A few problems of designing structural control systems are addressed, considering optimization of three design objectives: state error energy, control energy and stability robustness. Tradeoff relationships among these selected design objectives are investigated by solving multiple objective optimization problems. Various measures of robustness (tolerance of model errors and disturbances) are also reviewed carefully in the present study and throughout the dissertation, robust control design methodologies are emphasized. Presented in the first part of the dissertation are three new feedback design algorithms: 1) a generalized linear-quadratic regulator (LQR) formulation, 11) a generalized LQR formulation based on Lyapunov stability theorem, and 111) an eigenstructure assignment method using Sylvester's equation. The performance of these algorithms for multi-criterion optimizations are compared by generating three dimensional surfaces of wh1ch d1splay the tradeoff among the three design objectives. In the second part, a noniterative robust e1genstructure assignment algorithm via a projection method is introduced. This algorithm produces a fairly well-conditioned eigenvector matrix and provides an excellent starting solution for optimizations of various design criteria. We also present a specialized version of the projection method for second order differential equatlons, wh1ch offers useful insights to design strategies in regards to conditioning (robustness) of the eigenvectors. Finally, to illustrate the ideas presented in this study, we adopt numerical examples in two sets: 1) 6th order mass-spring systems and 11) various reduced order models of a flexible system. The numerical results confirm that multi-criterion optimizations by using a minimum correction homotopy technique is a useful tool with significant potential for enhanced computer—aided design of control systems. The proposed robust eigenstructure assignment algorithm is successfully implemented and tested for a 24th reduced order model, which establishes the approach to be applicable to systems of at least moderate dimensionality. We show analytically and computationally that constraining closed—loop eigenvectors to equal open-loop eigenvectors generally does not lead to either optimal conditioning (robustness) of the closed-loop eigenvectors or minimum gain norm. / Ph. D. / incomplete_metadata

This thesis examines the use of a linear DC motor as a proof mass actuator for the control of large space structures. A model for the actuator, including the current and force compensation used, is derived. Because of the force compensation, the actuator is unstable when placed on a structure. Relative position feedback is used for actuator stabilization. This method of compensation couples the actuator to the mast in a feedback configuration. Three compensator designs are proposed. The physical limits of the LDCM place limits on the bandwidth of the closed loop actuator. A ten mode finite element model of a flexible space structure was used in simulations to examine all aspects of the actuator's performance. The performance of the actuator is compared for the three compensator designs. The actuator bandwidth is seen to be important in the actuator's effectiveness. Increasing actuator bandwidth resulted in a saturation nonlinearity in the actuator. The excitation capability of the actuator was examined to determine the authority of the actuator. The damping of the mast modes was examined to determine the effect of the feedback configuration of the actuator/mast system. Root locus techniques were used to explain changes in the vibrational modes of the structure due to the actuator compensation. Disturbance analysis was performed to quantify the effect of corrupted measurements on the purity of force generated by the actuator. / Master of Science

Traditional large space structure construction incorporates the use of lightweight tubular metal alloys that have good strength to weight and stiffness to weight ratio. Recently, however, space structure construction has shifted focus on materials that are ultra lightweight, have high strength, have low package volume and possess excellent damping characteristics. Substantial damping is required in space since there is no surrounding medium to provide damping. Such a construction uses composites in a fabric form that displays viscoelastic behavior. The viscoelastic behavior is attributed to energy dissipation because of the shear stresses between the various fibrous strands that are kept in place by constraining viscoelastic layers. This type of vibration control falls under the rubric of passive damping of structures and has been found to have certain advantages over active damping such as less complexity as it does not require sensors, actuators and power supply that are needed for active damping. One such material consists of woven carbon strands constrained by layers of viscoelastic damping material. Dynamics and buckling behavior of a structure in the form of a tube made from this material with metallic end caps is modeled and analyzed using commercially available Finite Element Analysis code ABAQUS®. The current analysis deals with the non-pressurized tube since the structure can maintain the tubular configuration as well as support end caps on account of the stiffness provided by the composites. Since no simple analytical approaches are available to predict damping of these materials, experimental data was used to estimate the damping characteristics of the material. The mass of the end cap was also estimated from the experimental impulse response as exact mass of the end cap (that was rigidly fixed to the tube) was unknown. / Master of Science

