US 20130124177Al
(19) United States
(12) Patent Application Publication (10) Pub. N0.: US 2013/0124177 A1
FALANGAS
(54)
(43) Pub. Date:
METHOD OF MODELING DYNAMIC
(52)
CHARACTERISTICS OF A FLIGHT VEHICLE
US. Cl.
CPC ................................ .. G06F 17/5095 (2013.01)
USPC
(71) Applicant: ERIC T. FALANGAS, FOUNTAIN
VALLEY, CA (US)
(72)
Inventor
'
(21)
A 1 NO _ 13/739 on
pp '
ERIC T FALANGAS FOUNTAIN
VALLES'K CA (Us) ’
"
ABSTRACT
invention alloWs a user to de?ne the complexity of a ?ight
vehicle model, and such models may be simple rigid body
’
'
703/8
The present invention models dynamic behavior of ?ight
vehicles for simulation, analysis, and design. The present
models, models of medium complexity, or very complex
Jan 11 2013
'
............................................................ ..
(57)
’
(22) Filed
May 16, 2013
models including high order dynamics comprising hundreds
’
of structural ?exibility modes and variables related to aero
Related U‘s‘ Application Data
elasticity, fuel sloshing, various types of effectors, tail-Wags
dog dynamics, complex actuator models, load-torque feed
(63) Continuation of application No. 12/592,651, ?led on
back, Wind gusts, and other parameters impacting ?ight
Dec. 1, 2009, noW Pat. No. 8,380,473.
vehicles. The present invention accommodates and analyzes
multiple vehicle and actuator concepts and con?gurations as
Publication Classi?cation
(51) Int. Cl.
G06F 17/50
de?ned in ?ight vehicle input data, Which speci?es ?ight
vehicle parameters at a steady-state condition for modeling
?ight vehicle response to dynamic forces and ?ight control
commands With respect to steady state operation.
(2006.01)
Vehicle Input
Data
x.inp
Systems File
containing the
110
vehicle state
130
/100
X,m0d
x. nod
—>'
:
—>-
Flight Vehicle
Mode/mg Program
.
Modal Data
120
Input Files
140
x.gaf
Aero-E/astic
Data
space model
150
Patent Application Publication
May 16, 2013 Sheet 1 0f 3
US 2013/0124177 A1
Vehicle Input
Data
Systems File
containing the
110
vehicle state
130
r100
x.mod
x. nod
’
:
—>-
Modal Data
Flight Vehicle
Modeling Program
.
A
Input F/les
140
space model
120
v
xgaf
User
Aero-E/astic
Data
FIG‘ 1
150
f 11 0
[120
Input File
Systems File
(xxxJnp)
(xxx.Qdr)
M
r 200
M
System Modi?cation
:
Program
User
:
FIG. 2
Patent Application Publication
May 16, 2013 Sheet 2 0f3
Mixing Logic
US 2013/0124177 A1
300
Inputs
f?rector
r
Commands
320
310 3
0
%
'= 310
g
07(1)
R ll
dz(1)
_
dy(2)
Pitch
(12(2)
3—>-
Q 3103
Yaw
i
g
I,
Engine
.
:320 Deflect/ons
dthmtg)
320 Thrust
nit/7,0113) C320 Variations
AyAcce/erat
(D
320
dthrot?) C320
AxAcce/erat
g
>
320 Pitch/Yaw
'“
s,
"5
0.)
/_
7
—>'
dsun‘?)
AzAcce/erat
C320
dsurfw
320 Control
d
FIG 3
2
320
(ye/6V com
r400
E/evon
32“
300\
: Actuat
HMe/
r100
>
I
Vehicle
:
Outputs
I
"
7
F400
Mixing
F320
Logic
‘sail com_
>
' Ai/eron
:
Vehicle
> Actuat
:
Model
HMa/l
320
r400
5rud com
320
\
>
" Rudder
:
= Actuat
_
Q HMrud
4
Surface
5””:(3) t 3,0 De?ections
Hinge Moments
Patent Application Publication
May 16, 2013 Sheet 3 0f 3
US 2013/0124177 A1
Gust Input
r300
r400
Mixing
_
Logic
R’
I
320
Actuator
r100
_
Vehicle
7
Model
ro/l, pitch, yaw iI310
demands
r500
—--
Command
FCS
<
Measurements
Inputs
FIG. 5
Output
May 16,2013
US 2013/0124177 A1
METHOD OF MODELING DYNAMIC
CHARACTERISTICS OF A FLIGHT VEHICLE
a comprehensive ?ight vehicle modeling tool that aggregates
all input data and is easy and convenient to use and yet
versatile enough to apply to different types of ?ight vehicles
CROSS-REFERENCE TO RELATED PATENT
APPLICATIONS
[0001] This application claims priority to a provisional
application having Ser. No. 61/268,434, ?led Jun. 13, 2009,
the contents of Which are hereby incorporated by reference in
and varying parameters and complexity of modeling.
BRIEF SUMMARY OF THE INVENTION
[0006] The present invention is a utility softWare product
used to create linear dynamic models of ?ight vehicles that
their entirety. This application is also a continuation of non
can be used for simulation purposes and also for control
provisional patent application having Ser. No. 11/592,651,
analysis and design. Flight vehicles include but are not lim
ited to aircraft, gliders, spacecraft, space shuttles, space sta
?led Dec. 1, 2009, the contents of Which are also hereby
incorporated by reference in their entirety.
BACKGROUND OF THE INVENTION
tions, launch vehicles, rocket planes, missiles, and any other
vehicles capable of ?ight. The present invention alloWs a user
to de?ne the complexity of the models created, and such
models may be simple rigid body models for preliminary
[0002]
The present invention generally relates to a method
of modeling dynamic characteristics of ?ight vehicles. Spe
analysis, models of medium complexity, or very complex
models including high order dynamics that include hundreds
ci?cally, the present invention relates to a method of compil
of structural ?exibility modes and variables related to aero
ing input data de?ning characteristics of a ?ight vehicle and
elasticity, fuel sloshing, various types of effectors, tail-Wags
dog dynamics, complex actuator models, load-torque feed
generating system output data for performing simulation,
analysis, and design on the ?ight vehicle control system.
[0003] Existing methods of modeling high order ?ight
vehicle dynamics and generating an out-put ?le for use in
simulation, analysis, and design of ?ight vehicle controls are
complicated and time consuming. The performance quality of
?ight vehicles, such as launch vehicles, re-entry vehicles, and
high performance aircraft, is generally studied in tWo distinct,
though related, phases. The ?rst one deals With orbital
back, Wind gusts, etc. Other aspects of ?ight vehicles that can
be modeled With the present invention include any number of
thrust vector control (TVC) engines, a number of throttling
engines, a number of RCS jets, a number of control surfaces,
control moment gyros (CMG), or reaction Wheels, etc.
[0007] The present invention is not tailored to any speci?c
vehicle application, but can accommodate and analyZe mul
mechanics, vehicle guidance, and the shaping of point mass
tiple vehicle concepts and con?gurations. Vehicle con?gura
tion is de-?ned in the input data, Which speci?es ?ight vehicle
trajectories assuming that the vehicle can be perfectly steered
along the desired path. This analysis is usually referred to as
parameters at a steady-state condition for modeling variables
“long period dynamics.” The second study deals With small
of ?ight vehicle response to dynamic forces during steady
state operation of the ?ight vehicle, and Which may include,
variations or perturbations of the vehicle from its nominal
but is not limited to data relating to mass properties, aerody
trajectory. The perturbation dynamics have a shorter period
namic data, trajectory data, engine data, slosh, control surface
data, hinge moment coe?icients, aero-elastic coef?cients,
and they are also referred to as “short period dynamics.”
Flight vehicles are modeled as linear state-space representa
tions used for analyZing the ?ight control system stability and
performance With respect to guidance commands, Wind gust
disturbances, failures, etc.
[0004]
Although vehicle parameters such as mass proper
ties, aero data, trajectory, and others are constantly changing
throughout a mission, ?ight control system (PCS) gains and
CMG, reaction Wheel data, sensor types, and other variables.
[0008] Input data is compiled and applied to multiple utility
subprograms that perform functions such as ?ight vehicle and
actuator modeling, designing mixing logic for combining
various types of effectors, reading modal data ?les, selecting
important bending modes and rescaling the mod-al data,
modifying scaling and reducing state-space systems, and
?lters are traditionally designed at ?xed, mission critical
?ight conditions, called “time slices.” Critical conditions for
rocket vehicles are at high dynamic pressures, lift-off, maxi
combining subsystems together. The various utility subpro
mum slosh, before and after staging, high angles of attack (a),
alloW a user to control performance of the pre-sent invention.
grams are selected from menus on a graphical user interface
(GUI) using WindoWs and dialog boxes to accept data and
etc. The ?ight control system gains are interpolated or
[0009]
phased-in betWeen the time slices using “gain scheduling.”
?les, including input data ?les, modal data ?les, and output
For an aircraft one estimates the range of ?ight envelope in
terms of alphas versus Mach number, and design ?ight con
trol system gains at as many alpha and Mach number combi
nations as necessary to cover the ?ight envelope. Look-up
tables of gains versus alphas and Mach numbers are coded in
modeling softWare and the gains are interpolated at interme
diate values.
[0005] There is a need for a modeling tool that can easily
create vehicle state-space models for control design and
system ?les. An input data ?le consists of sets of data, each set
of data designated to provide data speci?c to a utility subpro
gram. An input data ?le has a speci?c extension, and it is
analysis directly from vehicle parameters at different ?ight
conditions, for ?ight vehicle models ranging from simple
rigid-body models for preliminary ?ight control system
design to more complex ones that include high order reso
nances used for detailed design, stability analysis and perfor
mance evaluation in presence of disturbances. The present
invention is therefore motivated at least in part by the need for
The present invention utiliZes different types of data
dedicated to a speci?c project. Each input data ?le may con
tain several sets of ?ight vehicle or other utility program data.
For example, the input data ?le may include ?ight vehicle
data for creating a vehicle system, actuator data for creating
actuator systems, system modi?cation data, and system inter
connection data, all designated for a speci?c vehicle model
ing project. A user of the present invention does not need to
create the input data ?les from scratch, but the present inven
tion includes GUI utilities for entering the input data for a
vehicle, actuator, etc. The vehicle parameters are saved by the
program in the input data ?le.
[0010] Outputs are linear state-space systems and matrices.
They are saved in system ?les that also have a speci?c ?le
May 16,2013
US 2013/0124177 A1
name extension. The present invention also includes utilities
that convert the output systems or matrices to ?le formats for
third party programs such as Matlab® so that they can easily
be imported into such a program for control analysis and
simulations.
[0011] The present invention includes additional GUI utili
ties for maintaining the input and out-put data ?les and for
making them more presentable to the user. Each system con
tained With an input or output data ?le is de?ned by a title, a
short functional description, and also de?nitions of its inputs,
states, and outputs. There are graphic utilities for vieWing
such system ?les via menus and dialog displays. After an
output data ?le is generated With the present invention, state
space matrices created by the system data therein can be
graphically displayed With color-coded elements. User-de
?ned comments may be displayed on the side of the system
[0016] The present invention may also be used to create an
actuator state-space model using one of the actuator modeling
options using a set of actuator parameters. Sensor models
may also be created from transfer functions. The ?ight vehicle
model may be combined With the actuator and sensor models
together to create a bigger plant model. If the controller is in
the Z-domain, the present invention may transform the plant
model using a Z-transform option.
[0017] The plant model may be combined With the control
ler systems together in open-loop and closed-loop forms
using a systems combination option. The open-loop and
closed-loop models are used to analyZe the overall system
stability and performance in the frequency and time do -main.
