Finite element appendange equations for hybrid coordinate dynamic analysis
Development of hybrid coordinate equations of motion for finite element model of flexible appendage attached to rigid base undergoing unrestricted motions
Likins, P. W.↗
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Stabilizing the elastic modes of the Space Shuttle vehicle during launch.
The influence of vibration modes on the vehicle control system stabilization problem is examined with a conventional, nonadaptive, single-rate-sensor autopilot. The linear stability analyses are based upon symmetric and antisymmetric modal data generated from flexible-beam models. Primary emphasis is placed upon using only the three orbiter engines as control effectors. Principal control system variables considered are the effective autopilot rate and attitude gains, rate and attitude sensor locations, and lead/lag stability compensation. Results indicate that a multiple-sensor autopilot configuration will be necessary to achieve satisfactory vibration mode stability margins.
Greiner, H. G.↗
Attitude control concepts for precision-pointing nonrigid spacecraft
Literal criteria are developed for the controllability and observability of general models of flexible spacecraft. Results are interpreted in special cases and in physical terms, permitting in some cases the identification of uncontrollable and unobservable states simply by examination of scalars composed of modal parameters and location matrices for sensors and actuators. A procedure is established for isolation of uncontrollable states, whereby sensor and actuator configurations assure that uncontrollable flexible mode states are also unobservable; in many applications such states can then be removed by coordinate truncation.
Likins, P. W.↗
A vector-dyadic development of the equations of motion for N-coupled flexible bodies and point masses
The equations of motion for a system of coupled flexible bodies, rigid bodies, point masses, and symmetric wheels were derived. The equations were cast into a partitioned matrix form in which certain partitions became nontrivial when the effects of flexibility were treated. The equations are shown to contract to the coupled rigid body equations or expand to the coupled flexible body equations all within the same basic framework. Furthermore, the coefficient matrix always has the computationally desirable property of symmetry. Making use of the derived equations, a comparison was made between the equations which described a flexible body model and those which described a rigid body model of the same elastic appendage attached to an arbitrary coupled body system. From the comparison, equivalence relations were developed which defined how the two modeling approaches described identical dynamic effects.
Frisch, H. P.↗
Rocket/launcher structural dynamics
The equations of motion describing the interactions between a rocket and a launcher were derived using Lagrange's Equation. A rocket launching was simulated. The motions of both the rocket and the launcher can be considered in detail. The model contains flexible elements and rigid elements. The rigid elements (masses) were judiciously utilized to simplify the derivation of the equations. The advantages of simultaneous shoe release were illustrated. Also, the loading history of the interstage structure of a boosted configuration was determined. The equations shown in this analysis could be used as a design tool during the modification of old launchers and the design of new launchers.
Ferragut, N. J.↗
Dynamic response and stability analysis of flexible, multibody systems
A general version of Lagrange's equations, including auxiliary nonholonomic, rheonomic conditions of constraint, is used in the dynamic simulation and stability analysis of interconnected flexible bodies. Modeling of the nonlinear flexible/rigid dynamic coupling effects, the interaction forces/torques, and the elastic deformation effects is discussed. A digital computer program is developed to obtain time-domain solution for the nonlinear response of systems represented as a collection of individual bodies, numerical linearization of system-governing equations, time-domain solution for the perturbation response about a nominal state, and a frequency-domain stability analysis corresponding to the linearization. The digital simulation code is employed to study the dynamic behavior of a typical satellite and a spacecraft with deployable experiment booms.
Bodley, C. S.↗
The use of parametric cost estimating relationships for transport aircraft systems in establishing initial Design to Cost Targets
This paper provides a brief overview of Design to Cost (DTC). Problems inherent in attempting to estimate costs are discussed, along with techniques and types of models that have been developed to estimate aircraft costs. A set of cost estimating relationships that estimate the total production cost of commercial and military transport aircraft at the systems level is presented and the manner in which these equations might be used effectively in developing initial DTC targets is indicated. The principal point made in this paper is that, by using a disagregated set of equations to estimate transport aircraft costs at the systems level, reasonably accurate preliminary cost estimates may be achieved. These estimates may serve directly as initial DTC targets, or adjustments may be made to the estimates obtained for some of the systems to estimate the production cost impact of alternative designs or manufacturing technologies. The relative ease by which estimates may be made with this model, the flexibility it provides by being disaggregated, and the accuracy of the estimates it provides make it a unique and useful tool in establishing initial DTC targets.
