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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. 


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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 


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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 

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Entry 

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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 


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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 


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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 


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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] 


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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 


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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 


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commanded bank angle: Michael 7 c 6 minion 


3 l A >i: i 

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: : 4\ 

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i i si ■ r- 
v ..i . m ... 

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E 5 0 

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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