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

Deployable structures serve a large number of space missions. They are vital since spacecraft are launched by placing them inside launch vehicle payload fairings of limited volume. Traditional spacecraft design often involves large components. These components could have power, communication, or optics applications and include booms, masts, antennas, and solar arrays. Different stowing methods are used in order to reduce the overall size of a spacecraft. Some examples of stowing methods include simple articulating, more complex origami inspired folding, telescoping, and rolling or wrapping. Wrapping of a flexible component could reduce the weight by eliminating joints and other components needed to enable some of the other mechanisms. It also is one of the most effective methods at reducing the compaction volume of the stowed deployable. In this study, a generic unfurlable structure is optimized for maximum natural frequency at its fully deployed configuration and minimal strain energy in its stowed configuration. The optimized stowed structure is then deployed in simulation. The structure consists of a rectangular panel that tightly wraps around a central cylindrical hub for release in space. It is desired to minimize elastic energy in the fully wrapped panel and hinge to ensure minimum reaction load into the spacecraft as it deploys in space, since that elastic energy stored at the stowed position transforms into kinetic energy when the panel is released and induces a moment in the connected spacecraft. It is also desired to maximize the fundamental frequency of the released panel as a surrogate for the panel having sufficient stiffness. Deployment dynamic analysis of the finite element model was run to ensure satisfactory optimization formulation and results. / Master of Science / Spacecraft, or artificial satellites, do not fly from earth to space on their own. They are launched into their orbits by placing them inside launch vehicles, also known as carrier rockets. Some parts or components of spacecraft are large and cannot fit in their designated space inside launch vehicles without being stowed into smaller volumes first. Examples of large components on spacecraft include solar arrays, which provide power to the spacecraft, and antennas, which are used on satellite for communication purposes. Many methods have been developed to stow such large components. Many of these methods involve folding about joints or hinges, whether it is done in a simple manner or by more complex designs. Moreover, components that are flexible enough could be rolled or wrapped before they are placed in launch vehicles. This method reduces the mass which the launch vehicle needs to carry, since added mass of joints is eliminated. Low mass is always desirable in space applications. Furthermore, wrapping is very effective at minimizing the volume of a component. These structures store energy inside them as they are wrapped due to the stiffness of their materials. This behavior is identical to that observed in a deformed spring. When the structures are released in space, that energy is released, and thus, they deploy and try to return to their original form. This is due to inertia, where the stored strain energy turns into kinetic energy as the structure deploys. The physical analysis of these structures, which enables their design, is complex and requires computational solutions and numerical modeling. The best design for a given problem can be found through numerical optimization. Numerical optimization uses mathematical approximations and computer programming to give the values of design parameters that would result in the best design based on specified criterion and goals. In this thesis, numerical optimization was conducted for a simple unfurlable structure. The structure consists of a thin rectangular panel that wraps tightly around a central cylinder. The cylinder and panel are connected with a hinge that is a rotational spring with some stiffness. The optimization was solved to obtain the best values for the stiffness of the hinge, the thickness of the panel, which is allowed to vary along its length, and the stiffness or elasticity of the panel's material. The goals or objective of the optimization was to ensure that the deployed panel meets stiffness requirement specified for similar space components. Those requirements are set to make certain that the spacecraft can be controlled from earth even with its large component deployed. Additionally, the second goal of the optimization was to guarantee that the unfurling panel does not have very high energy stored while it's wrapped, so that it would not cause large motion the connected spacecraft in the zero gravity environments of space. A computer simulation was run with the resulting hinge stiffness and panel elasticity and thickness values with the cylinder and four panels connected to a structure representing a spacecraft. The simulation results and deployment animation were assessed to confirm that desired results were achieved.

Thin-ply composite materials display remarkable versatility and hold great promise for applications in the space industry. They are characterized by exceptional attributes such as a high strength-to-weight ratio, fatigue resistance, and the ability to conform to high curvatures without failure. This study investigates the behavior of thin-ply composite materials and structures, with a particular emphasis on their relevance to deployable space applications. Deployable structures such as solar sails, are large structures that are designed to be compactly folded into small volumes to fit inside the spacecraft for the purpose of carrying them to space. These structures utilize the strain energy during folding, to facilitate the deployment sequence and attain the intended original configuration of the structure. However, the viscoelastic nature of the composite material leads to a reduction of strain energy over the storage period, leading to shape inaccuracies after deployment. Our research includes an in-depth analysis of the viscoelastic properties of the composite material and the behavior of structures following folding and subsequent deployment. The viscoelastic mechanical properties of the materials were assessed through a numerical multi-scale homogenization approach. We examined thin-ply laminates with varying orientations and ply arrangements and conducted experimental studies to validate the numerical models. We subsequently incorporated the viscoelastic properties of the laminates into the simulation of deployable structures. The laminate properties were evaluated both at the ply level and at the laminate level. Numerical simulations were conducted to study the behavior of a composite boom during folding, stowage, deployment, and subsequent shape recovery. Our research extended to characterizing the composite material based on available test data, as well as examining the stowage and recovery behavior of a structure constructed from unidirectional composites.

