Dynamics and Stability and Control Characteristics of the X-37

10 Pages·2001·0.54 MB·English

by  Chaudhary, Ashwani

AIAA-2001-4383
DYNAMICS AND STABILITY AND CONTROL CHARACTERISTICS
OF THE X-37
A. Chaudhary*, V. Nguyen t, H. Tran _, D. Poladian §, and E. Falangas*
Boeing Phantom Works
Abstract are presented. The level of maneuvering control
This paper presents the stability and control power is assessed. Vehicle trim with multiple
analysis and the control design results for the surfaces is discussed. Special challenges where
Boeing/NASA/AFRL X-37. The X-37 is a flight the wings loose roll effectiveness are discussed
demonstrator vehicle that will go into space and and solutions are presented. Aerodynamic
after its mission, autonomously reenter and land uncertainties and flexibility modeling issues are
on a conventional runway. This paper studies the presented. Control design results and robustness
dynamics and control of the X-37 from analysis methods are presented. Results are
atmospheric reentry through landing. A nominal provided for the Entry, Terminal Area Energy
trajectory that lands on the Edwards Air Force Management (TAEM), and Approach and Land
Base Lakebed is considered for all the analysis phases.
and design. The X-37's longitudinal and
lateral/directional bare-airframe characteristics
7
Figure 1,The X-37 Configuration
*Principal Engineer
tBoeing Tech. Fellow, and Lead GN&C
*Principal Engineer, AIAA Senior Member
Engineering Specialist
Copyright @2001 by Boeing. Published by the American Institute of Aeronautics and Astronautics, Inc
with permission. NASA support per Cooperative Agreement NCC8-190 is acknowledged.
1
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Introduction During reentry, a_located jets are used to assist
in trim and control. Figure 3shows the locations
The Boeing/NASA/AFRL X-37, as shown in of the multiple, aft jets that are used. There is
Figure 1,is part of the Future-X Pathfinder roll-yaw coupling and impingement force
program. The Future-X Pathfinder Program is interaction as the jets are fired. The X-37 control
designed to field flight vehicles and technologies system is designed to manage the redundant jets
quickly and inexpensively, and to use them in and compensate for the non-linearities.
reliable and safe flight operations. The goal is to
advance the state of the art in low cost, reusable RU LU
launch vehicle technologies that are ready,
through flight-testing and qualification, to be
RR'_ _k
applied to operational systems.
An important predecessor to the X-37 program LL
was the X-40A flight test program _.Boeing first
flight-tested the X-40A in 1998, and a majority
of the analysis and design methodologies RD LD
presented here were tested and validated in that
program. The X-37 provides Orbital test and
Figure 3 - Locations of the Aft RCS jets
return capability that is new to all the other
current X programs.
Trajectory
A successful X-37 configuration is the result of
The dynamic pressure and angle-of-attack of the
numerous iterations between multiple
nominal trajectory are shown as a function of
disciplines. The stability and control analysis
Mach Number in Figure 4.
presented here supports the evolution of the
design to help provide an optimal design.
Nominal Trajectory
Control Effectors
[255
Figure 2 shows the atmospheric control surfaces
F20o
available for flight stabilization and
maneuvering.
_155_
-100][
Ruddervator
-50
o°
25 20 15 10 5
M_h Number
Figure 4 - X-37 Nominal Trajectory
Flaperon Jets
The nominal trajectory consists of a42-degree
Figure 2 -Atmospheric Control Effectors angle-of-attack profile after entry from an orbital
inclination. The angle-of-attack flown is atrade
The Ruddervators provide pitch control when
between heat load, heat rate, range, and cross
deflected symmetrically (de) and yaw control
range, and it is modulated as required until the
when deflected asymmetrically (dr). The
Approach and Land phase.
Flaperons are for providing roll when deflected
asymmetrically (da) and drag modulation when Inthe initial part of the trajectory, the bank angle
deflected symmetrically (Flaps). The Body Flap is used to control drag and stay below the heat
is used primarily for trimming, but itcan be used rate limit.
as a control device to assist in pitch
maneuvering. The Speedbrake is used to do drag The X-37 has across range modulation
(velocity and flight path) control in the TAEM capability and roll reversals are used to control
and approach and land phases. cross range.
