AIAA-98-4411
X-33 Attitude Control System Design
for
Ascent, Transition, and Entry Flight Regimes
/A' &
375
Charles E. Hall ++ , Michael W. Gallaher ++ , Neal D. Hendrix +
NASA Marshall Space Flight Center
Huntsville, Alabama, 35812
Abstract
The Vehicle Control Systems Team at Marshall Space Flight Center, Systems Dynamics Laboratory, Guidance
and Control Systems Division is designing, under a cooperative agreement with Lockheed Martin Skunkworks, the
Ascent, Transition, and Entry flight attitude control system for the X-33 experimental vehicle. Ascent flight control
begins at liftoff and ends at linear aerospike main engine cutoff (MECO) while Transition and Entry flight control
begins at MECO and concludes at the terminal area energy management (TAEM) interface. TAEM occurs at
approximately Mach 3.0. This task includes not only the design of the vehicle attitude control systems but also the
development of requirements for attitude control system components and subsystems. The X-33 attitude control
system design is challenged by a short design cycle, the design environment (Mach 0 to about Mach 15), and the X-
33 incremental test philosophy. The X-33 design-to-launch cycle of less than 3 years requires a concurrent design
approach while the test philosophy requires design adaptation to vehicle variations that are a function of Mach
number and mission profile. The flight attitude control system must deal with the mixing of aerosurfaces, reaction
control thrusters, and linear aerospike engine control effectors and handle parasitic effects such as vehicle flexibility
and propellant sloshing from the uniquely shaped propellant tanks. The attitude control system design is, as usual,
closely linked to many other subsystems and must deal with constraints and requirements from these subsystems.
I. Introduction
The X-33 is comprised of both rocket and aircraft
vehicle design and requires analytical methods for
evaluating the flight performance that draws from, but
is not limited to, each field [7]. The propulsion
system design, mission specific trajectory constraints
and engine out abort capability are among many of
the challenges.
Ascent attitude control is provided by rocket
engine thrust vector control (TVC) and aerosurfaces.
The vehicle uses two linear aerospike engines with
upper and lower banks of thrusters on each engine as
depicted in figure i. Unlike conventional launch
vehicles, however, TVC is accomplished by
differentially throttling the upper and lower banks of
thrusters for pitch and roll, and differentially
throttling the left and right engines (both upper and
lower banks) for yaw.
++ Aerospace Engineer, Flight Mechanics, GN&C Systems Branch
+ Team Leader, Flight Mechanics, GN&C Systems Branch
Copyright © 1998 by the American Institute of Aeronuatics and Astronautics, Inc. No copyright is asserted in the
United States under Title 17, U.S. Code. TheU.S. government has royalty-free license to exercise all rights under the
copyright claimed herein for Governmental Purposes. All other rights are reserved under the copyright owner.
1
American Institute of Aeronautics and Astronautics
night acmsurfaccs are used for ascent and entry
control; four elevens, two flaps and two rudders, as
shown in figure 2. Inherent to using aerosurfaces are
concerns about cross axis control torque coupling and
aerodynamic loading on the surfaces.
Figure 1: Linear Aerospike Engine.
Due to the shape of the lifting body fuselage,
complex tank structures were included in the vehicle
design. There are two liquid hydrogen tanks located
aft in the vehicle, and one liquid oxygen tank located
in the nose. Extensive analysis was required to derive
the degree of propellant damping required to provide
attitude control stability and stability margins during
ascent for all missions.
concepts [ I,2|. Due to the short design cycle and the
need for rapid prototyping, a well tested and reliable
attitude control system architecture was chosen for
the X-33. This design provides excellent ascent
trajectory tracking and is robust to wind disturbances
and non-linearities such as control effector deadzones
and control effector saturation. Concurrent with
analyses using the chosen design, research in attitude
control with Sliding Modes [9] looks promising, and
could find application in the full scale Reusable
Launch Vehicle.
Flight control design and analysis required
analytical software tailored to time and frequency
domain analysis with rapid prototyping in mind.
