Interest in large flexible space structures has grown considerably over the last decade. These distributed parameter systems exhibit vibration characteristics such as low, closely spaced natural frequencies and light damping, which, when coupled with the stringent pointing accuracy and vibration control requirements imposed on these systems, bring about interesting control problems. Addressing these problems has called for the use of active vibration control. Up to now, two of the most popular means for active vibration control of large space structures have been proof mass and reaction wheel actuators. These actuators are inertial-type actuators in that they operate by applying forces or moments to masses whose reaction forces, imposed on the structure, act to dampen the vibrations of the structure. A new class of actuators, variable geometry trusses (VGT's), has been recently introduced. These actuators are actually built into the structure, and they operate by varying their link lengths to apply forces to the structure or to change the shape of the structure itself. This study compared the effectiveness of four actuators in controlling the planar vibrations of a cantilevered truss-beam. The actuators chosen for the study were a proof mass actuator, a reaction wheel actuator, and two VGT's, the planar truss actuator, and the planar truss proof mass actuator (a combination VGT/inertial type actuator). Numerical simulations of each beam/actuator system were performed in response to initial condition inputs. A full-state, LQR optimal feedback control law was used with each system. These simulations provided information such as time response of the closed-loop system, damping provided to the beam, and power required by each actuator. This information can be used to determine the "best" actuator for a given purpose. The results of these simulations show that the VGT's are preferable in terms of damping added to the beam. The proof mass actuator is more efficient as far as power required to do the control, however, the efficiencies for all actuators are very similar. / Master of Science

Ever since the advent of the Moment-Distribution procedure (1) for analyzing continuous frames, it has been possible to solve many problems conveniently which previously had required laborious solutions. Indeed, the current literature of the engineering profession finds the Cross method being adopted in new fields and being applied to new problems. The classical methods of analysis, while still retaining some measure of their former utility, are being superseded by this and other methods involving less time and labor. Yet, even with this new impetus to the field of structural analysis, the rigid space frame has received far less attention than seems justified. Here is a class of structure devoid of practically any analytical investigation and even less experimental research. The desired characteristic of all current designs has been continuity, and yet there exists this paradoxical neglect of the third dimension, without which all structures would be non-existent. The reasons for this apparent indifference are not difficult to ascertain. Practicing engineers are practical men and as such require reasonably accurate results, obtained with a minimum of effort. Economy has dictated that refinements of analysis be saved for the classroom. A two-plane analysis is generally substituted for the more complex three-dimensional case. The write feels that the interaction of members in different planes of certain structures may be quite important in some cases and that a complete, convenient analysis is justified to determine the extent of such action. / Master of Science

The control problem of a large-order flexible system in the form of a beam-lattice is presented using the Independent Modal-Space Control (IMSC) method. The method is based on a transformation of the system equations of motion to modal space, yielding internally independent modal equations of motion. The control laws are designed in the modal space, permitting independent control of each mode, providing complete decoupling of the equations of motion. Linear optimal control with quadratic performance index is designed to control the response of the elastic as well as the rigid body modes, using the IMSC method. Actuators placement is of fundamental importance in the control of two-dimensional domains if IMSC is used. A method is presented as to the selection of actuators configuration in order to avoid singularity in the mode participation matrix, guaranteeing system controllability. The minimum-fuel problem is a very important one in the design of various space structures. Solution of the minimum-fuel problem is feasible in a coupled form for a fourth order system at most, but will be of insurmountable computational difficulty in the control of a flexible structure, since the model of such system will require a large number of degrees of freedom. A reformulation of the problem in the framework of "Modal Minimum-Fuel Problem" is presented, using the IMSC method. By this method, the complexity inherent in a high-order system is reduced, thus treatment of the coupled high-order system is avoided. Numerical examples for linear optimal control, with quadratic performance index, as well as for the minimum-fuel problem, are presented. / Ph. D.

In this thesis, we examine the Linear DC Motor in a configuration such that it provides the forces necessary to damp vibrations in a large flexible structure. The design is broken down into three steps where in each step, a feedback loop is placed around the actuator and/or the structure. The first loop is a motor compensation loop which effectively decouples the motor model from the structure model by removing the effect of the velocity of the structure on the motor's performance. The second loop stabilizes the relative position response of the combined actuator/structure model. This loop also shapes the magnitude response of the system, thus determining the bandwidth of the actuator. Two designs are developed: a narrow bandwidth design and a wide bandwidth design. The third loop is the vibration suppression design loop and can be designed a number of ways. In this thesis, we develop two decentralized designs and a centralized design. The final system is simulated to check design results. The various nonlinearities of the proof mass actuator are considered and their effect on results noted. These nonlinearites, the stroke and current limits, determine the effectiveness of each vibration suppression design. The linear model is checked for robustness to parameter uncertainty. Results for the various designs are tabulated and discussed. / M.S.

