The aim of this thesis is to show that it is possible to damp mechanical vibrations in a given frame, constituted by Euler beam governed by the equations of an elastica, by means of piezoelectric actuators glued on every beam and interconnected each other via electrical networks.Since we believe that the most efficient way to damp mechanical vibrations by means of electrical networks, is to realize a strong modal coupling between the electrical and the mechanical motion, we will synthesize a distributed circuit analog to the Euler beam.We will approach this synthesis problem following the black box approach to mechanical systems, studied by many engineers and scientists during the 1940's in an attempt to design analog computers.It will be shown that it is possible to obtain a quick energy exchange between its mechanical and electrical forms, using available piezoelectric actuators.Finally we will study a numerical simulation for the damping of transverse vibrations of a beam clamped at both ends. / Master of Science

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Space satellite technology is heading in the direction of ultra-large, lightweight structures deployable on orbit. Minimal structural mass translates into minimal launch costs, while increased satellite bus size translates into significant bandwidth improvement for both radar and optical applications. However, from a structural standpoint, these two goals are in direct conflict with one another, as large, flexible structures possess terrible dynamic properties and minimal effective bandwidth. Since the next level of research will require active dynamic analysis, vibration control, and shape morphing control of these satellites, a better-suited name for this technology is Super Precise Intelligent Deployables for Engineered Reconnaissance, or SPIDER. Unlike wisps of cobweb caught in the wind, SPIDER technology will dictate the functionality and versatility of the satellite much like an arachnid weaving its own web. In the present work, a rigorous mathematical framework based on distributed parameter system theory is presented in describing the dynamics of augmented membranous structures. In particular, Euler-Bernoulli beam theory and thin plate theory are used to describe the integration of piezoelectric material with membranes. In both the one and two dimensional problems, experimental validation is provided to support the developed models. Next, the linear quadratic regulator (LQR) control problem is defined from a distributed parameter systems approach, and from this formulation, the functional gains of the respective system are gleaned. The functional gains provide an intelligent mapping when designing an observer-based control system as they pinpoint important sensory information (both type and spatial location) within the structure. Further, an experimental investigation into the dynamics of membranes stretched over shallow, air-filled cavities is presented. The presence of the air-filled cavity in close proximity to the membrane creates a distributed spring and damping effect, thus creating desirable system dynamics from an optical or radar application perspective. Finally, in conjunction with the use of a pressurized cavity with a membrane optic, a novel basis is presented for describing incoming wavefront aberrations. The new basis, coined the clamped Zernike polynomials, provides a mapping for distributed spatial actuation of a membrane mirror that is amiable to the clamped boundary conditions of the mechanical lens. Consequently, based on the work presented here and being carried out in cooperation with the Air Force Research Laboratory Directed Energy Directorate (AFRL / DE), it is envisioned that a 1 m adaptive membrane optic is on the verge of becoming a reality. / Ph. D.

Emerging large-scale modular power converters are pursuing high-performance distributed control systems. As opposed to the centralized control architecture, the distributed control architecture features shared computational burdens, pulse-width modulation (PWM) latency compensation, simplified fiber-optic cable connection, redundant data routes, and greatly enhanced local control capabilities. Modular multilevel converters (MMCs) with conventional control are subjected to large capacitor voltage ripples, especially at low-line frequencies. It is proved that with appropriate arm current shaping in the timescale of a switching period, referred as the switching-cycle control (SCC), such line-frequency dependence can be eliminated and MMCs are enabled to work even in dc-dc mode. Yet the SCC demands multiple times of arm current alternations in one switching period. To achieve the high-bandwidth current regulation, hybrid modulation approach incorporating both the carrier-based modulation and the peak-current-mode (PCM) modulation is adopted. The combined digital and analog control and the extreme time-sensitive nature together pose great challenges on the practical implementation that the existing distributed control systems cannot cope with. This dissertation aims to develop an optimized distributed control system for SCC implementation. The critical analog PCM modulation is enabled by the intelligent gate driver with integrated rogowski coil and field programmable gate array (FPGA). A novel distributed control architecture is proposed accordingly for SCC applications where the hybrid modulation function is shifted to the gate driver. The proposed distributed control solution is verified in the SCC-based converter operations. Accompanied by the growing availability of medium-voltage silicon carbide (SiC) devices, fast-switching-enabled novel control schemes raise a high synchronization requirement for the communication network. Power electronics system network (PESNet) 3.0 is a proposed next-generation communication network designed and optimized for a distributed control system. This dissertation presents the development of PESNet 3.0 with a sub-nanosecond synchronization error (SE) and a gigabits-per-second data rate dedicated for large-scale high-frequency modular power converters. The White Rabbit Network technology, originally developed for the Large Hadron Collider accelerator chain at the European Organization for Nuclear Research (CERN), has been embedded in PESNet 3.0 and tailored to be suited for distributed power conversion systems. A simplified inter-node phase-locked loop (N2N-PLL) has been developed. Subsequently, stability analysis of the N2N-PLL is carried out with closed-loop transfer function measurement using a digital perturbation injection method. The experimental validation of the PESNet 3.0 is demonstrated at the controller level and converter level, respectively. The latter is on a 10 kV SiC-MOSFET-based modular converter prototype, verifying ±0.5 ns SE at 5 Gbps data rate for a new control scheme. The communication network has an impact on the converter control and operation. The synchronicity of the controllers has an influence on the converter harmonics and safe operation. A large synchronization error can lead to the malfunction of the converter operation. The communication latency poses a challenge to the converter control frequency and bandwidth. With the increased scale of the modular converter and control frequency, the low-latency requirement of communication network becomes more stringent. / Doctor of Philosophy / Emerging silicon carbide (SiC) power devices with 10 times higher switching frequencies than conventional Si devices have enabled high-frequency high-density medium-voltage converters. In the meantime, the power electronics building block (PEBB) concept has continually benefited the manufacturing and maintenance of modular power converters. This philosophy can be further extended from power stages to control systems, and the latter become more distributed with greatly enhanced local control capabilities. In the distributed control and communication system, each PEBB is equipped with a digital controller. In this dissertation, a real-time distributed control architecture is designed to take the advantage of the powerful processing capability from all digital control units, achieving a minimized digital delay for the control system. In addition, pulse-width modulation (PWM) signals are modulated in each PEBB controller based on its own clock. Due to the uncontrollable latency among different PEBB controllers, the synchronicity becomes a critical issue. It is necessary to ensure the synchronous operation to follow the desired modulation scheme. This dissertation presents a synchronized communication network design with sub-ns synchronization error and gigabits-per-second data rate. Finally, the impact of the communication network on the converter operation is analyzed in terms of the synchronicity, the communication latency and fault redundancy.

The focus of this dissertation is on developing novel methods and extending existing ones to improve the security and reliability of fixed-wing unmanned aircraft systems (UAS). Specifically, we focus on three strands of work: i) designing UAS controllers with performance guarantees using the robust control framework, ii) developing tools for detection and mitigation of physical-layer security threats in UAS, and iii) extending tools from compositional verification to design and verify complex systems such as UAS. Under the first category, we use the robust H-infinity control approach to design a linear parameter-varying (LPV) path-following controller for a fixed-wing UAS that enables the aircraft to follow any arbitrary planar curvature-bounded path under significant environmental disturbances. Three other typical path-following controllers, namely, a linear time-invariant H-infinity controller, a nonlinear rate-tracking controller, and a PID controller, are also designed. We study the relative merits and limitations of each approach and demonstrate through extensive simulations and flight tests that the LPV controller has the most consistent position tracking performance for a wide array of geometric paths. Next, convex synthesis conditions are developed for control of distributed systems with uncertain initial conditions, whereby independent norm constraints are placed on the disturbance input and the uncertain initial state. Using this approach, we design a distributed controller for a network of three fixed-wing UAS and demonstrate the improvement in the transient response of the network when switching between different trajectories. Pertaining to the second strand of this dissertation, we develop tools for detection and mitigation of security threats to the sensors and actuators of UAS. First, a probabilistic framework that employs tools from statistical analysis to detect sensor attacks on UAS is proposed. By incorporating knowledge about the physical system and using a Bayesian network, the proposed approach minimizes the false alarm rates, which is a major challenge for UAS that operate in dynamic and uncertain environments. Next, the security vulnerabilities of existing UAS actuators are identified and three different methods of differing complexity and effectiveness are proposed to detect and mitigate the security threats. While two of these methods involve developing algorithms and do not require any hardware modification, the third method entails hardware modifications to the actuators to make them resilient to malicious attacks. The three methods are compared in terms of different attributes such as computational demand and detection latency. As for the third strand of this dissertation, tools from formal methods such as compositional verification are used to design an unmanned multi-aircraft system that is deployed in a geofencing application, where the design objective is to guarantee a critical global system property. Verifying such a property for the multi-aircraft system using monolithic (system-level) verification techniques is a challenging task due to the complexity of the components and the interactions among them. To overcome these challenges, we design the components of the multi-aircraft system to have a modular architecture, thereby enabling the use of component-based reasoning to simplify the task of verifying the global system property. For component properties that can be formally verified, we employ results from Euclidean geometry and formal methods to prove those properties. For properties that are difficult to be formally verified, we rely on Monte Carlo simulations. We demonstrate how compositional reasoning