Lock Acquisition and Sensitivity Analysis of Advanced LIGO Interferometers

Laser interferometer gravitational wave observatory (LIGO) consists of two complex large-scale laser interferometers designed for direct detection of gravitational waves from distant astrophysical sources in the frequency range 10Hz - 5kHz. Direct detection of space-time ripples will support Einstein's general theory of relativity and provide invaluable information and new insight into physics of the Universe.

Initial phase of LIGO started in 2002, and since then data was collected during six science runs. Instrument sensitivity was improving from run to run due to the effort of commissioning team. Initial LIGO has reached designed sensitivity during the last science run, which ended in October 2010.

In parallel with commissioning and data analysis with the initial detector, LIGO group worked on research and development of the next generation detectors. Major instrument upgrade from initial to advanced LIGO started in 2010 and lasted till 2014.

This thesis describes results of commissioning work done at LIGO Livingston site from 2013 until 2015 in parallel with and after the installation of the instrument. This thesis also discusses new techniques and tools developed at the 40m prototype including adaptive filtering, estimation of quantization noise in digital filters and design of isolation kits for ground seismometers.

The first part of this thesis is devoted to the description of methods for bringing interferometer to the linear regime when collection of data becomes possible. States of longitudinal and angular controls of interferometer degrees of freedom during lock acquisition process and in low noise configuration are discussed in details.

Once interferometer is locked and transitioned to low noise regime, instrument produces astrophysics data that should be calibrated to units of meters or strain. The second part of this thesis describes online calibration technique set up in both observatories to monitor the quality of the collected data in real time. Sensitivity analysis was done to understand and eliminate noise sources of the instrument.

Coupling of noise sources to gravitational wave channel can be reduced if robust feedforward and optimal feedback control loops are implemented. The last part of this thesis describes static and adaptive feedforward noise cancellation techniques applied to Advanced LIGO interferometers and tested at the 40m prototype. Applications of optimal time domain feedback control techniques and estimators to aLIGO control loops are also discussed.

Commissioning work is still ongoing at the sites. First science run of advanced LIGO is planned for September 2015 and will last for 3-4 months. This run will be followed by a set of small instrument upgrades that will be installed on a time scale of few months. Second science run will start in spring 2016 and last for about 6 months. Since current sensitivity of advanced LIGO is already more than factor of 3 higher compared to initial detectors and keeps improving on a monthly basis, upcoming science runs have a good chance for the first direct detection of gravitational waves.

Stochastic optimal control

H. J. Kushner has obtained the differential equation satisfied by the optimal feedback control law for a stochastic control system in which the plant dynamics and observations are perturbed by independent additive Gaussian white noise processes. However, the differentiation includes the first and second functional derivatives and, except for a restricted set of systems, is too complex to solve with present techniques.

This investigation studies the optimal control law for the open loop system and incorporates it in a sub-optimal feedback control law. This suboptimal control law's performance is at least as good as that of the optimal control function and satisfies a differential equation involving only the first functional derivative. The solution of this equation is equivalent to solving two two-point boundary valued integro-partial differential equations. An approximate solution has advantages over the conventional approximate solution of Kushner's equation.

As a result of this study, well known results of deterministic optimal control are deduced from the analysis of optimal open loop control.

Distributed Control and Optimization for Communication and Power Systems

We are at the cusp of a historic transformation of both communication system and electricity system. This creates challenges as well as opportunities for the study of networked systems. Problems of these systems typically involve a huge number of end points that require intelligent coordination in a distributed manner. In this thesis, we develop models, theories, and scalable distributed optimization and control algorithms to overcome these challenges.

This thesis focuses on two specific areas: multi-path TCP (Transmission Control Protocol) and electricity distribution system operation and control. Multi-path TCP (MP-TCP) is a TCP extension that allows a single data stream to be split across multiple paths. MP-TCP has the potential to greatly improve reliability as well as efficiency of communication devices. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We clarify how algorithm parameters impact TCP-friendliness, responsiveness, and window oscillation and demonstrate an inevitable tradeoff among these properties. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new algorithm Balia (balanced linked adaptation) which generalizes existing algorithms and strikes a good balance among TCP-friendliness, responsiveness, and window oscillation. We have implemented Balia in the Linux kernel. We use our prototype to compare the new proposed algorithm Balia with existing MP-TCP algorithms.