If the stability and performance requirements are not satis
?ed, the ?ight control system gains may be modi?ed, and
lead-lag and notch ?lters may be added, and the analysis
matrices together With the de?nitions of the system inputs,
states, and outputs.
[0012] The present invention also includes GUI utilities for
vieWing, editing, and executing in-put data ?les. A user may
repeated.
access menus and dialogs for selecting data sets Within an
torques and other dynamic effects to a satisfactory level of
input data ?le, and is capable of modifying data sets, copying
complexity.
data sets to another ?lename, introducing user de?ned com
[0019] The present invention therefore addresses the needs
of the ?ight control analyst, Who can easily transform the
ments and notes, and executing data sets using the appropriate
utility subprogram. Accordingly, a utility subprogram can
either be selected to run from the main menu or from an input
data ?le GUI utility.
[0013] The present invention also has a batch processing
option, Where several sets of input data Within a single input
data ?le can be processed together instead of executing each
program individually. The program requires a batch input,
Which is a set of commands, to be included in the input data
?le. Each command line Within the batch calls a utility sub
program With the title of a data set containing the appropriate
input data. Batch processing greatly reduces the time required
to create a vehicle model since many times one needs to
modify the input data and recreate the model. There is also a
utility for creating batch data.
[0014] In addition to dynamic modeling the present inven
tion also performs static stability and static performance
[0018] The analyst may gradually increase the complexity
of the ?ight vehicle models by adding parameters such as
tail-Wags-dog, slosh, bending, detailed actuator models, load
trajectory, aero, and mass properties data into linear state
space models for a quick evaluation of system performance at
?xed ?ight conditions, all Within one modeling tool. The
program can be used to analyZe various ?ight vehicles such as
launch vehicles, rocket-planes, reentry vehicles, space sta
tions, satellites, and high performance aircraft that use rocket
engines, reaction jets, differential throttling, control moment
gyros (CMG), reaction Wheels (RW), and control surfaces. A
model can easily be modi?ed to a different con?guration by
changing the input data. The input data comprises trajectory
data, aerodynamic data, mass properties, engine parameters,
reaction control thrusters, orientation angles, control sur
faces, CMG, RW, Wind gust, locations of sensors and effec
tors, slosh parameters, bending mode frequencies, aero-elas
formance along a desired trajectory using mass properties,
tic coe?icients, mode shapes, and various types of actuator
models using actuator parameters. The analyst may also
gradually add more details and increase complexity in the
vehicle model. Starting With a simple rigid body model that
aerodynamic coe?icients, engine data, etc. They evaluate
can be used for an initial evaluation of a neW ?ight vehicle
trimability, static stability, time to double amplitude, and
other lateral performance parameters Which give a good indi
cation of a vehicle concept’s ?yability. The static perfor
present invention into a very complex one as the con?guration
design matures by including more details such as fuel slosh
analysis. There are utilities Which evaluate the vehicle per
concept, the model may evolve using the modeling tool of the
mance utilities are great for quick initial evaluation of neW
ing, bending, tail-Wags-dog (TWD), load-torque feedback,
vehicle concepts.
[0015] A typical vehicle modeling, design, and ?ight con
trol analysis procedure With the present invention begins With
a simple rigid-body vehicle model. The ?ight vehicle model
high order actuator models, control surface hinge moments,
ing program of the present invention is used to obtain a linear
state-space model from the vehicle input data. The state
space model is saved in a system ?le. A mixing logic program
may be used to create a gain matrix that converts roll, pitch,
and yaW demands to engine or surface de?ections. The mix
ing logic matrix may be combined With the simple vehicle
model to create the design plant model in the systems ?le. The
present invention may also be used to combine the vehicle
system With the mixing logic matrix connected at the vehicle
input. If neces sary, these may also be decoupled into pitch and
thrust-vector-control (TVC), aero-surface mixing logic, and
others. The present invention also includes options for creat
ing actuator models, selecting the dominant ?exible modes
from modal data ?les, and generating mixing logic matrices
that combines engine thrust vectored control (TVC), reaction
jets (RCS), and control surfaces.
[0020] The present invention reads the vehicle and actuator
data from the input data ?le and creates state-space models of
the vehicle and actuator Which are saved in the system ?le.
There are other utility programs Which also read information
from the input ?le and save systems or gain matrices in the
system ?le. The output state-space representation is com
monly used for control system analysis. In fact, linear state
lateral subsystems for use separately to design preliminary
space plant models are the standard input to most robust
control modes, and the present invention may also be used to
control design and analysis tools such as LQG, H-in?nity, etc.
The output state-space vehicle models include pitch and lat
extract the pitch and lateral subsystems from bigger systems.
May 16,2013
US 2013/0124177A1
eral dynamics coupled together but the present invention
provides additional utilities that decouple the systems,
modify them, or extract a subsystem of selected inputs, states,
and outputs from a bigger system. There are also situations
Where additional out-puts are needed in the state-space
model. For example, outputs that may be needed to evaluate
vehicle performance in control synthesis or simulation mod
els, such as outputs coming from states, state derivatives, or
output derivatives. The present invention includes a system
modi?cation utility that performs such operations. System
prising providing a system, Wherein the system comprises
distinct softWare modules each embodied in a computer hard
Ware environment and comprising at least a data collection
module, a data conversion module having a plurality of sub
modules each analyZing data relating to speci?c parameters
de?ning ?ight vehicle movement, a data processing module,
and an output ?le generation module, and compiling an input
data ?le from input data de?ning a ?ight vehicle, executing
the input data ?le to convert the input data de?ning a ?ight
vehicle into a state-space system ?le comprising data de?ning
?les use a standard format Which includes the system title,
folloWed by some comment lines that describe the system,
at least one system, extracting the data de?ning at least one
folloWed by the matrices (A, B, C, D), and the de?nitions of
data de?ning the at least one system to a ?le format for
the state variable inputs, states, and outputs at the bottom of
each system, beloW the matrices. Utility options are also
simulating performance of the ?ight vehicle.
available to convert the state-space systems a format for Mat
lab® and also from Matlab® ?les.
includes a system for modeling dynamic characteristics of a
[0021] The present invention therefore includes, in one
embodiment, a method of modeling dynamic characteristics
system from the state-space system ?le, and exporting the
[0025]
In yet another embodiment, the present invention
?ight vehicle, comprising a computer readable program,
embodied on at least one module in a computer hardWare
of a ?ight vehicle, comprising collecting input data specify
environment, con?gured to compile an input data ?le from
input data de?ning a ?ight vehicle, a computer readable pro
ing ?ight vehicle parameters at a steady-state condition for
modeling variables of ?ight vehicle response to dynamic
forces during steady-state operation of the ?ight vehicle, con
verting the input data into state-space systems data for use by
Ware environment, con?gured to execute the input data ?le to
convert the input data de?ning a ?ight vehicle into a state
space system ?le comprising data de?ning at least one sys
at least one utility program module to create a state-space
tem, a computer readable program, embodied on at least one
system modeling one or more components of ?ight vehicle
activity, the at least one utility pro- gram module generating a
systems data output ?le comprising at least one matrix map
module in a computer hardWare environment, con?gured to
ping the input data to the state-space systems data, and gen
erating an output ?le for simulating ?ight vehicle design and
performance based on at least one matrix mapping the input
data to the state-space systems data.
[0022]
In another embodiment, the present invention
includes a method of modeling dynamic characteristics of a
gram, embodied on at least one module in a computer hard
extract the data de?ning at least one system from the state
space system ?le, and a computer readable program, embod
ied on at least one module in a computer hardWare environ
ment, con?gured to export the data de?ning the at least one
system to a ?le format for simulating performance of the
?ight vehicle.
[0026] Other features and advantages of the present inven
tion Will become more apparent from the folloWing descrip
tion of the embodiments, taken together With the accompa
?ight vehicle, comprising compiling an input data ?le from
input data de?ning a ?ight vehicle, executing the input data
nying draWings, Which illustrate, by Way of example, the
?le to convert the input data de?ning a ?ight vehicle into a
principles of the invention.
state-space system ?le comprising data de?ning at least one
system, extracting the data de?ning at least one system from
the state- space system ?le, and exporting the data de?ning the
at least one system to a ?le format for simulating performance
of the ?ight vehicle.
[0023] In another embodiment, the present invention
includes a method of batch modeling dynamic characteristics
of a ?ight vehicle, comprising compiling a batch input data
?le from multiple sets of batch input data de?ning ?ight
vehicle parameters at a steady-state condition and de?ning a
set of commands for modeling ?ight vehicle characteristics,
calling a speci?c utility program module de?ned in the batch
input data ?le Within a title of the set of commands for the
speci?c utility program module included Within input data
appropriate for the speci?c utility program module to convert
the input data de?ning ?ight vehicle parameters at a steady
state condition into a state-space system ?le comprising data
de?ning at least one system, extracting the data de?ning at
least one system from the state-space system ?le, and export
ing the data de-?ning the at least one system to a ?le format
for simulating performance of the ?ight vehicle.
[0024]
In still another embodiment, the present invention
includes a computer program product, comprising a com
puter usable medium having a computer readable program
code embodied therein, the computer readable program code
adapted to be executed to implement a method for modeling
dynamic characteristics of a ?ight vehicle, the method com
BRIEF DESCRIPTION OF THE SEVERAL
VIEWS OF THE DRAWINGS
[0027]
FIG. 1 is block diagram of inputs and outputs of a
?ight vehicle modeling program according to the present
invention;
[0028] FIG. 2 is block diagram of inputs and outputs of a
system modi?cation utility of a ?ight vehicle modeling pro
gram according to one embodiment of the present invention;
[0029] FIG. 3 is block diagram of inputs and outputs of a
mixing logic utility of a ?ight vehicle modeling program
according to one embodiment of the present invention;
[0030] FIG. 4 is block diagram of inputs and outputs of a
mixing logic utility and actuator utilities of a ?ight vehicle
modeling program according to one embodiment of the
present invention; and
[0031] FIG. 5 is block diagram of inputs and outputs of a
mixing logic utility and actuator utilities of a ?ight vehicle
modeling program according to another embodiment of the
present invention.
DETAILED DESCRIPTION OF THE INVENTION
[0032]
In the folloWing description of the present invention
reference is made to the accompanying draWings Which form
a part thereof, and in Which is shoWn, by Way of illustration,
exemplary embodiments illustrating the principles of the
May 16,2013
US 2013/0124177 A1
present invention and hoW it may be practiced. It is to be
understood that other embodiments may be utilized to prac
tice the present invention and structural and functional
changes may be made thereto Without departing from the
scope of the present invention.
Introduction
[0033]
The present invention is a collection of ?ight vehicle
modeling and analysis programs and other related utilities,
used to create complex state-space models of ?ight vehicles
for linear stability and performance analysis. The dynamic
models may vary, from simple rigid body to very complex
models that may include high order dynamics, such as actua
?ight vehicle modeling program 100 inputs and outputs,
shoWing types of input data ?les 110 and the output system
?le 120.
[0036] Referring to FIG. 1, for every vehicle or ?ight con
dition analysis a pair of ?les, an input data ?le 110 and a
system ?le 120 are created speci?cally for that project. The
input data ?le 110 includes sets of data or instructions for the
Flixan utility programs. Each input data ?le 110 may contain
many sets of data for the various utility programs. On the top
of each data set a label identi?es the utility program for Which
the data belongs to and that Will be processed by this utility
program. BeloW the label a short title de?nes the data. The
same title is also used to de?ne the system Which is created by
tors, tail-Wag-dog, slosh and ?exibility With hundreds of
that data after being processed by the corresponding utility
structural modes. The program is interactive and uses a
program. BeloW the title there may be some optional com
graphical user interface (GUI) With WindoWs and menus to
ments or user notes describing in more detail the purpose,
conditions, intention, or any other details a user 150 may Want
interface With a user-analyst. The present invention, also
referred to herein as the Flixan program package, the Flixan
program, or simply Flixan, includes and performs the linear
iZed equations of motion applicable to ?ight vehicles such as
airplanes, gliders, launch vehicles, rockets, missiles, space
to add for documentation purposes. There are interactive utili
ties Within mo st Flixan programs that guide the user 150 in the
preparation of the input data sets.