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Off-nominal trajectories and variations about authority. In such diagrams, the vectors that
them are also considered in the full design cycle, represent the aileron, rudder, angle-of-sideslip,
but for the kind of results shown in this paper, an CG in the ydirection, and jet rolling and yawing
analysis about the nominal trajectory provides a can be drawn to size up the lateral/directional
good overall understanding. trim authority. The size of the uncertainty on
each vector can also be included in the diagram.
Bare Airframe Stability and Control
Figure 6shows such a normalized vector
Characteristics diagram at subsonic speeds. The boxes at the end
of the vectors represent uncertainties. It can be
Trim Characteristics seen that the aileron and rudder vectors can add
up to cancel the dynamics created due to the
In the upper part of the trajectory, just after angle-of-sideslip and asymmetries due to the y
reentry where the atmosphere is very thin, the X-
CG. At subsonic speeds, the jet vector is short
37 uses jets, Flaps, Ruddervators, and Body Flap and does not have any authority. At hypersonic
as needed to trim out the longitudinal dynamics.
speeds when the dynamic pressure is very low,
As the dynamic pressure rises, the Body Flap the jet vector is very effective and is responsible
and Ruddervators alone areused to trim all the
for trimming and controlling the X-37. As
way to touchdown. The Body Flap and illustrated in Figure 6, the aileron (da) vector
Ruddervator combination was sized such that the
swings from the right side to the left, with
only small deflections of the Ruddervator are ramifications for controllability that are
used for trimming. Figure 5 shows the discussed later.
deflections required, as a percentage of full
authority, to trim out the longitudinal dynamics.
At each analysis point in the trajectory, the
vehicle was trimmed for forward and aft center- HypSerhsioftnic
of-gravity (CG) variations combined with
trajectory perturbations. The maximum
deflection for the Ruddervator and Body Flap
that resulted from these variations is shown in
Figure 5.
*'60
....... ....i.......i.......... Beta
5O
....i.......i..........
"_ 40
U_ !ii
0
Cn
m
_'
Figure 6- Lateral/Directional Trim Authority
o
The Speedbrake and the Flaps are modulated for
drag control, which is required for headwind and
n. 0 10 15 20 25 30 tailwind compensation. Ideally, the
MachNumber
Ruddervator's deflection, as it holds trim, should
change only slightly as the Speedbrake and Flaps
Figure 5- X-37 Pitch Trim Authority
are modulated. Large changes indeflection
As shown in Figure 5, there is sufficient pitch would use up all the deflection budgets as well
authority during the flight envelope. The trim as require gain schedules to be a function of the
schedule is able to accommodate changes in the Speedbrake and Flaps. Figure 7 shows the
CG and other uncertainties. The Ruddervator change in Ruddervator required along the
deflection is minimal such that there is enough trajectory for full deflections of the Flaps and
deflection left over for control. Speedbrake. As can be seen from Figure 7, full
deflections of the Speedbrake and Flaps require
Vector diagrams that plot rolling moment only a 5 to 10% change in the Ruddervator
coefficients against the yawing moment deflection. At lower Mach numbers, where drag
coefficients can assess Lateral/Directional trim
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modulation is most active, the change in amount of instability can be handled by the
Ruddervator deflection iseven less. control power available.
15
The maximum instability as shown in Figures 8
and 9 can be related to static margins and mode
times-to-double and used to size a configuration.
4 ; ;
rr i, _:
t_ 3 ....... i' i : '_
2 : .... '-....... i...... -'_--
"_" I ....................... i.,......Xx _ :_.....
:_ l: i: _x, wix
"_ 0 .... _*.... -*-_--,-_-_-,_-_* .... ,_-
0 0.5 1 1.5 2 25 _E_-1 ............. ---,,....... •...... _.x.x .....