The work that is reported herein deals with system identification methods for large flexible structures. Proposed space missions for the future include the deployment of large flexible structures, e.g., NASA's proposed space station. These structures must be controlled to maneuver the structure to desired locations and to suppress unwanted vibration. Before controlling any structure, it is necessary to have an accurate model which may include accurate estimates of the structure's natural frequencies and mode shapes. System identification is an important process that precludes system control. Precision structures such as those proposed for the Space Based Laser or the Aerospace Plane require high performance control systems which will require robust, computationally efficient system identification algorithms. This work attempts to experimentally verify, develop, and compare existing identification algorithms to determine their properties and improve their efficiency towards potential applicability in a space environment. To this end, we consider the Temporal Correlation Method and the Eigensystem Realization Algorithm. The algorithms are implemented on the Astronautics Laboratory Grid structure, and the results of the algorithms are compared in the presence of damping, noise, and residual modes. In addition, the Temporal Correlation Method is shown to be a constrained version of the Eigensystem Realization Algorithm for cases of light damping. / Master of Science

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1994. / Vita. Abstract. Includes bibliographical references (leaves 69-72). Also available via the Internet.

Neste trabalho são descritas análises estática e dinâmica em regime elástico de pórticos espaciais com incerteza no carregamento utilizando o método de elementos finitos (MEF). A abordagem do problema dinâmico estrutural de vibrações forçadas será feita dentro do regime elástico linear com amortecimento viscoso. O pórtico é abordado com teoria de viga fina onde são considerados os acoplamentos devido às forças normais e a torção sobre o modelo de flexão em viga fina de Bernoulli-Euler. A formulação forte do problema dinâmico da viga com carga axial é obtida a partir das equações de equilíbrio de Euler-Lagrange, decorrentes do princípio variacional de Hamilton e, a formulação forte do problema dinâmico do eixo longo sujeito a torção é determinada utilizando o modelo de torção de Saint-Venan. Para a determinação da formulação fraca para o elemento de viga tridimensional foi aplicado o método dos resíduos ponderados Galerkin. Também é descrita neste trabalho, a análise da confiabilidade estrutural considerando a incerteza no carregamento e, em algumas propriedades mecânicas dos materiais, utilizando o método de Monte Carlo (MMC). A série de Neumann foi utilizada como alternativa para reduzir o tempo de processamento do problema dinâmico. A análise simultânea das diversas variáveis foi abordada utilizando a estatística multivariada. Os resultados da analise estática e de vibrações livres dos exemplos numéricos são apresentados com o intuito de validar os métodos contidos neste trabalho comparando-os com resultados obtidos utilizando um software comercial de análise estrutural. / Submitted by Ana Guimarães Pereira (agpereir@ucs.br) on 2015-11-23T16:10:16Z No. of bitstreams: 1 Dissertacao Samuel Cornelli.pdf: 2680799 bytes, checksum: bcb4daa1a00ba8c03aafdea11fa42778 (MD5) / Made available in DSpace on 2015-11-23T16:10:16Z (GMT). No. of bitstreams: 1 Dissertacao Samuel Cornelli.pdf: 2680799 bytes, checksum: bcb4daa1a00ba8c03aafdea11fa42778 (MD5) / In this thesis, static and dynamic analysis of elastic space frames with regime uncertainty in loading using the finite element method (FEM) are described. A structural approach to the dynamic problem of forced vibrations will be made within the linear elastic regime with viscous damping. The structure is approached with thin beam theory which the couplings are considered normal forces due to twisting and bending about the model thin Bernoulli-Euler beam. The strong formulation of the dynamic problem of the beam with axial load is obtained from the equilibrium equations of Euler-Lagrange equations arising from the variational principle of Hamilton and the strong formulation of the dynamic problem of the long shaft under torsion is determined using the model of twist of Saint-Venan. To determine the weak formulation for three-dimensional beam element applies the Galerkin method of weighted residues. Is also described in this study, the analysis of structural reliability considering the uncertainty in loading and some mechanical properties of materials using the Monte Carlo method (MMC). Neumann series will be used as an alternative to reduce the processing time of the dynamic problem. The simultaneous analysis of several variables is addressed using multivariate statistics. Some results of numerical examples are presented in order to validate the methods contained in this work compared with the results obtained from structural analysis of commercial software.

