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NASA NTRS1987

Maneuvering and vibration control of flexible spacecraft

This paper is concerned with the problem of slewing a large structure in space and suppressing any vibration at the same time. The structure is assumed to undergo large rigid-body motions and small elastic deformations. A perturbation method permits a maneuver strategy independent of the vibration control. Optimal control and pole placement techniques, formulated to include first-order actuator dynamics, are used to suppress the vibration during maneuver. The theory is illustrated by simultaneous maneuvering and vibration control of the Spacecraft Control Laboratory Experiment (SCOLE) model in a space environment.

Meirovitch, L.↗

NASA NTRS1988

Synchronous response modelling and control of an annular momentum control device

Research on the synchronous response modelling and control of an advanced Annular Momentun Control Device (AMCD) used to control the attitude of a spacecraft is described. For the flexible rotor AMCD, two sources of synchronous vibrations were identified. One source, which corresponds to the mass unbalance problem of rigid rotors suspended in conventional bearings, is caused by measurement errors of the rotor center of mass position. The other sources of synchronous vibrations is misalignment between the hub and flywheel masses of the AMCD. Four different control algorithms were examined. These were lead-lag compensators that mimic conventional bearing dynamics, tracking notch filters used in the feedback loop, tracking differential-notch filters, and model-based compensators. The tracking differential-notch filters were shown to have a number of advantages over more conventional approaches for both rigid-body rotor applications and flexible rotor applications such as the AMCD. Hardware implementation schemes for the tracking differential-notch filter were investigated. A simple design was developed that can be implemented with analog multipliers and low bandwidth, digital hardware.

Hockney, Richard↗

NASA NTRS1982

The Development of a Handbook for Astrobee F Performance and Stability Analysis

An astrobee F performance and stability analysis is presented, for use by the NASA Sounding Rocket Division. The performance analysis provides information regarding altitude, mach number, dynamic pressure, and velocity as functions of time since launch. It is found that payload weight has the greatest effect on performance, and performance prediction accuracy was calculated to remain within 1%. In addition, to assure sufficient flight stability, a predicted rigid-body static margin of at least 8% of the total vehicle length is required. Finally, fin cant angle predictions are given in order to achieve a 2.5 cycle per second burnout roll rate, based on obtaining 75% of the steady roll rate. It is noted that this method can be used by flight performance engineers to create a similar handbook for any sounding rocket series.

Wolf, R. S.↗

NASA NTRS1986

Dynamics and Control of Flexible Spacecraft During and After Slewing Maneuvers

The dynamics and control of slewing maneuvers of a large flexible spacecraft, namely, NASA Spacecraft Control Laboratory Experiment (SCOLE) test article are studied. The dynamical equations obtained for slewing maneuvers are highly nonlinear and coupled. The maneuver is expressed in terms of four Euler parameters and is specified as the angular displacement about an arbitrary axis. The slew maneuver control problem is developed in terms of rigid-body slewing and suppression of two elastic modes is analyzed using the method of nonlinear decoupling.

Kakad, Y. P.↗

NASA NTRS1973

Aeroelastic analysis of sounding rocket vehicles.

Rigid-body stability analysis can be extended to treat aeroelastic effects by allowing the structure to deflect under airloads as a simple beam. Linear aerodynamics and the bent shape then define the airloads. The resulting equations are indeterminant but can be manipulated to show the basic aeroelastic effects of flexibility, dynamic pressure, and angle of attack. The FLMD quasi-static program can solve these equations by iteration and compute stability for a specific vehicle/payload combination. Given the proper distributed inputs for the instant of time investigated, the FLMD predicts the center of pressure and related parameters, such as static margin.

Meyers, S. C.↗

NASA NTRS1982

Semi-implicit transient analysis procedures for structural dynamics analysis

A semi-implicit direct time integration procedure is presented which avoids factorization of the implicit difference solution matrix. The procedure, if properly implemented, requires only vectorial calculations and hence needs the same computer core space as explicit integration procedures. Guidelines for splitting the stiffness matrix into upper and lower matrices are established, which among other things are designed to satisfy a correct transmission of rigid-body motions from element (or grid) to its adjacent elements.

Park, K. C.↗

NASA NTRS1988

Element-by-element and implicit-explicit finite element formulations for computational fluid dynamics

Preconditioner algorithms to reduce the computational effort in FEM analyses of large-scale fluid-dynamics problems are presented. A general model problem is constructed on the basis of the convection-diffusion equation and the two-dimensional vorticity/stream-function formulation of the Navier-Stokes equations; this problem is then analyzed using element-by-element, implicit-explicit, and adaptive implicit-explicit approximation schemes. Numerical results for the two-dimensional advection and rigid-body rotation of a cosine hill, flow past a circular cylinder, and driven cavity flow are presented in extensive graphs and shown to be in good agreement with those obtained using implicit methods.