Beltramo, M. N.↗
SPS antenna pointing control
The pointing control of a microwave antenna of the Satellite Power System was investigated emphasizing: (1) the SPS antenna pointing error sensing method; (2) a rigid body pointing control design; and (3) approaches for modeling the flexible body characteristics of the solar collector. Accuracy requirements for the antenna pointing control consist of a mechanical pointing control accuracy of three arc-minutes and an electronic phased array pointing accuracy of three arc-seconds. Results based on the factors considered in current analysis, show that the three arc-minute overall pointing control accuracy can be achieved in practice.
Hung, J. C.↗
Video distribution system cost model
A cost model that can be used to systematically identify the costs of procuring and operating satellite linked communications systems is described. The user defines a network configuration by specifying the location of each participating site, the interconnection requirements, and the transmission paths available for the uplink (studio to satellite), downlink (satellite to audience), and voice talkback (between audience and studio) segments of the network. The model uses this information to calculate the least expensive signal distribution path for each participating site. Cost estimates are broken downy by capital, installation, lease, operations and maintenance. The design of the model permits flexibility in specifying network and cost structure.
Gershkoff, I.↗
Controllability and observability for flexible spacecraft
Current interest in extended sensing and actuation for the control of flexible spacecraft has led to the use of modern multivariable control theory and the associated concepts of controllability and observability. This paper shows how to evaluate these properties on a mode-by-mode basis for flexible spacecraft control analysis. Relatively simple criteria are derived which indicate the degree of controllability (observability) of each mode in simple literal terms. These criteria provide physical insight and practical guidance on the type, number, and positioning of sensors and actuators. The results are interpreted for force and torque actuators, and for attitude and deformation measurements. To illustrate these ideas, sample controllability and observability 'surfaces' are presented for the Purdue generic flexible spacecraft model.
Hughes, P. C.↗
Structural concept trends for commercial supersonic cruise aircraft design
Structural concept trends for future commercial supersonic transport aircraft are considered. Highlights, including the more important design conditions and requirements, of two studies are discussed. Knowledge of these design parameters, as determined through studies involving the application of flexible mathematical models, enabled inclusion of aeroelastic considerations in the structural-material concepts evaluation. The design trends and weight data of the previous contractual study of Mach 2.7 cruise aircraft were used as the basis for incorporating advanced materials and manufacturing approaches to the airframe for reduced weight and cost. Structural studies of design concepts employing advanced aluminum alloys, advanced composites, and advanced titanium alloy and manufacturing techniques are compared for a Mach 2.0 arrow-wing configuration concept. Appraisals of the impact of these new materials and manufacturing concepts to the airframe design are shown and compared. The research and development to validate the potential sources of weight and cost reduction identified as necessary to attain a viable advanced commercial supersonic transport are discussed.
Sakat, I. F.↗
An approach to simulation of the finite element machine
The paper describes the simulation approach for the finite element machine (FEM), a special-purpose computer for structural analysis calculations under development at the NASA-Langley Research Center. The FEM consists of an array (1000 or more) of general-purpose microcomputers performing structural analysis in an asychronous parallel manner. A simulator of sufficient flexibility to model the behavior of the FEM on many levels has been designed and coded, and verification has begun using the experimental FEM hardware. The structure of the simulator is described, and preliminary simulation results are presented.
Sawyer, P. L.↗
Control technology development
The main objectives of the control technology development task are given in the slide below. The first is to develop control design techniques based on flexible structural models, rather than simple rigid-body models. Since large space structures are distributed parameter systems, a new degree of freedom, that of sensor/actuator placement, may be exercised for improving control system performance. Another characteristic of large space structures is numerous oscillatory modes within the control bandwidth. Reduced-order controller design models must be developed which produce stable closed-loop systems when combined with the full-order system. Since the date of an actual large-space-structure flight is rapidly approaching, it is vitally important that theoretical developments are tested in actual hardware. Experimental verification is a vital counterpart of all current theoretical developments.