Neste trabalho são descritas análises estática e dinâmica em regime elástico de pórticos espaciais com incerteza no carregamento utilizando o método de elementos finitos (MEF). A abordagem do problema dinâmico estrutural de vibrações forçadas será feita dentro do regime elástico linear com amortecimento viscoso. O pórtico é abordado com teoria de viga fina onde são considerados os acoplamentos devido às forças normais e a torção sobre o modelo de flexão em viga fina de Bernoulli-Euler. A formulação forte do problema dinâmico da viga com carga axial é obtida a partir das equações de equilíbrio de Euler-Lagrange, decorrentes do princípio variacional de Hamilton e, a formulação forte do problema dinâmico do eixo longo sujeito a torção é determinada utilizando o modelo de torção de Saint-Venan. Para a determinação da formulação fraca para o elemento de viga tridimensional foi aplicado o método dos resíduos ponderados Galerkin. Também é descrita neste trabalho, a análise da confiabilidade estrutural considerando a incerteza no carregamento e, em algumas propriedades mecânicas dos materiais, utilizando o método de Monte Carlo (MMC). A série de Neumann foi utilizada como alternativa para reduzir o tempo de processamento do problema dinâmico. A análise simultânea das diversas variáveis foi abordada utilizando a estatística multivariada. Os resultados da analise estática e de vibrações livres dos exemplos numéricos são apresentados com o intuito de validar os métodos contidos neste trabalho comparando-os com resultados obtidos utilizando um software comercial de análise estrutural. / In this thesis, static and dynamic analysis of elastic space frames with regime uncertainty in loading using the finite element method (FEM) are described. A structural approach to the dynamic problem of forced vibrations will be made within the linear elastic regime with viscous damping. The structure is approached with thin beam theory which the couplings are considered normal forces due to twisting and bending about the model thin Bernoulli-Euler beam. The strong formulation of the dynamic problem of the beam with axial load is obtained from the equilibrium equations of Euler-Lagrange equations arising from the variational principle of Hamilton and the strong formulation of the dynamic problem of the long shaft under torsion is determined using the model of twist of Saint-Venan. To determine the weak formulation for three-dimensional beam element applies the Galerkin method of weighted residues. Is also described in this study, the analysis of structural reliability considering the uncertainty in loading and some mechanical properties of materials using the Monte Carlo method (MMC). Neumann series will be used as an alternative to reduce the processing time of the dynamic problem. The simultaneous analysis of several variables is addressed using multivariate statistics. Some results of numerical examples are presented in order to validate the methods contained in this work compared with the results obtained from structural analysis of commercial software.

Surface errors on parabolic reflector antennas degrade the overall performance of the antenna. They cause amplitude and phase errors in the aperture field which lower the gain, raise the side lobes, and fill in the nulls. These are major problems in large ->space reflector antenna systems. F or example, future multiple beam antenna systems requiring spatial isolation to allow frequency reuse could be rendered useless if high side lobes are present. Space antenna structures are difficult to build. They must maintain a nearly perfect parabolic shape in a harsh environment while remaining lightweight. The restrictions on the structure become more severe as science and technology requirements demand electrically large antennas. Mechanically, there are technologies [4)r building antennas with adaptive surfaces that can compensate for many of the larger distortions caused by thermal and gravitational forces. However, as the frequency and size of the reflectors increase, the subtle surface errors become significant and degrade the overall radiation pattern. It is for this reason that another method must be used to further improve the radiation pattern. Electromagnetic compensation for surface errors in large apace reflector antennas has been the topic of several research studies. Most of these studies try to correct the focal plane fields of the reflector near the radiation pattern. The compensation is implemented by weighting the elements of an array feed. In most of the studies, a precise knowledge of the reflector surface is required. An alternative approach to electromagnetic compensation is presented in this study. The proposed technique uses pattern synthesis to compensate for the surface errors. It differs from previous methods in two major respects. The previous studies used global algorithms that try to correct the entire focal plane field near the focal point or the aperture plane field and, hence, modify the entire radiation pattern. The pattern synthesis approach uses a localized algorithm in which pattern corrections are directed specifically towards portions of the pattern requiring improvement. The second major difference is that the pattern synthesis technique does not require knowledge of the reflector surface, but instead uses radiation pattern data to perform the compensation. / Ph. D.

Recent demands in large space structure technology have suggested the use of active control actuators integral to a structures' construction. The concept of a 3-D (triangular cross-sectioned) active truss is presented. The linear equations of motion for one plane of the truss are derived. A model for a generic flexible beam is then appended to the planar truss model. A linear time-invariant optimal control law is found, followed by a presentation of an experimental planar truss built to test the concept. Physical parameters are then substituted into the dynamic model and several sets of control gains are found. The "Kalman'' gains are applied to the experimental structure. Experimental results are compared to expected theoretical results with good (30%) correlation. Conclusions are drawn and suggestions are made for further research. / Master of Science