J Control Theory Appl 2011 9 (2) 231–236
DOI 10.1007/s11768-011-9099-1
Dynamics modeling and control of large transport
aircraft in heavy cargo extraction
Yanli FENG, Zhongke SHI, Wei TANG
College of Automation, Northwestern Polytechnical University, Xi’an Shaanxi 710072, China
Abstract: In this paper, a novel version of six-degree-of-freedom nonlinear model for transport aircraft motion in
cargo extraction is developed and validated by the theoretical mechanics and flight mechanics. In this model constraint
force and moment reflecting the flight dynamic effects of inner moving cargo are formulated. A methodology for a control
law design in this phase is presented, which linearizes the aircraft dynamics making use of piecewise linearization and
utilizes robust control technique for interval system to achieve specified handling qualities with robustness to uncertainties.
The simulations demonstrate adequate effectiveness and excellent robustness of the proposed controller.
Keywords: Cargo extraction; Transport aircraft; Flight dynamic model; Equilibrium; Interval system; Robust control
1 Introduction
Airdropping has practical applications in a variety of mil-
itary and civilian fields, e.g., goods transportation, rapid
deployment of ammunition and supplies, dealing with emer-
gencies, etc. In the process of heavy cargo airdrop, cargo
extraction makes the resultant force and moment acted on
the carrier airplane change substantially and it eventually
leads to a considerable deviation of the velocity, attitude
and trajectory from the original flight states. Therefore, it is
essential to pose operations on the controls, which can serve
to minimize the states deviation of the carrier aircraft when
cargo moves in it and restore the straight-and-level flight
after extraction.
At present, most of the studies about large transport air-
craft in heavy cargo extraction focus on analysis and sim-
ulation of the cargo’s movement [1∼3] and parachute’s
dynamics [4∼6]. The performance of the carrier aircraft in
this process has not been reported on yet in the literature.
This paper deals with the problem of designing a controller
to ensure the security and stability of the airplane in this
flight condition.
The successful design of such a control system first
requires a model of transport aircraft dynamics in cargo
extraction. With significant effects from added force and
moment produced by inner cargo, the dynamics of a trans-
port aircraft in cargo extraction are markedly different from
traditional flight conditions [7, 8]. In this paper, the equa-
tions of transport aircraft motion in cargo extraction are
established first. Then, the solution to the aircraft trim prob-
lem in cargo extraction is formulated and the open-loop
dynamics are analyzed across a range of extraction condi-
tions. Finally, a controller is designed for aircraft in heavy
cargo extraction. The closed-loop performance is presented
and simulation results reported for a specific case study ver-
ify the feasibility of the proposed approach.
2 Modeling of the aircraft motion in cargo
extraction
In derivation of the flight dynamic model, for simplic-
ity, the cargo is considered as a particle. Accordingly, the
load is represented by a set of constraint force and moment
acting on the carrier aircraft. Besides, the effects of atmo-
spheric turbulence are ignored. There are three coordinate
systems to be used in the following modeling process: the
earth-fixed reference frame, the body-fixed reference frame
and the track-axes reference frame. Definition of these co-
ordinate systems are shown in [9].
2.1 Dynamic equations
Following the previous flight dynamics analyses [10,11],
the classical system of scalar dynamic equations of a rigid,
constant mass airplane in proximity of a flat-Earth with
symmetric layout in the body-axis reference can be depicted
by
⎧
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎩
˙u =
F
Ax
m
a
+(vr −wq),
˙v =
F
Ay
m
a
+(wp − ur),
˙w =
F
Az
m
a
+(uq − vp),
(1)
⎧
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎩
˙p =
I
z
L+I
zx
N +I
zx
(I
z
+I
x
−I
y
)pq+(I
y
I
z
−I
2
z
−I
2
zx
)qr
I
x
I
z
−I
2
zx
,
˙q =
M +(I
z
−I
x
)pr+I
zx
(r
2
−p
2
)
I
y
,
˙r =
I
zx
L+I
x
N +(I
2
x
−I
x
I
y
+I
2
zx
)pq+I
zx
(I
y
−I
z
−I
x
)qr
I
x
I
z
−I
2
zx
,
(2)
In the above equations m
a
denotes the mass of the air-
craft, F
Ax
, F
Ay
, F
Az
, are the external forces acting on the
airplane with respect to the body axis. u, v, and w are the
components of the velocity in body-x, body-y, and body-z
direction respectively. p is the roll rate, q is the pitch rate,
and r is the yaw rate. L is the roll moment, M is the pitch
moment and N is the yaw moment. I
x
, I
y
, and I
z
are mo-
ments of inertia, I
zx
is the product moment of inertia.
In the process of cargo extraction, the resultant force
and moment acting on the carrier aircraft are composed of
aerodynamic, gravitational, propulsive contributions and the
force and moment produced by the inner cargo.
The equation of motion for the cargo can be derived from
Received 31 May 2009; revised 28 March 2010.
This work was supported by the Aviation Science Foundation of China (No. 2007ZD53053).
c
South China University of Technology and Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2011
资源评论