MARS Y AS (MARshall SYstem for Aerospace
Simulation) [3] was employed for the control system
design and development. The MARSYAS simulation
system has been under continuous development at
Marshall Space Flight Center since the 1960’s and
has been used for the analysis of a variety of launch
vehicles, spacecraft and the Space Shuttle Main
Engine. Dynamic modeling can be realized quickly
using the MARSYAS simulation language and
assembled into a full system simulation very quickly.
MARSYAS is capable of time domain and frequency
domain 6 Degree-of-Freedom (6DOF) analysis using
the same models for both domains.
Although MARSYAS can be used for time
domain analysis, it must process the simulation code
in a translation phase that converts the simulation
code to C, then links to C libraries to form an
executable simulation. The equations are arranged to
make them amenable to frequency response and
eigenvalue analysis. This requires more CPU time
making MARSYAS inefficient for large sets of
simulations as required for dispersion analysis. For
dispersion analyses with higher fidelity models,
MAVERIC (Marshall Aerospace VEhicIe
Representation In C) [4] was used. MAVERIC can be
used for 6DOF or 3DOF simulation from lift off to
TAEM, and can produce Monte Carlo analysis of
both ascent and entry profiles.
II. Reference Mission Profile
The control law design was based upon past
launch vehicle experience and upon analysis of two
other Single Stage To Orbit Reusable Launch Vehicle
The X-33 will launch from Edwards Air Force
Base, California and land at one of two sites. A
reference flight profile from launch to TAEM is
2
American Institute of Aeronautics and Astronuatics
shown in figure 3. One typical mission’s ascent phase
of tlight lasts 203 seconds and places the vehicle at an
altitude of roughly 1 80,000 feet and a speed of Mach
10. During ascent, variations in engine throttle (100%
to 63% nominal power level) and rigorous attitude
maneuvers must be accomodated by the control
system in order to meet the required MECO
conditions on altitude, velocity, angles of attack (a)
and side slip (P) before hand-over to transition and
entry flight control. Guidance is open nominally loop
for ascent, and the attitude control system follows
commanded inertial roll, pitch, yaw angles and body
rates. After MECO, the transition phase, which lasts
approximately 25 seconds, re-configures the control
mixing from main engines with aerosurfaces to
aerosurfaces with RCS. The attitude control system
for the transition and entry phases of flight follow
commanded a, a rate, P, bank and bank rate profiles
generated by guidance. Guidance is closed loop
during the entry phase. The entry phase of flight
brings the vehicle from an altitude of approximately
191,000 feet and a speed of Mach 9.8 down to an
altitude of 89,000 feet and a speed of Mach 3.0.
MEct | Enuy
i . Ida **c i » zn
|—r-r-r-i-
\
M»cf> - to a Mich
:.i | J
» 1
[
—
—
t i!
Irani it Jon
Entry
V ■" ,
/ ; 1
!
■ft 1
L ■ i.
t
I Lijfc>*
Li. . . i ..... i .... i
400 350 300 250 200 150 100 50 0
range lo TAEM (NM)
Figure 3: Reference Mission Profile
III. Ascent Flight Control
before flight. The AFCS is designed to accommodate
an engine failure. It requires no re-configuration lo do
this; instead, a different set of control gains are used,
chosen as a function of the time of failure.
Figure 4: AFCS Block Diagram
In the case of an aerosurface actuator failure, the
AFCS computes torque commands using nominal
gains, Filters them and passes them to a
reconfigurable control algorithm that essentially
redistributes the control to the remaining operable
surfaces, taking advantage of the multi-axis torque
capability of each one [8]. An air data control
augmentation system is in place for load relief, that
uses measured a and P as inputs, and generates
augmented pitch and yaw attitude and rate error
commands. It is activated by a software flag that is set
at a pre-determined time of flight or Mach number.
This paper includes only analysis results from the
AFCS without air data augmentation, however. The
capability to include Programmed Test Inputs (small,
temporary open loop commands) was built in so that
engine and aerodynamic characteristics could be
studied from post flight data.