[0037] System ?les 120 include quadruple systems de?ned
craft, and other such vehicles capable of motion in air, space,
by state-space matrices (a, b, c, d), control design state-space
or the atmosphere, and creates state-space systems at ?xed
conditions. The level of the complexity of the model is adjust
able and customiZable according to the preferences and needs
models, or individual matrices. They are created by various
programs in the Flixan program package. A system ?le 120
may include many systems, such as a simple rigid-body
of the user.
vehicle and a complex high order vehicle created by the ?ight
[0034]
vehicle modeling pro-gram 100. It may also include several
actuator models for each aero-surface or engine TVC. The
system ?le 120 may also have ?ight control or sensor systems
implemented in terms of transfer-function combinations
using the transfer-functions combination program. The sys
tem ?le 120 may also include systems derived by combining
Among the many Flixan utility programs is an
actuator modeling program that performs various hydraulic
and electro-mechanical actuator models for engine thrust
vector control (TVC) and for control surface sleWing. The
Flixan program package also includes a TVC/throttle control/
aero-surfaces mixing logic program that creates an effector
mixing logic matrix based on the engine parameters and the
smaller subsystems using the systems combination utility
control surfaces’ aero coef?cients. When this matrix is
program. There may also be discrete systems derived from
included at the input of the ?ight vehicle model it decouples
continuous systems by using the Z-transformation utility. The
the fully-coupled vehicle dynamics by reducing the interac
system ?le 120 may also include individual matrices such as
tion in some rotational directions, mainly in roll, pitch, and
gains or TVC matrices. The mixing logic program 300, for
example, creates mixing logic matrices that translate the
yaW. Some translational directions may also be included in
the mixing logic, such as motion along x or Z, if the vehicle
?ight control, roll, pitch, and yaW demands, into individual
has suf?cient control effectors to decouple motion along
these translational directions. The ?ight vehicle model often
needs to be combined together With actuator models, the
aero-surface and TVC de?ections. The Flixan program pack
age further includes utilities used to create, process, edit,
delete, vieW, or copy data sets containing input data for vari
mixing logic matrix, and the ?ight control system for control
analysis. The Flixan package includes additional utility pro
ous Flixan programs.
grams to combine state-space systems and matrices together,
create state systems from transfer function interconnections,
and to modify or extract subsystems from other systems. Still
other utility programs perform other functions such as
Z-transform analysis of continuous systems to discrete state
difference systems sampled at some sampling rate (dT), man
Input and Output Files
extension (.inp) and include ?ight vehicle data, actuator,
transfer functions, system interconnections, system modi?
cation data, etc. The ?ight vehicle modeling program 100
aging data ?les, creating control design models for LQR or
processes the input data and creates a system or a matrix. The
H-in?nity, and transferring systems or matrices to third party
?rst line of each set of input data in an input data ?le 110
identi?es What type of data folloWs, such as for example
programs such as Matlab®.
[0035]
The present invention therefore provides a suite of
vehicle modeling modules, all of Which are selectable from a
system of menu in the Flixan program’s GUI. The present
invention includes a ?ight vehicle modeling program 100 that
reads the vehicle parameters, combines it With other ?ight
[0038]
As noted above, the input data ?les 110 have an
FLIGHT VEHICLE INPUT DATA, or INTERCONNEC
TION OF SYSTEMS, or ACTUATOR INPUT DATA, or
MIXING LOGIC, etc. The second line is a unique title for the
data. The same title is also used to identify the system or the
matrix Which is created by the program and it is saved in a
vehicle data such as the modal data de?ning structural ?ex
separate system ?le 120. The lines beloW the title, starting
ibility modes, and generates the ?ight vehicle state-space
With an exclamation mark (l), are comment lines Which are
system data. TWo main types of ?les are contemplated for the
inserted there by the user 150, either directly by editing the
?ight vehicle modeling program 100: input data ?les 110 that
input data ?le 110, or via other utility programs. Such com
ment lines assist the user 150 in formulating a modeling
have a ?lename extension (.inp), and system ?les 120 With a
?lename extension (.qdr). FIG. 1 is a block depiction of the
project. The comment lines appear in a dialog display Where
May 16,2013
US 2013/0124177 A1
they can be modi?ed, and they may also be transferred to the
larly, each accelerometer can be speci?ed to measure along
state-space model in the system ?le 120. A sample input data
the vehicle x, y, or Z axes. Although they are referred to as
?le 110 is shoWn beloW.
accelerometers, they can be de?ned to measure either: linear
[0039]
position (ft), velocity (ft/sec), or translational acceleration
(ft/sec2). Accelerometer measurements include rigid-body
The input data ?le 110 includes vehicle parameters
at a steady-state, or trimmed, condition. The input data ?le
110 also contains input data such as mass properties, trajec
tory, aerodynamic derivatives, engine data, control surface
plus ?ex motion, and can also be con?gured to measure only
the ?ex motion. One must also specify the location of the
data, slosh parameters, various sensors, Wind-gust, and ?ex
accelerometer in vehicle coordinates. The vane sensors mea
ibility data. An input data ?le 110 may include more than one
sure the angles of attack and sideslip, and are normally
located in front of the ?ight vehicle. As With accelerometers,
set of ?ight vehicle data. For example, the input data ?le 110
may include a rigid-body set of ?ight vehicle data and a
one must also specify the vane location in vehicle coordi
?exible vehicle set of ?ight vehicle data, and it may also
include a number of structural ?exibility modes, actuator
data, and interconnection info.
nates.
[0040]
Referring to the above sample input data ?le 110,
are included, the Flixan program requires the slosh mass
the line beloW the vehicle title and the comment lines is the
?ags line. There are four ?ags Which turn on different mod
(slugs), the sloshing frequency in l g in (rad/sec), the damp
ing coef?cient, and the un-de?ected (x, y, Z) location of the
[0043]
Also de?ned in the ?ight vehicle data set, are the
propellant sloshing parameters. When sloshing parameters
eling options. The ?rst ?ag is for resolving body rates, and can
slosh mass in vehicle coordinates. If there is no sloshing, the
be set to either “Body Axes” (default) or “Stability Axes.” The
second ?ag determines the attitude output, can be set to either
“AttitudeIEuler Angles” (default) or “AttitudeIRate lnte
gral.” The third ?ag relates to aero-elastic data, and may be set
number of slosh masses is set to Zero.
to either “Without GAFD” (default) or “Include GAFD”
When there is a GAFD data ?le available. The fourth ?ag
relates to tum-coordination logic. If the vehicle ?ight soft
Ware includes turn-coordination logic for an airplane, and the
user 150 prefers the tum-coordination logic to be included in
the plant model instead (in order to simplify the control
design so that one does not have to carry it the controller), the
?ag is set to “With Turn Coordination.” OtherWise, if the user
150 does not Want to include tum-coordination, the ?ag is set
to the default state.
[0041]
Within the input data ?le 110, the ?rst group of ?ight
vehicle data beloW the ?ags relates to parameters such as
mass properties, lnertias, CG, trajectory parameters, alpha,
beta, attitude, altitude, nominal rates, accelerations, Wind
gust disturbance, aero parameters, aero derivatives, etc. Other
types of ?ight vehicle data in the input data ?le 110 includes
the control surfaces in-formation, such as trim position, max
[0044]
The ?ight vehicle data set may also include modal
data Which de?nes ?ex information. If a model is to be a
rigid-body model the “Number of Bending Modes: 0” must
be set, otherWise, the number of ?ex modes must be entered.
If the number of bending modes is greater than Zero, then the
?ight vehicle data set Will also include the title of the selected
modal data that Will be combined With the rigid vehicle data.
Modal data and ?ex modeling are discussed in full herein.
[0045] The selected modes are another set of ?ight vehicle
data that should also be saved in the same input data ?le 110
together the vehicle rigid-body data. Note that in the present
invention, When the term “input data ?le” is used, the ?ight
vehicle data comprising the input data ?le 110 includes all
?ight vehicle data to be modeled: rigid-body vehicle data,
modal data, etc. Modal data is collected using a separate
module of the Flixan program package knoWn as the mode
se-lection program. The mode selection process is described
further herein but until noW it has been assumed that the
selected modal data is already in the input data ?le 110 and
ready to be processed together With the ?ight vehicle data.
The title of the selected modes is placed, during mode selec
de?ection, hinge line orientation, surface mass properties,
moment arm, surface chord, hinge line location, hinge
tion, on the top of the selected modal data. Different sets of
moment coef?cients, aero-force and moment increments due
to de?ection, etc. The ?rst line before the control surface data
and therefore the input data ?le 110 may contain more than
speci?es the number of surfaces and also the tail-Wags-dog
(TWD) ?ag, either “Include TWD” or “No TWD” (default).
one set of selected modes under different titles, a similar
concept to containing more than one set of vehicle data. This
Engine data is also included, comprising the nominal engine
thrust and the maximum thrust (if the engine is throttable). If
the engine is not throttable, (variable thrust), the maximum
is hoW the Flixan program package identi?es Which set of
modal data is to be combined With a ?ight vehicle data set.
The selected modes in the input data ?le 110 are identi?ed by
the Flixan program from the id label, “SELECTED MODAL
thrust is set equal to the nominal thrust. The engine data also
includes a label that de?nes Whether the engine is “Gimbal
ing,” “Throttling,” or both, since one may have a situation
Where some engines are gimbaling and some are throttling, or
both. Other engine parameters include mounting angles, the
maximum pitch and yaW de?ections (if gimbaling, otherWise
they are assumed to be Zero), the engine mass properties for
computing the TWD force, and the engine gimbal location in
vehicle coordinates. A short label that identi?es each engine
or RCS thruster may also be included.
[0042]
Among sensor data in the ?ight vehicle input data
?le 110, there are three types of sensors: gyros, accelerom
eters, and vane sensors. Each gyro is speci?ed to measure
either in roll, pitch, or yaW rotations. Although referred to as
selected modes may also be present including different titles,
DAT ,” above the title.
[0046] The Flixan program package includes tWo utility
programs for managing the input data ?les 110: an input data
set processing utility, and a utility for creating and processing
batch data sets. The input data set processing utility is used to
clean and manage input data ?les 110. It per-forms tasks such
as selecting and editing an input data ?le 110, executing an
individual pro-gram/data combination or a batch set, deleting
or relocating a data set inside the same data ?le, or copying a
number of selected data sets to another data ?le. A batch is a
set of input instructions that command a utility program to
process various sets of input data sequentially Without any
gyros, these sensors can be de?ned to measure either: angular
user 150 intervention, instead of requiring a separate execu
tion of each program With its data. The batch mode execution
position (rad), rate (rad/ sec), or acceleration (rad/sec2). Simi
speeds up the reprocessing of the input data ?les 110 after
May 16,2013
US 2013/0124177 A1
some data modi?cations. The batch creation utility described
here is not only used to create neW batch data sets, but also to
modify existing ones and save them under a different title in
an input data ?le 110. To create a set of batch mode instruc
tions one must ?rst plan the data processing sequence and test
batch utility can be used to create a set of batch instructions
eters, gyros, and the angle of attack sensors, the locations of
the slosh masses, and a disturbance input for applying a
disturbance force.
