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Gain determination from dynamic /on line/ solutions to Riccati equation for model reference adaptive control applicable to multiple input/ output or stochastic systems
The effects of a pulse shape on the transient response of a cylindrical shell are presented. Uniaxial, membrane, and bending theories for isotropic shells were used in this study. In addition to the results of the analytical study, the preliminary results of an experimental study into the generation and measurement of shear waves in a cylindrical shell are included.
Efficient computation of natural frequencies and associated free vibration modes of spinning flexible structures is required to accurately determine the nature of interaction between the flexible structure and the attitude control system, which is vital in relating control torques to attitude angles. While structural discretization is effected by the finite element method, the resulting eigenvalue problem is solved by a combined Sturm sequence and inverse iteration procedure that yields a few specified roots and associated vectors. An eigenvalue procedure, based on a simultaneous iteration technique, provides efficient computation of the first few roots and vectors; a modal synthesis procedure proves to be useful for eigenproblem solutions of unusual structures such as spacecraft.
The application of NASTRAN to design studies of two very large-area lightweight structures is described. The first is the Satellite Solar Power Station, while the second is a deployable three hundred meter diameter antenna. A brief discussion of the operation of the SSPS is given, followed by a description of the structure. The use of the NASTRAN program for static, vibration and thermal analysis is illustrated and some results are given. Next, the deployable antenna is discussed and the use of NASTRAN for static analysis, buckling analysis and vibration analysis is detailed.
Efficient computation of natural frequencies and associated free vibration modes of spinning flexible structures is required to accurately determine the nature of interaction between the flexible structure and the attitude control system, which is vital in relating control torques to attitude angles. While structural discretization is effected by the finite element method, the resulting eigenvalue problem is solved by a combined Sturm sequence and inverse iteration procedure that yields a few specified roots and associated vectors. An eigenvalue procedure, based on a simultaneous iteration technique, provides efficient computation of the first few roots and vectors; a modal synthesis procedure proves to be useful for eigenproblem solutions of unusual structures such as spacecraft.
Attitude control techniques for the pointing and stabilization of very large, inherently flexible spacecraft systems were investigated. The attitude dynamics and control of a long, homogeneous flexible beam whose center of mass is assumed to follow a circular orbit was analyzed. First order effects of gravity gradient were included. A mathematical model which describes the system rotations and deflections within the orbital plane was developed by treating the beam as a number of discretized mass particles connected by massless, elastic structural elements. The uncontrolled dynamics of the system are simulated and, in addition, the effects of the control devices were considered. The concept of distributed modal control, which provides a means for controlling a system mode independently of all other modes, was examined. The effect of varying the number of modes in the model as well as the number and location of the control devices were also considered.
The equations of motion of an arbitrary flexible body in orbit were derived. The model includes the effects of gravity with all its higher harmonics. As a specific example, the motion of a long, slender, uniform beam in circular orbit was modelled. The example considers both the inplane and three dimensional motion of the beam in orbit. In the case of planar motion with only flexible vibrations, the pitch motion is not influenced by the elastic motion of the beam. For large values of the square of the ratio of the structural modal frequency to the orbital angular rate the elastic motion was decoupled from the pitch motion. However, for small values of the ratio and small amplitude pitch motion, the elastic motion was governed by a Hill's 3 term equation. Numerical simulation of the equation indicates the possibilities of instability for very low values of the square of the ratio of the modal frequency to the orbit angular rate. Also numerical simulations of the first order nonlinear equations of motion for a long flexible beam in orbit were performed. The effect of varying the initial conditions and the number of modes was demonstrated.
Polyimide membranes of a thickness range from under 0.01 micron m to greater than 1 micron m can be produced at an estimated cost of 50 cents per sq m (plus the cost of the polymer). The polymer of interest is dissolved in a solvent which is solube in water. The polymer or casting solution is allowed to flow down an inclined ramp onto a water surface where a pool of floating polymer develops. The solvent dissolves into the water lowering the surface tension of the water on equently, the contact angle of the polymer pool is very low and the edge of the pool is very thin. The solvent dissolves from this thin region too rapidly to be replenished from the bulk of the pool and a solid polymer film forms. Firm formation is rapid and spontaneous and the film spreads out unaided, many feet from the leading edge of the pool. The driving force for this process is the exothermic solution of the organic solvent from the polymer solution into the water.
A mathematical and computational analysis capability has been developed for calculating the effective mechanical properties of three-dimensional periodic truss-like structures. Two models are studied in detail. The first, called the octetruss model, is a three-dimensional extension of a two-dimensional model, and the second is a cubic model. Symmetry considerations are employed as a first step to show that the specific octetruss model has four independent constants and that the cubic model has two. The actual values of these constants are determined by averaging the contributions of each rod element to the overall structure stiffness. The individual rod member contribution to the overall stiffness is obtained by a three-dimensional coordinate transformation. The analysis shows that the effective three-dimensional elastic properties of both models are relatively close to each other.