Control System Description
The function of the Ascent Flight Control System
(AFCS) is to provide stable control of the vehicle
from liftoff to MECO while following the prescribed
ascent trajectory provided by the Guidance function.
A block diagram of the AFCS is given in figure 4.
The attitude quaternion, body rate, engine throttle and
mixture ratio commands are received from Guidance
at a lhz rate. The AFCS functions are executed at a
50 hz rate, which requires smoothing the commands.
Gains, limits and flex filter coefficients are pre-
computed for each separate mission and loaded
Control Effectors
The X-33 uses two linear aerospike rocket
engines and eight aerosurfaces for attitude control
during ascent. The linear aerospike engines, which
use liquid oxygen and hydrogen propellants, provide
207,000 pounds thrust each. The design allows the
exhausted gasses to expand against the atmosphere,
as opposed to a bell shaped nozzle like conventional
engines, and is self-compensating with altitude. Each
engine has a bank of ten thrusters across the top and
bottom which can be throttled independently of one
3
American Institute of Aeronautics and Astronuatics
another. Thrust Vector Control (TVCj is done by
differentially throttling each bank of thrusters, so that
the need tor a gimbal system is eliminated.
Furthermore, the engine can be integrated into the
thrust structure, stiffening the design and saving
weight. Effects of the linear aerospike engines on the
aerodynamics of the vehicle and aerodynamic effects
on the engine’s performance must be accounted for,
however. Since this type of engine has never been
used on any vehicle, these effects had to be derived
through a combination of computational fluid
dynamic analysis and wind tunnel testing of an X33
model with a simulated engine. This data will be
augmented by data from planned flight tests of a
subscale aerospike engine ramp on the SR-71.
Figure 5 illustrates how TVC is accomplished
using differential throttling. If no TVC is required,
both the top and the bottom banks of thrusters have
the same throttle setting. For roll control, one
engine’s thrusters are commanded differentially to
produce a pitch torque, and the other engine is
commanded in the same way to produce pitch torque
of opposite sign.
Figure 5: Aerospike Engine; a) No TVC, b) pitch
up differential throttle, c) pitch down differential
throttle
For pitch control, the differential throttle command is
the same for both engines. To produce yaw torque,
the overall throttle command for one engine is higher
than the other one. In nominal operation, each
engine’s Gas Generators (GG) are throttled for yaw
TVC. The oxygen and hydrogen feed lines from the
GG’s to the TVC valves are interconnected and can
be opened or closed by isolation valves. These valves
are closed under nominal conditions. In the case of an
engine failure, they can be opened allowing one GG
to provide flow to both engines thus providing TVC
operation similar to the nominal, but with reduced
thrust.
Figure 2 illustrates the aerosurface configuration.
On ascent, the vertical rudders are used for yaw, the
elevons and flaps are used for roll and pitch control.
There are two elevons on each canted fin, but the
AFCS treats them as one surface, sending the same
deflection command to both.
