Optomechanical Inertial Sensors and Feedback Cooling

The optomechanical interaction is an extremely powerful tool with which to measure mechanical motion. The displacement resolution of chip-scale optomechanical systems has been measured on the order of 1⁄10th of a proton radius. So strong is this optomechanical interaction that it has recently been used to remove almost all thermal noise from a mechanical resonator and observe its quantum ground-state of motion starting from cryogenic temperatures.

In this work, chapter 1 describes the basic physics of the canonical optomechanical system, optical measurement techniques, and how the optomechanical interaction affects the coupled mechanical resonator. In chapter 2, we describe our techniques for realizing this canonical optomechanical system in a chip-scale form factor.

In chapter 3, we describe an experiment where we used radiation pressure feedback to cool a mesoscopic mechanical resonator near its quantum ground-state from room-temperature. We cooled the resonator from a room temperature phonon occupation of <n> = 6.5 million to an occupation of <n> = 66, which means the resonator is in its ground state approximately 2% of the time, while being coupled to a room-temperature thermal environment. At the time of this work, this is the closest a mesoscopic mechanical resonator has been to its ground-state of motion at room temperature, and this work begins to open the door to room-temperature quantum control of mechanical objects.

Chapter 4 begins with the realization that the displacement resolutions achieved by optomechanical systems can surpass those of conventional MEMS sensors by an order of magnitude or more. This provides the motivation to develop and calibrate an optomechanical accelerometer with a resolution of approximately 10 micro-g/rt-Hz over a bandwidth of approximately 30 kHz. In chapter 5, we improve upon the performance and practicality of this sensor by greatly increasing the test mass size, investigating and reducing low-frequency noise, and incorporating more robust optical coupling techniques and capacitive wavelength tuning. Finally, in chapter 6 we present our progress towards developing another optomechanical inertial sensor - a gyroscope.

Distributed Optimal Control of Cyber-Physical Systems: Controller Synthesis, Architecture Design and System Identification

The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation.

The identification of quadratic invariance as an appropriate means of "convexifying" distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification.

We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H-infinity optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H-infinity norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

Design and control of an ultraprecision stage used in grating tiling

In petawatt laser system, the gratings used to compose pulse compressor are very large in size which can be only acquired currently by arraying small aperture gratings to form a large one instead, an approach referred to as grating tiling. Theory and experiments have demonstrated that the coherent addition of multiple small gratings to form a larger grating is viable, the key technology of which is to control the relative position and orientation of each grating with high precision. According to the main factors that affect the performance of the grating tiling, a 5-DOF ultraprecision stage is developed for the grating tiling experiment. The mechanism is formed by serial structures. The motion of the mechanism is guided by flexure hinges and driven by piezoelectric actuators and the movement resolution of which can achieve nanometer level. To keep the stability of the mechanism, capacitive position sensors with nanometer accuracy are fixed on it to provide feedback signals with which to realize closed-loop control, thus the positioning precision of the mechanism is within several nanometers range through voltage control and digital PID algorithm. Results of experiments indicate that the performance of the mechanism can meet the requirement of precision for grating tiling.}

Comparativa entre distintos sistemas comerciales de feedback de la profundidad y frecuencia de las compresiones torácicas durante la Reanimación Cardiopulmonar realizada en un tren de larga distancia.

[Es]En este trabajo se analiza la posibilidad de utilizar los sistemas de feedback comerciales más conocidos (TrueCPR de la empresa Physio-Control y CPRmeter de Laerdal) en un tren de larga distancia. Se trata de estudiar su habilidad y precisión tanto en profundidad de compresión como en frecuencia. Para nes comparativos, también ha sido necesario analizar la precisión de ambos equipos en condiciones de laboratorio.