[0049] The mode selection utility program uses also a
smaller ?le associated With the modal data ?le 130. This
smaller ?le is a nodes lookup table, also referred to as map,
having an extension (.nod), and is created by the user 150. It
contains a list of the structural nodes Which are in the modal
data ?le 130. This lookup ?le includes a title folloWed by
several lines, each line de?ning a node. Each line contains a
that Will automate the entire process by running the batch data
instead of the individual program steps. This utility may also
node number starting from 1 to as many nodes as they are in
be used to test the batch set by making sure that it runs
the table, the node ID Which is a large and unique number that
successfully before saving it in the input data ?le 110.
identi?es the node in the Nastran model, and the x, y, and Z
location of the node in vehicle coordinates. The number of
nodes and their sequence in the map corresponds to the num
ber of nodes and the node sequence in the modal data ?le 130.
it outside the batch utility by running each individual program
separately to make sure that each pro gram/data pair runs
successfully by itself and that there are no errors in the input
data. In other Words, debug each step individually. Then the
Modal Data and Flex Modeling
short description of the corresponding vehicle location, a
[0047] As mentioned above, modal data de?ning structural
?exibility modes is input data sepa-rate from input data de?n
ing rigid-body ?ight vehicle parameters, and is entered and
collected separate from such rigid-body data and maintained
The lookup ?le is used by the mode selection program in
menus and dialogs that help the user 150 to identify vehicle
locations that correspond to actuator and sensor positions.
in a separate modal data ?le 130 having a ?le extension
(.mod). The mode selection program, Which is a utility pro
Flexibility Mode Selection
gram Within Flixan, post-processes the modal data ?le, scales,
and extracts a smaller set of modes to be processed and
[0050] In embodiments introducing ?exibility into the
?ight vehicle modeling program 100, the present invention
combined With the ?ight vehicle rigid-body data. The
requires a selected set of ?exure modes Which are processed
selected set of ?ex modes is included and saved in the same
together With the rigid-body ?ight vehicle data. The selected
input data ?le, beloW the vehicle rigid body data, under the
modes are not the same ones de?ned in the modal data ?le
130, but are a smaller set of modes Which are combined into
label “SELECTED MODAL DATA.” The ?ight vehicle mod
eling program 100 combines and processes the selected
modal data With the rigid-body data Which are both included
the input data ?le 110. Mode selection is the process of going
1 1 0 includes data from the rigid-body input data and selected/
rescaled modal data parameters for the desired ?ight vehicle
through the modal data ?le 130 and extracting a smaller set of
modal frequencies at feWer vehicle locations, i.e. only at the
locations Which are speci?ed in the vehicle input data. A
utility program facilitates mode selection and performs this
modeling.
mode selection process to prepare the smaller set of modes
[0048] The structural ?exibility of the ?ight vehicle is char
acteriZed by a number of bending modes, each de?ned by
parameters such as mode frequency, damping coe?icient,
generaliZed mass, and the generaliZed mode shapes at key
?ight vehicle locations (nodes), such as the force application
that Will be processed by the ?ight vehicle modeling program
in the input data ?le. The resulting compiled input data ?le
points and the sensors. Modal data includes a large number of
mode frequencies and shapes and is derived from a ?nite
elements model of the structure at a ?xed con?guration. A full
modal data ?le 130 has a title Which identi?es the ?ight
vehicle con?guration folloWed by a line that de?nes hoW
many modes and hoW many nodes are included. The modal
data ?le 130 also includes a group of mode shapes data at each
modal frequency. Each line represents a node and contains the
node ID and six mode shapes at each mode, three translations
along the vehicle x, y, Z axes, and three rotations about the x,
y, Z axes. A typical modal data ?le 130 includes hundreds of
100.
[0051] The modal data ?le 130 includes several hundred
bending modes. Most frequently, hoW-ever, a small number
of modes (less than 50) Will be su?icient to determine the
vehicle stability and performance With suf?cient accuracy.
The original modal data ?le 130 may also include many
locations (nodes), most of Which may not be needed for a
particular model. Only the nodes that correspond to vehicle
locations Which are de?ned in the input data, such as the
engines, sur-faces, and sensors, need to be included in the
selected set of modes. The mode selection program provides
the capability to compare the modes in terms of strength and
select a smaller number of modes Which are strong in a certain
direction betWeen different parts of the vehicle. The selection
is based on the modal strength Which is a measure of com
modes from a Nastran output at a number of locations and is
bined controllability and observability of each mode betWeen
created by post-processing the Nastran output data using a
separate user-supplied program to reformat the data in the
the actuators and sensors. The selected mode frequencies and
shapes are saved in the input data ?le 110 to be used by the
standard (.mod) format required by the ?ight vehicle model
?ight vehicle modeling program 100. The mode selection
ing program 100. When generating a modal data ?le 130 from
utility program also scales the modal data to match the vehicle
data. The modal data is usually computed by a ?nite elements
modeling program in units and axial directions different from
those de?ned in the ?ight vehicle data. The utility program
provides the user 150 With the capability to scale the selected
modal data and converts them to units compatible With the
a big Nastran output, one should select a suf?cient number of
nodes (locations on the structure, typically 20 to 40 nodes),
even if one is not sure that all of them Will be needed. This is
because it is easier to ignore some of the nodes When devel
oping the vehicle model than to need it later, in case one needs
an additional sensor, for example, and not have a node for it.
Some important nodes to include in the modal data ?le 130
are locations of the engine gimbals, control surface hinges,
CMGs, reaction Wheels, sensors such as IMU, accelerom
vehicle rigid body parameters before saving them.
[0052] In one example of mode selection, the user 150 may
also select a range of modes to be compared. In the folloWing
example, the user 150 speci?es the number of excitation force
May 16,2013
US 2013/0124177 A1
and torque points (Which do not necessarily correspond to
modes With the vehicle data. The selected modal data consist
vehicle actuator points, but they are used strictly for mode
selection purposes), the number of translational and rota
tional sensor points (Which do not necessarily correspond to
vehicle sensor points, but they are used strictly for mode
selection purposes), the axis of interest (i.e. modes Which are
dominant in roll, pitch, or yaW directions), and the number of
modes to be selected. The mode selection program provides
of the mode shapes and slopes (three translations along x, y, Z,
the option to either auto-select the strongest modes or manu
ally select the strongest modes by means of a graphic display
of modal strengths.
[0053] The user 150 may repeat the mode selection by
trying different number of actuator and sensor points, types,
and directions to see hoW the mode selection results may vary.
The user 150 then also identi?es the excitation and sensor
points on the structure to be used for mode selection only. In
the example, in Which the user 150 speci?ed force excitation
points for mode-selection, it is notable these locations are
only for mode selection purposes and need not represent
actual vehicle locations at the gimbals and the ?ight control
sensors, Which Will be de?ned later. The next step in the
example is to identify the nodes for the excitation points, and
the nodes for the translational and rotational sensors. The
mode selection program provides menus Where the user 150
de?nes these excitation and sensorpoints and also their direc
tions. The program displays the nodes map in menu form
Which helps the user 150 to select the excitation and sensor
locations. The selection points to a node number and its
corresponding mode shapes in the modal data ?le. Based on
and three rotations about x, y, Z) at every selected mode
frequency.
Output Systems File
[0057]
The ?ight vehicle state-space system data forms
quadruple matrices Which are saved as a system in the output
data ?le 120, also referred to herein the system ?le 120. A
system ?le 120 has a ?lename extension (.qdr) and may
include several systems or single matrices related to a certain
vehicle con?guration or ?ight condition study. Each system
or matrix is identi?ed by a unique title. The ?ight vehicle
system uses the same title as the title in the input data ?le 110.
The user 150 notes that Were entered as comments beloW the
title in the input data ?le 110 Will also be transferred as
comment lines into the system ?le 120, beloW the system title.
De?nitions of the vehicle model inputs, states, and outputs are
also included beloW the (A, B, C, D) matrices.
[0058]
The present invention includes a ?le management
utility for maintaining clean and organiZed system ?les 120 in
control analysis projects. It is similar to the input data ?le
processing utility With some differences. The user 150 can
delete some older systems or matrices from the system ?le
120, move them to a different location from the top of the
system ?le 120 in a logical sequence, edit the system ?le 120
and sensor points the pro-gram calculates the modal strength
at each mode frequency.
using a standard text editor, display the system matrices using
color coded graphics instead of actual numbers, display tables
of the system inputs, states and outputs, Write and display
[0054]
comments/user notes that describe a system or a gain matrix,
the mode shapes (translations and rotations) at the excitation
The modal strength for each mode is determined by
the values of the mode shapes at the nodes Where the forces
and torques are applied and their directions, and also by the
values of the mode shapes or slopes at the sensors and their
measured directions. High mode shape values at the excita
tion and sensor points imply strong contribution from that
mode. The mode selection program calculates the mode
strength for each mode and saves it in a separate ?le.
[0055] Before alloWing the user 150 to select Which modes
and mod-ify them graphically using WindoWs and dialogs.
The user 150 may also transfer some systems or gain matrices
to different system ?les 120. Maintaining organiZed system
?les by means of comments, labeling the system inputs,
states, and outputs, keeping the systems and matrices in a
sequential order, and deleting the unused older versions can
be a very attractive feature for documenting, especially When
the user 150 discontinues the analysis for a While to resume it
to retain from the modal data ?le 130, the user 150 enters
additional information. The mode selection program Will cre
ate a much smaller subset of the original modal data set and
save it in the input data ?le 110. The selected modal data set
later.
Will contain only the selected feW dominant modes and modal
shapes only at a feW locations that play important role in the
?ight vehicle model. A very similar selection process is used
mark {l}, (c) the system siZe in terms of number of: Inputs,
in selecting nodes that correspond to vehicle engines, control
surfaces, torque actuators, sloshing fuel, a disturbance point,
and ?ight control sensors as de?ned in the vehicle input data.
[0056] At this point the mode comparison is complete and
[0059] Each system ?le 120 may contain several systems
and matrices. Each state-space system includes: (a) a title, (b)
some comment lines (optional) starting With an exclamation
States, and outputs, (d) the sampling period (dT) if the system
is discrete (otherWise Zero), (e) the (a, b, c, d) matrix data, and
(f) de?nitions of the system states, inputs, and outputs Which
are also optional.A sample of system data in a system ?le 120
is shoWn beloW.
the user 150 selects the dominant modes, either automatically
or graphically by means of a bar chart displaying modal
strength versus mode number. Before exiting mode selection
the user 150 may type in some comment notes regarding the
mode selection process, describing, for example, What types
of modes have been selected, and the conditions of mode
selection, excitation points, measurement points, directions,
ROCKET
STATE-SPACE
PLANE
SYSTEM
AT MACH=0.85, Q=l50, T=l778.0 sec (Pitch RB)
v
! Pitch Axis Model Extracted from the Coupled Rigid Body Axes Model
I
etc. This information Will be included as comment lines near
Number of Inputs, States, Outputs, Sample Time dT (for discrete) = 3 2 3
the top of the selected modes, beloW the title. A default title
de?ning the selected modes is placed on the top of the data.
