This thesis aims to investigate the controllability and observability of the discrete fractional linear time-invariant state-space model. First, we will establish key concepts and properties which are the tools necessary for our task. In the third chapter, we will discuss the discrete state-space model and set up the criteria for these two properties. Then, in the fourth chapter, we will attempt to apply these criteria to the discrete fractional model. The general flow of our objectives is as follows: we start with the first-order linear difference equation, move on to the discrete system, then the fractional difference equation, and finally the discrete fractional system. Throughout this process, we will develop the solutions to the (fractional) difference equations, which are the basis of our criteria.

The objective of this whole study was to evaluate a LiDAR sensor for high-resolution remote sensing in agriculture. A linear motion system was developed to precisely control the dynamics of LiDAR sensor in effort to remove uncertainty in the LiDAR position/velocity while under motion. A user control interface was developed to operate the system under different velocity profiles and log LiDAR data synchronous to the motion of the system. The LiDAR was then validated using multiple test targets with five different velocity profiles to determine the effect of sensor velocity and height above a target on measurement error. The results indicated that the velocity of the LiDAR was a significant factor affecting the error and standard deviation of the LiDAR measurements, although only by a small margin. Then the concept of modeling the alfalfa using the linear motion system was introduced. Two plots of alfalfa were scanned and processed to extract height and volume and was compared with photogrammetric and field measurements. Insufficient alfalfa plots were scanned which prevented any statistical analysis from being used to compare the different methods. However, the comparison between LiDAR and photogrammetric data showed some promising results which may be further replicated in the future.

Satellite power systems can be understood as islanded dc microgrids supplied by specialized and coordinated solar cell arrays augmented by electrochemical battery systems to handle high-power loads and periods of eclipse. The periodic availability of power, the limited capacity of batteries, and the dependence of all mission service on power consumption create a unique situation in which temporal power and energy scarcity exist. A multi-period model of an orbital satellite power system’s performance over a mission’s duration can be constructed. A modular power system architecture is used to characterize the system’s constraints. Using mathematical programming, an optimization problem can be posed such that the optimal power and energy ratings for the power system are determined for any load schedule imposed by a given mission’s requirements. The optimal energy trajectory of the electrical power system over a mission’s duration is also determined when the mathematical programming problem is solved. A generic set of mission requirements is identified to test this approach, but the objective function of the resulting optimization problem can be modified to return different results. These results can provide a clear illustration of the trade-offs that designers of such power systems consider in the design process.

This thesis presents a new modular structure of the axial flux Switched Reluctance Motor (SRM). The design consists of four stator disks with each adjacent disk rotated 30 degrees apart and four rotor disks connected to a common shaft. The proposed design aims to reduce the unwanted radial force, mitigate the torque ripple, and improve the efficiency. The modular structure distributes the radial force and torque strokes along the axial length of the motor, potentially damping the torque pulsation. In addition, the modular structure would deliver the rating power at a lower current level, reducing the overall ohmic loss. Moreover, if a fault occurs on a motor disk or its control unit, the motor would still operate through other disks, increasing the reliability of the system. To verify the effectiveness of the proposed design, the magneto-static and transient performance of the motor are compared with the conventional single layer structure using 3-D Finite-Element (FE) software tool to see that the proposed motor performs better with lower torque ripple and lower radial force than a conventional single layer structure.

The new Field Programmable Gate Array (FPGA) technologies and their structures have opened up new approaches to logic design and synthesis. The main feature of an FPGA is an array of logic blocks surrounded by a programmable interconnection structure. Cellular FPGAs are a special class of FPGAs which are distinguished by their fine granularity and their emphasis on local cell interconnects. While these characteristics call for specialized synthesis tools, the availability of logic gates other than Boolean AND, OR and NOT in these architectures opens up new possibilities for synthesis. Among the possible realizations of Boolean functions, XOR logic is shown to be more compact than AND/OR and also highly testable. In this dissertation, the concept of structural regularity and the advantages of XOR logic are used to investigate various synthesis approaches to cellular FPGAs, which up to now have been mostly nonexistent. Universal XOR Canonical Forms, Two-level AND/XOR, restricted factorization, as well as various Directed Acyclic Graph structures are among the proposed approaches. In addition, a new comprehensive methodology for the investigation of all possible XOR canonical forms is introduced. Additionally, a new compact class of XOR-based Decision Diagrams for the representation of Boolean functions, called Kronecker Functional Decision Diagrams (KFDD), is presented. It is shown that for the standard, hard, benchmark examples, KFDDs are on average 35% more compact than Binary Decision Diagrams, with some reductions of up to 75% being observed.

