Dissertation (Ph.D.)--Auburn University, 2008. / Abstract. Includes bibliographic references (p.73-80).

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Newton; globalized; inexact Newton. Includes bibliographical references (p. 61).

We study local well-posedness of the Cauchy problem for two geometric wave equations that can be derived from Anti-Self-Dual Yang Mills equations on R2+2. These are the space-time Monopole Equation and the Ward Wave Map. The equations can be formulated in different ways. For the formulations we use, we establish local well-posedness results, which are sharp using the iteration methods. / text

published_or_final_version / Mathematics / Master / Master of Philosophy

published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

The objective of this thesis is to study a cycle-to-cycle control approach called Terminal Iterative Learning Control (TILC) and apply it to the process of plastic sheet heating in a thermoforming oven. Until now, adjustments to the oven heater temperature setpoints have been made manually by a human operator following a trial and error approach. This approach causes financial losses, because plastic sheets are wasted during the period of time when the adjustments are made at the beginning of a production run. Worse, the heater setpoints are subject to modification because of variation in the ambient temperature, which has an important impact on the sheet reheat process. / The TILC approach is analyzed by studying the closed-loop system in the discrete cycle domain through the use of the z-transform. The system, which has dynamic behaviour in the time domain, becomes a static linear mapping in the cycle domain. One can then apply on this equivalent system a traditional control approach, while considering that the system output is sampled once at the end of the cycle. On the other hand, from the standpoint of the real system, this control approach can be viewed as cycle-to-cycle control. / The stability and rate of convergence of the TILC algorithm can be analyzed through the location of the closed-loop system poles in the cycle domain. This analysis is relatively easy for a first-order TILC but becomes more complex for a higher-order TILC algorithm. The singular value decomposition (SVD) is used to simplify the convergence analysis while decoupling the system in the cycle domain. The SVD technique can be used to facilitate the design of higher-order TILC algorithms. / Internal Model Control (IMC) is another approach that can make the ILC design easier, because there is only one parameter per filter to adjust. The IMC technique has an interesting feature. In the case where the system is nominal, the closed-loop transfer function of the system is the same as the IMC filter's transfer function. Therefore, the adjustment of the filter parameter allows the designer to select the desired system response. / For industrial processes such as thermoforming ovens, it is important that the systems controlled by TILC algorithms are stable and have good performance. For thermoforming ovens, the terminal sheet temperature response must not be too oscillatory from cycle to cycle, since this may lead to high heater temperature setpoints. In the most serious case, high heater temperatures can cause the sheet to melt and spill on the heating elements at the bottom of the oven. / The performance aspect must not be neglected, since it is important to minimize the number of wasted plastic sheets, particularly at process startup. To avoid such waste of time and material, it is necessary that the TILC algorithm converge as quickly as possible. However, the robustness and performance objectives are conflicting and an acceptable compromise must be achieved. The control engineer must define specifications to describe these two constraints. Tools such as the Hinfinity Mixed-Sensitivity Analysis and mu-Analysis can be used to check the compliance of a given TILC algorithm with the robustness and performance specifications defined before the analysis. One can therefore compare various TILC algorithms quantitatively, through a computed measure obtained with one of the two approaches. These same tools can be used for the design of TILC algorithms, using weighting functions representing the specifications. / Simulation and experimental results obtained on industrial thermoforming machines show the effectiveness of the various approaches in this thesis. Many examples are also presented throughout the chapters.

The objectives of this project are (1) to reduce the excursions between real heater temperatures and the desired values, and (2) to realize cyclic production of plastic sheets on the AAA thermoforming machine. / At first, present relevant knowledge and modeling of the AAA machine are covered. A programmable pre-processing module is inserted before the heaters to prevent the input commands from delaying in heater response. The results prove that the excursions can be theoretically reduced to zero. / Based on the Terminal Iterative Learning Control (TILC) algorithm, a hybrid dual-mode cascade-loop system is designed: the inner loop monitors the real-time temperatures for PID control in Mode 0, while the outer loop reads temperatures and commands once per cycle to decide the necessity of switching mode. A more realistic version with flexible cycle length and instant response to operator's commands is also designed to simulate the real operating circumstance.

No description available.

Thesis (Ph. D.)--West Virginia University, 2008. / Title from document title page. Document formatted into pages; contains vi, 77 p. Includes abstract. Includes bibliographical references (p. 75-77). WVU users: Also available in print for a fee.

Thesis(M.S.)--Auburn University, 2006. / Abstract (p.34-35). Vita. Includes bibliographic references.