Engineering topics
Publications and source records attributed to Das, A..
Action planning in robot automated operations requires intelligent task level programming. Invoking intelligence necessiates a typical blackboard based architecture, where, a plan is a vector between the start frame and the goal frame. This vector is composed of partially ordered bases. A partial ordering of bases presents good and bad sides in action planning. Partial ordering demands the use of a temporal data base management system.
A number of future DOD and NASA spacecraft such as the space based radar will be not only an order of magnitude larger in dimension than the current spacecraft, but will exhibit extreme structural flexibility with very low structural vibration frequencies. Another class of spacecraft (such as the space defense platforms) will combine large physical size with extremely precise pointing requirement. Such problems require a total departure from the traditional methods of modeling and control system design of spacecraft where structural flexibility is treated as a secondary effect. With these problems in mind, the Air Force Rocket Propulsion Laboratory (AFRPL) initiated research to develop dynamics and control technology so as to enable the future large space structures (LSS). AFRPL's effort in this area can be subdivided into the following three overlapping areas: (1) ground experiments, (2) spacecraft modeling and control, and (3) sensors and actuators. Both the in-house and contractual efforts of the AFRPL in LSS are summarized.
Requirements indicate the need for much larger, more accurate, and in some cases, very dynamic satellites. Large control system bandwidths are needed to meet accuracy and response requirements while maintaining tight control over appendage oscillations. Studies in recent years have shown that linear quadratic Gaussian (LQG) controllers can achieve the desired performance if the system is linearized and if the system model is accurate. Results of an LQG controller applied to a single axis satellite with large solar arrays, are given. A reduced order model (ROM) comprises rigid body motion with dominant structural modes. Optimal control and estimation gains are calculated based on an extremely conservative 0.0005 critical damping ratio. In order to examine stability characteristics, single-input single-output (SISO) frequency response concepts are generalized to develop a method of displaying open loop frequency response of multi-input multi-output (MIMO) control system.
A numerical study was performed on the effects of stochastic geometry and random environmental torques on the pointing accuracy of spinning and three-axis stabilized satellites. The Euler equations for the motions of satellites yielded the stochastic principal moments and a Fokker-Planck analog simulation was employed to model the response vector of a rigid satellite. White noise inputs were obtained from a random number generator. Attention was given to both fast and slow spin satellites. Responses grew with time in all cases. The growth was initially exponential and eventually reached stable values. In comparison with other theoretical techniques, the Fokker-Planck model detailed the most responses and showed that spin-stabilization is preferable for satellites with low inertial noise levels.
A unified method is presented for deriving the influence functions of moving singularities which determine the field quantities in aerodynamics and aeroacoustics. The moving singularities comprise volume and surface distributions having arbitrary orientations in space and to the trajectory. Hence one generally valid formula for the influence functions which reveal some universal relationships and remarkable properties in the disturbance fields. The derivations used are completely consistent with the physical processes in the propagation field, such that treatment renders new descriptions for some standard concepts. The treatment is uniformly valid for subsonic and supersonic Mach numbers.
The present investigation is concerned with the effects of stochastic geometry and random environmental torques on the pointing accuracy of spinning and three-axis stabilized satellites. The study of pointing accuracies requires a knowledge of the rates of error growth over and above any criteria for the asymptotic stability of the satellites. For this reason the investigation is oriented toward the determination of the statistical properties of the responses of the satellites. The geometries of the satellites are considered stochastic so as to have a phenomenological model of the motions of the flexible structural elements of the satellites. A widely used method of solving stochastic equations is the Fokker-Planck approach where the equations are assumed to define a Markoff process and the transition probability densities of the responses are computed directly as a function of time. The Fokker-Planck formulation is used to analyze the response vector of a rigid satellite.
Simplified models of the vortex distribution over cylindrical surfaces are developed. The effect of a change of vortex strength was analyzed quantitatively by menas of potential theory. The considerable bulging of the cylindrical vortex sheet as a consequence of the change of the vortex strength is discussed. The coiling-up of the vortices rotation in opposite directions over the cylindrical surface renders the condition for instability and the subsequent large spreading of the vortex core. These processes occur without a positive pressure gradient being necessary in the field of flow surrounding the coiled up vortex sheet.
It is demonstrated that by monitoring the deformations of the flexible elements of a satellite, the effectiveness of the satellite control system can be increased considerably. A simple model of a flexible satellite was analyzed in the first part of this work. The same model is used here for digital computer simulations.