0.0000
This title can be changed as needed to better de?ne the
selected modes. The title of the selected modes must also be
included in the last line of the vehicle input data set (beloW the
line that speci?es the number of ?ex modes) in order for the
?ight vehicle modeling program 100 to associate the selected
Matrices: (A,B,C,D)
MatrixA
Size = 2 X 2
l-Column
l-RoW —0.30l38585E+00
2-RoW 0.99731876E+00
2-Colurnn
—0.39838865E+01
—0.29373747E+00
May 16,2013
US 2013/0124177 A1
8
-continued
Matrix B
1-Column
l-ROW —O.36336I6IE+0I
2-ROW —0.2l43505lE-0l
Matrix C
Size = 2 X 3
2-Column
—O.36336I6IE+0I
—0.2l43505lE-0l
-continued
De?nition of System Variables
Inputs = 3
3-Column
—0.25937799E—02
—0.22487362E—03
Size = 3 X 2
1-Row
1-Column
0.10000000E+01
2-ROW
0.00000000E+00
0.10000000E+0l
3-Row —0.22074682E+01
—0.25042853E+03
M?UiX D
1-Column
Left Rudder Deflection (rad)
Right Rudder Deflection (rad)
3
Gust Azim, Elevat Angles=(45, 45) (deg)
States = 2
2-Column
0.00000000E+00
SiZ? = 3 X 3
2-Column
I
2
I
2
Pitch Rate
Angle ofattack
( q -rigid)
(alfa-rigid)
(rad/sec)
(radians)
Outputs = 3
1
Pitch Rate (q-stab) (rad/sec)
2
Angle of attack, alfa, (radians)
3
CG Acceleration along Z axis, (ft/sec?2)
3-Column
l-ROW
0.00000000E+00
0.00000000E+00
0.00000000E+00
2-ROW
0.00000000E+00
0.00000000E+00
0.837l2588E-03
3-Row —0.17702788E+02
—0.17702788E+02
—0.18556683E+00
_
[0060]
_
_
AS noted earller, an output ?le may also Include, In
addition to systems, a single matrix. The example below
shows a system ?le comprised of a single gain matrix.
GAIN MATRIX FOR
Vehicle, Coupled Model, MaxiQ T=55 sec
l
1 This is a matrix that was created using the Flixan 2 program.
1 One more comment. It is a TVC Mixing Logic. It translates the
1 Roll, Pitch, and Yaw acceleration demands into pitch and yaw
! engine deflection commands. The inputs and outputs are de?ned
! below.
Matrix K2
Size = 10 X 3
1-Column
1 — Row
2-Column
3-Column
0.00000000E+00
—0.33481212E+00
0.00000000E+00
—0.76731573E—02
2- Row
0.42072877E-01
—0.34527500E+00
3 — Row
—0.42072877E—01
—0.34527500E+00
0.76731573E-02
4- Row
0.25131532E+00
—0.55578813E+00
—0.45 834326E-01
5 — Row
—0.25131532E+00
—0.55578813E+00
0.45834326E-01
6- Row
0.28624342E+00
0.00000000E+OO
—0.41166570E+00
7- Row
0.20227759E+00
0.00000000E+OO
—0.40758536E+00
8- Row
0.20227759E+00
0.00000000E+OO
—0.40758536E+00
9- Row
—0.14377220E—01
0.00000000E+OO
—0.59408361E+00
1 O- Row
—0.14377220E—01
0.00000000E+OO
—0.59408361E+00
De?nitions of Matrix Inputs (Columns): 3
Roll Acceleration About Vehicle X Axis
Pitch Acceleration About Vehicle Y Axis
Yaw Acceleration About Vehicle Z Axis
De?nitions of Matrix Outputs (Rows): 10
TVC Output #
I to Engine No: I
Pitch
De?ect
TVC Output #
2 to Engine No: 2
Pitch
De?ect
TVC Output #
3 to Engine No: 3
Pitch
De?ect
TVC Output #
4 to Engine No: 4
Pitch
De?ect
TVC Output #
5 to Engine No: 5
Pitch
De?ect
TVC Output #
6 to Engine No: I
Yaw
De?ect
TVC Output #
7 to Engine No: 2
Yaw
De?ect
TVC Output #
8 to Engine No: 3
Yaw
De?ect
TVC Output #
9 to Engine No: 4
Yaw
De?ect
TVC Output #
10 to Engine No: 5
Yaw
De?ect
May 16,2013
US 2013/0124177 A1
[0061]
The ?le management utility also includes menus to
alloW a user 150 to perform various operations on a system
?le 120. For example, a user 150 may move a system or a gain
matrix from its current position inside the system ?le 120 to a
neW position relative to the top of the system ?le 120. A user
150 may also delete some systems or gain matrices from the
system ?le 120. A user 150 may also graphically vieW a
system or a gain matrix using color codes instead of actual
numbers. Each matrix element appears like a small square
and is a convenient Way of vieWing large matrices, instead of
reading the actual numbers, since the color indicates the
magnitude of each element, Which in general is suf?cient
information. In one embodiment, numbers With high positive
exponent gravitate toWard the green, blue, and cyan, and
shoWn With a minus sign on the top of the matrix element. The
user 150 must also enter the system title, a short description of
the system (optional comments), and may also de?ne the
system inputs, states, and outputs. Initially the inputs, states,
and outputs are assigned some default de?nitions by the pro
gram. To change the input labels into something more
descriptive, the user 150 overWrites the old label With a neW
input label, and may select another input and enter a neW
label.
[0065]
Referring to FIG. 2, the present invention also
includes a utility program 200 used to modify, recondition or
simplify an existing state-space system. For example, the
orange, red, and broWn. Zeros are black and ones are bright
analyst may Want to replace the system outputs With a neW set
of outputs, or change the units of the system parameters, or to
eliminate some unnecessary inputs, states, or outputs. The
system modi?cation program 200 reads the state-space sys
White. Negative numbers have the minus (—) sign in front of
tem from a system ?le 120 and can create a neW system by
the colored square. The actual value of each element can be
seen at the bottom of a display dialog. The user 150 may also
modifying the old system’ s inputs, states, and outputs and by
performing certain operations. These include an operation to
rescale the original system variables by converting the units
numbers With high negative exponent gravitate toWard the
read or modify the element value using the number entry ?eld
at the bottom of the display. All the available information
The ?le management utility also alloWs users 150 to
of the old system’s inputs, states, and outputs into a different
set of units. The conversion is performed by scaling the old
state-space system variables by a constant (S), Where the old
units:(S) times the neW units. Another such operation creates
select some state-space systems or matrices from a system
a neW system by replacing the old system outputs With a neW
120 ?le and copy them to another system ?le 120. After
selecting a source ?le from the ?lename selection menu, the
titles of the systems or gain matrices Which are currently
saved in that system ?le 120 are displayed. All the system
of the old system’s outputs, states, and the derivatives of the
old system outputs and states. This option is useful for
extracting derivatives of outputs Which are often needed for
titles, gain matrices, and control synthesis model titles are
listed in the order that they appear inside the system ?le 120.
Where state or output derivatives are often included in the
about the system or matrix can be vieWed or modi?ed by this
dialog.
[0062]
[0063]
A user 150 may also choose a destination system ?le
120 Where the data Will be copied to. After selecting the
destination system ?le 120, the display shoWs the highlighted
systems or matrices that Were selected from the source ?le to
be copied in the destination system ?le 120. The selected
systems or matrices Will be added in the destination system
?le 120, and the display Will change shoWing the titles of all
the systems Which are noW present in the destination system
?le 120. The previous systems and matrices that Were in that
set of outputs Which are made up from a combination of some
optimization in LQG or H-in?nity control design models,
criteria optimization vector. The system modi?cation pro
gram 200 can also be used to simplify a system by eliminating
some of the old system’s inputs, states, or outputs Which are
not needed, or it can be used to decouple state-space systems,
separating, for example, a coupled ?ight vehicle model into
separate pitch and lateral systems by eliminating the variables
Which belong to the other axis. This option can also be used to
change the sequence of the neW system’s inputs, states, or
outputs.
selected system ?le 120.
[0064] The present invention includes additional system
and matrix creation utilities. One such utility is for creating a
[0066] In the system modi?cation program 200, the input
data ?le 110 includes the system modi?cation instructions,
assuming that the instructions set has already been saved
there from a previous application. OtherWise, the user 150
Will de?ne (by means of GUI utilities) the system modi?ca
tion instructions Which Will be saved in the input data ?le 110
neW state-space system or a neW matrix from scratch by
for a later use. The system ?le 120 includes the state-space
system ?le 120 Will remain on the top and the neWly copied
ones Will be added at the bottom of the system ?le 120. The
present invention also includes a text editor to vieW or edit the
inputs, states, and outputs, and the sampling period if it is a
discrete system described in terms of state-space difference
system that Will be modi?ed by the program using the re
conditioning instructions. The modi?ed system Will also be
placed in the same system ?le 120.
[0067] When the system modi?cation instructions are
already in the input data ?le 110, the user 150 need only to
equations. OtherWise, for a continuous system the sampling
de?ne the tWo ?le names and select the neW system title. A set
entering the non-Zero numbers in the matrix and saving it in a
system ?le 120. When selecting this utility the user 150
de?nes the neW system title, its siZe in terms of number of
period is set to Zero. The user 150 also de?nes the system ?le
120 Where the neW system or matrix must be saved. Using a
of input instructions for system modi?cation is recogniZed by
tool for entering the matrix elements and its state-space vari
the system modi?cation program 200 from a label in the input
data ?le 110. The system modi?cation program 200 searches
ables, non-Zero numbers are entered individually. In one
through the input data ?le 110, identi?es all the system modi
embodiment of the present invention, after entering the num
bers, each matrix element appears in different colors depend
ing on the magnitude of the element. Small magnitude ele
ments appear in one color, While large magnitude elements
appear in a different, distinguishable color. Ones appear
?cation data sets and lists their titles in a menu. The user 150
selects one of the titles from the menu, and the neW system
bright White, Zeros are black, and there is a range of colors in
betWeen de-pending on the magnitude. Negative numbers are
Will be identi?ed by this title. The system modi?cation pro
gram 200 reads the input instructions and computes the modi
?ed state-space system from the old system.
[0068] If the system modi?cation instructions are not in
input data ?le 110, the systems modi?cation program 200 can
May 16,2013
US 2013/0124177A1
create a new set of system modi?cation instructions. The
system modi?cation program 200 obtains the system recon
ditioning instructions as directed by the user 150, saves them
in the input data ?le 110 and runs them. The user 150 selects
the system to be modi?ed and the system modi?cation pro
gram 200 reads the state-space matrices of the selected sys
tem and creates a title for the neW system. The user 150 can
tiplying With the scaling factor the corresponding roW in
matrices C and D. Rescaling the states affects only matrices
A, B, and C. The user 150 need not rescale the states in order
to combine tWo systems together.