Our second focus is on designing computationally efficient algorithms for electricity distribution system operation and control. First, we develop efficient algorithms for feeder reconfiguration in distribution networks. The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed integer nonlinear program and hence hard to solve. We propose a heuristic algorithm that is based on the recently developed convex relaxation of the optimal power flow problem. The algorithm is efficient and can successfully computes an optimal configuration on all networks that we have tested. Moreover we prove that the algorithm solves the feeder reconfiguration problem optimally under certain conditions. We also propose a more efficient algorithm and it incurs a loss in optimality of less than 3% on the test networks.

Second, we develop efficient distributed algorithms that solve the optimal power flow (OPF) problem on distribution networks. The OPF problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. Traditionally OPF is solved in a centralized manner. With increasing penetration of volatile renewable energy resources in distribution systems, we need faster and distributed solutions for real-time feedback control. This is difficult because power flow equations are nonlinear and kirchhoff's law is global. We propose solutions for both balanced and unbalanced radial distribution networks. They exploit recent results that suggest solving for a globally optimal solution of OPF over a radial network through a second-order cone program (SOCP) or semi-definite program (SDP) relaxation. Our distributed algorithms are based on the alternating direction method of multiplier (ADMM), but unlike standard ADMM-based distributed OPF algorithms that require solving optimization subproblems using iterative methods, the proposed solutions exploit the problem structure that greatly reduce the computation time. Specifically, for balanced networks, our decomposition allows us to derive closed form solutions for these subproblems and it speeds up the convergence by 1000x times in simulations. For unbalanced networks, the subproblems reduce to either closed form solutions or eigenvalue problems whose size remains constant as the network scales up and computation time is reduced by 100x compared with iterative methods.

Synthetic molecular machines for active self-assembly : prototype algorithms, designs, and experimental study

Computer science and electrical engineering have been the great success story of the twentieth century. The neat modularity and mapping of a language onto circuits has led to robots on Mars, desktop computers and smartphones. But these devices are not yet able to do some of the things that life takes for granted: repair a scratch, reproduce, regenerate, or grow exponentially fast–all while remaining functional.

This thesis explores and develops algorithms, molecular implementations, and theoretical proofs in the context of “active self-assembly” of molecular systems. The long-term vision of active self-assembly is the theoretical and physical implementation of materials that are composed of reconfigurable units with the programmability and adaptability of biology’s numerous molecular machines. En route to this goal, we must first find a way to overcome the memory limitations of molecular systems, and to discover the limits of complexity that can be achieved with individual molecules.

One of the main thrusts in molecular programming is to use computer science as a tool for figuring out what can be achieved. While molecular systems that are Turing-complete have been demonstrated [Winfree, 1996], these systems still cannot achieve some of the feats biology has achieved.

One might think that because a system is Turing-complete, capable of computing “anything,” that it can do any arbitrary task. But while it can simulate any digital computational problem, there are many behaviors that are not “computations” in a classical sense, and cannot be directly implemented. Examples include exponential growth and molecular motion relative to a surface.

Passive self-assembly systems cannot implement these behaviors because (a) molecular motion relative to a surface requires a source of fuel that is external to the system, and (b) passive systems are too slow to assemble exponentially-fast-growing structures. We call these behaviors “energetically incomplete” programmable behaviors. This class of behaviors includes any behavior where a passive physical system simply does not have enough physical energy to perform the specified tasks in the requisite amount of time.

As we will demonstrate and prove, a sufficiently expressive implementation of an “active” molecular self-assembly approach can achieve these behaviors. Using an external source of fuel solves part of the the problem, so the system is not “energetically incomplete.” But the programmable system also needs to have sufficient expressive power to achieve the specified behaviors. Perhaps surprisingly, some of these systems do not even require Turing completeness to be sufficiently expressive.

