The purpose of this study was to review the history of financing public school facilities in Virginia with primary emphasis on the period of the public schools, 1870 through 1987. An ancillary purpose of the study was to review alternative methods of financing public school capital facilities in Virginia in 1987 and certain considerations in the determination of school plant needs and implementation of a capital improvements plan. A combination topical-chronological synthesis research plan was employed within time frames of twenty-six to thirty-year periods from 1870-1987. As a result of this study, the following findings and conclusions were made: / Ph. D.

The use of active control actuators integral to a structure's construction has been suggested in large space structure technology. A 3-D active truss is presented and analyzed and control of the actuators to reduce the vibration of a flexible rod attached to the structure is discussed. A state feedback control law is used. Experiments are performed using digital control implementation. Some experimental results are acceptable compared to expected theoretical analysis. Conclusions and recommendations are made for future research. / M.S.

An analytical and experimental investigation into the position and vibration control of beam-like structures within a gravity field using only root actuation was performed. Two methods were used to linearize the system's equations of motion. This, in turn, allowed for the use of powerful Modern Control Theory pole-location techniques to determine proper feedback-control gains. The control law was implemented on an IBM PC capable of analog/digital conversion. A DC servo motor served as the control actuator. Gains were computed for a continuous controller rather than for one having a sampled-data nature. Both simulation and experimental response were good, and were seen to correspond well with computed system-eigenvalues. If gains were chosen to cause more negative eigenvalues, the system's response speed increased, as it should. If eigenvalues are forced to become too negative, however, the system becomes too fast for the controller, and response deteriorated. / M.S.

In this study three types of optimized controllers are developed and tested on two laboratory structures. The two structures represented a progression in complexity and challenge to the controllers. The first structure was simple enough to be accurately modeled so the analytical frequencies and mode shapes agreed with the experimental measurements. The second structure being more complex was more difficult to model so differences between the analytical results and experimental measurements were present. These differences required the application a correction method to the reduced models developed for the second structure. The correction method was shown to work with good results on one reduced model and with poor results on the second reduced model. Two direct rate feedback control laws and a linear quadratic regulator with state estimation (LQG controller) were designed and implemented on both structures. It was shown that the performance of the LQG controller can be approached with a much simpler direct rate feedback controller with better analytical-experimental agreement. The best analytical-experimental agreement occurred with the simplest controller applied analytically to the corrected reduced model demonstrating the validity of the correction method as well as giving a strong reason to use simpler controller designs. / Ph. D.

This study examines the characteristics of four methods for the control of flexible structures and investigates the control performances of each method. The investigation is concerned with various control performance measures, such as control gain magnitude, settling time and overshoot in transient response, actuator phase and gain margins, and stability in the presence of actuator failure. In conjunction with the system performance, a systematic approach to the choice of weighting matrices for optimal control is presented. The approach shows a relation between the weighting matrices and the closed-loop eigenvalues. Since the approach is based on a set of independent second·order modal dynamics, the dimensionality of the system is no longer a problem in obtaining the optimal control law. The newly developed Minimum Gain Pole Placement (MGPP) is an optimal method in the sense that it minimizes an objective function, where the objective function is taken as control gain magnitudes with constraints of exact pole placement for any set of modes. The robustness of Independent Modal Space Control (IMSC) is examined. In general, the parameters of the control system are usually approximated, so that the designed controller, based on a postulated model, will not perform on the actual system as expected. This study shows that when the IMSC method is used with collocated sensors and actuators, the modelling errors in the postulated system cannot lead to instability of the closed-loop system containing control modes and residual modes.However, in the case of coupled control (MGPP), this property cannot be shown. This points to the robustness of IMSC method with respect to modelling errors. The IMSC method requires the same number of actuators as the number of control modes. The method can be extended to the cases of fewer actuator and more actuator by using the pseudo-inverse of modal particification matrix, an approach referred to as pseudo-independent modal-space control (PIMC). It is shown that PIMSC also yields some form of optimal control and that it is robust as well. Modal filters are introduced to detect and identify failure of control components in large space structures. The failure mode is investigated in the modal space so that a simple failure detection and identification (FDI) based on modal dynamics is established. Moreover the information obtained from the modal analysis provides some guidelines for the identification of faulty components. The integral form of the modal filters provides the ability to mitigate the effects of noise, disturbances and parameter uncertainties pointing to the robustness of the method. The detection process proposed in this study reduces the computational effort and permits an assessment of the system stability. / Ph. D. / incomplete_metadata

This thesis presents a unique method of damage detection in large space structures. The goal is to develop an efficient algorithm which can be automated in an on-line format, and can asses damage in many elements. Theses are goals not realized by current methods. Damage incurred in a structural member is modeled as a linear reduction in that member's modulus of elasticity. The damaged structure's global stiffness matrix is expressed as the healthy global stiffness matrix minus some perturbation matrix. A vector expression of the perturbation matrix allows the percent reduction in damage to be solved for exactly in an equation involving the healthy truss model and a mode identified from the damaged structure. An algorithm for locating and estimating single-element damage is built around this equation. Simulations of the algorithm are performed on two planar truss models. The vector expression of the damage perturbation is shown to lead to a mode shape - strain energy relationship. From this, it is shown that a smaller truss model can be computed from element stiffness vectors. Damage can then be detected as existing among a small group of elements. Simulations show detection in one group to be independent from damage in other groups. From this information, a dimensionally expanded version of the single-element detection method can be used to exactly locate and estimate damage in many elements simultaneously. This process is presented as a sequential algorithm which meets all of the desired criteria. / M.S.

MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1980. / Includes bibliographical references. / by Jeffrey Hastings Lang. / Ph.D.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 207-211). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 207-211). Also available on the Internet.

This dissertation is concerned with developing new time-optimal control techniques for higher-order linear and weakly nonlinear systems. As an application, we consider the simultaneous slewing and vibration suppression of a flexible beam, possibly with a tip mass. This application arises in the design of large space structures and flexible lightweight and accurate robotic arms. The solution of the soft-constrained time-optimal control problem is expressed in terms of the controllability Grammian. The properties of the open-loop solution are studied. A closed-loop control algorithm, which takes into account the mUltiplicity of extremal solutions, is then developed. The algorithm is based on the concept of continuation and reduces the computational complexity by as much as two orders of magnitude when compared to the brute-force approach. The amplitude of the soft-constrained time-optimal control is found to saturate as the state norm becomes large, thus suggesting a simpler but suboptimal feedback implementation. We develop and discuss the concept of saturating controls for linear systems, and we develop a design approach that generates a family of saturating control laws in which the speed of the response and amount of available control action can be explicitly traded off. The soft-constrained time-optimal cheap-control problem is formulated and solved using singular-perturbation theory. The solution procedures are illustrated with an example solved using the MACSYMA symbolic manipulation language. Regular-perturbation theory is then used to find the open-loop hard-constrained time-optimal control for a class of weakly nonlinear systems. The control is found by solving a nonlinear two-point boundary value problem (TPBVP) characterizing the control of the linearized system, and a second linear TPBVP. / Ph. D.