Mach Number
' * XX
-2................ r....... !........_........ J
Figure 7 - Effect On Trim Of Other Surfaces
-3................ i....... i...._ .......
Dynamic Characteristics
-4 -3 -2 -1 0 1
The short period and phugoid modes of the X-37
Real (rad/s)
along the nominal trajectory space are shown in
Figure 8.The vehicle is stable along the nominal Figure 9 - Bare Airframe Lateral/Directional
trajectory with the short period mode frequencies Eigenvalues
increasing as the dynamic pressure increases
with decreasing altitude. As shown, some After trimming, there must be sufficient control
combinations of angle-of-attack in the transonic acceleration left over for maneuvering. All along
region give an unstable airframe, but analysis the trajectory, at trimmed conditions, surface
shows that there is sufficient control power for deflections, required to generate a minimum
stability augmentation. acceleration to execute maneuvers demanded by
guidance, were computed. The results are shown
4 ': : : : : in Figure 10along with a limit line that shows
i , i , i
that solutions above that line will require jet
, , × [( J , assistance in order to prevent saturating the
,: ,:X xxxXX:* q: '' ,
surfaces.
, X XX *Xx J ,
'_ '', *IxX k_ , *', 103
_-1 i .... ";....... ; .........".._'ILr "l.......
_0 102
, , _ _ ,
E-1
tJetAssisted Control__ A
3--
', k xx 'xx x : . I0_
-2 ........ '....... 4..... ..Xb ....... ,....... 4.......
: _ xxx : ' : rr
3 ....!........".._:.x._.",._._..E.......!..........
100
', : ', × , ,
&'9
-2 -1.5 -1 -0.5 0 0.5
104
Real (rad/s)
Figure 8 - Bare Airframe Longitudinal
Eigenvalues 10.2 ! I I I I
0 5 10 15 20 25 30
MachNumber
Figure 9presents the eigenvalues of the
lateral/directional bare airframe that correspond Figure 10 - Surface Deflections Required to
Produce Minimum Acceleration
to the dutch roll, spiral, and the roll modes. The
dutch roll mode can be seen as a low damped,
From the results, it can be seen that there is
low frequency mode. The dutch roll gets
sufficient maneuvering authority to produce
unstable at lower mach numbers, although the
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acceleratioanssrequired. At the very high Mach Figure 12shows the weather cock stability or the
Numbers, the amount of surfaces required to directional stability derivative, Cnl3, for the flight
produce accelerations gets prohibitively high. regime to be mostly negative. Again, three
This is due to the low dynamic pressure at these trajectory cases are presented as error bars about
high Mach Numbers and the resulting low the nominal trajectory. The negative values of
surface effectiveness. In the high Mach Number
Cnl_ do not necessarily imply instability, for Cnl3
region, jets are used to assist in maneuvering.
dynamic includes the effect of angle-of-attack
and presents a more accurate measure of
Stability Derivatives
stability.
Ultimately, it is the vehicle transfer function
eigenvalues and transmission zeros that
determine exact open loop stability and
maneuverability. However, there is along
history of looking atthe vehicle's pitch,
directional, and lateral stability derivatives to get
aquick idea of the configuration athand.
Looking at these derivatives assists in quickly
: i i i i
sizing up the configuration and examining any
special regimes from astability and control
perspective.
From the trim vectors presented in Figure 6, it
can be seen that at subsonic speeds, the X-37 has
0 5 10 15 20 25
a-C113(stable), a+Cnfl (stable), and that adverse
Mach Number
roll isprovided by the rudder and proverse yaw
by the aileron. This section shows the
Figure 12 - Directional Derivative, Cnl5
characteristics of the configuration as afunction
of Mach Number along the trajectory.
Cnl3 dynamic, as shown in Figure 13, shows that
there are some regions of instability, depending
on the Mach and Alpha combinations. It is for
{D these regions that control power availability must
¢-
be checked. Figure 13 also compares well with
the instability level shown by the dutch roll
eigenvalues for the nominal trajectory in Figure
9.
