220978-1-5386-7255-6/18/$31.00 ©2018 IEEE
Fixed-Time Nonsingular Terminal Sliding Mode
Control for Unmanned Aerial Vehicles
Dou Zhang, Guo-Ping Jiang, Ying-Jiang Zhou, You-Hong Wan, Zhen Jia
School of Automation, Nanjing University of Posts and Telecommunications,
Nanjing, Jiangsu Province, 210023, China
E-mail: zhouyj@njupt.edu.cn (Ying-Jiang Zhou)
Abstract—This paper proposes a fixed-time nonsingular
terminal sliding mode control methodology for Unmanned
Aerial Vehicles with the presence of nonlinearity and external
disturbance. A fixed-time terminal sliding surface is
constructed and the settling time is independent of initial
system states. Nonsingular terminal sliding mode control
strategy based on switching saturation function is employed to
enable avoidance of the singularity problem. The control
method is proved to be effective by simulation results.
Keywords—Unmanned Aerial Vehicles, Fixed-Time,
Terminal Sliding Mode Control, Nonsingular.
I. INTRODUCTION
Unmanned aerial vehicle (UAV) has aroused the close
attention of the researchers because of its wide application.
The UAV can be divided into single rotor, double rotor and
multi rotor according to the number of its rotor. Quad-rotor
UAV is also called quad-rotor aircraft, which is the
simplest and most popular one of the multi rotor UAVs. It
has been widely applied in aerial photography, geological
exploration, pipeline inspection, environmental assessment
and other fields. Sliding mode control of UAV has become
a hot topic in the research field of UAV[1].
Sliding mode control (SMC) is a nonlinear control
method[2], which forces the system to slide along a
prescribed switching manifold. Due to its simplicity, high
robustness to external disturbances and low sensitivity to
the system parameter variations, it has aroused great
interest in scientific research. In the branch of SMC,
terminal sliding mode control (TSMC)[3] has been widely
studied and employed in industrial applications, including
motor control[4], process control[5], robotics[6],
aircrafts[7], power systems[8], networks[9] and so on. On
the basis of ensuring stability, TSMC can achieve fast
tracking of reference input and retain the high robustness of
SMC.
TSMC has the characteristics of finite time convergence.
Finite-time TSMC is studied[10], where system state
variables will reach the fast terminal sliding manifold
within a desired finite time. However, the settling time in
the finite-time control depends on initial states of the
system. If the initial conditions is unavailable in advance, it
will prohibit their practical applications. Zuo[11] presents a
fixed-time TSMC concept of non-linear systems. The
guaranteed closed-loop convergence time independent of
initial states is derived. TSMC also applies consensus
tracking for second-order multi-agent networks[12]. A
nonsingular fixed-time TSMC method is proposed to
achieve the trajectory tracking within a fixed-time time[13].
Unfortunately, there comes across a challenging issue: the
singularity in the controller.
Therefore, it is necessary to
further study the singularity problem in the TSMC
system
s[14-16].
In this paper, the fixed-time TSMC are designed and the
singularity phenomena of the systems are further studied in
detail. The concept of fixed-time TSMC is extended from
the global finite-time TSMC, the fixed-time stability can be
guaranteed by the proposed TSMC design. The closed-loop
convergence time independently of initial system states can
be estimated a priori by the control parameters. We extend
the framework to second-order non-linear systems in the
presence of uncertainties and external disturbances. Based
on a new sliding surface expanded from TSMC, a
switching control method is introduced into the control law
design to avoid the singularity. The proof of the global
stability of the nonsingular TSMC systems is also given in
this paper. The simulation results verify the effectiveness
of the proposed method.
The remainder of this paper is organized as follows.
Section 2 presents the Model of the UAV system and some
basic lemmas. Section 3 states the fixed-time TSMC
design and a new ideal sliding surface. A systematic
nonsingular method is proposed in section 4 to overcome
the singularity problem. Simulation examples is presented
in Section 5. Conclusions are drawn in Section 6.
II. PRELIMINARIES
A. Model of UAV
In this section, the dynamics model of the UAV is
introduced. The ground coordinate system is used to
determine the position of the aircraft relative to the ground,
and uses the body coordinate system to describe the
position motion and the attitude angle motion of the aircraft.
The UAV is a complex dynamic system in the course of
flight, so it is difficult to deduce its motion equation
accurately. For the sake of simplicity, we ignore the
influence of the earth's rotation, the elastic deformation of
aircraft and some other rotating parts.
The earth fixed axis system is used to determine the
position of the UAV to the ground, and the body axis
This work is supported by the National Natural Science Foundation of
China [grant number 61374180, 61603196]; the Natural Science Foundation
of Jiangsu Province of China [grant number BK20150851]; the Project funded
by China Postdoctoral Science Foundation [grant number 2015M581842]; the
Project funded by Jiangsu Province Postdoctoral Science Foundation [grant
number 1601259C]; the Sponsored by NUPTSF [grant number NY215011];
the Postgraduate Research & Practice Innovation Program of Jiangsu
Province[grant number KYCX17_0793].
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