[0071] Another system modi?cation option in the system
modi?cation program 200 is titled Instructions to Create a
NeW Set of Outputs and is used to create a neW system With a
then de?ne the neW system title, choose one of the three
system modi?cation program options, and enter some com
ments or notes describing the neW system. To choose modi
?cation options, a menu beloW the title shoWs the three sys
tem modi?cation options appears, and the user 150 highlights
one of the options. Before selecting an option the user 150
may also type in some system description comments. The
folloWing: (a) the old system outputs, (b) its output deriva
tives, (c) the old system states, and (d) the derivatives of the
states. This utility is useful in preparing synthesis models for
control system design Which require additional output criteria
to be optimiZed. After selecting the system to be modi?ed the
user notes Will also be inserted as comments in the data ?les
user 150 may enters the neW system title and some user 150
and Will become available to other utility programs.
reference notes at the bottom. The process can be repeated
many times until all the desired outputs are included, one at a
neW set of outputs from an old system that already exists in the
system ?le 120. The neW outputs can be selected from the
[0069] The system modi?cation program 200 is then ready
to accept the system modi?cation instructions provided
directly by the user 150. Each system modi?cation option
requires different instructions and it Will be described sepa
time, from the four groups. The system modi?cation program
200 returns to the previous system modi?cation options menu
and the system modi?cation program 200 executes the
rately herein. The system modi?cation instructions are saved
in the input data ?le 110 and the system modi?cation program
200 runs them in order to generate the modi?ed system. A
neW system With the neWly selected outputs and the modi?ed
title is saved in the same system ?le 120, beloW the original
instructions of creating a neW system With neW outputs. The
user 150 may Want to include more than one modi?cation in
system. The de?nitions of the neW system variables are also
the same data set. Therefore, after completing one set of
instructions the system modi?cation program 200 returns to
the menu beloW Where an additional modi?cation option can
printed beloW the system (A, B, C, D) matrices.
be included in the set before creating the ?nal system. The
[0072] Another system modi?cation option is titled Enter
ing Instructions to Truncate the System’s Inputs, States, or
Outputs, and is a utility that extracts a subsystem from the
system modi?cation program 200 runs the neW instructions
original sys-tem by selecting some of the old system’s inputs,
and creates the neWly-modi?ed system, and this neWly-modi
states, and outputs to be retained in the neW system. It can be
used to eliminate any uncontrollable and unobservable states,
or to decouple a large system into smaller sub-systems. For
example, it can be used to separate an aircraft model obtained
from a six degrees of freedom modeling tool into tWo separate
pitch and a lateral models Which are decoupled. If the system
truncation data is not in the input data ?le 110 from the
?ed system’s matrices are saved in the same systems ?le
under the neWly-modi?ed title.
[0070] One system modi?cation option is titled Entering
Instructions to Rescale a System and is used for converting
the units of some of the system inputs, states, or output vari
ables from one type of units to another. Converting, for
example, a system Whose inputs are de?ned in pounds and its
outputs in feet to a dynamically equivalent system Whose
inputs are de?ned in kilograms and its outputs are in meters.
This utility can be used, for example, to transform a given
plant model in order to combine it With a controller or an
actuator systems that have been de?ned in different units. In
order to rescale a state-space variable from an old set of units
to a neW set of units the user 150 must specify a scaling factor
de?ned so that one old unit is equal to “S” times the neW unit.
If a force input, for example, Was de?ned in (lb) and it must be
converted to (02), the scaling factor S:l6. If the old system
output Was in (feet) and it must be converted to (inches), the
scaling factor S:l2. For this option, the user 150 is prompted
to select the system inputs, states, or outputs that need to be
scaled. The user 150 selects one set of variables to be trans
formed at a time, that is, either the inputs, the states, or the
outputs. If, for example, the user 150 Wants to transform some
of the inputs, the systems modi?cation program 200 opens
another menu listing the system inputs as they are de?ned in
the system ?le beloW the matrices. The user 150 selects one of
the inputs from the inputs name-list, and enters the unit con
version factor “S.” The system modi?cation program 200
returns to the list of inputs and the user 150 can rescale
another input. After ?nishing re-scaling the inputs the user
?lename selection menu push the “Enter a NeW Set” button as
before. The user 150 then enters the neW system title, the
option of truncating a system, and some user notes as shoWn
in the space beloW, and selects the system title to be modi?ed.
The user 150 then de?nes the inputs, states, and outputs that
Will remain in the neW system. All the other system variables
are eliminated. The system modi?cation program 200 pre
sents a dialog having tabs Which list the old sys-tem inputs,
states, and outputs, and the user 150 highlights the variables
to be retained in each tab. The system modi?cation program
200 then asks the user 150 to con?rm before saving the
modi?ed system in the system ?le 120.
Running the Flight Vehicle Modeling Program
[0073] Once all input data to be used to model a ?ight
vehicle have been collected, the user 150 selects the input data
?le 110 and the system ?le 120 Where the vehicle state-space
system Will be saved. The ?ight vehicle modeling program
100 looks for the input data ?le 110 and starts searching for
?ight vehicle input data, Which Will be so labeled in the input
data ?le 110. An in-put data ?le 110 may contain more than
one set of vehicle data. Immediately beloW the ?ight vehicle
label there is a title Which identi?es the vehicle data. Each set
of vehicle data has a different title. When the ?ight vehicle
150 may rescale some of the outputs or some of the states.
modeling program 100 identi?es vehicle data sets, it displays
Re-scaling a system’s input is performed by dividing With the
scaling factor the corresponding column in matrices B and D.
their corresponding titles in a menu. The user 150 may select
some or all of the vehicle data sets to compile With the ?ight
Similarly, rescaling a system’s output is per-formed by mul
vehicle modeling program 100.
May 16,2013
US 2013/0124177 A1
[0074] The ?ight vehicle modeling program 100 reads the
selected vehicle data from the input data ?le 110 and displays
the data in dialog form. The dialog may include many tabs
that can be selected to vieW one group of vehicle data at a
time. The title of the vehicle data Which Will also become the
system title also appears in the dialog display.
[0075] The tabs alloW vieWing or entering data, one tab
group at a time. Each tab displays different types of vehicle
data. Different types of vehicle data shoWn in the tabs
includes, but is not limited to, mass properties, trajectory,
[0081] After inspection of all the dialog tabs to verify that
all vehicle data have been entered and read correctly, the ?ight
vehicle modeling program 100 Will create the vehicle state
space system and save it in the system ?le 120. The system
de?ned in the system ?le 120 Will have the same title as the
title used in the input data ?le 1 1 0. The vehicle notes that Were
entered as comments beloW the title in the input data ?le 110
Will also be transferred as comment lines into the system ?le
120 beloW the system title. De?nitions of the system’s inputs,
states, and outputs Will also be printed beloW the (A, B, C, D)
aerodynamic forces, gyros, control surfaces, engines, slosh
data, accelerometers, and ?exibility. The mass properties tag
matrices.
includes the vehicle mass, moments and products of inertia,
CG location, local value of g, and the radius of the earth. The
trajectory data tab shoWs the inertial velocity and accelera
tion, the sensed acceleration resolved along the body x, y, and
Z axes, the 0t, [3 trim angles, 0t, [3 rates, the Euler angles, the
cally creates de?nition labels for the vehicle state-space vari
dynamic pressure, the steady-state body rates, vehicle alti
tude, Mach number, etc.
[0076]
The aero forces tab shoWs the aero force coe?icients
at the trimmed condition (CAO, CZO) and also the aero force
derivatives per degree along (—x, +y, +Z). CZ is de?ned to be
along the Z axis, in the opposite direction from the normal
force coe?icient CN. The partials of the force co-e?icients
With respect to altitude change (l/feet), and also the partials of
the force coe?icients With respect to velocity change in (l/ft/
sec) are included in this group.
[0077] The gyros tab displays the gyros info as speci?ed in
the vehicle data, such as for example a pitch rate gyro. The
dialog also shoWs its x, y, Z location. The gyros may be
de?ned in different Ways, such as in rotations (radians), and
can also be de?ned to measure rate in (rad/ sec), and angular
[0082]
The ?ight vehicle modeling program 100 automati
ables based on the vehicle con?guration information as
de?ned in the in-put data ?le 110. The vehicle control inputs
include control surface de?ections, TVC engine de-?ections,
or engine thrust variations (normaliZed). When the tail-Wags
dog (TWD) option is turned on We also have tWo additional
inputs per surface or engine dof, the de?ection rate and angu
lar acceleration. All three inputs (de?ection, rate, and accel
eration) come from an actuator state-space model, discussed
herein. When the TWD option for the engines or aero-sur
faces is off, there is only one input per surface or engine dof,
the de?ection in (rad), in Which case the actuator can be
simpli?ed as a ?rst or second order transfer function.
Aero-Elasticity
[0083] Aero-elasticity is the dynamic coupling betWeen
aerodynamics and structural ?exibility. To model aero-elas
ticity in the present invention, the ?ight vehicle modeling
program 100 re-quires a GeneraliZed Aero Force Derivative
(GAFD) ?le that contains the aero-elastic coe?icients that
acceleration in (rad/sec2).
couple ?exibility With aerodynamics and also the inertial
[0078] The control surfaces tab includes the data for the
vehicle control surfaces at a speci?ed ?ight condition. The
engines tab displays the information for the vehicle thruster
engines. The engines are de?ned to be either gimbaling, or
throttling, or both. The slosh tab includes parameters used for
effects betWeen the ?exible vehicle and the control surface
accelerations. The GAFD data includes several sets of coef
?cients. The GAFD data are located in a separate aero-elastic
data ?le 140 that has a ?lename extension (.gaf) containing
modeling propellant sloshing. Fuel sloshing inside a tank is
represented by an oscillatory motion of a slosh mass resolved
in tWo orthogonal directions (y and Z) Which are perpendicu
lar to the sensed vehicle acceleration vectorAT. The folloWing
parameters are needed for each tank: the slosh mass (slugs),
slosh frequency (rad/ sec), the damping coe?icient (I), and
also the location in (ft) of the slosh mass (un-de?ected) With
respect to the vehicle coordinates.
[0079]
The accelerometers tab displays the accelerometers
info as it is read from the vehicle input data ?le 110. Although
referred to as accelerometers they can also be de?ned to
measure position in (feet) or velocity in (ft/ sec) along the x, y,
or Z directions. The accelerometer location in vehicle coordi
nates is also required because the accelerometer measure
ment is also sensing vehicle rotational acceleration. With the
accelerometer sensors the user 150 has the option to turn off
the rigid-body component from the measurement because
there are some cases Where it can be useful. The menus in the
accelerometers tab are either used for setting or for vieWing
the accelerometer speci?cations.
[0080] A bending tab may also be included that displays the
title of the ?ex modes that Will be combined With the vehicle
data. Also included is a “User Notes” tab used to display the
comment lines in the vehicle input data, or to enter neW
comment lines When starting a neW set of data.
coupling coef?cients used to model the inertial coupling
the coef?cients required for the implementation of aero-elas
ticity, and also the inertial coupling coef?cients. If the default
?ag “Without GAFD” option is used in the vehicle input data,
the ?ight vehicle modeling program 100 ignores the aero
elastic effects and creates a simpli?ed ?ex model using only
modal data, assuming that ?exibility is excited at the hinges
by rigid surface rotations and accelerations, and also that the
aero forces at the hinges are generated by ?at panel rotations
from their trimmed positions.
[0084] The GAFD ?le includes various sets of coef?cients.
The ?rst set of coe?icients describes hoW the vehicle aerody
namic forces and moments are affected by the modal dis
placements and modal rates. A second set of coe?icients
describe hoW the generaliZed modal displacement of a mode
is excited by the vehicle motion, such as changes in angle of
attack, sideslip, body rates, accelerations, control surface
de?ections, surface rates, and also by modal displacement,
rate, and acceleration interactions With other modes. A third
set of coe?icients describe hoW the moments at the hinges of
the control surfaces are affected by changes in the angles of
attack, side-slip, body rates, accelerations, modal displace
ments, modal rates, and also by the control surface de?ections
and rates. The hinge moments affect the actuator perfor
mance. The GAFD data also includes the rigid-body aerody
namic force and moment derivatives due to changes in angle
of attack, sideslip, body rates, accelerations, control surface
May 16,2013
US 2013/0124177A1
12
de?ections, and surface rates. These coe?icients, however,
[0089]
are not included in the aero-elastic data ?le 140, because the
?ight vehicle modeling program 100 uses more accurate
aero-coe?icients and aero-derivatives Which are de-rived
from Wind tunnel tests and are included in the vehicle input
data.
ent vehicle effector inputs. For example, gimbaling engines
Separate actuator programs 400 are used for differ
may utiliZe tWo actuator programs 400, one for pitch and one
for yaW de-?ections. FIG. 4 shoWs a typical interconnection
betWeen the ?ight vehicle modeling program 100 and the
control surface actuator programs 400. The actuator pro
Running the Vehicle Modeling Program With the Aero-Elastic
grams 400 generate outputs Which are de?ections in (radi
Data File
ans), de?ection rates, and accelerations (rad/sec2), and Which
drive the other ?ight vehicle modeling program 100 inputs.