..D
i
¢D
d:l
i i i i i
0 5 10 16 20 2'5
MachNumber
d_
Figure 11 - Lateral Stability Derivative, Cll3
r-
Figure 11 shows the lateral stability derivative,
i I ! ¢ |
0 5 10 15 20 25
C1[3,as function of Mach Number for three Mach Number
different trajectory cases, presented as error bars
about the nominal trajectory values. It can be
Figure 13 - Directional Derivative, Cnl5 dyn,
seen that Clfl is stable throughout the trajectory. With Alpha Effects
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LCDP Transition Region also be combined with an aileron to rudder
interconnect gain, if required.
As the X-37 goes from high angles of attack in
the entry phase to the lower angle-of-attacks in mo -El-- LCDPAileron
the TAEM phase, the airflow over the Flaperons -e- LCDPRuddervator
m
causes a change in roll responses (reversal to
E
normal) and starts creating proverse yaw by the
I,,,,,
aileron. This is a critical region since it is not O
Z
known exactly when the Flaperons will go I°
through this change, but they must still carry out
a minimal level of maneuvering.
._.9.
This phenomenon can be graphically observed 17)
O ' iD 11-I ir
by looking at Figure 6, presented earlier. As the _J
aileron vector swings from the left to the right O ii i
quadrant (from hypersonic to transonic), CnSa
becomes zero and changes signs. This change in "O
Cn(Sa, in combination with Cll3, causes a change i : , ,,
in roll responses. Finally during this transition ID
>
period for CnSa, when it is exactly in line with 0 5 10 15 20 25
the beta vectors, no roll rate control occurs. Mach Number
Fortunately, during all this, the rudder
derivatives do not change sign and do not cause Figure 14 - LCDP of the aileron changes signs
alignment problems with the beta vector.
Finally, Figure 15 shows that the derivative,
Algebraically, it is seen that the Lateral Control cn_, changes signs and may be unknown, due to
Departure Parameter may be defined as2: uncertainties, for a large region around the
LCDP transition region. Cn& is always produces
Clo Cn& ) [i] adverse yaw and can be counted on in any
LCDP = (Cna Cl& control startegy.
During the transition from high to low angle-of-
>..
attacks, the LCDP changes signs. As it changes
signs, there is a period where there is no roll
effectiveness from the aileron. To see why this is >
9
so, consider the transfer function relating the a..
aileron to the roll rate: 1'
J,
_SbCl& Is2+-qS.b)o(Cn.Cos(cO-C_.l_,C'an,a Cos(a))] [2] m
P-L= lxx Izz " Cl&, >-
_a ®
s(s2+_sb(Cn,Cos(_,__c,,C_l,Sin(ct)))
Izz Ixx ®
<
The LCDP term appears in the numerator of the
transfer function, and as the LCDP changes
signs, the zero in the transfer function goes from
the left-hand plane to the right hand plane.
However due to aerodynamic uncertainties, there
] I [ I I
is a wide region in the trajectory where the 5 10 15 20 25
numerator zero is near zero in the right hand MachNumber
plane and the aileron can't be counted on for any
Figure 15 - cnSa reversals and predictable
performance.
cnSr
Figure 14 shows the change in the LCDP
parameter for the aileron and for the The control solution for this region is to not use
Ruddervator. In closed loop control, the two may the Cn_Saderivative based gains and to use the
powerful control available from the
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Ruddervators when the aileron goes through the the rudders and the sensors in both pitch and
roll response change. The uncertainties in this lateral axes, and that active gain compensation
area will have to be scrutinized and good must be used to attenuate the modes.
robustness shall have to be provided by the
control system.
Flexible Characteristics
It is extremely important to characterize the
flexible vehicle properties since effects of the
surface panels, the linkages, the actuators, and
the backup structure must be understood.
The system must be specified and designed such
that the first surface mode is above the actuator
bandwidth frequency. Any mode frequency must
be the combined contribution of the end-to-end d
system.
