The swing equations for renewable generators connected to the grid are developed and a wind turbine is used as an example. The swing equations for the renewable generators are formulated as a natural Hamiltonian system with externally applied non-conservative forces. A two-step process referred to as Hamiltonian Surface Shaping and Power Flow Control (HSSPFC) is used to analyze and design feedback controllers for the renewable generators system. This formulation extends previous results on the analytical verification of the Potential Energy Boundary Surface (PEBS) method to nonlinear control analysis and design and justifies the decomposition of the system into conservative and non-conservative systems to enable a two-step, serial analysis and design procedure. The first step is to analyze the system as a conservative natural Hamiltonian system with no externally applied non-conservative forces. The Hamiltonian surface of the swing equations is related to the Equal-Area Criterion and the PEBS method to formulate the nonlinear transient stability problem. This formulation demonstrates the effectiveness of proportional feedback control to expand the stability region. The second step is to analyze the system as natural Hamiltonian system with externally applied non-conservative forces. The time derivative of the Hamiltonian produces the work/rate (power flow) equation which is used to ensure balanced power flows from the renewable generators to the loads. The Second Law of Thermodynamics is applied to the power flow equations to determine the stability boundaries (limit cycles) of the renewable generators system and enable design of feedback controllers that meet stability requirements while maximizing the power generation and flow to the load. Necessary and sufficient conditions for stability of renewable generators systems are determined based on the concepts of Hamiltonian systems, power flow, exergy (the maximum work that can be extracted from an energy flow) rate, and entropy rate. This paper will present the analysis and numerical simulation results for two nonlinear control design examples that include: (1) the One-Machine Infinite Bus (OMIB) system with a Unified Power Flow Controller (UPFC) and (2) the swing equation for a wind turbine connected to an infinite bus through a UPFC to determine the required performance of the UPFC to enable the maximum power output of a wind turbine subject to stochastic inputs while meeting the power system constraints on frequency and phase. The energy storage requirements will also be identified from the UPFC and/or FACTS devices while working in combination with the wind turbine.
Collective systems are typically defined as a group of agents (physical and/or cyber) that work together to produce a collective behavior with a value greater than the sum of the individual parts. This amplification or synergy can be harnessed by solving an inverse problem via an information-flow/communications grid: given a desired macroscopic/collective behavior find the required microscopic/individual behavior of each agent and the required communications grid. The goal of this report is to describe the fundamental nature of the Hamiltonian function in the design of collective systems (solve the inverse problem) and the connections between and values of physical and information exergies intrinsic to collective systems. In particular, physical and information exergies are shown to be equivalent based on thermodynamics and Hamiltonian mechanics.
The development of tools for complex dynamic security systems is not a straight forward engineering task but, rather, a scientific task where discovery of new scientific principles and math is necessary. For years, scientists have observed complex behavior but have had difficulty understanding it. Prominent examples include: insect colony organization, the stock market, molecular interactions, fractals, and emergent behavior. Engineering such systems will be an even greater challenge. This report explores four tools for engineered complex dynamic security systems: Partially Observable Markov Decision Process, Percolation Theory, Graph Theory, and Exergy/Entropy Theory. Additionally, enabling hardware technology for next generation security systems are described: a 100 node wireless sensor network, unmanned ground vehicle and unmanned aerial vehicle.
This paper 1 develops a novel control system design methodology that uniquely combines: concepts from thermodynamic exergy and entropy; Hamiltonian systems; Lyapunov's direct method and Lyapunov optimal analysis; electric AC power concepts; and power flow analysis. Relationships are derived between exergy/entropy and Lyapunov optimal functions for Hamiltonian systems. The methodology is demonstrated with two fundamental numerical simulation examples: 1) a Duffing oscillator/Coulomb friction nonlinear model that employs PID regulator control and 2) a van der Pol nonlinear oscillator system. The control system performances and/or appropriately identified terms are partitioned and evaluated based on exergy generation and exergy dissipation terms. This novel nonlinear control methodology results in both necessary and sufficient conditions for stability of nonlinear systems.
Exergy is the elixir of life. Exergy is that portion of energy available to do work. Elixir is defined as a substance held capable of prolonging life indefinitely, which implies sustainability of life. In terms of mathematics and engineering, exergy sustainability is defined as the continuous compensation of irreversible entropy production in an open system with an impedance and capacity-matched persistent exergy source. Irreversible and nonequilibrium thermodynamic concepts are combined with self-organizing systems theories as well as nonlinear control and stability analyses to explain this definition. In particular, this paper provides a missing link in the analysis of self-organizing systems: a tie between irreversible thermodynamics and Hamiltonian systems. As a result of this work, the concept of ''on the edge of chaos'' is formulated as a set of necessary and sufficient conditions for stability and performance of sustainable systems. This interplay between exergy rate and irreversible entropy production rate can be described as Yin and Yang control: the dialectic synthesis of opposing power flows. In addition, exergy is shown to be a fundamental driver and necessary input for sustainable systems, since exergy input in the form of power is a single point of failure for self-organizing, adaptable systems.