Optimal Control Effector Selection Algorithm
An Optimal Control Effector Selection Algorithm
[5] was employed to generate the gains used in the
mixing logic for the AFCS. A function of control
effector deflections is formed:
f(5) = 5 t Q5 (l)
where <5 is a 8x1 vector of effector deflections, and
Q is a positive symmetric matrix (8x8) of weighting
or penalty factors. A constraint equation is written
that equates commanded torque (T c ) about the roll,
pitch, and yaw axes of the vehicle to the
corresponding effector deflections:
<t>(5) = D5-T c = 0 (2)
where D , called the sensitivity matrix, is a (3x8)
matrix of partial derivatives of torque about roll,
pitch, and yaw with respect to each effector
deflection. A new functional of the form
#(<$) = /(5) + A T <I>(<5) (3)
is written, where A is the lagrange multiplier and is
independent of <5 . For a minimum set of deflections
5 that satisfy the constraints (2), the equation
4
American Institute of Aeronautics and Astronuatics
dS
(4)
must be satisfied. Substituting (1) and (2) into (3) and
substituting the resultant into (4) yields the following
result for 8 :
Over 190 modes were identified in the frequency
range of interest, 0 to 25 hz, by Finite Element Model
analysis. Modes were selected, based on kinetic
energy, for various propellant loads. The modes were
modeled by a second order differential equation that
describes the motion due to flex at the sensor
location. The angular rates and displacements due to
flex were added to the rigid body rates and
displacements. The equation for flex is [6]:
5 = -^Q~ [ D t s l
(5)
Vi +20,7), +W, 2 r7,
Substituting (5) into (2) and solving for A yields
X = -2[dQ-'D t ]t c (6)
Using LaGrange multipliers and making the
appropriate substitutions yields the control deflection
vector, 8 :
8 = Q-'D t [dQ- x D t Yt c (7)
where B v = Q l D T [DQ 'D r ] is the allocation
(mixing gain) matrix. Equation (7) yields the
deflections that minimize the functional in equation
(1) and satisfies the constraint equation (2).
The allocation matrix B v is precomputed at 10
second intervals for each trajectory. Through real
wind dispersed simulation analysis, the weighting of
each effector is fine-tuned such that each one is used
approximately the same percentage.
Flexible Body Dynamics and Flex Filter Design
Flexure in the vehicle structure can be sensed by
the rate gyros. Instability can occur when flex modes
are excited by the control effectors. Attitude and
attitude rates containing flexible body effects are fed
back to the attitude control system. For this reason the
flexible body dynamics must be accurately modeled
and a filter must be designed that attenuates the
sensor response to the undesirable modes.
Where q,, co ii are the the modal coordinate,
generalized damping, and natural frequency of mode
i; Fj are the generalized forces for mode i at node j.
The generalized forces are input to the structure at 14
nodes representing aerosurface actuator and engine
hard points. The flex contribution of each mode to the
angular velocity measured at the sensor is:
CO — d) 71
x,y,z rx,y,z h
Where 0 ^ is the normalized mode shape at the
sensor location.
Filtering the sensor output due to flex modes was
accomplished by two digital filters in the Inertial
Navigation Unit (INU) and digital notch filters in the
AFCS software. The filters in the INU are effectively
low pass filters designed to attenuate signals above 10
hz. The AFCS filters were designed to attenuate
particular flex modes.
Slosh Dynamics and Damping Requirements
Propellant sloshing is another potential source of
instability for the attitude control system. Like flex
dynamics, slosh is a parasitic effect that must be
modeled in the controls analysis software. Testing
was done at Marshall Space Flight Center on sub-
scale X-33 tank sections in order to help characterize
slosh frequencies in the oxygen and hydrogen tanks.
These data, in conjunction with analytical results,
were used to define the necessary parameters to
model slosh. These parameters, slosh mass, slosh
5
American Institute of Aeronautics and Astronuatics
mass location, and frequency were generated as a
function of liquid height in the tanks.
A spring-mass-damper model was used for each
slosh mass in the control analysis f 10]. Slosh
dynamics in the Z body axis or pitch direction, and in
the Y body axis or yaw direction for each slosh mass
was modeled by second order differential equations,
with inputs a function of vehicle accelerations:
Zs i + 2£s t cas t Zs + (OsfZs - /(0,0,Z) (8)
Ys t + 2£s. cos* Ys + cos? Ys = (9)
Where £ s i,toSi are the damping coefficient and natural
frequency for slosh mode i, 0,0,1// are vehicle roll,
pitch, and yaw angular accelerations, Z, Y are
vehicle Z and Y axis accelerations.
Through linear analysis with slosh, damping
requirements for the propellant tanks were derived by
increasing the damping coefficients in equations (8)
and (9) until gain and phase margins in all rotational
axes were met. This data was used to design baffles in
the oxygen tank. No baffles were needed in the
hydrogen tanks because internal septums provided
sufficient damping. A plot of the pitch axis damping
requirement is shown in figure 6.
