Effect of Structure Flexibility on Attitude Dynamics of Modernizated Microsatellite

Research Objectives and Tasks
Micro satellite Configuration
Reference frames
Mathematical Models of flexible space structures
Major Findings and Results
Recommendations for Future Research
Overview

The major objective of this research is to study the effect of structure flexibility on attitude behavior (Euler angles and angular velocities ) of micro satellites and the degree of such effect
Research Objectives and Tasks

The research objectives and tasks of this study are as follows :
Develop mathematical models of flexible space structures
Determine the attitude accuracy
Research Objectives and Tasks

The construction of micro satellite can consist of main parts: base plate, mounting plate, walls, blocks and the payloads.
Each part and subpart of this construction will be replaced by the equivalent solid mass and moment of inertia with respect to the real construction.
Micro Satellite Configuration

Micro Satellite Configuration

Micro Satellite Configuration

Reference Frames
Inertial coordinate system (ICS)
Orbital coordinate system (OCS)
Design coordinate system (DCS)
Body axes system (BAS)

Mathematical Models of Flexible Space Structures
A mathematical model of the satellite takes into account flexible body components (solar panels, antennas, booms etc…);
This kind of modelling consists of two parts one related to rigid body motion and the other to flexible body motion.

Mathematical Models Of Flexible Space Structures
Two kind of software will be used ANSYS and MATLAB;
ANSYS software will be used to calculate the modal analysis (natural frequencies and mode shapes) ;
MATLAB software will be used to integrate the system of equations .

Mathematical Models Of Flexible Space Structures
Finite Element Model :

Mathematical Models Of Flexible Space Structures
The dynamic equations of motion around center of mass taken into account the elastic oscillations of a housing of satellite and solar panels can be written in the following form :

The calculation of flexible modes elements (Gαi) are usually determined by the following way in BAS :
ρb : is a radius vector that connects satellite COM to any arbitrary point of the satellite construction;
Uαi : is a vector to describe the mode shape.
Mathematical Models Of Flexible Space Structures

Mathematical Models Of Flexible Space Structures
Lines of micro satellite used for representing flexible elements.

Mathematical Models Of Flexible Space Structures
The satellite kinematics equations will be in the following form :
ωbo : is the satellite body angular velocity with respect to the OCS;
θ, φ,ψ : are EULER angles pitch, roll and yaw respectively.

Finding and Major Results
Average values for frequencies (fi) for the first six tones groups are equal to: 14; 26.7; 65.5; 86.9; 90.2; 113 Hz respectively;
It is noted that the first five tones groups is related to the solar panels of the satellite and at the group tone number six is for the housing.

Finding and Major Results
Micro satellite solar panels 2nd tones groups.
26.85
HZ
27.02
HZ
26.99
HZ
27.03
Hz

Finding and Major Results
113.36
HZ
Micro satellite housing 1st tone.

Finding and Major Results
The simulations of satellite dynamics (Euler angles and angular velocities) is carried out using MATLAB software on the following two cases :
On the satellite as a RIGID BODY
On the satellite as a FLEXIBLE BODY (taking into account vibration modes of the satellite)

On both the above situations the gravitational moment is the only external moment
Result of simulation are shown in the following figures. From this results it is noted that their is unobserved different between rigid and flexible body simulations
Finding and Major Results

Finding and Major Results
Simulation of attitude dynamics (angular velocities) with and without flexible moments

Simulation of attitude dynamics (Euler angles ) with and without flexible moments
Finding and Major Results

Finding and Major Results
Error of attitude dynamics (Euler angles and angular velocities) due to flexible moment in 20 sec