Tezduyar, T. E.↗

NASA NTRS1981

Dynamic Moire Methods for Detection of Loosened Space Shuttle Tiles

Moire fringe methods for detecting loose space shuttle tiles were investigated with a test panel consisting of a loose tile surrounded by four securely bonded tiles. The test panel was excited from 20 to 150 Hz with in-plane sinusoidal acceleration of 2 g (peak). If the shuttle orbiter can be subjected to periodic excitation of 1 to 2 g (peak) and rigid-body periodic displacements do not mask the change in the Moire pattern due to tile looseness, then the use of projected Moire fringes to detect out-of-plane rockin appears to be the most viable indicator of tile looseness since no modifications to the tiles are required.

Snow, W. L.↗

NASA NTRS1984

Decoupled control analysis of a large flexible space antenna with linear quadratic regulator comparisons

A decoupled-control analysis was performed for a large flexible space antenna. Control involved commanding changes in the rigid-body modes or nulling disturbances in the flexible modes. The study provides parametric-type data which could be useful in the final design of a large space antenna control system. Results are presented to illustrate the effect on control requirements of (1) the number of modes controlled; (2) the number, type, and location of control actuators; and (3) variations in the closed-loop dynamics of the control system. Comparisons are given between the decoupled-control results and those obtained by using a linear quadratic regulator approach. Time history responses are presented to illustrate the effects of the control procedures.

Young, J. W.↗

NASA NTRS1986

Solving large-scale dynamic systems using band Lanczos method in Rockwell NASTRAN on CRAY X-MP

The improved cost effectiveness using better models, more accurate and faster algorithms and large scale computing offers more representative dynamic analyses. The band Lanczos eigen-solution method was implemented in Rockwell's version of 1984 COSMIC-released NASTRAN finite element structural analysis computer program to effectively solve for structural vibration modes including those of large complex systems exceeding 10,000 degrees of freedom. The Lanczos vectors were re-orthogonalized locally using the Lanczos Method and globally using the modified Gram-Schmidt method for sweeping rigid-body modes and previously generated modes and Lanczos vectors. The truncated band matrix was solved for vibration frequencies and mode shapes using Givens rotations. Numerical examples are included to demonstrate the cost effectiveness and accuracy of the method as implemented in ROCKWELL NASTRAN. The CRAY version is based on RPK's COSMIC/NASTRAN. The band Lanczos method was more reliable and accurate and converged faster than the single vector Lanczos Method. The band Lanczos method was comparable to the subspace iteration method which was a block version of the inverse power method. However, the subspace matrix tended to be fully populated in the case of subspace iteration and not as sparse as a band matrix.

Gupta, V. K.↗

NASA NTRS1976

Free-interface methods of substructure coupling for dynamic analysis

Benfield, et al. (1972) showed that among fixed-interface, free-interface, and hybrid substructure coupling methods, the fixed-interface methods as the most accurate and the free-interface methods are the least accurate. In the present note, a substructure coupling method is proposed which employs free-interface substructure modes supplemented by 'reduced flexibility.' Substructure coupling based on the improved substructure model is discussed, and a numerical comparison with Hou's free-interface method is given. To simplify representation of the method proposed, the substructure equations are developed first for constrained substructures, and then the equations representing substructures with rigid-body modes are given. Finally, the equations for coupling of substructures are derived. Example calculations are included.

Craig, R. R., Jr.↗

NASA NTRS1977

Solar sail attitude dynamics and control

This paper describes some results of an attitude dynamics and control study for a solar sailing vehicle. This type of vehicle is currently under study and evaluation at JPL and has very high potential for interplanetary missions in and beyond the 1980s. Crucial to the success of such a vehicle would be the performance of its onboard attitude control system. Because of the vehicle's large size and its flexibility, vehicle deformations may have a potential for causing a degradation in vehicle performance. It may therefore be necessary for the control system to take into account the vehicle deformations as well as its rigid-body motions. Distributed parameter system analysis techniques are used in the paper to study certain fundamental aspects of such a control system for the sail vehicle. The techniques can, however, be more generally applicable to other large flexible vehicles.

Rodriguez, G.↗

NASA NTRS1975

A generalized tensor formulation of atmosphere and seas dynamics

A generalized mathematical model was developed for simulation of the dynamics and transport of both the atmosphere and seas. A nearly horizontal bottom coordinate surface conforms to the land-to-air interface and the sea-floor-to-water interface, which simplifies computations. General vertical motion of the other quasi-horizontal coordinate surfaces is allowed; external gravity waves can be represented by the top coordinate surface, and meteorological fronts and inversion layers in the atmosphere and refractive layers in the seas can be represented with enhanced resolution by the internal quasi-horizontal coordinate surfaces. A tensor reformulation of the standard subgrid mixing theory departs significantly from the standard theory in allowing, as a solution under adiabatic conditions, rigid-body rotation of the atmosphere.