is effective in reducing the use of simulations/tests needed in the verification process, thereby increasing the reliability of the unmanned multi-aircraft system. / Doctor of Philosophy / Given the safety-critical nature of many unmanned aircraft systems (UAS), it is crucial for stake holders to ensure that UAS when deployed behave as intended despite atmospheric disturbances, system uncertainties, and malicious adversaries. To this end, this dissertation deals with developing novel methods and extending existing ones to improve the security and reliability of fixed-wing UAS. Specifically, we focus on three key areas: i) designing UAS controllers with performance guarantees, ii) developing tools for detection and mitigation of security threats to sensors and actuators of UAS, and iii) extending tools from compositional verification to design and verify complex systems such as UAS. Pertaining to the first area, we design controllers for UAS that would enable the aircraft to follow any arbitrary planar curvature-bounded path under significant atmospheric disturbances. Four different controllers of differing complexity and effectiveness are designed, and their relative merits and limitations are demonstrated through extensive simulations and flight tests. Next, we develop control design tools to improve the transient response of multi-mission UAS networks. Using these tools, we design a controller for a network of three fixed-wing UAS and demonstrate the improvement in the transient response of the network when switching between different trajectories. As for the contributions in the second area, we develop tools for detection and mitigation of security threats to the sensors and actuators of UAS. First, we propose a framework for detecting sensor attacks on UAS. By judiciously using knowledge about the physical system and techniques from statistical analysis, the framework minimizes the false alarm rates, which is a major challenge in designing attack detection systems for UAS. Then, we focus on another important attack surface of the UAS, namely, the actuators. Here, we identify the security vulnerabilities of existing UAS actuators and propose three different methods to detect and mitigate the security threats. The three methods are compared in terms of different attributes such as computational demand, detection latency, need for hardware modifications, etc. In regard to the contributions in the third area, tools from compositional verification are used to design an unmanned multi-aircraft system that is tasked to track and compromise an aerial encroacher, wherein the multi-aircraft system is required to satisfy a global system property pertaining to collision avoidance and close tracking. A common approach to verifying global properties of systems is monolithic verification where the whole system is analyzed. However, such an approach becomes intractable for complex systems like the multi-aircraft system considered in this work. We overcome this difficulty by employing the compositional verification approach, whereby the problem of verifying the global system property is reduced to a problem of reasoning about the system’s components. That being said, even formally verifying some component properties can be a formidable task; in such cases, one has to rely on Monte Carlo simulations. By suitably designing the components of the multi-aircraft system to have a modular architecture, we show how one can perform focused component-level simulations rather than conduct simulations on the whole system, thereby limiting the use of simulations during the verification process and, as a result, increasing the reliability of the system.

Massive infrastructure networks such as electric power, natural gas, or water systems play a pivotal role in everyday human lives. Development and operation of these networks is extremely capital-intensive. Moreover, security and reliability of these networks is critical. This work identifies and addresses a diverse class of computationally challenging and time-critical problems pertaining to these networks. This dissertation extends the state of the art on three fronts. First, general proofs of uniqueness for network flow problems are presented, thus addressing open problems. Efficient network flow solvers based on energy function minimizations, convex relaxations, and mixed-integer programming are proposed with performance guarantees. Second, a novel approach is developed for sample-efficient training of deep neural networks (DNN) aimed at solving optimal network dispatch problems. The novel feature here is that the DNNs are trained to match not only the minimizers, but also their sensitivities with respect to the optimization problem parameters. Third, control mechanisms are designed that ensure resilient and stable network operation. These novel solutions are bolstered by mathematical guarantees and extensive simulations on benchmark power, water, and natural gas networks. / Doctor of Philosophy / Massive infrastructure networks play a pivotal role in everyday human lives. A minor service disruption occurring locally in electric power, natural gas, or water networks is considered a significant loss. Uncertain demands, equipment failures, regulatory stipulations, and most importantly complicated physical laws render managing these networks an arduous task. Oftentimes, the first principle mathematical models for these networks are well known. Nevertheless, the computations needed in real-time to make spontaneous decisions frequently surpass the available resources. Explicitly identifying such problems, this dissertation extends the state of the art on three fronts: First, efficient models enabling the operators to tractably solve some routinely encountered problems are developed using fundamental and diverse mathematical tools; Second, quickly trainable machine learning based solutions are developed that enable spontaneous decision making while learning offline from sophisticated mathematical programs; and Third, control mechanisms are designed that ensure a safe and autonomous network operation without human intervention. These novel solutions are bolstered by mathematical guarantees and extensive simulations on benchmark power, water, and natural gas networks.

