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.

The design of feedback control laws for discrete models of flexible structures is addressed. Two strategies are proposed. First, a parameter optimization method is used, in which the behavior of the controller is described by a performance measure and numerically optimized. A second method, based on continuation maps, allows several performance criterion to be met. These performance measures are quite general in nature; they may be functions of eigenvalues, eigenvectors, sensitivities, and other mission specific quantities. A model of a cantilevered flexible beam is developed and used to demonstrate capabilities and problems with the design methods. / M.S.

This thesis reports a study in the area of active vibration damping focused primarily on reconfiguration of control actuators following failure of one or more components. Several related issues concerning practical implementation were considered, and these also were discussed. These subjects were studied with reference to a particular laboratory structure, a hanging plane grid in the Spacecraft Controls Branch at NASA Langley Research Center. The structure had dynamics representative in many respects of a large, highly flexible space structure (LSS), and this study was intended to contribute toward the development of vibration control for LSS. A numerical analysis of the reconfiguration by computer simulation is presented. The possible future experimental validation of this numerical analysis motivated examination of some auxiliary problems related to implementation of vibration control with real, nonideal hardware. One of these problems is the effect of the dynamics of real sensors, actuators, and filters on a vibration control system. An experimental analysis of this problem was conducted, and the results presented here include hardware induced performance degradation and system instability. Another problem considered is prediction of response for use in feedback control by a digital controller that introduces a significant computational delay. A prediction technique is described, and some results of open-loop experimental evaluation of this technique are presented. Also, a computer simulation of closed-loop application of this technique was conducted, and the results, which include system instabilities, are presented. / M.S.

During the past decade, researchers have shown much interest in control and identification of Large Space Structures (LSS). Our inability to model these LSS accurately has generated extensive research into robust controllers capable of maintaining stability in the presence of large structural uncertainties as well as changing structural characteristics. In this work the performance of Model Reference Adaptive Control - (MRAC) is studied in numerical simulations and verified experimentally, to understand how differences between the plant and the reference model affect the control effort. MRAC is applied analytically and experimentally to a single-degree-of-freedom system and analytically to a multi-degree-of-freedom system with multi-inputs and multi-outputs. Good experimental and analytical agreement is demonstrated in control experiments and it is shown that MRAC does an excellent job of controlling the structures and achieving the desired performance even when large differences between the plant and ideal reference model exist. However, it is shown that reasonable differences between the reference model and the plant significantly increase the required control effort. The effects of increased damping in the reference model are considered, and it is shown that requiring the controller to provide increased damping actually decreases the required control effort when differences between the plant and reference model exist. This result is very useful because one of the first attempts to counteract the increased control effort due to differences between the plant and reference model might be to require less damping, however, this would actually increase the control effort. The use of optimization to successfully improve performance and reduce control effort is shown to be limited, because the actual control-structure system can not realize all the performance improvements of the analytical optimal system. Finally, it is shown that very large sampling rates may be required to accurately implement MRAC. / Ph. D.

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

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

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.