[0085]
After the aero-elastic data is de?ned and assuming
that an aero-elastic data ?le 140 has been prepared for all
aero-surfaces and at frequencies that correspond to the
selected mode frequencies (there may be more GAFD fre
quencies than selected modal frequencies but there should be
a GAFD frequency for each of the selected mode frequencies)
the ?ight vehicle modeling program 100 is ready to run With
aero-elasticity included. After selecting the ?lenames, and
vehicle data, the ?ight vehicle modeling program 100 brings
The actuator program 400 inputs are de?ection commands in
(radian) and hinge moments in (ft-lb). The hinge moments
include load-torque feedback in a mechanical loop from the
?ight vehicle modeling program 100 representing external
loading on the actuator due to vehicle motion.
[0090] The present invention also includes the capability to
specify actuator models for further modeling of the ?ight
vehicle in a speci?c actuator program 400. Flight vehicles are
you to the dialog With the tabs that display the vehicle data.
The ?ight vehicle modeling program 100 displays more
controlled by engines that rotate about a gimbal or by control
menus and dialogs because it must locate the GAFD ?le and
process the data. It displays a menu that lists all GAFD
actuator system is to provide the force that is needed to gimbal
?lenames Which are in the project directory.
[0086] The ?ight vehicle modeling program 100 reads the
modal data for the selected ?ex modes, and also reads the
GAFD frequencies and data from the aero-elastic data ?le
140. It is possible for the aero-elastic data ?le 140 to contain
more frequencies than the selected modes. While some
modes in the selected set of modes may have been excluded,
We already have those frequencies included in the aero-elastic
data ?le 140. It is also possible that the aero-elastic data ?le
140 may contain more control surfaces than those de?ned in
the vehicle model. The user 150 instructs the ?ight vehicle
modeling program 100 Which GAFD frequencies need to be
selected, and also Which surfaces, corresponding to the ones
included in the vehicle data. The ?ight vehicle modeling
program 100 uses a dialog to select the GAFD frequencies
that correspond to the selected modal data, and also the con
trol surfaces in the aero-elastic data ?le 140 that correspond to
the surfaces de?ned in the vehicle data. The set of frequencies
include selected mode frequencies (via the mode selection
utility). The user 150 selects only the GAFD frequencies that
correspond to the selected mode frequencies.
[0087] The user 150 also speci?es control surfaces because,
just like the aero-elastic data ?le 140 may contain more fre
quencies than the modal frequencies, the GAFD ?le 140 may
also contain more surfaces than the number of surfaces in the
vehicle model. Once this has been the completed the ?ight
vehicle modeling program 100 is able to compute the aero
elastic vehicle state-space model and save it in the system ?le
120 under the same title as the title used in the input data ?le
110.
surfaces rotating about a hinge. The purpose of a servo
the engine or to rotate the aero-surfaces in the direction
needed to control the vehicle. In launch vehicles, a small
rotation of the thrust vector angle about the gimbal (typically
betWeen 15° and 110° in pitch and in yaW) is suf?cient to
generate a signi?cant amount of normal or lateral force at the
gimbal that can be used to stabiliZe and steer the vehicle,
overcome the Wind-gust disturbances, and balance the aero
dynamic moments. In an aircraft the control surface de?ec
tions are larger, in the order of :400 from the trim position.
The surface rotates about a hinge line parallel to a Wing or a
vertical stabiliZer, and the actuator provides the force to rotate
it against the aerodynamic loads. In some aircraft the Whole
Wing, ?ap, or rudder is rotating and not just the trailing end of
the control surface. The rotation of the surface changes the
air?oW around the aircraft and creates the aerodynamic forces
and moments needed to trim and to control the ?ight vehicle.
[0091] Thrust forces are transmitted to the vehicle through
the gimbal. The launch vehicle gimbals are usually tWo
directional alloWing the engines to rotate both in pitch and
yaW directions. The actuator is a mechanical servo device that
is used to control the de?ection (6) of the engine. A TVC
engine is controlled by tWo orthogonal actuators, typically in
pitch and yaW directions. The actuator length can be varied by
means of hydraulic or electro-mechanical forces Which ex
tend or retract the shaft. One end of the actuator is attached to
the ?ight vehicle and the other end of the shaft is attached to
the noZZle. The angular position of the noZZle is controlled by
adjusting the length of the actuators. During ?ight, the desired
pitch and yaW changes in engine rotation are computed by the
?ight control system and the actuators are commanded to
either extend or retract in order to achieve the required
Actuator Models and Modeling
changes in noZZle de?ection.
[0092] In order to properly model the dynamic coupling
[0088] The actuator is an important element in modeling
?ight vehicle dynamics. In the present invention the actuator
betWeen the ?ight vehicle and the con-trol surfaces or the
TVC engines, some standard actuators must be derived that
dynamics are created as a separate block that can later be
are included as selectable model options. Each actuator mod
integrated With the vehicle model. The actuator model does
eling program 400 reads the actuator parameters from the
input data ?le 110 and creates different types of actuator
state-space models Which are saved in the system ?le 120.
The actuator state-space models are combined With the ?ight
vehicle models in order to capture dynamic effects such as
not only include the piston translation dynamics but also the
engine or control surface rotational dynamics Which include
the load moment of inertia, vehicle back-up stiffness, moment
arms, viscous damping, and other actuator parameters. FIG. 4
and FIG. 5 are interconnection diagrams shoWing inputs to
actuator programs 400 With respect to the ?ight vehicle mod
eling program 100 and mixing logic 300.
tail-Wags-dog, hinge moment, and load-torque feedback,
Which couple also With vehicle structural bending. Actuator
parameters may include piston area, moments of inertia of the
US 2013/0124177 A1
load, ampli?er gains, friction coe?icients, piston and backup
stiffnesses, compensator transfer functions, etc. The actuator
modeling program 400 operation is very similar to the ?ight
vehicle modeling program 100. The output is a state-space
system that captures the actuator plus load dynamics. It is
saved in a system ?le 120 With its in-puts, states, and output
variables de?ned beloW the matrices. Actuator models usu
ally have tWo inputs and three outputs. The tWo inputs are: (1)
engine de?ection command (6c) in radians, coming from the
?ight control system output, and (2) the load torque (TL) in
(ft-lb), Which is an external loading torque on the actuator due
to the vehicle motion. The three outputs are: (1) engine
de?ection angle (6) in (radians), (2) engine rate in (radians/
sec), and (3) engine acceleration in (rad/sec2).
[0093]
The selection of an actuator device is determined
mainly by the poWer requirement of the load. The poWer is
determined by the aerodynamic forces and the speed of
response. A ?ight vehicle can be better controlled When it is
marginally stable. If the vehicle is passively unstable and it
diverges too fast, then the actuator has to respond fast enough
in order to catch up With the instability and prevent it. On the
other hand, if the vehicle is too stable it also requires a lot of
actuator poWer in order to steer it. Other factors to be consid
ered for the selection of an actuator include the dynamic
May 16,2013
actuator shaft ex-tension. The position sensor measures the
actuator shaft translation Which includes also the error due to
the shaft deformation. The measurement does not see the
backup structure or load deformation. All three stiffnesses
should be included in the actuator model When: (a) the vehicle
is a rigid body, or (b) vehicle is ?exible but the actuator link
stiffnesses are set to “rigid” in the ?nite-elements-model.
When the ?ight vehicle is ?exible and the backup and load
structure compliances are included, they should not be
included in the actuator. Only the piston stiffness should be
included, otherWise, the stiffnesses Will be included tWice.
[0096] The actuator modeling tool includes several actua
tor modeling options, some of Which are described herein by
Way of example. Electro-hydraulic actuators are most com
monly used for launch vehicle thrust-vector-control, and have
great poWer capability and can deliver larger torques than
electrical equipment of comparable siZe and Weight. For con
tinuous operation, they offer a minimum (equipment/poWer)
ratio. Where intermittent operation is required, a hydraulic
system can provide large amount of poWer from a small
volume of accumulator. Their dynamic characteristics are
expressed by small time constants, and they develop higher
(peak torque/inertia) ratios.
[0097] The most common form of utiliZation of hydraulic
servos in vehicle control loops consists of a high pressure
characteristics, the poWer sources available, the reliability of
the equipment, and other physical and economic limitations.
supply (pump), an electro-hydraulic servo valve, a hydraulic
Combining a Flexible Vehicle Model With Actuators
actuator (cylinder), a feedback transducer, and a servo-am
[0094]
pli?er. The hydraulic poWer supplies currently used are of tWo
main types. The ?rst type employs a variable displacement
The actuator models include the rotational dynam
ics of the load and calculate the angular position, velocity and
acceleration of the engine or aero-surface relative to the
vehicle. This relative motion of the load is used as an input to
pump Whose output ?oW is controlled by means of a servo
the ?ight vehicle model Which generates the control and
relief valve is also connected from the high pressure side to
the loW pressure side to minimiZe pressure transients above
reaction forces. In FIG. 4, three control surfaces actuator
models 400 are shoWn, created by the actuator modeling
program. They are knoWn as elevon, aileron, and rudder
actuators. There is a mixing logic 300 matrix that converts the
?ight control system 500 output as shoWn in FIG. 5 to actuator
system inputs 320. The control surface de?ection, rate, and
acceleration outputs drive the vehicle dynamic model created
by the ?ight vehicle modeling program 100. In addition to
other outputs the ?ight vehicle model also generates the hinge
moment outputs Which are fed back to close the mechanical
sensing the high pressure side of the hydraulic system. A
the operating pressures of the system. For normal operations
the valve remains closed, opening only When the pressure
exceeds a value overcoming the pre-load on the relief valve.
The second type of poWer supply uses a ?xed displacement
pump With a relief valve to maintain the supply pressure
Within set limits, as Well as to meet the normal ?oW require
ments. In this system the relief valve is normally open so that
supply pressure and valve opening maintain ?oW through the
relief valve equal to the ?oW output of the ?xed displacement
hinge-moments feedback loop at the control surface hinge
pump. When there is a ?oW demand the relief valve closes and
moment inputs. In the present invention, the actuator models
the supply pressure is reduced. The dynamics of both poWer
supply and relief valve exhibit a fairly ?at response With small
phase shift Within the bandWidth of the overall servo loop,
therefore, the supply pressure Will be assumed to be constant
400 are combined With the ?ight vehicle models 100 using a
systems combination utility, or by using other commercially
available tools.
[0095] The user 150 should take care in selecting stiff
nesses When putting together vehicle and actuator models.
There are three types of stiffnesses involved When dealing
With actuators and they combine in series to de?ne the com
bined load resonance: (1 ) the stiffness of the backup structure,
Which is the structural stiffness at the point Where the actuator
piston is attached to the vehicle, (2) the actuator shaft stiffness
consisting of piston plus oil or electrical stiffness, and (3) the
load stiffness due to the ?exibility of the aero-surface itself, or
the engine noZZle. When We are dealing With a rigid vehicle
model, all three stiffnesses must be included in the actuator
mod-el and the actuator model captures the local resonance of
the load oscillating at the pivot. The de?ection (6), the rate,
and the acceleration outputs consist not only of rigid surface
rotation, but also the additional de?ections due to the com
bined spring constant (KT) from all three stiffnesses. The
position feedback loop in the actuator is a measurement of the
at the value of Zero ?oW demand. Electro -hydraulic valves are
designed for ?oW or pressure control. These units are highly
complex devices and exhibit high order non-linear responses.