This dissertation aims to realize the goal of deploying legged robots that cooperatively walk to transport objects in complex environments. More than half of the Earth's continent is unreachable to wheeled vehicles---this motivates the deployment of collaborative legged robots to enable the accessibility of these environments and thus bring robots into the real world. Although significant theoretical and technological advances have allowed the development of distributed controllers for complex robot systems, existing approaches are tailored to the modeling and control of multi-agent systems composed of collaborative robotic arms, multi-fingered robot hands, aerial vehicles, and ground vehicles, but not collaborative legged agents. Legged robots are inherently unstable, unlike most of the systems where these algorithms have been deployed. Models of cooperative legged robots are further described by high-dimensional, underactuated, and complex hybrid dynamical systems, which complicate the design of control algorithms for coordination and motion control. There is a fundamental gap in knowledge of control algorithms for safe motion control of these inherently unstable hybrid dynamical systems, especially in the context of collaborative work. The overarching goal of this dissertation is to create a formal foundation based on scalable optimization and robust and nonlinear control to develop distributed and hierarchical feedback control algorithms for cooperative legged robots to transport objects in complex environments. We first develop a hierarchical nonlinear control algorithm, based on model predictive control (MPC), quadratic programming (QP), and virtual constraints, to generate and stabilize locomotion patterns in a real-time manner for dynamical models of single-agent quadrupedal robots. The higher level of the proposed control scheme is developed based on an event-based MPC that computes the optimal center of mass (COM) trajectories for a reduced-order linear inverted pendulum (LIP) model subject to the feasibility of the net ground reaction force (GRF). QP-based virtual constraint controllers are developed at the lower level of the proposed control scheme to impose the full-order dynamics to track the optimal trajectories while having all individual GRFs in the friction cone. The analytical results are numerically verified to demonstrate stable and robust locomotion of a 22 degree of freedom (DOF) quadrupedal robot, in the presence of payloads, external disturbances, and ground height variations. We then present a hierarchical nonlinear control algorithm for the real-time planning and control of cooperative locomotion of legged robots that collaboratively carry objects. An innovative network of reduced-order models subject to holonomic constraints, referred to as interconnected LIP dynamics, is presented to study quasi-statically stable cooperative locomotion. The higher level of the proposed algorithm employs a supervisory controller, based on event-based MPC, to effectively compute the optimal reduced-order trajectories for the interconnected LIP dynamics. The lower level of the proposed algorithm employs distributed nonlinear controllers to reduce the gap between reduced- and full-order complex models of cooperative locomotion. We numerically investigate the effectiveness of the proposed control algorithm via full-order simulations of a team of collaborative quadrupedal robots, each with a total of 22 DOFs. The dissertation also investigates the robustness of the proposed control algorithm against uncertainties in the payload mass and changes in the ground height profile. Finally, we present a layered control approach for real-time trajectory planning and control of dynamically stable cooperative locomotion by two holonomically constrained quadrupedal robots. An innovative and interconnected network of reduced-order models, based on the single rigid body (SRB) dynamics, is developed for trajectory planning purposes. At the higher level of the control scheme, two different MPC algorithms are proposed to address the optimal control problem of the interconnected SRB dynamics: centralized and distributed MPCs. The MPCs compute the reduced-order states, GRFs, and interaction wrenches between the agents. The distributed MPC assumes two local QPs that share their optimal solutions according to a one-step communication delay and an agreement protocol. At the lower level of the control scheme, distributed nonlinear controllers are employed to impose the full-order dynamics to track the prescribed and optimal reduced-order trajectories and GRFs. The effectiveness of the proposed layered control approach is verified with extensive numerical simulations and experiments for the blind, robust, and cooperative locomotion of two holonomically constrained A1 robots with different payloads on different terrains and in the presence of external disturbances. It is shown that the distributed MPC has a performance similar to that of the centralized MPC, while the computation time is reduced significantly. / Doctor of Philosophy / Future cities will include a complex and interconnected network of collaborative robots that cooperatively work with each other and people to support human societies. Human-centered communities, including factories, offices, and homes, are developed for humans who are bipedal walkers capable of stepping over gaps, walking up/down stairs, and climbing ladders. One of the most challenging problems in deploying the next generation of collaborative robots