controllers for discrete-time systems and time-delayed systems. By using bilinear transformation and orthogonal transformation, earlier research results obtained in the continuous-time case are extended to discrete-time situation. The complete set of stabilizing PID controllers for the discrete-time systems is thus obtained. Moreover, this set remains to be a union of convex sets when one particular parameter is fixed. Thus a method to design robust and non-fragile digital PID controllers is proposed by following a similar design procedure for the continuous-time systems. In order to find the stabilizing controller set for systems with time-delays, the relationship between the Nyquist Criterion and Pontryagin’s theory is investigated. The conditions under which one can correctly apply the Nyquist Criterion to time-delayed systems are derived. Then, the complete set of stabilizing PID controllers for arbitrary order LTI systems with time-delay up to a given value is obtained. Furthermore, the stability issue of a system with fixed-delay is also studied and a formula which provides complete knowledge of the distribution of the closed-loop poles is presented. Based on this formula, stabilizing P and PI controller sets for the system with fixed-delay can be computed.

Based on the Lyapunov stability theorem, an adaptive sliding mode control scheme is proposed in this thesis for a class of systems with mismatched state-delayed perturbations to solve regulation problems. The main idea is that some adaptive mechanisms are embedded both in the sliding surfaces and in the controllers, so that not only the mismatched perturbations are suppressed during the sliding mode, but also the information of upper bound of perturbations is not required. The sliding surface functions are firstly designed through the usage of designed pseudo controllers, which is capable of stabilizing the reduced-order systems. The number of the sliding surface functions required by the proposed control scheme depends on the relationship between systems's dimension and number of inputs. The second step is to design the controllers so that the trajectories of the controlled system are able to reach sliding surface in a finite time. Once the controlled system enters the sliding mode, the asymptotical stability is guaranteed. Two numerical examples and one practical experiment are given for demonstrating the feasibility of the proposed control scheme.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

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Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Ray T. Chen. Vita. Includes bibliographical references.

Thesis (Ph. D.)--West Virginia University, 2004. / Title from document title page. Document formatted into pages; containsxi, 230 p. : ill. (some col.). Vita. Includes abstract. Includes bibliographical references (p. 215-225).

A dynamic model is developed for the purpose of predicting stability characteristics of an industrial-scale, swirl-stabilized premixed combustor located at the National Energy Technology Laboratory (NETL) in Morgantown, WV. The model consists of modular blocks that assemble into an open-loop transfer function depicting the frequency response of the thermoacoustic system. These blocks include the system acoustic response to unsteady heat release forcing, the air-side coupling of acoustic particle velocity to inlet fuel mass fraction, transport delays present in the mixing nozzle and combustion chamber, and dynamic heat release excitation from unsteady inlet fuel mass fraction. By examing the frequency response with linear stability techniques, the existence of limit cycles due to linear instabilities is predicted. Further, the frequency response analysis is used to predict limit cycle frequencies in the case of predicted instability. The analysis predictions are compared with the results of tests performed at NETL, demonstrating a capability of replicating many of the observed stability characteristics. / Ph. D.