This dissertation is concerned with some topics in the modeling and control of large flexible structures. In the finite element convergence toward the natural modes and frequencies of a structure, it is found that two mechanisms limiting the accuracy of higher modes are, first, a decrease in the number of active degrees of freedom for higher mode approximations due to orthogonality constraints, and, second, the fact that lower computed, rather than actual, eigenfunctions appear in the orthogonality constraints, so that inaccuracy in lower modes inhibits convergence to higher modes. Refining the elements using the hierarchical p-version proves to be far superior to refining the mesh, as demonstrated by numerical examples. In the third chapter, a method is presented for solving the algebraic eigenvalue problem for a structure, which combines attractive features of the subspace iteration method and the component-mode synthesis methods. Reduced substructure models are generated automatically and coupled exactly to form a reduced structure model, whose eigensolution is used to refine the substructure models. Convergence is much faster than in the subspace iteration method, as demonstrated by numerical examples. In the fourth chapter, the effectiveness of modal control (IMSC) and direct feedback control, in which the actuator force depends only on the local velocity and displacement, are investigated for suppressing traveling waves on a string and on a beam, both with slight material damping. Direct feedback proves superior for the string, as more modes must be controlled than can be handled by modal control with a limited number of actuators, but inferior for the beam, as effort is wasted suppressing motion in higher modes where damping is pervasive, while modal control focuses effort on those lower modes which need to be controlled. The optimal vibration control for a distributed system subjected to persistent excitation is not available, so a two-part control is proposed in chapter five for suppressing the motion of a distributed system with a moving support. The first part cancels the moving support's excitation to an optimal extent, and the second is a direct velocity feedback control. A numerical example demonstrates the effectiveness of this control method. / Ph. D. / incomplete_metadata

The analytical study presented here is concerned with by two types of sensitivity of active vibration control of large space structures (LSS). The first one required for assessing robustness, is the sensitivity of the performance and stability of the control system to changes in structure and to model reduction. The second type is the sensitivity of the optimum design of the control system to changes in the structure. This sensitivity is of interest in assessing the need for integrated structure/control design. Three direct rate feedback (DRF) control techniques are studied for a laboratory structure which has characteristics of LSS and then compared to standard linear quadratic (LQ) control. The baseline design of each control system is obtained first and then sensitivity analysis conducted. An uncoupled DRF control law which minimized the sum of gains subject to requirements on performance was not robust to structural changes, and small changes in the structure caused notable increase in performance compared to that of the baseline design and therefore a potential gain from simultaneous structure/control design was indicated. Two coupled DRF techniques are proposed. A Minimum Force DRF (MF-DRF) law minimized maximum force of any actuator, while a Linear Quadratic DRF (LQ-DRF) law minimized the standard quadratic performance index for initial conditions in the shape of the first six natural modes. Both techniques guaranteed system stability. The LQ control law was found to be only slightly better than the simpler MF·DRF law in terms of the quadratic performance index and poorer than the LQ-DRF law. However the LQ control requires model reduction and was found to be sensitive to errors in that process. For example, the LQ design lost its stability when the structure was modified by adding a non-structural mass to it. A separate experimental study was conducted simultaneously with this study to verify theoretical results. Good agreement was found between analytical results and experimental measurements for the investigated control techniques. / Ph. D.

Active control of large flexible space structures is typically implemented to control only a few known elastic modes. Linear Quadratic Regulators (LQR) and Kalman-Bucy Filter (KBF) observers are usually designed to control the desired modes of vibration. Higher modes, referred to as residual modes, are generally ignored in the analysis and may be excited by the controller to cause a net destabilizing effect on the system. This is referred to as the spillover phenomenon. This dissertation considers the stabilization of the neglected dynamics of the higher modes of vibration. It aims at designing modal controllers with improved spillover stability properties. It is based on the premise that the structural dynamicist will be able to predict more vibration modes than would be practical to include in the design of the controller. The proposed method calls for designing the observer so as to improve spillover stability with minimum loss in performance. Two formulations are pursued. The first is based on optimizing the noise statistics used in the design of the Kalman-Bucy Filter. The second optimizes directly the gain matrix of the observer. The influence of the structure of the plant noise intensity matrix of the Kalman-Bucy Filter on the stability margin of the residual modes is demonstrated. An optimization procedure is presented which uses information on the residual modes to minimize spillover (i.e., maximize the stability margin) of known residual modes while preserving robustness vis-à-vis the unknown dynamics. This procedure selects either the optimum plant noise intensity matrix or the optimum observer gain matrix directly to maximize the stability margins of the residual modes and properly place the observer poles. The proposed method is demonstrated for both centralized and decentralized modal control. / Ph. D.

This study concerns the active damping of structural vibrations through the application of various forms of velocity feedback control. Active damping will be required for large space structures which are performance-sensitive to motion or inaccurate pointing. Several control forms, including modal-space active damping and direct rate feedback, are analyzed theoretically, and three laboratory models are described. A previous, unsuccessful attempt at control is reviewed and explained. The remaining control forms developed in the theoretical section were implemented successfully and the results compare favorably with theoretical predictions. Each control form is analyzed relative to its own merits and in comparison with other methods. An important point is the stability assured by a dual (colocated) configuration. of velocity sensors and control force actuators. Modal-space active damping is shown to be an effective control method with predictable performance in controlled modes and beneficial spillover into residual (non-controlled) modes. / Ph. D. / incomplete_metadata