Ope_Loop Phase(deg)
A detailed aero-elastic analysis is being done
Figure ]7 - Flex Model, Laterai/Directlonal
with Generalized Aerodynamics Force Axis
Derivatives (GAFD) data, which is used to
model the dynamic effects of aero-elasticity. Controls
GAFD data provides coefficients that describe
how the vehicle basic aerodynamic forces and The design was performed using Hinfinity
moments are affected by modal displacements controls and a fixed gain structure. The Hinfinity
and rates. A second set of coefficients describes setup allows the attachment of uncertainties into
how the modal displacement of a flex mode is the synthesis model and allows for a faster
excited by the vehicle motion. A third set of turnaround time.
coefficients describes how the moments at the
Aerosurfaee Control
hinges of the control surfaces are affected by
The X-37 lateral/directional control system is a
changes in attitudes, rates, and deflections.
roll rate demand system. Cross range is
Ruddervator analysis has shown that there isa controlled by the guidance by demanding bank
torsional and a "diving board "mode. The angle tracking, which in turn demands a crisp
"diving board" mode frequency isabove control roll rate response.
frequencies and is not affected by the actuator
The X-37 rolls about the stability axis to
and back-up stiffnesses.
minimize the angle-of-sideslip while
maneuvering. Ideally, the angle-of-sideslip
should be kept as small as possible because of
increased non-linearities in the vehicle dynamics
with increasing angle-of-sideslip. Since the
- , angle-of-sideslip is not available on an
atmospheric reentry vehicle due to the high
temperatures that would burn off any probe, the
angle-of-sideslip is estimated from the side
acceleration. The control system is designed to
decouple, to the maximum extent possible while
._I \u / meeting other requirements, the roll rate
responses and the angle-of-sideslip. Inertial turn
Op4m-LO__ (_g) compensation along with the estimated angle-of-
sideslip feedback is used to obtain a coordinated
Figure 16 - Flex Model, Longitudinal Axis
roll.
The resultsfor theother modes shownin the
Figure 18shows the roll rate step responses for
Nichols plotsof Figures 16and !7 indicatethat
the Approach and Land, Terminal Area Energy
there is a significant amount of bending between
Management, and Entry flight phases. These
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responses have been superimposed on a The time domain responses in the longitudinal
requirements envelope developed for the Space axis show that there is enough control power to
Shuttle. Step responses are a good way to gauge meet requirements. Step responses such as these
whether the control system will meet the tracking also help form acontrols budget to show that
and speed demands of the guidance outer loops adequate surfaces are available for both trim and
and whether the response times will be fast control. The control system has been flown on
enough for maneuvers executed without the the 6Degree-Of-Freedom (6DOF) simulation
guidance in the loop. and has helped many trajectory, actuation, and
other subsystem sizing studies.
The responses for the X-37 in all phases are
crisper than those demanded by the shuttle. The 21 -- - -: : i I
final responses for the X-37 will be a trade off
between what the guidance demands and what
can be given due to requirements of robustness -2--i I ; 1 •
and other design constraints.
0 2 4Time (sec)6 8 10
21- ..._- "-----" ', I
".:...1....
_21 I IAppr°a ,ch& Land,phase [
_1-__ "..... :__.c_ ....... 1
.21 i i i i ,
0 2 4Time (sec)G 8 10
2
30 2 4Time(sec)6 8 10 i I I I
iii
_o gt.ne-: .........
v l i i i
4m I o i i l ........ oa mo _o i
-2
I I I I
o
0 2 4Time (secl 6 8 10
0 2 4Time(sec)6 B 10
_'21 I I = = 1
Figure 19 - Nz and Alpha Responses in the 3
_" 'I .... , ...... -%:,-...... ::___-"--r-----, Phases
1
Blended Aerosurface and Jet Control
0 2 4 Time(sec)6 B 10
Figure 20 plots the dynamics and controls
Figure 18 - Roll Rate Response in the 3 vectors from the hypersonic region. It shows that
Phases the jets are a very powerful device for
lateral/directional control in the region when the
In the longitudinal axis, the flight controls uses aerosurfaces are becoming effective for control.
pitch rate and normal acceleration feedback for As scaled on the plot, only half of the jet vector
low supersonic and subsonic flight. In the is shown, and it is enough to control dynamics
hypersonic and high supersonic regimes, pitch due to the angle-of-sideslip.
rate and estimated angle-of-attack feedback is
used. The angle-of-attack is estimated from
inertial velocities and is used for feedback, gain
scheduling, and conversion of body rates to
stability axis rates. However, the accuracy
required on the angle-of-attack is not critical
because of the high inertial velocities in the
hypersonic regime and the slow variation of the
aerodynamics with angle-of-attack when it is
used for gain scheduling.
