c
Abstract—A robust adaptive type-2 fuzzy logic controller is
designed for the longitudinal dynamics of a flexible
air-breathing hypersonic vehicle. The aircraft’s pitch motion
and flexible vibration are strongly coupled explicitly in the
dynamic equations. The throttle setting is designed to control
the velocity by dynamic inversion control method. The elevator
deflection is designed to stabilize the pitch rate and flexible
modes and in the end control the altitude in a stepwise manner
by backstepping control method. The flexible modes are actively
used in the control design in order to counteract both the
tracking errors and the flexible vibrations. The virtual control
signals in backstepping control as well as their derivatives are
obtained by command filters whose magnitudes, bandwidths
and rate limit constraints can be set. The transition processes of
the velocity and altitude commands are also obtained by
command filters. Uncertainties are estimated online by interval
type-2 adaptive fuzzy logic system. The adaptive law of the fuzzy
logic system is derived by Lyapunov synthesis approach.
Simulation results demonstrate the effectiveness and robustness
of the proposed controller and also validate type-2 fuzzy logic is
more capable of handling uncertainties than type-1 fuzzy logic.
NOMENCLATURE
V
: velocity, ft/s h : altitude, ft
: flight path angle, rad
α
: angle of attack, rad
q
: pitch rate, rad/s
: lift, lb
: drag, lb
T
: thrust, lb
: gravitational acceleration
: pitching moment, lb·ft
m
: mass, slug
y
: moment of inertia, lb·ft
2
S
: reference area, ft
2
c : mean aerodynamic chord, ft
q : dynamic pressure, lb/ft
2
: density of air, slugs/ft
3
c
: throttle setting instruction
: fuel equivalence ratio
e
δ
: elevator deflection, rad
L
C
: lift coefficient
D
C
: drag coefficient
T
C
: thrust coefficient
M
C
: pitching moment coefficient
,
fa
η
: forebody and aftbody general elastic mode
,
fa
: forebody and aftbody coupling coefficient
,
fa
ωω
: forebody and aftbody natural frequency
,
fa
: forebody and aftbody damping ratio
Fang. Yang, Ruyi. Yuan, Jianqiang. Yi are all with the Institute of
Automation, Chinese Academy of Sciences, Beijing 100190 China
(corresponding author phone: +86-010-82544639; fax: 86-010-82544640;
e-mail: ruyi.yuan@ ia.ac.cn).
This work was supported by National Natural Science Foundation of
China under Grant 61203003, 61273149 and 60904006, Knowledge
Innovation Program of the Chinese Academy of Sciences under Grant
YYYJ-1122, and Innovation Method Fund of China under Grant
2012IM010200.
I. INTRODUCTION
YPERSONIC vehicle has been widely researched since
1960s due to its high speed (at least 5 Mach), high
thrust-to-weight ratio and reusability. It will
dramatically reduce the flight time between continents and
bring great development in civil and military applications.
Although hypersonic vehicle has these advantages, its flight
control law design is still highly challenging. Early research
is mainly focused on a rocket-powered hypersonic vehicle
called generic hypersonic flight vehicle (GHFV) [1]. GHFV
is in winged-coned configuration which has complete ground
test data. Its flight control law design neglected the flexible
effects and viewed it as a rigid body. Xu designed an adaptive
sliding mode controller on the high-order feedback linearized
model and got good control effect and robustness under a
certain degree of parametric uncertainty [2]. Some other
representative control methods also can be seen in [3], [4].
The successful flight of scramjet-powered X-43 series
promoted more research work on air-breathing hypersonic
vehicle (AHV). AHV is in wave-rider configuration whose
long-thin fuselage causes non-negligible structural vibration
problem. Furthermore, due to AHV’s special integrated
engine-frame configuration, there exist tight and complex
interactions between aerodynamics, structural dynamics and
the propulsion system. Bolender developed a nonlinear model
(called heave model) for the longitudinal dynamics of an
AHV using Lagrange method [5], [6].
But heave model is too
complex for control design. Three kinds of simplified models
are derived from heave model as table
Ⅰshows. Rigid-body
modes are nearly independent on flexible modes in model A.
Relevant papers can be found in [7]. Model B gets the most
widely used recently. It displays no coupling explicitly in
dynamic equations but the flexible modes affect the
aerodynamic and propulsive coefficients and therefore
indirectly affect the rigid-body modes. Kuipers designed an
adaptive linear quadratic controller based on the linearized
rigid AHV model [8]. Lisa introduced the canard deflection
as an additional control variable and designed the parameter
adaptive law to guarantee the stability of the rigid-body
dynamics and the flexible dynamics [9]. Parker also added the
canard to eliminate the non-minimum phase character of the
rigid-body dynamics and stabilized the flexible dynamics
[10]. In this paper, we study model C which displays strong
coupling in dynamic equations especially between the pitch
motion and the flexible vibration but neglects the flexible
effects on coefficients. Up to now, for model C, few papers
have actively used flexible modes to design a control law.
Model A and C adopt two-cantilever-beam assumptions and
Robust Adaptive Type-2 Fuzzy Logic Controller Design for a Flexible
Air-breathing Hypersonic Vehicle
Fang. Yang, Jianqiang. Yi, Xiangmin. Tan, and Ruyi. Yuan
H
2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
July 6-11, 2014, Beijing, China
978-1-4799-2072-3/14/$31.00 ©2014 IEEE