Research Article
Robust PD+ Control Algorithm for Satellite Attitude Tracking for
Dynamic Targets
Gao Shan,
1
Li You ,
2
Xue Huifeng,
1
and Yao ShuYue
2
1
School of Automation, Northwestern Polytechnical University, Xi’an, China
2
School of Aerospace Science and Technology, Xidian University, Xi’an, China
Correspondence should be addressed to Li You; liyou@xidian.edu.cn
Received 30 December 2020; Revised 1 June 2021; Accepted 30 June 2021; Published 27 July 2021
Academic Editor:
Javier Moreno-Valenzuela
Copyright © 2021 Gao Shan et al. 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.
In this paper, a PD + controller combined with the sliding mode surface is proposed to improve system convergence rate and
efficiency on control torque for satellite attitude tracking control. A sliding mode surface with the maneuver stage is constructed
by the Euler axis; hence, the constant angular velocity is achieved. e PD + controller with the variable structure and auxiliary
term is constructed to track the desired sliding mode surface. e Lyapunov function in PD control analysis is modified to simplify
stability analysis. Model uncertainty, external disturbance, control torque constraint, and angular velocity constraint are taken
into consideration, and a novel method to reduce the overshoot of angular velocity is proposed. e performance and superiority
of the proposed method are demonstrated by numerical simulation results.
1. Introduction
In the rapid development of aerospace science technology
and a series of practical processes of science and technology
works, researchers have paid extensive attention and worked
on the attitude tracking control of satellites. Among these
works, PD control algorithm is the industry’s most mature
and widely used method. e PD control law for satellite
attitude control was proposed by Wie [1, 2] when solving the
attitude tracking control issue. At the same time, Wie
summarized some related Lyapunov functions and gave the
general stability proof methods. And recently, for the sat-
ellite attitude control problem, James [3] proposed a passive
PD control law for satellite attitude stabilization control, and
it was pointed out that the attitude system governed by the
PD controller is energy consumed. e directional cosine
matrix was treated as an equivalent proportional term in this
paper. Generally, standard PD control algorithm is a mature
method, and since it is a very mature method, researchers
did not focus on this field for almost a decade.
e reason why the PD control method can be deeply
developed and widely applied for a long time is its obvious
advantages, such as uncomplicated structure, clear physical
meaning, and strong robustness. However, it also has the
following limitations: (1) the initial control torque is too
large, and the control torque drops drastically with the
decrease of system state, so the utilization efficiency of the
control law is low. (2) e convergence rate is slow, and the
rapid declination in attitude angular velocity causes the drop
of the convergence rate of the attitude quaternion. (3) e
modeled system is not fully utilized, and in reality, we can
partially determine the system’s rotational inertia
parameters.
For the aforementioned problems, Jovan et al. [4]
designed a robust attitude tracking control law. In order to
improve the convergence rate of the standard PD controller,
Verbin et al. [5–7] applied the backstepping method to
design an angular velocity curve with fast convergence
characteristics, and the control law designed by Verbin
enables the actual state to track the designed reference
trajectory. In [5, 6], the problem of satellite control torque
limitation is discussed, while in [5, 7], the satellite angular
velocity limitation is discussed, but [5–7] lacked the dis-
cussion about the uncertainty of system’s moment of inertia.
Cao et al. [8] considered the uncertainty of rotational inertia,
added external disturbance moments, and designed a
Hindawi
Mathematical Problems in Engineering
Volume 2021, Article ID 6680994, 15 pages
https://doi.org/10.1155/2021/6680994
