Research Article
Continuous high order sliding mode controller design for a fl exible
air-breathing hypersonic vehicle
Jie Wang
a,
n
, Qun Zong
b
, Rui Su
b
, Bailing Tian
b
a
School of Control Science and Engineering, Hebei University of Technology, Tianjin 300130, China
b
School of Electrical and Automation Engineering, Tianjin University, Tianjin 300072, China
article info
Article history:
Received 31 January 2013
Received in revised form
22 December 2013
Accepted 5 January 2014
Available online 16 February 2014
This paper was recommended
for publication by Jeff Pieper.
Keywords:
Flexible air-breathing hypersonic vehicle
Continuous high order sliding mode control
Sliding mode disturbance observer
Finite-time stability
abstract
This paper investigates the problem of tracking control with uncertainties for a flexible air-breathing
hypersonic vehicle (FAHV). In order to overcome the analytical intractability of this model, an Input–
Output linearization model is constructed for the purpose of feedback control design. Then, the
continuous finite time convergence high order sliding mode controller is designed for the Input–Output
linearization model without uncertainties. In addition, a nonlinear disturbance observer is applied to
estimate the uncertainties in order to compensate the controller and disturbance suppression, where
disturbance observer and controller synthesis design is obtained. Finally, the synthesis of controller and
disturbance observer is used to achieve the tracking for the velocity and altitude of the FAHV and
simulations are presented to illustrate the effectiveness of the control strategies.
& 2014 ISA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
Air-breathing hypersonic vehicles (AHVs) are crucial to the
development of new technologies in affordable space access and
speedy global reach. Compared with ordinary aircrafts, AHVs adopt
airframe integrated with scramjet engine configuration, which leads
to strong interactions among the elastic airframe, the propulsion
system, and the structural dynamics. In addition, the requirements
of flight stability and high speed response, the existence of various
random interference factors and large uncertainties, the design of a
robust controller for AHVs using a nonlinear uncertainty model is
highly challenging [1,2].
Because of the slender geometries and light structures of this
generic vehicle, significant flexible effects cannot be neglected in
the controller design [3], since these modes may be harmful to
system stability. In order to ensure the safety and reliability, fight
control design for AHVs must guarantee stability of the flight
system and provide a satisfying control performance [4]. Recently,
a FAHV model, which includes the flexible dynamics, was devel-
oped in [5–7]. Based on this kind of FAHV models, several studies
on the flight controller design and simulation have been published
in recent years. The approach of linearizing FAHV model at given
operating points and design of a controller using linear control
design techniques has been widely used. In [8], the nonlinear
longitudinal dynamics of a FAHV was directly linearized at a
specified trim condition, and a linear quadratic regulator (LQR)
was presented for a region in the neighborhood of the operating
point. To ensure stability for a wide range of operating points, the
idea of feedback linearization attracted considerable attention in
[9,10]. The advantage of this method is that it could linearize the
nonlinear dynamics by linearizing the input–output map for all
values of the states x in a certain neighborhood of x
0
instead of the
operating point x
0
. After obtaining a linearized input–output map,
the linear controller can be designed in combination with the
feedback linearization law. In [11], approximate feedback linear-
ization was applied to transform the nonlinear FAHV model into a
MIMO model which provides an example of nonlinear controller
design. In [12,13], a tracking controller was constructed by using a
minimax LQR control approach together with feedback lineariza-
tion law for the nonlinear FAHV model developed by Serrani [14].
In practice, the atmospheric properties and aerodynamic char-
acteristics in the flight envelop of the F AHVs are difficult to be
measured or estimated. Therefore, robust control remains a key
choice for F AHV flight contro l. Sliding mode control (SMC) is
commonly favored as a powerful robust control method to handle
systems running under uncertain conditions [1 5,16]. However, it is
also well known that traditional SMC techniq ue may have the
shortcoming of chattering phenomenon in practice [17,18].Anumber
of methods have been proposed to reliably prevent chattering, such
as observer-based solution [16], the boundary lay er solution [19],and
theadaptiveslidingmodemethod[20]. High order sliding mode
(HOSM) control proposed in [21–24] has also been studied in the
context of chattering. In [21], the HOSM controller based on homo-
geneity properties is presented to achieve finite time convergence.
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/isatrans
ISA Transactions
0019-0578/$ - see front matter & 2014 ISA. Published by Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.isatra.2014.01.002
n
Corresponding author.
E-mail address: wangjie1314@tju.edu.cn (J. Wang).
ISA Transactions 53 (2014) 690–698