Figure 19shows the normal acceleration and
angle-of-attack responses from the three phases.
In the Approach and Land and TAEM phases,
normal acceleration responses to steps
commanded by guidance are shown. Higher up, I
0
in the Entry part of the trajectory, responses to
Cn
step commands in the angle-of-attack are shown.
Figure 20 - Jet Control Authority
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The jets were represented using results from Second, using modern control tools, a mu
describing function analysis and gains were analysis is performed after attaching the most
designed with the same methodology as that for important aerodynamic and mass properties
the aerosurfaces. uncertainties. The value of the mu analysis is that
it simultaneously perturbs the uncertainties in the
Figures 21 and 22 show the attitudes and rates worst possible way to point out weaknesses in
during a bank angle maneuver, and the amount
the design. Figure 23 shows just such a plot from
of jet firings required to complete the maneuver. the mu analysis. It can be seen that in this case
there isno possible instability for the magnitude
_.1ooI , !
of the uncertainties attached, and the biggest
0" 01 /1 i contributors are the aerodynamic derivatives,
io/ cnSa and clSa.
0_ .................... !....................... 035 ....
=".2/ 1 i _ cyb
031t / _ clb
,ot.-..._... ....,..................
/
la. ol / i _', 0.2'5 _..j .... cyda
clda
---- cnda
02 _,_ cydr
-_-- cldr
"_"0.57 _ ? 1p ,
_-o.s0l___ ""----.-----V..."..-..-.... ,i ....... 0.151 --+- c!nxdxr
0 5 10 15 01 --_,- izz
Figure 21 - Rate Contol during the upper
O. _.
Trajectory
10"z 10"l 10° 101....
Frequency (tad/s)
11111 1 Figure 23 - Mu analysis showing relative
contribution of each uncertainty
0 5 10 15
The third method to assure robustness, on the X-
37, is to subject the whole design to alot of
stress cases on the 6DOF simulation. In these
l i stress cases, numerous trajectory, aerodynamic,
°
0 5 10 15 actuator, sensor, and mass property parameters
'll t i 1 IIIIIII
aresimultaneously varied. The performance of
the vehicle along the trajectory is then assessed.
.......T...J.m.. lmtlllVll1111111
Conclusion
0 5 10 15
With the analysis and results presented in this
Figure 22 - Jet Firings in the upper trajectory
paper, the X-37 has been shown to be arobust,
for control
aerospace vehicle. A trim analysis showed that
Jet firings are actually determined by a complex there is excellent trim capability in all axes, and
jet selection logic that determines which jets that after trimming there is enough surface
have failed and which are available for optimal authority left for control of the vehicle. The
control. dynamics of the LCDP transition region were
presented, and it was shown how the X-37 can
Robustness Analysis be controlled in aregion where aerodynamic
alignments and uncertainties make the exact
The robustness of the X-37 design is assured in
dynamics unknown. Results of the control design
three ways. First, traditional gain and phase were presented and it was shown how the
margin analysis is performed since there is a
robustness of the design is ensured using
long history of successful aerospace programs classical and modern control methods.
using this methodology.
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References
_Nguyen, V., Chaudhary, A.K., Poladian, D.; "
X-40A Guidance and Control and Flight Test
Results," AAS paper no. 00-0015, February 3,
1999.
2pamadi, B., "Performance, Stability, Dynamics,
and Control of Airplanes," American Institute of
Aeronautics and Astronautics, 1998.
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