Then the frequency responses with slosh and with
Hex dynamics were computed. The stability margin
requirements were 6 db gain and 30 degrees phase for
the nominal vehicle. Figure 7a shows a frequency
response in the roll channel, opened at the output of
the controller, with only smooth wall (0.2%) damping
of the liquid oxygen (LOX) slosh modes. The stablity
margin boundary is represented by the triangle. A
damping of 4% was applied to the LOX slosh modes
so that the stability margin requirements could be
met. This frequency response in shown in figure 7b.
Figure 7: Frequency response with smooth wall
damping (a) and 4% damping (b) of slosh modes.
Figure 6: Oxygen tank pitch axis damping
requirement
Nonlinear Simuiations
Full, nonlinear six degree of freedom simulations
of all ascent trajectories were performed to verify the
performance of the AFCS for nominal, engine out
abort flights, as well as flights with wind and vehicle
dispersions. Figure 8 shows attitude errors from over
500 Monte Carlo simulations with wind and vehicle
dispersions. The AFCS appears to be robust to these
dispersions, ensuring good launch probability.
Stability Analysis
Stability of the vehicle was assessed at discrete
operating points along the reference ascent trajectory
by linear analysis. Nonlinear, time varying models
were used to calculate the PID and mixing gains.
v 0 50 too 150 200 250
a .) Tim* [nc]
6
American Institute of Aeronautics and Astronuatics
I0 , , - r r r r - ^
0 50 100 ISO 200 250
Tima (sac)
Figure 8: Minimum and maximum attitude errors
in (a) roll, (b) pitch and (c) yaw from Monte Carlo
simulations.
Figure 9 shows roll, pitch and yaw attitude errors
for a trajectory with an engine failure at 100 seconds.
The plot demonstrates that the AFCS handles the
transition from nominal to engine out flight very well
and follows the commanded attitude with good
transient response to the maneuvers.
Figure 9: Attitude errors with an engine failure at
100 seconds.
IV. Transition and Entry Control
Transition and Entry Control System Description
commands to the control effectors so that the
vehicle's attitude and attitude rates follow, to the
required degree, the commanded attitude and attitude
rates generated by the transition and entry guidances.
During transition, the maneuvers initiated by the
control system reorient the X-33 from its state at the
time of MECO to a state from which guidance can
begin to direct the vehicle through the appropriate
maneuvers for entry. During entry, the control system
initiates maneuvers which are considerably more
complex, and which modulate the vehicle's energy,
through lift and drag, to reach a targeted velocity,
altitude, and location over ground from which the
TAEM phase (which is responsible for directing the
X-33 to the landing site) can begin.
In order to effect the maneuvering for which it is
responsible, the transition and entry control system
generates commands to the various control effectors
available during these phases: a suite of eight
thrusters in the Reaction Control System (RCS) and
eight actuated aerosurfaces (two rudders, four
elevons, and two body flaps). Due to the difference in
computational frequency (guidance commands are
updated at 1 Hz, control is executed at 50 Hz) the
control system uses a smoothing function to
interpolate the commands, reducing the step function
effects that can result.
The commands generated by the transition and
entry guidances for input to the transition and entry
flight control system are expressed in terms of the
aerodynamic angles, a, P, and <})bk (bank angle). The
modulation of a affects the balance of lift and drag on
the vehicle, p is to be kept to a minimum to minimize
loads on the X-33. <j)bk maneuvers and a modulation
enable the vehicle control its drag in targeting the
desired TAEM conditions. The sign of <])bk controls
lateral motion. Guidance also provides a commanded
bank angle rate and angle of attack rate, which the
control system uses to incorporate appropriate
accelerations. Locally, the control system generates
commands for P angle rates; these are typically 0
deg/s, although they may be set to small values with
directions selected so that the P control signals will
contribute beneficially rather than adversely to a
particular commanded bank maneuver.