Building on a large variety of work by other scientists in the fields of DNA nanotechnology, chemistry and reconfigurable robotics, this thesis introduces several research contributions in the context of active self-assembly.

We show that simple primitives such as insertion and deletion are able to generate complex and interesting results such as the growth of a linear polymer in logarithmic time and the ability of a linear polymer to treadmill. To this end we developed a formal model for active-self assembly that is directly implementable with DNA molecules. We show that this model is computationally equivalent to a machine capable of producing strings that are stronger than regular languages and, at most, as strong as context-free grammars. This is a great advance in the theory of active self- assembly as prior models were either entirely theoretical or only implementable in the context of macro-scale robotics.

We developed a chain reaction method for the autonomous exponential growth of a linear DNA polymer. Our method is based on the insertion of molecules into the assembly, which generates two new insertion sites for every initial one employed. The building of a line in logarithmic time is a first step toward building a shape in logarithmic time. We demonstrate the first construction of a synthetic linear polymer that grows exponentially fast via insertion. We show that monomer molecules are converted into the polymer in logarithmic time via spectrofluorimetry and gel electrophoresis experiments. We also demonstrate the division of these polymers via the addition of a single DNA complex that competes with the insertion mechanism. This shows the growth of a population of polymers in logarithmic time. We characterize the DNA insertion mechanism that we utilize in Chapter 4. We experimentally demonstrate that we can control the kinetics of this re- action over at least seven orders of magnitude, by programming the sequences of DNA that initiate the reaction.

In addition, we review co-authored work on programming molecular robots using prescriptive landscapes of DNA origami; this was the first microscopic demonstration of programming a molec- ular robot to walk on a 2-dimensional surface. We developed a snapshot method for imaging these random walking molecular robots and a CAPTCHA-like analysis method for difficult-to-interpret imaging data.

The optoelectronic swept-frequency laser and its applications in ranging, three-dimensional imaging, and coherent beam combining of chirped-seed amplifiers

This thesis explores the design, construction, and applications of the optoelectronic swept-frequency laser (SFL). The optoelectronic SFL is a feedback loop designed around a swept-frequency (chirped) semiconductor laser (SCL) to control its instantaneous optical frequency, such that the chirp characteristics are determined solely by a reference electronic oscillator. The resultant system generates precisely controlled optical frequency sweeps. In particular, we focus on linear chirps because of their numerous applications. We demonstrate optoelectronic SFLs based on vertical-cavity surface-emitting lasers (VCSELs) and distributed-feedback lasers (DFBs) at wavelengths of 1550 nm and 1060 nm. We develop an iterative bias current predistortion procedure that enables SFL operation at very high chirp rates, up to 10^16 Hz/sec. We describe commercialization efforts and implementation of the predistortion algorithm in a stand-alone embedded environment, undertaken as part of our collaboration with Telaris, Inc. We demonstrate frequency-modulated continuous-wave (FMCW) ranging and three-dimensional (3-D) imaging using a 1550 nm optoelectronic SFL.

We develop the technique of multiple source FMCW (MS-FMCW) reflectometry, in which the frequency sweeps of multiple SFLs are "stitched" together in order to increase the optical bandwidth, and hence improve the axial resolution, of an FMCW ranging measurement. We demonstrate computer-aided stitching of DFB and VCSEL sweeps at 1550 nm. We also develop and demonstrate hardware stitching, which enables MS-FMCW ranging without additional signal processing. The culmination of this work is the hardware stitching of four VCSELs at 1550 nm for a total optical bandwidth of 2 THz, and a free-space axial resolution of 75 microns.

We describe our work on the tomographic imaging camera (TomICam), a 3-D imaging system based on FMCW ranging that features non-mechanical acquisition of transverse pixels. Our approach uses a combination of electronically tuned optical sources and low-cost full-field detector arrays, completely eliminating the need for moving parts traditionally employed in 3-D imaging. We describe the basic TomICam principle, and demonstrate single-pixel TomICam ranging in a proof-of-concept experiment. We also discuss the application of compressive sensing (CS) to the TomICam platform, and perform a series of numerical simulations. These simulations show that tenfold compression is feasible in CS TomICam, which effectively improves the volume acquisition speed by a factor ten.