Force equations of motion of the individual flexible elements of a satellite were obtained in a previous paper. Moment equations of motion of the composite bodies of a flexible satellite are to be developed using two sets of equations which form the basic system for any dynamic model of flexible satellites. This basic system consists of a set of N-coupled, nonlinear, ordinary, or partial differential equations, for a flexible satellite with n generalized, structural position coordinates. For single composite body satellites, N is equal to (n + 3); for dual-spin systems, N is equal to (n + 9). These equations involve time derivatives up to the second order. The study shows a method of avoiding this linearization by reducing the N equations to 3 or 9 nonlinear, coupled, first order, ordinary, differential equations involving only the angular velocities of the composite bodies. The solutions for these angular velocities lead to linear equations in the n generalized structural position coordinates, which can be solved by known methods.
This investigation has two distinct parts. In this first part the environmental and control torques experienced by a satellite are assumed to be random so as to account for the inherent errors in the control systems and the lack of exact models of the environmental torques. It has been shown that under this assumption the required stability criteria of a satellite is quite different from that obtained by a deterministic approach. It has also been shown that a flexible three-axes stabilized satellite can be made almost certainly asymptotically stable, while the same is not true for a flexible spinning satellite.
A singular perturbation formulation is used to study the responses of a flexible satellite when random measurement errors can occur. The random variables, at different instants of time, are assumed to be uncorrelated. Procedures for obtaining maxima and minima are described, and a variation of the linear method is developed for the formal solution of the two-point boundary-value problems represented by the variational equations. Random and deterministic solutions for the structural position coordinates are studied, and an analytic algorithm for treating the force equation of motion is developed. Since the random system indicated by the variational equation will always be asymptotically unstable, any analysis of stability must be based on the deterministic system.
The analytical models for flexible satellites have been reported earlier. Numerical results comparing the pointing accuracy of three-axes stabilized, spinning, and dual-spin satellites are presented here. The responses are compared for deterministic and random models with and without external torques. The performances of a uniform control system have been compared to a time-optimal control system for the same base-line configurations.
Techniques for measuring attitude deviations in the Nimbus 6 and Nimbus G 3-axis stabilized, zero-momentum, earth observation satellites are presented. The on-orbit telemetered data include scanner roll and pitch error signals, an illuminated DSAS which can read the azimuth and elevation of the sunline when the spacecraft is not in the umbra, the signal from the single gyro in the RMP, and the momenta of the reaction wheels. Mathematical methods for interpreting the measured data are described with attention to filter equations, especially the Kalman filter because of its ability to eliminate high frequency noise.
The article reviews research on pointing accuracies of flexible satellites with regard to derived equations of motion of individual elements and composite bodies. The solution of these equations may be achieved through the formulation of a set of singularly perturbed equations by eliminating the generalized position vector. These equations are generally solved by a method of asymptotic expansions if certain convergence criteria are satisfied. The analysis may be applied to dual-spin flexible satellites.
The formulation and existence of a generalized force in the singularly perturbed formulation of flexible satellites is described. The concept of this force sharply reduces the number of degrees of freedom and the equations of motion of satellites with a large number of flexible elements. The force is analyzed to demonstrate its existence and convergence criteria. The complete solution has been obtained in three time zones - the inner boundary layer, the outer boundary layer, and the large time extending beyond these boundary layers. A stability criterion is proposed for this generalized force.
Models of thermally induced flutter of the flexible elements of a satellite, such as beams, circular plates, and cylindrical shells, have been obtained. These models form the necessary blocks for analyzing the motion of satellites. The heat input is considered to be caused by solar radiation. The partial differential equations for all the elements of the satellite are linear in the space-dependent variables and nonlinear in the time-dependent variables. These equations are coupled through the motion of the center of mass of the satellite. Galerkin's method has been used to remove the space-dependence of these equations.
A modification of optimal spinning satellite control theory is proposed, based on introducing an additional vector into the equation for control torque components. This modification essentially means that the amplitudes of the time-dependent satellite perturbation functions can be made small when the amplitudes of the control torque components are allowed to be different. An algorithm for computer simulation of the satellite control theory is provided. A singular perturbation scheme is used which greatly reduces the number of degrees of freedom in the flexible satellite motion equations.
The results of a study on the application of the magnetically anchored rate damper to gravity gradient stabilization of the Long Duration Exposure Facility (LDEF) are presented. The analyses and simulations required to investigate the use of an existing viscous magnetic rate damper for rate stabilizing the LDEF spacecraft were performed. The following tasks were included: linear performance estimates, capture and damper requirements, and performance prediction. Each of these tasks was performed for two gravity gradient stabilization configurations; an axisymmetric configuration for two-axis (pitch and roll) stability; and a non-axisymmetric configuration for three-axis stability. The results are presented by stabilization configuration.