Schaechter, D. B.↗
Dynamics and control of a Shuttle attached antenna experiment
Study results obtained to date identify the requirements for a large space system flight experiment. This paper considers the dynamics and control of an offset feed wrap-rib antenna attached to the Shuttle for such an experiment. Results reported in this paper are primarily based on the analysis and simulation of the combined Shuttle and antenna flexible dynamics model, and the Shuttle Vernier Reaction Control Subsystem. These results establish the technical feasibility of the Shuttle attached antenna flight experiment. Static and dynamic disturbances examined do not cause significant dynamic interactions to the experiment. Shuttle Vernier jets can be used for control purpose or as controlled excitation sources for experiment. Interface between the Shuttle and the antenna can be rigid or actively decoupled depending on the experiment objective. Key large space systems control technologies such as distributed sensing and actuation, system identification, figure estimation and control, and control for slew or reconfiguration can be validated with the experiment configuration described in this paper.
Wang, S. J.↗
Theoretical Thermodynamics of Mixtures at High Pressures
The development of an understanding of the chemistry of mixtures of metallic hydrogen and abundant, higher-z material such as oxygen, carbon, etc., is important for understanding of fundamental processes of energy release, differentiation, and development of atmospheric abundances in the Jovian planets. It provides a significant theoretical base for the interpretation of atmospheric elemental abundances to be provided by atmospheric entry probes in coming years. Significant differences are found when non-perturbative approaches such as Thomas-Fermi-Dirac (TFD) theory are used. Mapping of the phase diagrams of such binary mixtures in the pressure range from approx. 10 Mbar to approx. 1000 Mbar, using results from three-dimensional TFD calculations is undertaken. Derivation of a general and flexible thermodynamic model for such binary mixtures in the relevant pressure range was facilitated by the following breakthrough: there exists an accurate nd fairly simple thermodynamic representation of a liquid two-component plasma (TCP) in which the Helmholtz free energy is represented as a suitable linear combination of terms dependent only on density and terms which depend only on the ion coupling parameter. It is found that the crystal energies of mixtures of H-He, H-C, and H-O can be satisfactorily reproduced by the same type of model, except that an effective, density-dependent ionic charge must be used in place of the actual total ionic charge.
Hubbard, W. B.↗
Approximation of Optimal Infinite Dimensional Compensators for Flexible Structures
The infinite dimensional compensator for a large class of flexible structures, modeled as distributed systems are discussed, as well as an approximation scheme for designing finite dimensional compensators to approximate the infinite dimensional compensator. The approximation scheme is applied to develop a compensator for a space antenna model based on wrap-rib antennas being built currently. While the present model has been simplified, it retains the salient features of rigid body modes and several distributed components of different characteristics. The control and estimator gains are represented by functional gains, which provide graphical representations of the control and estimator laws. These functional gains also indicate the convergence of the finite dimensional compensators and show which modes the optimal compensator ignores.
Gibson, J. S.↗
Computing Benefits and Costs for Propulsion Systems
Flexible computer model developed for evaluating benefits and costs of placing large space systems into operational orbits. Model contains performance envelopes of three primary propulsion systems for orbit transfer based on three low-thrust engines. Allows for any mission model to be input into program. Model also allows user to easily vary program to examine effects of various ratings and weighting of benefit parameters for baseline engines. Program written in FORTRAN IV for use on IBM 370 computer.
Hamlyn, K.↗
Fault-tolerant control of large space structures using the stable factorization approach
Large space structures are characterized by the following features: they are in general infinite-dimensional systems, and have large numbers of undamped or lightly damped poles. Any attempt to apply linear control theory to large space structures must therefore take into account these features. Phase I consisted of an attempt to apply the recently developed Stable Factorization (SF) design philosophy to problems of large space structures, with particular attention to the aspects of robustness and fault tolerance. The final report on the Phase I effort consists of four sections, each devoted to one task. The first three sections report theoretical results, while the last consists of a design example. Significant results were obtained in all four tasks of the project. More specifically, an innovative approach to order reduction was obtained, stabilizing controller structures for plants with an infinite number of unstable poles were determined under some conditions, conditions for simultaneous stabilizability of an infinite number of plants were explored, and a fault tolerance controller design that stabilizes a flexible structure model was obtained which is robust against one failure condition.
Razavi, H. C.↗