Large complex teams (e.g., DOE labs) must achieve sustained productivity in critical operations (e.g., weapons and reactor development) while maintaining safety for involved personnel, the public, and physical assets, as well as security for property and information. This requires informed management decisions that depend on tradeoffs of factors such as the mode and extent of personnel protection, potential accident consequences, the extent of information and physical asset protection, and communication with and motivation of involved personnel. All of these interact (and potentially interfere) with each other and must be weighed against financial resources and implementation time. Existing risk analysis tools can successfully treat physical response, component failure, and routine human actions. However, many ''soft'' factors involving human motivation and interaction among weakly related factors have proved analytically problematic. There has been a need for an effective software tool capable of quantifying these tradeoffs and helping make rational choices. This type of tool, developed during this project, facilitates improvements in safety, security, and productivity, and enables measurement of improvements as a function of resources expended. Operational safety, security, and motivation are significantly influenced by ''latent effects'', which are pre-occurring influences. One example of these is that an atmosphere of excessive fear can suppress open and frank disclosures, which can in turn hide problems, impede correction, and prevent lessons learned. Another is that a cultural mind-set of commitment, self-responsibility, and passion for an activity is a significant contributor to the activity's success. This project pursued an innovative approach for quantitatively analyzing latent effects in order to link the above types of factors, aggregating available information into quantitative metrics that can contribute to strategic management decisions, and measuring the results. The approach also evaluates the inherent uncertainties, and allows for tracking dynamics for early response and assessing developing trends. The model development is based on how factors combine and influence other factors in real time and over extended time periods. Potential strategies for improvement can be simulated and measured. Input information can be determined by quantification of qualitative information in a structured derivation process. This has proved to be a promising new approach for research and development applied to personnel performance and risk management.
Because of the inevitable depletion of fossil fuels and the corresponding release of carbon to the environment, the global energy future is complex. Some of the consequences may be politically and economically disruptive, and expensive to remedy. For the next several centuries, fuel requirements will increase with population, land use, and ecosystem degradation. Current or projected levels of aggregated energy resource use will not sustain civilization as we know it beyond a few more generations. At the same time, issues of energy security, reliability, sustainability, recoverability, and safety need attention. We supply a top-down, qualitative model--the surety model--to balance expenditures of limited resources to assure success while at the same time avoiding catastrophic failure. Looking at U.S. energy challenges from a surety perspective offers new insights on possible strategies for developing solutions to challenges. The energy surety model with its focus on the attributes of security and sustainability could be extrapolated into a global energy system using a more comprehensive energy surety model than that used here. In fact, the success of the energy surety strategy ultimately requires a more global perspective. We use a 200 year time frame for sustainability because extending farther into the future would almost certainly miss the advent and perfection of new technologies or changing needs of society.
This report describes an integrated approach for designing communication, sensing, and control systems for mobile distributed systems. Graph theoretic methods are used to analyze the input/output reachability and structural controllability and observability of a decentralized system. Embedded in each network node, this analysis will automatically reconfigure an ad hoc communication network for the sensing and control task at hand. The graph analysis can also be used to create the optimal communication flow control based upon the spatial distribution of the network nodes. Edge coloring algorithms tell us that the minimum number of time slots in a planar network is equal to either the maximum number of adjacent nodes (or degree) of the undirected graph plus some small number. Therefore, the more spread out that the nodes are, the fewer number of time slots are needed for communication, and the smaller the latency between nodes. In a coupled system, this results in a more responsive sensor network and control system. Network protocols are developed to propagate this information, and distributed algorithms are developed to automatically adjust the number of time slots available for communication. These protocols and algorithms must be extremely efficient and only updated as network nodes move. In addition, queuing theory is used to analyze the delay characteristics of Carrier Sense Multiple Access (CSMA) networks. This report documents the analysis, simulation, and implementation of these algorithms performed under this Laboratory Directed Research and Development (LDRD) effort.
As part of DARPA's Software for Distributed Robotics Program within the Information Processing Technologies Office (IPTO), Sandia National Laboratories was tasked with identifying military airborne and maritime missions that require cooperative behaviors as well as identifying generic collective behaviors and performance metrics for these missions. This report documents this study. A prioritized list of general military missions applicable to land, air, and sea has been identified. From the top eight missions, nine generic reusable cooperative behaviors have been defined. A common mathematical framework for cooperative controls has been developed and applied to several of the behaviors. The framework is based on optimization principles and has provably convergent properties. A three-step optimization process is used to develop the decentralized control law that minimizes the behavior's performance index. A connective stability analysis is then performed to determine constraints on the communication sample period and the local control gains. Finally, the communication sample period for four different network protocols is evaluated based on the network graph, which changes throughout the task. Using this mathematical framework, two metrics for evaluating these behaviors are defined. The first metric is the residual error in the global performance index that is used to create the behavior. The second metric is communication sample period between robots, which affects the overall time required for the behavior to reach its goal state.
A robust nonlinear adaptive control (NAC) system was designed for the rotational slewing of an active structure. The control laws were developed for both motor torque control and beam vibration control actuation. The experiments validated the control system performance. Robustness to parameter variations were tested increasing the tip mass, that reduced the first-mode bending frequency. It was found that the control system performance results were similar to the zero tip mass case.