International Journal of Recent Technology and Engineering (IJRTE)
ISSN: 2277-3878, Volume-7, Issue-6S, March 2019
253
Blue Eyes Intelligence Engineering
Retrieval Number: F02490376S19/19©BEIESP
Abstract: This paper explores attitude control algorithms using
thrusters and momentum wheels for satellite tracking
manoeuver. The attitude reference trajectory is generated to track
a ground object on the rotating Earth and to keep the Sun vector
perpendicular to the solar panel to maximize the solar power.
The dynamic model is derived based on Newton-Euler approach
and Modified Rodrigues Parameters (MRPs) are used to
represent attitude kinematics. The control algorithms are derived
based on the Lyapunov stability control theory to ensure the
asymptotic stability of the control law. MATLAB software
package is used as a simulation environment to develop and test
the performance of the proposed tracking control algorithms
using a Graphical User Interface (GUI) tool that can be
expanded for future development.
Keywords: Attitude tracking; Lyapunov stability; Satellite
dynamics and control.
I. INTRODUCTION
Attitude Determination and Control System (ADCS) is
used to orient the satellite payload in space and or to observe
an object with certain accuracy [1-3]. For example, Hubble
Space Telescope (HST) is pointed to observe astronomical
objects with very high accuracy. The HST antenna is
accurately pointed to a ground station to focus the radio
beam and to reduce the power requirements while the HST
solar panel is rotated such that the Sun direction becomes
perpendicular to maximize the generated solar power [4-6].
Therefore, the ADCS designer must design the system to
meet the pointing and accuracy requirements. Design trades
are necessary to select the ADCS sensors, actuators and
control algorithms based on the satellite mission
requirements. In this paper, momentum wheels and thrusters
are investigated as actuators for attitude tracking maneuvers.
The control algorithms are derived based on Lyapunov
control theory and reference trajectory is generated similar
to HST mission. The payload is pointed to view and track a
particular target on ground, and to generate maximum power
by rotating around the payload boresight axis to orient the
solar panel perpendicular to the Sun direction.
In literature, Hanblai and Shaube et al. investigate ideal
reference trajectories for target tracking [7-9]. In Hablani’s
ideal tracking, the final angular velocity of the target is not
zero and the payload axis is initially facing the zenith
direction. The tracking commands utilizes 2-1-3 Euler angle
sequence. Shaube et al. computes the tracking commands in
terms of a Modified Rodrigues Parameters (MRPs) because
it is close to be optimal and less in computation. In addition
Revised Manuscript Received on March 10, 2019.
Mohamed Okasha, Department of Mechanical Engineering,
International Islamic University Malaysia, PO Box 10, 50728 Kuala
Lumpur, Malaysia (Email: mokasha@iium.edu.my)
Moumen Idres, Department of Mechanical Engineering, International
Islamic University Malaysia, PO Box 10, 50728 Kuala Lumpur, Malaysia
Alia Ghaffar, Department of Mechanical Engineering, International
Islamic University Malaysia, PO Box 10, 50728 Kuala Lumpur, Malaysia
to target tracking, Kalweit computes ideal attitude
commands for Sun tracking. The payload initially facing the
Nadir direction. The ideal solar rotation angle is computed
to reorient the payload about the yaw axis so that the solar
panel normal direction points to the Sun [10]. In this paper,
both target tracking and Sun tracking constraints are
considered to generate the ideal reference tracking
commands.
Schaub et al. and Hall et al use Lyapunov control theory
to develop nonlinear tracking controllers. To guarantee
global asymptotic stability, they choose the Lyapunov
function and drive the control law such that the Lyapunov
function derivative is negative definite. A virtual rigid body
with the same properties as the real satellite is used to derive
the ideal tracking trajectory. Similar controllers are
presented in this paper to track the desired virtual
trajectories using thrusters and momentum wheels. Thrusters
are used to perform large and coarse attitude maneuvers
while Momentum wheels provide fine attitude maneuvers to
eliminate the tracking errors [4-6]. Attitude kinematics are
described using MRPs because they are minimal set and
their singularities can be efficiently avoided [11]. MATLAB
software package is used as a simulation environment to
develop and test the performance of the proposed tracking
control algorithms using a Graphical User Interface (GUI)
tool that can be expanded for future development [12].
This papers are organizes as follow: Section 1 gives an
introduction; Section 2 presents dynamic and kinematics
model with definition of reference frames an attitude
description; Section 3 derives the ideal reference trajectory for
target alignment and Sun tracking including attitude, angular
velocity and angular acceleration commands. The
development of Lyapunov attitude controller are presented in
Section 4; Section 5 shows the simulation results and the
controller performance followed by a conclusion in Section 5.
II. DYNAMICS MODEL
The rotational equations motion for satellite with N
momentum wheels, in body frame, can be written as [4-6].
1x
b b b a e
aa
b b s s
h h J h Ah g
hg
h I AI
where h
b
is the satellite angular momentum vector, I is the
3×3 moment of inertia matrix of the entire satellite, I
s
is the
N×N wheels axial moment of inertia matrix, A is the 3×N
matrix containing the axial unit vectors of the momentum
wheels, h
a
is the N×1 matrix of the axial angular momentum
Satellite attitude tracking control using
Lyapunov control theory
Mohamed Okasha, Moumen Idres, Alia Ghaffar
