Aerospace and Electronic Systems Magazine April 2018 - 5
Pegasus XL rocket, Photo credit: NASA
analysis is extended to cover many points, including (1) extensive
robustness analysis, (2) evaluation of different flight and operation
conditions, (3) evaluation of different input and control profiles,
and (4) investigation of the real-time implementation structure and
computational cost for sampling time analysis.
The report is organized as follows. In the problem statement,
insights are provided regarding the major problem at hand. The
framework of real-time nonlinear RHC methodology is then introduced, and solution strategies are discussed. Simulation and
noise tolerance results are provided, and then some conclusions
and thoughts on possible future work are presented.
PROBLEM STATEMENT
LAUNCH VEHICLE
Launching a standard rocket (with some form of payload) into orbit has traditionally used fairly simple guidance methodologies.
The rocket is launched in a certain direction, begins a slow turn,
transitions into a gravity turn, and finally achieves a certain orbit
that allows the placement of the payload.
As mentioned previously, early control systems for such
launch vehicles tended to use precalculated position and velocity profiles, which assumed that the launch conditions were well
known. Even in the best realistic case, there are some uncertainties of interactions between the rocket and its surroundings, and
high precision of placement may not always be achievable. These
uncertainties become more pronounced when the launch platform
is not stationary but rather has some movement, such as in the
case of launching from an airplane or a ship. Although a small
percentage of variation in final orbital parameters may be fine
for some payloads, others may require a more precise result. In
light of this, more sophisticated control methodologies may need
to be implemented.
α = ( cos 2 (α ) ( mu ) ) QS ( aα 3 + bα 2 + cα + eδ ) + q
(
q = QSd fα 3 + hα 2 + iα + jδ
)
Iy
(1)
(2)
where α is the angle of attack, q is the pitch rate, Q is the dynamic
pressure, S is the reference area, d is the diameter, m is the mass, Iy
is the pitch moment of inertia, u is the velocity component along
the center line (where u = velocity × cos(α)), and δ is the tail elevator deflection angle (a graphical representation of which can
be seen in Figure 1). Coefficients a, b, c, e, f, h, i, and j are values
provided by Reichert and Yost [14] (along with values for many
of the other variables), representing a specific flight condition for
such vehicles.
In this study, the scaled versions of EOMs from Reichert and
Yost [14] are implemented, which are given in detail in Lu [15].
The final forms used in the control system developed in this research are
α =
180 gQS
cos (πα 180 ) aα 3 + bα 2 + cα + eδ + q
π WV
(3)
q =
180QSd
f α 3 + hα 2 + iα + jδ
Iy
(4)
(
(
)
)
EQUATIONS OF MOTION
Compared with traditional rockets, missiles are more likely to exhibit additional complexities. Therefore, in terms of plant modeling, some missile control strategies have been investigated and implemented for the purposes of this research. In particular, Reichert
and Yost [14] supply equations of motion that can be used, such as:
APRIL 2018
Figure 1.
Generic representation of missile dynamics.
IEEE A&E SYSTEMS MAGAZINE
5
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