Modelling of a flexible satellite motion

S.Ye.Somov

Samara State Aerospace University named after acad. S.P. Korolev

34 Moskovskoye Shosse, Samara, 443086, Russia

For large-scale spacecraft (SC) the structure oscillations can render an essential influence on its spatial motion, it is especially for an initial mode after separation from a launcher. Modern computer technology allows to obtain a dynamic analysis and a video-display the spacecraft structure elements' deformations during the SC spatial motion. That it is very useful at designing and spacecraft flight support. In the paper the developed software for simulation and animation of a flexible spacecraft angular motion, is briefly presented. Communication satellite SESAT (Siberia Europe SATellite) with large-scale flexible solar array panels (SAPs) was developed by Research and Production Association of Applied Mechanics (NPO PM) named after acad. M.F. Reshetnev under the contract with European organization Eutelsat љand љwas removed љon љgeostationary orbit in April 2000. For this spacecraft necessary models of spatial motion are created at pulse-width modulation of control by jet engines and the SAPs' bend-turning oscillations, results of animation both the SC body and the SAPs motion are presented in the paper.

A lot of publications were devoted for a choice of dynamic schemes, methods for deriving and research the deformable SC motion equations, but the problem of development the effective methods and algorithms for modeling dynamics and imitation of the SC motion is remained actual. At deriving the approximate models of the flexible SC motion the Reley-Ritz-Galerkin method is most applied. In tasks of synthesis the SC dynamic models with non-rigid structure the method of fixed elements (MFE) is widely applied. Peculiarity of the applied approach consists in presentation of the structure elements' flexible oscillations by fixed number of tones.љ Moreover, calculation of the oscillation forms is carried out by the MFE with condensation (reduction) on the oscillation tones, the factor matrixes of interference for motions of all sub-structure are also calculated by computer.

Models of the attitude control system's љcomponents are presented - the orientation engine unit on the basis of six thermo-catalytic jet engines with width-pulse modulation of the thrust, a block of three one-axial angular rate sensors, the step-by-step gear driver and an angular position sensor by two SAPs' wings with respect to the SC body.

After branch a SC from accelerating block and disclosing the SAPs, at initial time moment the angular rate vector accepts some value from the limited convex area. Then the SC angular rate vector is determined which should be reached with the given accuracy for some acceptable duration of the damping mode. Requirement for performance of this mode for spacecraft such as Sesat consists in a simultaneous turning the flexible SAPs on the angle љconcerning the SC body. Thus, the SC tensor inertia and the torque vector of inertia-gyroscopic forces are change.

Linearized with respect to a rest position in inertial reference frame the continuous model of free (without the external torques) SC controlled motion in damping mode at fixed the SAPs position have been introduced. For constructing the logarithmic frequency characteristics of continuous controlled object the specialized algorithms based on Wilkinson QR-algorithm with Hesenberg reduction top form and Rosenbrok algorithm, are used. Analysis of the obtained results testifies to essential change of the logarithmic frequency characteristics on a yaw љand a roll љchannels depending on the SAPs position for all tones, and insignificant dependence the logarithmic frequency characteristics of the SC on pitch channel from the SAPs position for first two tones of their flexible oscillations. Such frequency analysis have allowed to obtain the necessary information for correct computer imitation and animation of the flexible spacecraft motion.

Imitation of the SC motion in Matlab environment is based on the elaborated models. Results of numerical imitation are displayed both in graphic windows and in 3 files - deviations of the SAPs' wings on tones of flexible oscillations and the SC body orientation quaternion. The basic dialogue window of the imitation environment for the flexible SC motion is presented. The analysis of the spacecraft dynamics in damping mode for various variants of initial conditions on coordinates by tones of oscillations was carried out, some results are presented in the paper.

Russian software environment Super Vision (SVN) - the NPO PM development was applied for animation of motion by the SC with flexible active SAPs. In used version of this software the requirement specification is applied for creation and tuning the reflected objects. Here the data loader carries out the important role. It is intended for loading, bufferization and distribution of data on requirements from any graphic and animation objects. At loading the data are "in-buffered" in individual file on the computer local disk and then their "up-pumping" is carried out for graphic reflection. The animation data are "in-buffered" directly in the computer operative memory.

Interface between components of the elaborated software complex for modeling and visualization of the SC flexible structure is carried out by files on hard disk. In first stage the SC damping mode modeling is fulfilled. Results of the subsystem work are graphics of the transient processes and the data files which are recorded on hard disk. In second stage the data preparation is carried out for reflection of the flexible SAPs' oscillations into the environment of visualization system SVN. Moreover in the Matlab environment the program Forsvm is up-running, besides that љfrom the disk there are read the files of forms on first 3 oscillation tones and a file which contains coordinates of the SAPs' main points. In result the file xyz.txt is appeared which contains the current coordinates of the SAPs' main points in the SAPs' reference frame verses a time.

The SVN environment have two tuning files: panel.svn and mnk.svn. In case of load the file panel.svn there will be reflected љthe SAPs' wing oscillations, and in case of load mnk.svn - the SC body motion.љ For reflection the SAPs' oscillations there are applied the data file xyz.txt, and for reflection of the SC body motion - the file mnk.txt. Indicated files are the text tables. The program have the line passing opportunity for variation of a reproduction speed by the motion process љon the display screen. At passing over in silence the file lines follow over 0.04 sec, that gives the image reproduction in real time - 25 frames (lines) per second if computer have enough efficiency. The animation frames of the SC attitude motion and the SAPs' turn-bend oscillations at the SC damping are presented in the paper.