The status of Langley Research Center development of the nestable column concept is reviewed including results of member and truss component tests, and planned assembly studies. In addition, more recent studies of alternative member concepts are presented. Preliminary results on relative efficiency of several types of truss-type columns are compared and future test plans discussed.
The composite material beam builder which will produce triangular beams from pre-consolidated graphite/glass/thermoplastic composite material through automated mechanical processes is presented, side member storage, feed and positioning, ultrasonic welding, and beam cutoff are formed. Each process lends itself to modular subsystem development. Initial development is concentrated on the key processes for roll forming and ultrasonic welding composite thermoplastic materials. The construction and test of an experimental roll forming machine and ultrasonic welding process control techniques are described.
The application of geometrical schemes to large sphere antenna reflectors was investigated. The purpose of these studies is to determine the shape and size of flat segmented surfaces which approximate general shells of revolution and in particular spherical and paraboloidal reflective surfaces. The extensive mathematical and computational geometry analyses of the reflector resulted in the development of a general purpose computer program. This program is capable of generating the complete design parameters of the dish and can meet stringent accuracy requirements. The computer program also includes a graphical self contained subroutine which graphically displays the required design.
The equations of planar motion for a flexible beam in orbit which includes the effects of gravity gradient torques and control torques from point actuators located along the beam was developed. Two classes of theorems are applied to the linearized form of these equations to establish necessary conditions for controlability for preselected actuator configurations. The feedback gains are selected: (1) based on the decoupling of the original coordinates and to obtain proper damping, and (2) by applying the linear regulator problem to the individual model coordinates separately. The linear control laws obtained using both techniques were evaluated by numerical integration of the nonlinear system equations. Numerical examples considering pitch and various number of modes with different combination of actuator numbers and locations are presented. The independent model control concept used earlier with a discretized model of the thin beam in orbit was reviewed for the case where the number of actuators is less than the number of modes. Results indicate that although the system is controllable it is not stable about the nominal (local vertical) orientation when the control is based on modal decoupling. An alternate control law not based on modal decoupling ensures stability of all the modes.
There is a need for means to construct large complex structures without having to spend a large amount of time for assembly. One approach to meeting this requirement is to erect the overall structure using highly efficient structural modules. The individual modules can then be packaged for launch, so as to utilize the volume of the Shuttle properly, and then expanded in orbit. The present paper describes several types of such modules that have been designed and tested.
Structural members that might be suitable for strain energy deployable structures, are discussed with emphasis on a thin-walled cylindrical tube with a cross-section that is called 'bi-convex'. The design of bi-convex tube test specimens and their fabrication are described as well as the design and construction of a special purpose testing machine to determine the deployment characteristics. The results of the first series of tests were quite mixed, but clearly revealed that since most of the specimens failed to deploy completely, due to a buckling problem, this type of tube requires some modification in order to be viable.
A mechanical attachment adapter was designed, constructed, and tested. The adapter was was included in a simulation program that investigated techniques for assembling erectable structures under simulated zero-g conditions by pressure-suited subjects in a simulated EVA mode. The adapter was utilized as an interface attachment between a simulated equipment module and one node point of a tetrahedral structural cell. The mating performance of the adapter, a self-energized mechanism, was easily and quickly demonstrated and required little effort on the part of the test subjects.
Assembly techniques and hardware configurations used in assembly of the basic tetrahedral cell by A7LB pressure-suited subjects in a neutral bouyancy simulator were studied. Eleven subjects participated in assembly procedures which investigated two types of structural members and two configurations of attachment hardware. The assembly was accomplished through extra-vehicular activity (EVA) only, EVA with simulated manned maneuvering unit (MMU), and EVA with simulated MMU and simulated remote manipulator system (RMS). Assembly times as low as 10.20 minutes per tetrahedron were achieved. Task element data, as well as assembly procedures, are included.
The dynamics, attitude, and shape control of a large thin flexible square platform in orbit are studied. Attitude and shape control are assumed to result from actuators placed perpendicular to the main surface and one edge and their effect on the rigid body and elastic modes is modelled to first order. The equations of motion are linearized about three different nominal orientations: (1) the platform following the local vertical with its major surface perpendicular to the orbital plane; (2) the platform following the local horizontal with its major surface normal to the local vertical; and (3) the platform following the local vertical with its major surface perpendicular to the orbit normal. The stability of the uncontrolled system is investigated analytically. Once controllability is established for a set of actuator locations, control law development is based on decoupling, pole placement, and linear optimal control theory. Frequencies and elastic modal shape functions are obtained using a finite element computer algorithm, two different approximate analytical methods, and the results of the three methods compared.