Stabilizing Parameterization for Uncertain Delay Systems

Ph.DDOCTOR OF PHILOSOPH

Stability Analysis and Decentralized Control of Coupled Oscillators with Feedback Delays

Most dynamic systems do not react instantaneously to actuation signals. The temporal evolution of some others is based on retarded communications or depends on information from the past. In such cases, the mathematical models used to describe these systems must include information about the past dynamics of the states. These models are often referred to as delay or retarded systems. Delays could channel energy in and out of a system at incorrect time intervals producing instabilities and rendering controllers\u27 performance ineffective. The purpose of this research is two folds. The first investigates the effect of inherent system delays on the stability of coupled oscillators subjected to decentralized control and the second studies the prospectus of augmenting the delay into a larger delay period that could actually stabilize the coupled system and enhance its damping characteristics. Towards these ends, a system of two linearly-coupled oscillators with decentralized delayed-proportional feedback is considered. A comprehensive linear stability analysis is utilized to generate maps that divide the controllers\u27 gain and delay domain into regions of stability for different coupling values. These maps are then used to draw definite conclusions about the effect of coupling on the stability of the closed-loop in the presence of delay. Once the stability maps are generated, the Lambert-W function approach is utilized to find the stability exponents of the coupled system which, in turn, is used to generate damping contours within the pockets of stability. These contours are used to choose gain-delay combinations that could augment the inherent feedback delays into a larger delay period which can enhance the damping characteristics and reduce the system settling time significantly. An experimental plant comprised of two mass-spring-damper trios coupled with a spring is installed to validate the theoretical results and the proposed control hypothesis. Different scenarios consisting of different gains and delays are considered and compared with theoretical findings demonstrating very good agreement. Furthermore, the proposed delayed-proportional feedback decentralized controller is tested and its ability to dampen external oscillations is verified through different experiments. Such a research endeavor could prove very beneficial to many vital areas in our life. A good example is that of the coupled system of the natural and artificial cardiac pacemakers where the natural pacemaker represents a rhythmic oscillating system and the coupled artificial pacemaker provides a stabilizing signal through a feedback mechanism that senses the loss in rhythm. In this system, even the minute amount of delay in the sensing-actuating could prove very detrimental. The result of this research contributes to the solution of this and similar problems

New results in relay feedback analysis and multivariable stability margins

Ph.DDOCTOR OF PHILOSOPH

Deep space communication and navigation study. Volume 1 - Summary

Comparison of alternative means for high data rate communication from deep space probes, and deep space navigation by orbiting spacecraf

Plantwide Control and Simulation of Sulfur-Iodine Thermochemical Cycle Process for Hydrogen Production

A PWC structure has developed for an industrial scale SITC plant. Based on the performance evaluation, it has been shown that the SITC plant developed via the proposed modified SOC structure can produce satisfactory performance – smooth and reliable operation. The SITC plant is capable of achieving a thermal efficiency of 69%, which is the highest attainable value so far. It is worth noting that the proposed SITC design is viable on the grounds of economic and controllability

Risk-based security-constrained optimal power flow: Mathematical fundamentals, computational strategies, validation, and use within electricity markets

This dissertation contributes to develop the mathematical fundamentals and computational strategies of risk-based security-constrained optimal power flow (RB-SCOPF) and validate its application in electricity markets. The RB-SCOPF enforces three types of flow-related constraints: normal state deterministic flow limits, contingency state deterministic flow limits (the N-1 criteria), and contingency state system risk, which depends only on contingency states but not the normal state. Each constraint group is scaled by a single parameter setting allowing tradeoffs between deterministic constraints and system risk. Relative to the security-constrained optimal power flow (SCOPF) used in industry today, the RB-SCOPF finds operating conditions that are more secure and more economic. It does this by obtaining solutions that achieve better balance between post-contingency flows on individual circuits and overall system risk. The method exploits the fact that, in a SCOPF solution, some post-contingency circuit flows which exceed their limits impose little risk while other post-contingency circuit flows which are within their limits impose significant risk. The RB-SCOPF softens constraints for the former and hardens constraints for the latter, thus achieving simultaneous improvement in both security and economy. Although the RB-SCOPF is more time-intensive to solve than SCOPF, we have developed efficient algorithms that allow RB-SCOPF to solve in sufficient time for use in real-time electricity markets. In contrast to SCOPF, which motivates market behavior to offload circuit flows exceeding rated flows, the use of RB-SCOPF provides price signals that motivate market behavior to offload circuit flows and to enhance system-wide security levels. Voltage stability testing has demonstrated that the dispatch result based on RB-SCOPF has higher reactive margins at normal state and after a contingency happens, thus has better static voltage stability performance

Robust identification and controller design for delay processes

Ph.DDOCTOR OF PHILOSOPH

Linear Covariance Analysis For Gimbaled Pointing Systems

Linear covariance analysis has been utilized in a wide variety of applications. Historically, the theory has made significant contributions to navigation system design and analysis. More recently, the theory has been extended to capture the combined effect of navigation errors and closed-loop control on the performance of the system. These advancements have made possible rapid analysis and comprehensive trade studies of complicated systems ranging from autonomous rendezvous to vehicle ascent trajectory analysis. Comprehensive trade studies are also needed in the area of gimbaled pointing systems where the information needs are different from previous applications. It is therefore the objective of this research to extend the capabilities of linear covariance theory to analyze the closed-loop navigation and control of a gimbaled pointing system. The extensions developed in this research include modifying the linear covariance equations to accommodate a wider variety of controllers. This enables the analysis of controllers common to gimbaled pointing systems, with internal states and associated dynamics as well as actuator command filtering and auxiliary controller measurements. The second extension is the extraction of power spectral density estimates from information available in linear covariance analysis. This information is especially important to gimbaled pointing systems where not just the variance but also the spectrum of the pointing error impacts the performance. The extended theory is applied to a model of a gimbaled pointing system which includes both flexible and rigid body elements as well as input disturbances, sensor errors, and actuator errors. The results of the analysis are validated by direct comparison to a Monte Carlo-based analysis approach. Once the developed linear covariance theory is validated, analysis techniques that are often prohibitory with Monte Carlo analysis are used to gain further insight into the system. These include the creation of conventional error budgets through sensitivity analysis and a new analysis approach that combines sensitivity analysis with power spectral density estimation. This new approach resolves not only the contribution of a particular error source, but also the spectrum of its contribution to the total error. In summary, the objective of this dissertation is to increase the utility of linear covariance analysis for systems with a wide variety of controllers and for whom the spectrum of the errors is critical to performance