We develop chirped-wave phase-locking techniques, and apply them to coherent beam combining (CBC) of chirped-seed amplifiers (CSAs) in a master oscillator power amplifier configuration. The precise chirp linearity of the optoelectronic SFL enables non-mechanical compensation of optical delays using acousto-optic frequency shifters, and its high chirp rate simultaneously increases the stimulated Brillouin scattering (SBS) threshold of the active fiber. We characterize a 1550 nm chirped-seed amplifier coherent-combining system. We use a chirp rate of 5*10^14 Hz/sec to increase the amplifier SBS threshold threefold, when compared to a single-frequency seed. We demonstrate efficient phase-locking and electronic beam steering of two 3 W erbium-doped fiber amplifier channels, achieving temporal phase noise levels corresponding to interferometric fringe visibilities exceeding 98%.

Active interaction control for civil structures

This thesis presents a civil engineering approach to active control for civil structures. The proposed control technique, termed Active Interaction Control (AIC), utilizes dynamic interactions between different structures, or components of the same structure, to reduce the resonance response of the controlled or primary structure under earthquake excitations. The primary control objective of AIC is to minimize the maximum story drift of the primary structure. This is accomplished by timing the controlled interactions so as to withdraw the maximum possible vibrational energy from the primary structure to an auxiliary structure, where the energy is stored and eventually dissipated as the external excitation decreases. One of the important advantages of AIC over most conventional active control approaches is the very low external power required.

In this thesis, the AIC concept is introduced and a new AIC algorithm, termed Optimal Connection Strategy (OCS) algorithm, is proposed. The efficiency of the OCS algorithm is demonstrated and compared with two previously existing AIC algorithms, the Active Interface Damping (AID) and Active Variable Stiffness (AVS) algorithms, through idealized examples and numerical simulations of Single- and Multi-Degree-of Freedom systems under earthquake excitations. It is found that the OCS algorithm is capable of significantly reducing the story drift response of the primary structure. The effects of the mass, damping, and stiffness of the auxiliary structure on the system performance are investigated in parametric studies. Practical issues such as the sampling interval and time delay are also examined. A simple but effective predictive time delay compensation scheme is developed.

Transition metal clusters supported by multinucleating ligand frameworks as models of biological active sites

This dissertation describes efforts to model biological active sites with small molecule clusters. The approach used took advantage of a multinucleating ligand to control the structure and nuclearity of the product complexes, allowing the study of many different homo- and heterometallic clusters. Chapter 2 describes the synthesis of the multinucleating hexapyridyl trialkoxy ligand used throughout this thesis and the synthesis of trinuclear first row transition metal complexes supported by this framework, with an emphasis on tricopper systems as models of biological multicopper oxidases. The magnetic susceptibility of these complexes were studied, and a linear relation was found between the Cu-O(alkoxide)-Cu angles and the antiferromagnetic coupling between copper centers. The triiron(II) and trizinc(II) complexes of the ligand were also isolated and structurally characterized.

Chapter 3 describes the synthesis of a series of heterometallic tetranuclear manganese dioxido complexes with various incorporated apical redox-inactive metal cations (M = Na⁺, Ca²⁺, Sr²⁺, Zn²⁺, Y³⁺). Chapter 4 presents the synthesis of heterometallic trimanganese(IV) tetraoxido complexes structurally related to the CaMn₃ subsite of the oxygen-evolving complex (OEC) of Photosystem II. The reduction potentials of these complexes were studied, and it was found that each isostructural series displays a linear correlation between the reduction potentials and the Lewis acidities of the incorporated redox-inactive metals. The slopes of the plotted lines for both the dioxido and tetraoxido clusters are the same, suggesting a more general relationship between the electrochemical potentials of heterometallic manganese oxido clusters and their “spectator” cations. Additionally, these studies suggest that Ca²⁺ plays a role in modulating the redox potential of the OEC for water oxidation.