The primary responsibility of the X-33 transition
and entry flight control system is to generate
As the X-33 flies at angles of attack ranging
between around 0 to around 50 degrees during
transition and entry, bank maneuvers must be
7
American Institute of Aeronautics and Astronuatics
accomplished by combinations of roll (about the x-
body axis) and yaw (about the z-body axis).
Maneuvers about these axes also contribute to p, so
the control system's efforts to effect bank must be
balanced with its efforts to maintain low p. The
commanded P rates can assist in this conflict by
forcing the P from an adverse toward a proverse
direction.
Complicating the control system’s responsibility
of controlling to aerodynamic angle commands is the
problem of estimating these angles. The relative
velocity vector is largely determined by the
orientation of the vehicle's velocity vector with
respect to the mass of air rotating with the Earth, but
winds also contribute to it. The X-33 has no sensors
to directly sense these winds and thus measure the
aerodynamic angles during most of the transition and
entry (a Flush Air Data System is onboard, but is not
usable at the higher Mach numbers). Therefore, the
navigation system supplies an estimate of a and P
computed without consideration of wind. These
estimates result in errors that can be significant to the
controller, and which must be accommodated with a
design that is robust enough to tolerate them.
different sign than is estimated in flight. Large P may
result in loss of control at higher dynamic pressures,
when the base aerodynamic torques can exceed the
control authority. While P angles of appropriate sign
can assist a commanded bank, it is difficult to
maneuver with certainty to a desired p, because the
error band is close to the limits to which the
controller attempts to constrain p. Early in the design,
aerodynamic coefficients dictated that the center of
gravity and moment reference point be nearly
coincident to provide adequate control authority for
angle of attack. This yielded nearly neutral static
stability of p. This produces undesirable
complications, offset by positive Cnp dynamic which
provides some dynamic stability. But P is routinely
disturbed during the bank maneuvers, since bank and
P are cross-coupled.
The commanded bank commands are limited in
magnitude by guidance. Banks can become very
large, and in some cases, overshoot may result in
transient periods during which the X-33 is flying
banked such that the lift vector is directed downward,
but the control system design goals are to avoid such
a state. Figure 10 shows a typical bank command
profile and simulated response for an early mission.
Figure 9 shows a typical commanded a profile for
transition and entry, with the simulated response.
Aside from some small perturbations that result from
trajectory optimization during design, the commands
are slow-changing and relatively non-complex. The
disturbances from wind may represent the most
significant of any abrupt errors introduced in the pitch
axis.
Angli of attack: Mlchitl 7i3
Figure 9: Angle of attack vs. commanded angle of
attack.
0 50 1 00 1 50 200 250 300 350
lim • from m iln •ngin* cut-off (s)
Figure 10: Commanded and simulated bank angle
The missions are designed to more aggressively test
various limits of the system, and consequently the
commanded profile becomes more challenging for the
control system. Figure 1 1 shows a bank command
profile for a later mission. Comparison with the
previous figure reveals a greater number of bank
reversals and more complex maneuvers.
The P angle is a crucial parameter to control. Due
to the navigation errors, this angle can actually be of a
8
American Institute of Aeronautics and Astronuatics
commanded bank angle: Michael 7 c 6 minion
3 l A >i: i
" .. J\ ' »
: : 4\
« 1
° n _ / •
i i si ■ r-
v ..i . m ...
0 ?
TD
C
*
1 f \]j
?, * \:
Vi
E 5 0
E
j V
jU j
0 50 100 150 200 250 300
lime If o m main engine cul-oll (*}
Figure 11: Commanded bank angle, Michael 7c6
Control Effectors: Aerosurfaces and Reaction
Control Jets
Figure 2 shows the general locations on the
vehicle body of the actuated aerodynamic surfaces
used during transition and entry control. The body
flaps offer their highest control authority in the pitch
axis, and generally exceed the other aerosurfaces in
their capacity to generate pitch torque. The elevons
are surfaces mounted on the canted fins on either side
at the rear of the X-33. The elevons are each split into
two surfaces, which are actuated in unison rather
than individually. The elevons provide a complex
blend of roll, pitch and yaw torque when deflected.