Avis, L. M.↗

NASA NTRS1972

Dynamic characteristics of a two-stage variable-mass flexible missile with internal flow

A general formulation of the dynamical problems associated with powered flight of a two stage flexible, variable-mass missile with internal flow, discrete masses, and aerodynamic forces is presented. The formulation comprises six ordinary differential equations for the rigid body motion, 3n ordinary differential equations for the n discrete masses and three partial differential equations with the appropriate boundary conditions for the elastic motion. This set of equations is modified to represent a single stage flexible, variable-mass missile with internal flow and aerodynamic forces. The rigid-body motion consists then of three translations and three rotations, whereas the elastic motion is defined by one longitudinal and two flexural displacements, the latter about two orthogonal transverse axes. The differential equations are nonlinear and, in addition, they possess time-dependent coefficients due to the mass variation.

Meirovitch, L.↗

NASA NTRS1977

Validation of a Flexible Aircraft TakeOff and Landing Analysis /FATOLA/ computer program using flight landing data

A multiple-degree-of-freedom takeoff and landing analysis, Flexible Aircraft TakeOff and Landing Analysis computer program (FATOLA), was used to predict the landing behavior of a rigid-body X-24B reentry research vehicle and of a flexible-body modified-delta-wing supersonic YF-12 research aircraft. The analytical predictions were compared with flight test data for both research vehicles. Predicted time histories of vehicle motion and attitude, landing-gear strut stroke, and axial force transmitted from the landing gear to the airframe during the landing impact and rollout compared well with the actual time histories. Based on the comparisons presented, the versatility and validity of the FATOLA program for predicting landing dynamics of aircraft has been demonstrated.

Carden, H. D.↗

NASA NTRS1987

Identifying Vibration Parameters in Large Structures

Analytical method separately examines low-frequency and highfrequency behavior. Report discusses techniques for identifying rigid-body parameters, flexible-body parameters, and quasi-static disturbances in large structures. Techniques developed to aid in planning space station. Though effort directed towards space station dynamic model and environment, proposed methodology for systems identification is generic enough to allow application to arbitrarily large space structures and spacecraft configurations.

Bayard, D. S.↗

NASA NTRS1988

Slewing and vibration control of the SCOLE

A discussion of Slewing and Vibration Control makes the following conclusions: (1) A 2-stage approach is feasible and promising for rapid slewing and precision pointing of SCOLE; (2) Not all bang-bang type of time-minimized slew maneuvers will excite large structural vibrations in SCOLE; and (3) Modal dashpots can be a concentrated high-power vibration control, as well as the usual diffuse (broadband, low-power (low-authority) control. The following recommendations are made: (1) Limit the magnitude of applied forces on reflector to either the 25-lb limit of vernier thrusters on the real Space Shuttle or the 150-lb level equivalent to the cold-gas jets of laboratory SCOLE; (2) to complete stage 2, add an integrated design of LQF/LTR (Linear-Quadratic-Gaussian/Loop-Transfer Recovery) and Modal Dashpots; and, (3) Validate the 2-stage approach using the SCOLE laboratory facility with a comprehensive sequence of integrated designs and experiments coupling nonlinear rigid-body motions with flexible-body dynamics.

Lin, Jiguan Gene↗

NASA NTRS1989

Explicit modeling and computational load distribution for concurrent processing simulation of the space station

Two important aspects of concurrent processing under development at TRW are discussed. These are: (1) the derivation of explicit mathematical models of multibody dynamic systems, and (2) a balanced computational load distribution (BCLD) among loosely coupled computational units (processors) of a concurrent processing system. The developed methodologies are demonstrated by way of an application to the Phase 1 of the Space Station - a task being performed by TRW under NASA/JSC contract NAS9-17778. The mathematical model of the Space Station consists of three interconnected flexible bodies capable of undergoing large, rigid-body motion with respect to each other. Body 1 is the main central body and contains the pressurized modules inboard of the two Alpha gimbals. Bodies 2 and 3 are the starboard and port bodies connected to Body 1 at the Alpha gimbals and include all components on the transverse booms outboard of the Alpha gimbals (including the solar arrays). The control systems in the model maintain Body 1 in a prescribed 3-axis attitude control mode, while producing large-angle rotations of the flexible solar arrays to position them normal to the sun-line.

Gluck, R.↗