Research Article
Design of Robust Observer-Based Backstepping Control for
a Satellite Control System
Saleh Alshamali and Elham Aljuwaiser
Department of Electrical Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
Correspondence should be addressed to Saleh Alshamali; s.alshamali@ku.edu.kw
Received 12 February 2019; Revised 23 April 2019; Accepted 9 May 2019; Published 26 May 2019
A
cademic
Editor: Xue-Jun Xie
Copyright © Saleh Alshamali and Elham Aljuwaiser. is is an open access article distributed under the Creative Commons
Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
is paper presents the attitude tracking of a class of satellite control systems under external disturbances. Once the error dynamics
of the satellite are obtained, a nonlinear transformation expresses them in a suitable representation for the design of a high-gain
observer and backstepping control. e observer-based backstepping controller is then designed to drive the angles of the satellite
dynamics to their desired values in the presence of exogenous disturbances. Closed-loop stability of the proposed controller is
demonstrated via Lyapunov theory, and its eectiveness is conrmed through numerical simulations.
1. Introduction
A great number of satellite systems are orbiting Earth for
various purposes. ese satellites are oen classied in
terms of their orbit, such as low Earth orbit, medium Earth
orbit, geostationary orbits, and geosynchronous orbits [,
]. Alternatively, they can be classied according to their
mechanism of control torque generation, such as thrusters,
reaction wheels, magnetic torquer rods, and control moment
gyroscopes [–]. e design of attitude tracking control
for satellite systems poses challenges to engineers, especially
when the satellite is under the inuence of external distur-
bances. erefore, a successful control design must ensure
stability of the closed-loop system.
Several strategies have been proposed for satellite control
systems (SCSs). For instance, actuator failure compensation
via adaptive backstepping control has been addressed in [].
In addition, a nonsingular terminal sliding mode control has
been proposed for attitude tracking of small satellites by using
a combined energy and attitude control system []. Likewise,
magnetic attitude control has been developed for SCSs with
uneven inertial distributions by combining Kalman ltering
and feedforward control to estimate and reject external
disturbances []. Nonlinear sliding mode control for attitude
tracking of a magnetically actuated satellite is introduced
in []. More recently, a three-stage sliding mode control
for attitude tracking of a satellite system with uncertain
inertia matrix and torque disturbance has been proposed [].
Attitude control of a rigid body with uncertain inertia matrix
using sliding mode control along with a state observer has
also been addressed []. In [], nonlinear model predictive
control is applied to a exible satellite, where the controller
parameters are optimized by a genetic algorithm. Satellite
attitude stabilization has also been addressed using the state-
dependent Riccati equation control method []. Horri et
al.[]developedagain-scheduledcontrollerforaSCS
based on inverse optimal control to improve the settling time
of a benchmark proportional–derivative controller. Attitude
control has also been addressed using an adaptive controller
based on a radial basis function neural network []. A fault-
tolerant control law based on sliding mode control has been
proposed for a SCS under solar perturbations and actuator
faults []. Xiao et al. [] addressed attitude tracking of a
exible spacecra via an adaptive sliding mode backstepping
controller.
Unlike previous studies, this work combines backstep-
ping control with a high-gain observer for attitude tracking
of a SCS under external disturbances. Backstepping control
is a simple, exible, and versatile approach that provides
Hindawi
Mathematical Problems in Engineering
Volume 2019, Article ID 7412194, 9 pages
https://doi.org/10.1155/2019/7412194