The balance between torque varies widely as a
function of Mach number and aerodynamic attitude.
The rudders are mounted on two side-by-side vertical
fins positioned at the top rear of the X-33, centered
about the roll axis.
At transition, the dynamic pressure is so low that
the rudder effectiveness is inconsequential. During
entry, the X-33 is at a large positive a so that the
rudders are blocked by the body of the vehicle from
most air flow, rendering them impotent. As the a is
decreased toward the end of entry, the rudders can
provide some useful torque generation capability, but
this capability is still far smaller than that provided by
the other surfaces.
has been structured to allow simple reallocation of the
surfaces through mission data loads. This mixing
logic, like the gains of the system, are input as a
function of Mach number, which, with a, are the
primary variables by which effectiveness is predicted.
The final configuration of control effectors is a rather
highly constrained one. The limited number of
aerosurfaces reduces options for redundancy. It is not
possible to dedicate each individual aerosurface to a
single axis of control (that is, to reserve one set of
surfaces for pitch, one for yaw, and one for roll
control).
The RCS jet general positions and orientations are
shown in Figure 12. These jets provide approximately
500 Ibf thrust each in nominal operation. The
configuration has been revised as the design
proceeded to maximize their usefulness: the
downward-thrusting jets on the upper sides are canted
so that their firings produce both yaw and roll in
directions favorable to banking at the missions' a
ranges. However, the RCS system is not capable, in
general, of providing pure moments. It may have
unpredicted influences on the aerodynamic
characteristics of the vehicle and its control surfaces.
Some jets fired alone can produce undesirable cross-
axis effects. The RCS system has primacy in the
control effectiveness strategy during the early part of
transition and entry, when the lower dynamic pressure
results in decreased effectiveness of the aerosurfaces,
but it remains active, to a mission-specifiable degree,
well after the aerosurfaces assume primary control.
This provides control authority should the aerosurface
deflections become saturated or disabled. This
phasing of control primacy is achieved through the
scheduling of deadbands of the jet selection logic and
the mixing logic gains. The RCS allocation strategy is
designed to yield a limited amount of redundancy
where available, and to meet requirements limiting
the number of thrusters that can be commanded on at
a given point in time. Violation of these requirements
could result in both temporary reductions in
effectiveness or permanent thruster failures.
A major challenge in relying primarily on the
aerosurfaces for control during entry is in designing a
system robust enough to handle dispersions from
predicted effectiveness. As updates to the
aerodynamic database have been developed, the
strategies have been rethought, and the control system
9
American Institute of Aeronautics and Astronuatics
' \
/ \
yaw yaw
Figure 12: RCS jet locations.
With the aerosurfaces, the primary control
allocation strategy is to use the body flaps for control
of pitch and yaw. A uniform component of the control
signal deflects both body flaps the same amount for
pitch, while a smaller differential component is added
to one and subtracted from the other, to produce yaw.
The elevons are deflected upwards to effect roll.
Upwards deflections are expected to produce far less
adverse yaw, so that small differential body flap
deflections can counter disturbances in that axis.
Deflections downwards are permissible for additional
pitch control, if the amount of downard deflection is
uniform. The control system generates a component
of deflection for each aerosurface in response to the
commands for torque in each axis, although the
factors are zero in many cases. This allows for the
revision of control strategy to accommodate updates
to the aerodynamic characteristic models that might
indicate effectiveness reversals or altered levels of
effectiveness.
system is essentially a proportional-integral-
derivative (PID) style control, using the estimated
angle of attack to transform the signals generated by
aerodynamic angle and rate errors into body axis
torque requests. The command signals are further
processed with the mixing logic, which allocates
these signals to the control effectors based upon a
Mach schedule.