Chapter 5 presents studies of the effects of the redox-inactive metals on the reactivities of the heterometallic manganese complexes discussed in Chapters 3 and 4. Oxygen atom transfer from the clusters to phosphines is studied; although the reactivity is kinetically controlled in the tetraoxido clusters, the dioxido clusters with more Lewis acidic metal ions (Y³⁺ vs. Ca²⁺) appear to be more reactive. Investigations of hydrogen atom transfer and electron transfer rates are also discussed.

Appendix A describes the synthesis, and metallation reactions of a new dinucleating bis(N-heterocyclic carbene)ligand framework. Dicopper(I) and dicobalt(II) complexes of this ligand were prepared and structurally characterized. A dinickel(I) dichloride complex was synthesized, reduced, and found to activate carbon dioxide. Appendix B describes preliminary efforts to desymmetrize the manganese oxido clusters via functionalization of the basal multinucleating ligand used in the preceding sections of this dissertation. Finally, Appendix C presents some partially characterized side products and unexpected structures that were isolated throughout the course of these studies.

Acceleration Sensing, Feedback Cooling, and Nonlinear Dynamics with Nanoscale Cavity-Optomechanical Devices

Light has long been used for the precise measurement of moving bodies, but the burgeoning field of optomechanics is concerned with the interaction of light and matter in a regime where the typically weak radiation pressure force of light is able to push back on the moving object. This field began with the realization in the late 1960's that the momentum imparted by a recoiling photon on a mirror would place fundamental limits on the smallest measurable displacement of that mirror. This coupling between the frequency of light and the motion of a mechanical object does much more than simply add noise, however. It has been used to cool objects to their quantum ground state, demonstrate electromagnetically-induced-transparency, and modify the damping and spring constant of the resonator. Amazingly, these radiation pressure effects have now been demonstrated in systems ranging 18 orders of magnitude in mass (kg to fg).

In this work we will focus on three diverse experiments in three different optomechanical devices which span the fields of inertial sensors, closed-loop feedback, and nonlinear dynamics. The mechanical elements presented cover 6 orders of magnitude in mass (ng to fg), but they all employ nano-scale photonic crystals to trap light and resonantly enhance the light-matter interaction. In the first experiment we take advantage of the sub-femtometer displacement resolution of our photonic crystals to demonstrate a sensitive chip-scale optical accelerometer with a kHz-frequency mechanical resonator. This sensor has a noise density of approximately 10 micro-g/rt-Hz over a useable bandwidth of approximately 20 kHz and we demonstrate at least 50 dB of linear dynamic sensor range. We also discuss methods to further improve performance of this device by a factor of 10.

In the second experiment, we used a closed-loop measurement and feedback system to damp and cool a room-temperature MHz-frequency mechanical oscillator from a phonon occupation of 6.5 million down to just 66. At the time of the experiment, this represented a world-record result for the laser cooling of a macroscopic mechanical element without the aid of cryogenic pre-cooling. Furthermore, this closed-loop damping yields a high-resolution force sensor with a practical bandwidth of 200 kHZ and the method has applications to other optomechanical sensors.

The final experiment contains results from a GHz-frequency mechanical resonator in a regime where the nonlinearity of the radiation-pressure interaction dominates the system dynamics. In this device we show self-oscillations of the mechanical element that are driven by multi-photon-phonon scattering. Control of the system allows us to initialize the mechanical oscillator into a stable high-amplitude attractor which would otherwise be inaccessible. To provide context, we begin this work by first presenting an intuitive overview of optomechanical systems and then providing an extended discussion of the principles underlying the design and fabrication of our optomechanical devices.

Optimum linear coding for additive noise systems using information feedback

The feedback coding problem for Gaussian systems in which the noise is neither white nor statistically independent between channels is formulated in terms of arbitrary linear codes at the transmitter and at the receiver. This new formulation is used to determine a number of feedback communication systems. In particular, the optimum linear code that satisfies an average power constraint on the transmitted signals is derived for a system with noiseless feedback and forward noise of arbitrary covariance. The noisy feedback problem is considered and signal sets for the forward and feedback channels are obtained with an average power constraint on each. The general formulation and results are valid for non-Gaussian systems in which the second order statistics are known, the results being applicable to the determination of error bounds via the Chebychev inequality.