Previous plasma imaging missions have used time-delay integration techniques that correct for uniform motion blur during integration. This was due to the assumed constant range-to-target of each pixel in the observed scene. ICON's low orbital altitude and twelve second integration time create non-uniform motion blur across the observed scene and necessitate a novel variable-range time-delay integration (TDI) algorithm be used to spatially resolve the two-dimensional images. The variable-range TDI algorithm corrects for each pixel moving at a different angular rate throughout image integration and transforms each raw image onto a surface where the spacecraft is moving at a constant angular rate with respect to every pixel in the image. Then as the raw images are co-added together the non-uniform motion of the observed scene is accounted for and will not geographically distort the final images, or any features seen within them. Through simulation using output from the SAMI3 model during plasma depletion formation it was determined that the structuring and gradients of plasma depletions can be recovered using this technique. Additionally, the effects of depletion width, solar activity level, and misalignment of the field-of-view with the local magnetic field were investigated. The variable-range TDI technique is able to recover the overall shape and depth of depletion of the depletions in all cases, however the determination of gradients observed at depletion walls is significantly degraded for very narrow plasma depletions and during periods of low solar activity. All simulated model conditions were shown to be representative of current ionospheric conditions. / Master of Science / Equatorial spread-F, also termed plasma bubbles, is a phenomenon that occurs in the equatorial region of Earth’s ionosphere, the charged region of Earth’s atmosphere. Plumes of less dense plasma, the charged material of the Ionosphere, rise through regions of higher density plasma. This causes disturbances to radio signals that travel through this region, which can lead to GPS range errors or loss of signal. ICON is a NASA Explorer mission aimed at, in part, understanding the sources of variability in the ionosphere. One instrument onboard ICON to accomplish this goal is the FarUltraviolet Imager which images airglow in the far-ultraviolet range. During nighttime, the FUV imager can observe plasma bubbles to study the instability and the mechanisms that produce it. This thesis looks at the ability of the variable-range time-delay integration (TDI) algorithm, used to produce images from ICON’s Farultraviolet imager, to spatially resolve the structure and gradients of observed plasma bubbles. However, due to the viewing geometry of ICON’s FUV imager, each pixel across the observed scene experiences a different angular rate of motion blur. The variable-range TDI algorithm removes this non-uniform motion blur by transforming each raw image onto a surface where the spacecraft moves at a constant angular rate with respect to every pixel in the image. Then raw images are integrated together such that the observed scene is not geographically distorted. It was concluded that the TDI process is able to spatially resolve a wide variety of plasma bubbles under various ionospheric conditions and imager configurations.

Constant time delay (CTD) and progressive time delay (PTD) are both evidence-based practices used to teach students with intellectual disability (ID). The prompt delay strategies have been used for instruction with academics, social, vocational, and communication skills. There is limited research regarding the differential effectiveness of the time delay variations for teaching academic content to students with ID. The present study compares the effects of CTD and PTD in the acquisition of academic content with four students with ID. An adapted alternating treatments design was used to compare the effectiveness and efficiency of the two procedures. Generalization was assessed across settings, participants, and materials. Results indicated that both strategies were effective but PTD was more efficient in regards to number of errors and average time to criterion.

The high-dimensional property of delay differential equations makes them useful for various purposes. The applications of systems modelled with delay differential equations demand different degrees of complexity. One solution to tune this property is to make the dynamics of the current state dependent on more delayed states. How the system responds to more delayed states depends on the system under study, as both decreases and increases in the complexity were observed in different nonlinear systems. However, it is also known that when there is an infinite number of delays that follow a continuous distribution, simpler dynamics usually expected due to the averaging over previous states that the delay kernel provides. The present thesis investigates the role of multiple delays in nonlinear time delay systems, as well as methods for evaluating their complexity. Through the use of pseudospectral differentiation, we first compute the Lyapunov exponents of such multi-delay systems. In systems with a large number of delays, chaos is found to be less likely to occur. However, in systems with oscillatory feedback functions, the entropy can increase just by adding a few delays. Our study also demonstrates that the transition to simpler dynamics in nonlinear delay systems can be either monotonous or abrupt. This is particularly true in first-order nonlinear systems, where increasing the width of the distribution of delays results in complexity collapse, even in the presence of a few discrete delays. The roots of the characteristic equation around a fixed point can be used to approximate the degree of complexity of the dynamics of such time-delay systems, as they can be linked to other dynamical invariants such as the Kolmogorov-Sinai entropy. The phenomenon of complexity collapse uncovered in our work was further studied in an 80/20 ratio excitatory-inhibitory neural network. We found that the smaller the time delay, the higher the likelihood of chaotic dynamics, and this also promotes asynchronous spiking activity. But for larger values of the delay, the neurons show synchronized oscillatory spiking activity. A global inhibition at a longer delay results in a novel dynamical pattern of randomly occurring epochs of synchrony within the chaotic dynamics. The final part of the thesis examines the behavior of time delay reservoir computing when there are multiple time delays. It is shown that the choice of spacing between time delays is crucial, and depends on the task at hand. The system was studied for a prediction task with one chaotic input as well as for a mixture of two chaotic inputs. It was found that, similar to the single delay case, there is a resonance when the difference between delays is equal to the clock cycle. Together, our research provides valuable insights into the dynamics and complexity of nonlinear multi-delay systems and the importance of the spacing between delays.