The parameters of the control system are selected
initially through a process of linearized stability
analysis, performed at several points in a given
mission. These parameters are selected to provide
acceptable response at representative phases in the
flight, covering the range of aerodynamic model
points and periods of critical performance. This
provides a set of mission data loads corresponding to
particular Mach numbers. By examining how these
parameters change between Mach, a good idea of
what ranges are appropriate and reasonable is
obtained, with an estimate of how different elements
of the controller must be weighted. The parameters of
the control system are tuned through a series of 6
degree-of-freedom simulations, assuring that the
performance displays the required response
characteristics. Control system robustness is further
verified by applying the Monte Carlo technique to the
simulation process, exposing the design to as full a
range of dispersions in parameters as possible. These
dispersions include the mechanical tolerances such as
thruster locations, analytic uncertainties such as
aerodynamic coefficient ranges, and statistical
dispersions generated with the Global Reference
Atmosphere Model [11] which simulates perturbed
winds and atmospheres.
Ultimately, the available set of control effectors
for the X-33 during transition and entry is a fairly
tightly-constrained one, and control allocation for
nominal and contingency operations is the major
challenge of the control system.
The dispersion analysis has not yet been
completed, but intermediate results have shown
increasing robustness. Gain sets developed for one
mission have been satisfactorily applied to nominal
simulations of another mission, suggesting that the
parameter selection methodology is in itself leading
to a robust control specification.
Transition and Entry Control Law
Figure 13 shows a simplified block diagram of the
first stage of the transition and entry flight control
system. Not depicted are certain filters which have
been reserved for modifying error signals and some
dead zones which can be used to tune responses. The
10
American Institute of Aeronautics and Astronuatics
prate
m
ajmird
agui
Yavarnnni
sigul
Figure 13: Transition and Entry Control System
Simplified
Dispersions that have been run have indicated the
system is insensitive to many mechanical tolerances.
Key dispersions appear to be aerodynamics (which
have relatively high uncertainties) and atmospheres,
which can lead to both recoverable events (such as
rollovers) and unrecoverable events (usually
manifested as loss of P control). Increasing tolerance
to these problems is a primary concern as the design
reaches its final stage, but the structure is expected to
permit development of solutions within the limits of
the available control authority.
[2] Reusable Launch Vehicle Single Stage To Orbit
VL001 Flight Mechanics Data Book, April 1995
[3] MARSYAS User’s Manual Revision 8, March 22,
1996
[4] Maveric User’s Guide, August 19, 1997
[5] Optimal Control Allocation for the X-33,
EDI 1(13-98-125), Mark E. Jackson, May 21, 1998
[6] Control System Model of an Airframe Flex Model
With Application to X-33, Mike Hannan, May 15,
1998
[7] Flight Dynamics and Stability and Control
Characteristics of the X-33 Vehicle, AIAA 98-4410,
H. P. Lee, M. Chang and M. K. Kaiser, Aug. 10,
1998
[8] Deterministic Reconfigurable Control Design for
the X-33 Vehicle, AIAA 98-4413, Elaine A. Wagner,
John J. Burken, Aug. 10, 1998
[9] "Sliding Mode Control of the X33VehicIe in
Launch and Re-entry Modes," Yuri Shtessel, James
McDuffie, Mark Jackson, Charles Hall, Don Krupp,
Michael Gallaher, and N. Douglas Hendrix,
AIAA98-4414, Proceedings of AIAA
Guidance, Navigation, and Control Conference,
Boston, MA, August 10-12, 1998
[10] The Dynamics of Liquids in Moving Containers
With Applications to Space Vehicle Technology,
Abramson, Ed., NASA SP- 106, 1966
[1 1] The NASA/MSFC Global Reference
Atmosphere Model - 1995 Version (GRAM - 95),
NASA TM 4715, C. G. Justus, W. R. Jeffries, S. P.
Yung, and D. L. Johnson, Aug. 1995
References:
[1] Reusable Launch Vehicle Single Stage To Orbit
WB001 Flight Mechanics Data Book, November 29,
1994
11
American Institute of Aerpnautics and Astronuatics
