogorov Complexity and Universal Probability. 14.12 Kolmogorov Sufficient Statistic. 14.13 Minimum Description Length Principle. Summary. Problems. Historical Notes. 15. Network Information Theory. 15.1 Gaussian Multiple-User Channels. 15.2 Jointly Typical Sequences. 15.3 Multiple-Access Channel. 15.4 Encoding of Correlated Sources. 15.5 Duality Between Slepian-Wolf Encoding and Multiple-Access Channels. 15.6 Broadcast Channel. 15.7 Relay Channel. 15.8 Source Coding with Side Information. 15.9 Rate Distortion with Side Information. 15.10 General Multiterminal Networks. Summary. Problems. Historical Notes. 16. Information Theory and Portfolio Theory. 16.1 The Stock Market: Some Definitions. 16.2 Kuhn-Tucker Characterization of the Log-Optimal Portfolio. 16.3 Asymptotic Optimality of the Log-Optimal Portfolio. 16.4 Side Information and the Growth Rate. 16.5 Investment in Stationary Markets. 16.6 Competitive Optimality of the Log-Optimal Portfolio. 16.7 Universal Portfolios. 16.8 Shannon-McMillan-Breiman Theorem (General AEP). Summary. Problems. Historical Notes. 17. Inequalities in Information Theory. 17.1 Basic Inequalities of Information Theory. 17.2 Differential Entropy. 17.3 Bounds on Entropy and Relative Entropy. 17.4 Inequalities for Types. 17.5 Combinatorial Bounds on Entropy. 17.6 Entropy Rates of Subsets. 17.7 Entropy and Fisher Information. 17.8 Entropy Power Inequality and Brunn-Minkowski Inequality. 17.9 Inequalities for Determinants. 17.10 Inequalities for Ratios of Determinants. Summary. Problems. Historical Notes. Bibliography. List of Symbols. Index.
45,034 citations
"Feedback for physicists: A tutorial..." refers background in this paper
...Recent papers by Touchette and Lloyd (2000, 2004) begin to explore more formally these links and derive a fundamental relationship between the amount of control achievable (“decrease of entropy” in their formulation) and the “mutual information” (Cover and Thomas, 1991) between the dynamical system and the controller created by an initial interaction....
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23,905 citations
Book•
01 Jan 1987
TL;DR: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis and praktische Anwendung der verschiedenen Verfahren zur IdentifIZierung hat.
Abstract: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis und praktische Anwendung der verschiedenen Verfahren zur Identifizierung hat. Da ...
20,436 citations
"Feedback for physicists: A tutorial..." refers methods in this paper
...For an introduction, see Dutton et al. 1997 ; for full details, see Ljung 1999 ....
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...Alternatively, there are a number of methods that avoid the transfer function completely: from a given input u(t) and measured response y(t), they directly fit to the coefficients of a time-domain model or directly give pole and zero positions (Ljung, 1999)....
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...Alternatively, there are a number of methods that avoid the transfer function completely: from a given input u t and measured response y t , they directly fit to the coefficients of a time-domain model or directly give pole and zero positions Ljung, 1999 ....
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TL;DR: In this paper, a simple model based on the power-law degree distribution of real networks was proposed, which was able to reproduce the power law degree distribution in real networks and to capture the evolution of networks, not just their static topology.
Abstract: The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them.
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network.
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other.
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.
18,415 citations
TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Abstract: Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
17,647 citations
"Feedback for physicists: A tutorial..." refers background in this paper
...The structure of such networks is a topic of intense current interest (Albert and Barabási, 2002; Newman, 2003)....
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