is maneuvering in those complex environments. Although significant theoretical and technological advances have allowed the development of distributed controllers for motion control of multi-agent robotic systems, existing approaches do not address the collaborative locomotion problem of legged robots. Legged robots are inherently unstable with nonlinear and hybrid natures, unlike most systems where these algorithms have been deployed. Furthermore, the evolution of legged collaborative robot teams that cooperatively manipulate objects can be represented by high-dimensional and complex dynamical systems, complicating the design of control algorithms for coordination and motion control. This dissertation aims to establish a formal foundation based on nonlinear control and optimization theory to develop hierarchical feedback control algorithms for effective motion control of legged robots. The proposed layered control algorithms are developed based on interconnected reduced-order models. At the high level, we formulate cooperative locomotion as an optimal control problem of the reduced-order models to generate optimal trajectories. To realize the generated optimal trajectories, nonlinear controllers at the low level of the hierarchy impose the full-order models to track the trajectories while sustaining stability. The effectiveness of the proposed layered control approach is verified with extensive numerical simulations and experiments for the blind and stable cooperative locomotion of legged robots with different payloads on different terrains and subject to external disturbances. The proposed architecture's robustness is shown under various indoor and outdoor conditions, including landscapes with randomly placed wood blocks, slippery surfaces, gravel, grass, and mulch.

With increasing advancement in material science and computational power of current computers that allows us to analyze high dimensional systems, very light and large structures are being designed and built for aerospace applications. One example is a reflector of a space telescope that is made of membrane structures. These reflectors are light and foldable which makes the shipment easy and cheaper unlike traditional reflectors made of glass or other heavy materials. However, one of the disadvantages of membranes is that they are very sensitive to external changes, such as thermal load or maneuvering of the space telescope. These effects create vibrations that dramatically affect the performance of the reflector. To overcome vibrations in membranes, in this work, piezoelectric actuators are used to develop distributed controllers for membranes. These actuators generate bending effects to suppress the vibration. The actuators attached to a membrane are relatively thick which makes the system heterogeneous; thus, an analytical solution cannot be obtained to solve the partial differential equation of the system. Therefore, the Finite Element Model is applied to obtain an approximate solution for the membrane actuator system. Another difficulty that arises with very flexible large structures is the dimension of the discretized system. To obtain an accurate result, the system needs to be discretized using smaller segments which makes the dimension of the system very high. This issue will persist as long as the improving technology will allow increasingly complex and large systems to be designed and built. To deal with this difficulty, the analysis of the system and controller development to suppress the vibration are carried out using vector second order form as an alternative to vector first order form. In vector second order form, the number of equations that need to be solved are half of the number equations in vector first order form. Analyzing the system for control characteristics such as stability, controllability and observability is a key step that needs to be carried out before developing a controller. This analysis determines what kind of system is being modeled and the appropriate approach for controller development. Therefore, accuracy of the system analysis is very crucial. The results of the system analysis using vector second order form and vector first order form show the computational advantages of using vector second order form. Using similar concepts, LQR and LQG controllers, that are developed to suppress the vibration, are derived using vector second order form. To develop a controller using vector second order form, two different approaches are used. One is reducing the size of the Algebraic Riccati Equation to half by partitioning the solution matrix. The other approach is using the Hamiltonian method directly in vector second order form. Controllers are developed using both approaches and compared to each other. Some simple solutions for special cases are derived for vector second order form using the reduced Algebraic Riccati Equation. The advantages and drawbacks of both approaches are explained through examples. System analysis and controller applications are carried out for a square membrane system with four actuators. Two different systems with different actuator locations are analyzed. One system has the actuators at the corners of the membrane, the other has the actuators away from the corners. The structural and control effect of actuator locations are demonstrated with mode shapes and simulations. The results of the controller applications and the comparison of the vector first order form with the vector second order form demonstrate the efficacy of the controllers. / Ph. D.