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An algorithm was developed and incorporated into a computer program for solving the damped, Timoshenko beam equations with free-free boundary conditions and prescribed initial data. A number of special cases are considered and, where appropriate, comparisons are made with known results.
A functional matrix of possible propulsion system characteristics for a spacecraft for deployable and assembled spacecraft structures shows that either electric propulsion or low thrust chemical propulsion systems could provide the propulsion required. The trade-off considerations of a single propulsion engine or multiengines are outlined and it is shown that a single point engine is bounded by some upper limit of thrust for assembled spacecraft. The matrix also shows several additional functions that can be provided to the spacecraft if a propulsion system is an integral part of the spacecraft. A review of all of the functions that can be provided for a spacecraft by an integral propulsion system may result in the inclusion of the propulsion for several functions even if no single function were mandatory. Propulsion interface issues for each combination of engines are identified.
The dynamics and stability of large orbiting flexible beams, and platforms and dish type structures oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid light-weight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam, the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate and shallow spherical shell in orbit with a two-degree-of freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for all the examples and a sensitivity study of the system response characteristics to the key system parameters is carried out.
The paper deals with the problem of system identifiability for a linear dynamical system. Two theorems are given relating the sufficient condition of system identifiability for certain linear structures to the total number of inputs and outputs. The principle of least squares, that seeks the minimization of a cost function is employed to carry out the system identification process. To illustrate the concept of the paper, a structural model of a beam with point masses is examined. Parameter identification methods are studied and a random search technique is introduced.
Various modifications were made to the tube design. The tubes were retested and analyzed, and the results are presented. One type of modified tube, the slotted tube, deployed successfully and reliably, and became the focus of detailed tests. Optimal design criteria, taking into consideration deployment as well as strength and buckling behavior were established.
The evaluation of several connector concepts in the neutral buoyancy simulator is discussed. Parameters for evaluating the fasteners included subject comments and hardware damage. Evaluation results include a rank ordering of the candidates with descriptions of the acceptable and unacceptable points of each. General design recommendations established as a result of neutral buoyancy testing are defined. Recommendations include detailed hardware and operational design requirements.
Theoretical developments and the results of laboratory experiments are treated as they apply to active attitude and vibration control, as well as static shape control. Modern control theory was employed throughout as the method for obtaining estimation and control laws.
The identification of the mass, damping and stiffness matrix for the finite-element formulation of a structure will be given. It will be shown that the quadrature integration procedure can be used to find the desired matrices when reasonable assumptions hold. The mass, damping and stiffness matrices of the matrix polynomial are identified by the algorithm.
The dynamics and attitude and shape control of very large, inherently flexible spacecraft systems were investigated. Increasingly more complex examples were examined, beginning with a uniform free-free beam, next a free-free uniform plate/platform and finally by considering a thin shallow spherical shell structure in orbit. The effects devices were modeled. For given sets of assumed actuator locations, the controllability of these systems was first established. Control laws for each of the actuators were developed based on decoupling techniques (including distributed modal control) pole placement algorithms and a application of the linear regulator problem for optical control theory.
Limited data on extensional and flexural damping of small specimens of graphite/epoxy and unreinforced epoxy resin were obtained. Flexural damping was measured using a forced vibration technique based on resonant flexural vibration of shaker excited double cantilever specimens. Extensional damping was measured by subjecting similar specimens to low frequency sinusoidal oscillation in a servohydraulic tensile testing machine while plotting load versus extensional strain. Damping was found to vary slowly and continuously over the frequency range 0.01 - 1000 Hz, and no drastic transitions were observed. Composite damping was found to be less than neat resin damping. Comparison of small specimen damping values with assembled column damping values seems to indicate that, for those materials, material damping is more important than joint damping. The data reported was limited not by the test apparatus, but by signal conditioning and data acquisition. It is believed that filtering of the strain gage signals and the use of digital storage with slow playback will make it possible to extend the frequency and amplitude ranges significantly.
