abort landing problem
aircraft
scheme
landing
This paper is concerned with the optimal transition and the near-optimum guidance of an aircraft from quasi-steady flight to quasi-steady flight in a windshear. The abort landing problem is considered with reference to flight in a vertical plane. In addition to the horizontal shear, the presence of a downdraft is considered.It is assumed that a transition from descending flight to ascending flight is desired; that the initial state corresponds to quasi-steady flight with absolute path inclination of −3.0 deg; and that the final path inclination corresponds to quasi-steady steepest climb. Also, it is assumed that, as soon as the shear is detected, the power setting is increased at a constant time rate until maximum power setting is reached; afterward, the power setting is held constant. Hence, the only control is the angle of attack. Inequality constraints are imposed on both the angle of attack and its time derivative.First, trajectory optimization is considered. The optimal transition problem is formulated as a Chebyshev problem of optimal control: the performance index being minimized is the peak value of the modulus of the difference between the instantaneous altitude and a reference value, assumed constant. By suitable transformations, the Chebyshev problem is converted into a Bolza problem. Then, the Bolza problem is solved employing the dual sequential gradient-restoration algorithm (DSGRA) for optimal control problems.Two types of optimal trajectories are studied, depending on the conditions desired at the final point. Type 1 is concerned with gamma recovery (recovery of the value of the relative path inclination corresponding to quasi-steady steepest climb). Type 2 is concerned with quasi-steady flight recovery (recovery of the values of the relative path inclination, the relative velocity, and the relative angle of attack corresponding to quasi-steady steepest climb). Both the Type 1 trajectory and the Type 2 trajectory include three branches: descending flight, nearly horizontal flight, and ascending flight. Also, for both the Type 1 trajectory and the Type 2 trajectory, descending flight takes place in the shear portion of the trajectory; horizontal flight takes place partly in the shear portion and partly in the aftershear portion of the trajectory; and ascending flight takes place in the aftershear portion of the trajectory. While the Type 1 trajectory and the Type 2 trajectory are nearly the same in the shear portion, they diverge to a considerable degree in the aftershear portion of the trajectory.Next, trajectory guidance is considered. Two guidance schemes are developed so as to achieve near-optimum transition from quasi-steady descending flight to quasi-steady ascending flight: acceleration guidance (based on the relative acceleration) and gamma guidance (based on the absolute path inclination).The guidance schemes for quasi-steady flight recovery in abort landing include two parts in sequence: shear guidance and aftershear guidance. The shear guidance is based on the result that the shear portion of the trajectory depends only mildly on the boundary conditions. Therefore, any of the guidance schemes already developed for Type 1 trajectories can be employed for Type 2 trajectories (descent guidance followed by recovery guidance). The aftershear guidance is based on the result that the aftershear portion of the trajectory depends strongly on the boundary conditions; therefore, the guidance schemes developed for Type 1 trajectories cannot be employed for Type 2 trajectories. For Type 2 trajectories, the aftershear guidance includes level flight guidance followed by ascent guidance. The level flight guidance is designed to achieve almost complete velocity recovery; the ascent guidance is designed to achieve the desired final quasi-steady state.The numerical results show that the guidance schemes for quasi-steady flight recovery yield a transition from quasi-steady flight to quasi-steady flight which is close to that of the optimal trajectory, allows the aircraft to achieve the final quasi-steady state, and has good stability properties.
place
optimal control problem
climb
https://doi.org/10.1007/bf00939681
control
values
gradient-restoration algorithm
guidance scheme
maximum power setting
yield
derivatives
index
power settings
2022-09-02T15:46
1988-08
reference values
shear
instantaneous altitude
portion
considerable degree
guidance
optimal control
recovery
optimal trajectories
inequality constraints
performance index
type 1
deg
peak value
only control
transformation
optimal transition
altitude
presence
articles
time derivative
transition problem
part
Bolza problem
point
trajectory guidance
boundary conditions
velocity recovery
vertical plane
downdrafts
constant time rate
branches
optimization
sequential gradient-restoration algorithm
Chebyshev problem
horizontal flight
addition
paper
flight guidance
flight recovery
quasi-steady flight
horizontal shear
shear portion
trajectory optimization
type 2
angle of attack
landing problem
windshear
stability properties
abort landing
good stability properties
sequence
conditions
absolute path inclination
state corresponds
algorithm
165-207
differences
rate
final point
ascending flight
state
corresponds
Quasi-steady flight to quasi-steady flight transition for abort landing in a windshear: Trajectory optimization and guidance
problem
modulus
angle
quasi-steady state
properties
article
final quasi-steady state
suitable transformation
degree
inclination
plane
ascent guidance
path inclination
optimum guidance
dual sequential gradient-restoration algorithm
reference
1988-08-01
optimum transitions
trajectories
constraints
https://scigraph.springernature.com/explorer/license/
recovery yield
time rate
numerical results
control problem
setting
attacks
transition
types
results
flight
false
flight transition
W. W.
Melvin
Miele
A.
Numerical and Computational Mathematics
pub.1036302239
dimensions_id
Mathematical Sciences
Journal of Optimization Theory and Applications
0022-3239
Springer Nature
1573-2878
Springer Nature - SN SciGraph project
10.1007/bf00939681
doi
58
T.
Wang
Aero-Astronautics Group, Rice University, Houston, Texas
Aero-Astronautics Group, Rice University, Houston, Texas
2
Airworthiness and Performance Committee, Air Line Pilots Association (ALPA), Washington, D.C.
Delta Airlines, Atlanta, Georgia
Airworthiness and Performance Committee, Air Line Pilots Association (ALPA), Washington, D.C.