This dissertation focused on the IRIS design since this will likely be one of the designs of choice for future deployment in the U.S and developing countries. With a net 335 MWe output IRIS novel design falls in the “medium” size category and it is a potential candidate for the so called modular reactors, which may be appropriate for base load electricity generation, especially in regions with smaller electricity grids, but especially well suited for more specialized non-electrical energy applications such as district heating and process steam for desalination. The first objective of this dissertation is to evaluate and quantify the performance of a Nuclear Power Plant (NPP) comprised of two IRIS reactor modules operating simultaneously with a common steam header, which in turn is connected to a single turbine, resulting in a steam-mixing control problem with respect to “load-following” scenarios, such as varying load during the day or reduced consumption during the weekend. To solve this problem a single-module IRIS SIMULINK model previously developed by another researcher is modified to include a second module and was used to quantify the responses from both modules. In order to develop research related to instrumentation and control, and equipment and sensor monitoring, the second objective is to build a two-tank multivariate loop in the Nuclear Engineering Department at the University of Tennessee. This loop provides the framework necessary to investigate and test control strategies and fault detection in sensors, equipment and actuators. The third objective is to experimentally develop and demonstrate a fault-tolerant control strategy using this loop. Using six correlated variables in a single-tank configuration, five inferential models and one Auto-Associative Kernel Regression (AAKR) model were developed to detect faults in process sensors. Once detected the faulty measurements were successfully substituted with prediction values, which would provide the necessary flexibility and time to find the source of discrepancy and resolve it, such as in an operating power plant. Finally, using the same empirical models, an actuator failure was simulated and once detected the control was automatically transferred and reconfigured from one tank to another, providing survivability to the system.

Model reduction is a powerful and ubiquitous tool used to reduce the complexity of a dynamical system while preserving the input-output behavior. It has been applied throughout many different disciplines, including controls, fluid and structural dynamics. Model reduction via proper orthogonal decomposition (POD) is utilized for of control of partial differential equations. In this thesis, the analytical expressions of POD modes are derived for the heat equation. The autocorrelation function of the latter is viewed as the kernel of a self adjoint compact operator, and the POD modes and corresponding eigenvalues are computed by solving homogeneous integral equations of the second kind. The computed POD modes are compared to the modes obtained from snapshots for both the one-dimensional and two-dimensional heat equation. Boundary feedback control is obtained through reduced-order POD models of the heat equation and the effectiveness of reduced-order control is compared to the full-order control. Moreover, the explicit computation of the POD modes and eigenvalues are shown to allow the computation of different n-widths approximations for the heat equation, including the linear, Kolmogorov, Gelfand, and Bernstein n-widths.

This thesis presents the design of an attitude determination system for small satellites that automatically corrects for attitude drift. Existing attitude determination systems suffer from attitude drift due to the integration of noisy rate gyro sensors used to measure the change in attitude. This attitude drift leads to a gradual loss in attitude knowledge, as error between the estimated attitude and the actual attitude increases. In this thesis a Kalman filter is used to complete sensor fusion which combines sensor observations with a projected attitude based on the dynamics of the satellite. The system proposed in this thesis also utilizes a novel sensor called the stellar gyro to correct for the drift. The stellar gyro compares star field images taken at different times to determine orientation, and works in the presence of the sun and during eclipse. This device provides a relative attitude fix that can be used to update the attitude estimate provided by the Kalman filter, effectively compensating for drift. Simulink models are developed of the hardware and algorithms to model the effectiveness of the system. The Simulink models show that the attitude determination system is highly accurate, with steady state errors of less than 1 degree.

Instrumented umanned aerial vehicles represent a new way of measuring turbulence in the atmospheric boundary layer. However, autonomous measurements require control methods with disturbance-rejection and altitude command-following capabilities. Filtered dynamic inversion is a control method with desirable disturbance-rejection and command-following properties, and this controller requires limited model information. We implement filtered dynamic inversion as the pitch controller in an altitude-hold autopilot. We design and numerically simulate the continuous-time and discrete-time filtered-dynamic-inversion controllers with anti-windup on a nonlinear aircraft model. Finally, we present results from a flight experiment comparing the filtered-dynamic-inversion controller to a classical proportional-integral controller. The experimental results show that the filtered-dynamic-inversion controller performs better than a proportional-integral controller at certain values of the parameter.

In preparation for the influx of renewable energy sources that will be added to the electrical system, flexible and adaptable control schemes are necessary to accommodate the changing infrastructure. Microgrids have been gaining much attention as the main solution to the challenges of distributed and intermittent generation, but due to their low inertia, they need fast-acting control systems in order to maintain stability. Multi-Agent Systems have been proposed as dynamic control and communication frameworks. Decentralized arrangements of agents can provide resiliency and the much-desired “plug and play” behavior. This thesis describes a control system that implements droop control and the diffusion communication scheme without the need of a centralized controller to coordinate the Microgrid agents to maintain the frequency and stable operating conditions of the system. Moreover, the inter-agent communication is unaffected by changing network configurations and can achieve optimal economic dispatch through distributed optimization.