The concept presented is intended to enhance astronaut assembly of truss structure that is either too large or complex to fold for efficient Shuttle delivery to orbit. The potential of augmented astronaut assembly is illustrated by applying the result of the tests to a barebones assembly of a truss structure. If this structure were assembled from the same nestable struts that were used in the Mobile Work Station assembly tests, the spacecraft would be 55 meters in diameter and consist of about 500 struts. The struts could be packaged in less than 1/2% of the Shuttle cargo bay volume and would take up approximately 3% of the mass lift capability. They could be assembled in approximately four hours. This assembly concept for erectable structures is not only feasible, but could be used to significant economic advantage by permitting the superior packaging feature of erectable structures to be exploited and thereby reduce expensive Shuttle delivery flights.
Modern control theory easily works with multiple input/multiple output systems. Two types of systems which fall into this category are flexible systems, where many measurements and several actuators are necessary to provide control over bending behavior, and articulated systems which consist of several rigid bodies connected together by pivoting connections. In this latter case, multiple controls are implemented as torquers at the joints.
A three axis mathematical representation of a modular assembled space platform consisting of interconnected discrete masses, including a deployable truss module, was derived for digital computer simulation. The platform attitude control system as developed to provide multilevel control utilizing the Gauss-Seidel second level formulation along with an extended form of linear quadratic regulator techniques. The objectives of the multilevel control are to decouple the space platform's spatial axes and to accommodate the modification of the platform's configuration for each of the decoupled axes.
A failure detection filter is applied to the detection of actuator and sensor failures on a free-free beam. Computer simulation tests are used to verify the filter design and study the effect of unmodeled modes on filter performance. In actuator tests, the failure signal to spillover noise ratio was found to be greatest when the filter bandwidth was 5 rad/sec beyond the input frequency. Observation spillover, however, was found to vary widely in tests run under similar conditions (same input frequency and filter poles) but with different detector gains. In sensor tests, the maximum signal-to-noise ratio for varying filter bandwidth depended upon the initial conditions placed on the unmodeled modes; the performance was good even for initial amplitudes on the first unmodeled mode 7.5% of that on the last modeled mode.
In most of the stable control designs for flexible structures, continuous time is assumed. However, in view of the implementation of the controllers by on-line digital computers, the discrete-time stability of such controllers is an important consideration. In the case of direct-velocity feedback (DVFB), involving negative feedback from collocated force actuators and velocity sensors, it is not immediately apparent how much delay due to digital implementation of DVFB can be tolerated without loss of stability. The present investigation is concerned with such questions. A study is conducted of the discrete-time stability of DVFB, taking into account an employment of Euler's method of approximation of the time derivative. The obtained result gives an indication of the acceptable time-step size for stable digital implementation of DVFB. A result derived in connection with the consideration of the discrete-time stability of stable continuous-time systems provides a general condition under which digital implementation of such a system will remain stable.
Large flexible communication satellite controller design is considered. The satellite that was developed for a "straw man' was configured as an offset fed paraboloid with a set of masts and booms that carry the antenna. The controllers were both a boom and mast actuator and a set of two degree of freedom actuators at the antenna to move it in order to satisfy both line of sight and defocus control.
Several assertions are argued regarding mode analysis of structural vibration. The idea of a "mode' is, in essence, a mathematical one. It is highly unlikely that any real structure can vibrate exactly so that all its points move in unison; in other words, it is highly unlikely that any structure has any modes. As an approximation, however, the use of a mode is an excellent one for many structures, especially for the "lower modes'. The agreement between experiment and theory for the "higher modes' tends to become weaker. In this approximate sense, most structures have a very large number of modes. It is elementary to show, however, that no real structure has an infinite number of modes. The only utility of the "infinite modes' idea is within the purely mathematical domain. Many "error indices' can be defined as guidelines for structural modal order reduction. Simple modal truncation, although suggested by experience with slender rods, is naive. The proper process is mode selection, based on a appropriate error criterion.
The problem of potential instability caused by actuator dynamics is examined. Two ways of overcoming it are discussed: rate feedback with compensation and position feedback with tuning filters.