Still, in the frequency range of interest, they can be repre
sented by a ?rst or second order transfer functions.
[0098] Other types of actuators are electro-mechanical
actuators, mainly because of their simplicity, reliability and
the reduced need for maintenance in comparison With the
hydraulic systems. In the heart of an electro-mechanical
actuator system there is a DC motor. At the rotor of the motor
there is a small gear driving a bigger gear for higher torque.
The bigger gear is connected to a screW gear that spirals as the
gears rotate. The spiral gear converts the rotational motion
into translation that drives the actuator shaft. The other end of
the shaft rod is connected by some linkage mechanism to the
load Which can pivot about a hinge With respect to the vehicle.
As the piston pushes against the load it rotates the noZZle or
May 16,2013
US 2013/0124177 Al
the control surface similar to the hydraulic actuator. The
electro-mechanical actuator system has tWo gear ratios. The
?rst gear ratio relates the number of motor spins to one rota
tion of the big gear, and the second gear ratio de-?nes the
number of motor spins for one inch extension of the piston. A
current ampli?er supplies the dc current required to drive the
motor. The servo loop is closed by means of a position mea
surement across the actuator. A rate feedback loop from the
motor velocity is also closed in order to achieve the desired
damping characteristics.
[0101]
The mixing logic option is embodied Within the
?ight vehicle modeling utilities in the Flixan program. The
?ight vehicle modeling program 100 requires the input data
?le 110 in order to obtain the vehicle mass properties and
effector data. It looks inside the input data ?le 110 and
searches for ?ight vehicle data sets and lists all the vehicle
data titles in a menu, from Where the user 150 selects a vehicle
set to be used for creating a mixing logic 300 matrix. The user
150 Will notice that the same vehicle input data set is also used
by the ?ight vehicle modeling program 100 to compute the
vehicle state-space model, Which is also saved in the same
Combining Effectors Via a Mixing Logic Matrix
[0099] Flight vehicles are controlled by forces and
moments generated by either gimbaling or throttling the
thruster engines, by ?ring reaction control jets, or by de?ect
ing control surfaces. The engines or surfaces are commanded
by the ?ight control system. The signals coming out of the
?ight control system as outputs 310 are the roll, pitch, yaW,
Ny, and NZ-demanded changes in the vehicle body rates. The
logic that interfaces betWeen the ?ight control system outputs
310 and the vehicle effectors is the mixing logic 300. Note,
that for a vehicle that has only gimbaling engines the mixing
output system ?le 120, together With the mixing logic 300
matrix.
[0102] The user 150 chooses a name for the mixing logic
3 00 matrix, and also the rotational and translational directions
to be controlled (for example, roll, pitch, yaW, and Z-accel
eration), Which serve as inputs 310. The directions chosen
should be accessible by the vehicle effectors. The three most
typical rotations are roll, pitch, and yaW. Translational direc
tions may also be included if the vehicle has the effectors to
provide control along these directions (such as speed brake,
?aps, throttle control, etc.). The mixing logic 300 reads the
vehicle mass properties, CG location, engine locations,
logic 300 is referred to as the Thrust Vector Control (TVC).
The more general effector mixing logic 300 is essentially a
matrix that converts the ?ight control system outputs 310 to
effector input commands 320. The mixing logic 300 therefore
translates the roll, pitch, and yaW angular accelerations
demanded by the ?ight control system 510 into commands
thrusts, maximum de?ections, aero-data for the control sur
faces, etc., and uses these vehicle parameters to compute the
320 such as engine or control surface de?ections, thrust varia
reaction control jets, or aero surfaces, as speci?ed in the
tions (for differential throttling), or RCS jet ignition com
vehicle input data.
[0103] The mixing logic matrix is integrated With the ?ight
mands. The mixing logic matrix 300 is generally time-vary
mixing logic matrix. The inputs 310 to the mixing logic 300
matrix are derived from the ?ight control system output as
shoWn in FIG. 5. The matrix outputs drive the vehicle control
effector inputs, such as gimbaling engines, throttling engines,
ing because it is a function of the vehicle geometry, thrust,
control softWare and converts the desired changes in vehicle
alpha, and mass properties. The mixing logic 300 algorithm
rates (roll, pitch, and yaW), and linear accelerations (along x,
that is presented here uses the pseudo-inverse method to
determine the best combination of controls to effectively
y, and Z) to outputs that serve as effector commands. The
number of roWs (outputs) is equal to the number of effector
achieve the required change in vehicle rates. By applying the
degrees of freedom. The number of columns (inputs) is equal
mixing logic in front of the vehicle model as in FIG. 5 it
to the number of vehicle degrees of freedom that must be
controlled (max number of 3 rotations plus max number of 3
attempts to diagonaliZe it, that is, the achieved vehicle accel
erations approach the commanded accelerations in the open
loop sense.
[0100]
The effector combination program generates the
mixing logic matrix by calculating the force and moment
variations in the vehicle body axes produced by each effector
independently. In other Words, it calculates the force and
moment variations due to gimbaling, throttling, and also due
translations). The number of vehicle degrees of freedom that
are included in the mixing logic 300 matrix should be limited
by the number of degrees of freedom Which can be accessible
by the effectors in the vehicle state model. The control
designer should knoW ahead of time Which vehicle directions
to a control surface de?ection. The effect of each effector in
the control directions is a column vector, and the vectors from
all effectors are combined together to form a matrix for the
total vehicle moments and forces due to the contributions
are controllable and select them using the six direction
options menu. Typically, three rotations are chosen and some
times one or tWo translations. For example, if the vehicle has
throttle control or a speed-brake you may also include the
x-axis acceleration. Flaps can also be used to control the
Z-axis acceleration.
from all the vehicle effectors. The mixing logic is the pseudo
inverse of that vector. One additional mixing logic 300 cal
matrix and it saves it in the system ?le 120 as a gain matrix.
culation is the maximum effectiveness of each effector. This
calculation is relevant here because the various engines or
tions accessible by effectors, the matrix has six columns,
aero surfaces may have different max gimbaling angles or
throttling capabilities. The mixing logic 300 therefore utiliZes
the effector contributions according to their effectiveness, by
spreading the control authority evenly among the effectors
proportionally according to their capabilities. This type of
mixing logic 300 maximiZes the control effectiveness by
alloWing all the effectors to reach saturation simultaneously.
For example, if tWo engines have equal thrust but different
gimbaling capabilities, the engine With the larger rotational
capability should be alloWed to de?ect at a larger angle.
[0104] The mixing logic 300 computes the mixing logic
For a vehicle system having three rotations and three transla
assuming of course that all six directions Were selected in the
appropriate menu. The six columns are the matrix inputs
coming from the ?ight control acceleration demands. The
?rst three correspond to the roll, pitch, and yaW angular
acceleration demands, and the next three correspond to trans
lational accelerations along x, y, and Z as shoWn in FIG. 3. For
a system With only three rotations and no translations the
matrix has only three columns corresponding to the roll,
pitch, and yaW demands. FeWer than three directions can also
be selected. In the case, for example, When We are interested
US 2013/0124177 A1
to control only the lateral directions after removing the pitch
vehicle subsystem. A reduced combination of rotations and
translations is also acceptable, such as, a pitch rotation in
combination With x-axis and Z-axis accelerations to be used
for a reduced pitch vehicle model. Also for a lateral model one
can choose the roll and yaW rotations together With the y-axis
acceleration.
[0105] The number of roWs in the mixing logic gain matrix
is equal to the number of effector degrees of freedom. Starting
May 16,2013
TVC engines (6e) With respect to their nominal trim posi
tions. Engine throttling is also used to control the vehicle by
varying the engine thrust by an amount (:6Te) from its nomi
nal thrust (Te). Entry vehicles, gliders, and aircraft are con
trolled by de?ections of the control surfaces (zocs) from their
nominal trim angle (Acs). The inputs to the dynamic model
include con-trol surface and engine de?ections in (radians),
thrust variations normaliZed by the nominal en-gine thrusts
(oTe/Te), and Wind gust velocity in (ft/ sec). The direction of
With the pitch de?ections of engine numbers: 1, 2, 3, . . . n,
the Wind gust is de?ned in the input data. The outputs include
folloWed by the yaW de?ections of engine numbers: 1, 2, 3, .
vehicle attitude, rate gyros, accelerations at the CG or at
. . n, folloWed by the engine de?ections that gimbal in a single
speci?c vehicle locations, angles of attack and sideslip (0t, [3)
“constrained” direction (yi), folloWed by the thrust variations
of engines: 1, 2, 3, . . . n, and ?nally With the de?ections of
and vane sensors Which measure (or, [3) With ?exibility at
speci?c locations. The vehicle models are created in state
control surfaces: 1, 2, 3, . . . n. The de?nitions of the matrix
space form, Which is a standard representation for applying
inputs (control dofs) and matrix outputs (effectors) are also
singular value robustness analysis techniques, LQG, and
H-in?nity control design methods.
included beloW the matrix.
[0106] The matrix generated by the mixing logic 300 deter
mines the pitch and yaW de?ection angles of the TVC engines
and control surfaces, or the variations in RCS thrust, and
attempts to uncouple the vehicle motion, Which means,
attempting to provide angular accelerations in the directions
demanded by the ?ight control system. FIG. 3 shoWs a typical
?ight control system using a mixing logic matrix. The mixing
logic 300 converts the ?ight control system 500 output signals
310 to effector input signals 320 as shoWn in FIG. 5. Since it
attempts to diagonaliZe the plant from the ?ight control sys
tem 500 output 310 to vehicle acceleration outputs, in the
event of an engine or control surface failure, the mixing logic
[0110] With the linear model, its state-variables describe
only variations from their nominal values. They do capture,
hoWever, the dynamic behavior of the ?ight vehicle for rela
tively small dispersions from its trimmed ?ight condition,
Which is acceptable for ?ight control design, stability and
performance analysis. The design assumption is that the
vehicle remains fairly close to its target trajectory or trim
condition and that the control system is able to provide a
reasonable amount of robustness to uncertainties and the
control authority to overcome small departures from the tar
only the mixing logic 300 changes.
get trajectory due to gust disturbances. The coef?cients of the
vehicle equations are time varying and they are functions of
the mass properties, aerodynamics, Mach number, alpha, and
other parameters Which are changing as the vehicle depletes
fuel and changes speed and altitude along a trajectory. Con
trol analysis, hoWever, is based on linear models at ?xed ?ight
conditions, With constant coef?cients. This assumption is
generally acceptable When the variation of vehicle parameters
Flight Vehicle Equations
associated With the vehicle dynamics. The time-slice model is
[0107] The present invention performs mathematical equa
tions of motion applicable to ?ight vehicles such as airplanes,
valid only for relatively short periods of time, (in the order of
300 must be recon?gured automatically during ?ight in order
to avoid ?ight control instabilities, assuming, of course, that
the vehicle has a suf?cient number of effectors remaining to
be able to control along the desired directions. The ?ight
control system remains unaffected by the effector failure,
gliders, launch vehicles, rockets, missiles, spacecraft, and
other such vehicles capable of motion in air, space, or the
atmosphere, and creates state-space systems at ?xed condi
tions. These equations of motion model the dynamic behavior
of these ?ight vehicles to describe hoW the vehicle Will move
in response to a combination of forces that are applied to the
vehicle.
[0108] The equations are presented in tWo forms: the non
linear large angle equations suitable for 6-DOF time-domain
simulations, and the lineariZed equations that describe small
variations of a vehicle from its nominal trim position. The
present invention uses the linear equations to create state
space systems for ?ight control analysis. The coe?icients of
the lineariZed equations are functions of the vehicle param
eters such as mass properties, aerodynamics, trajectory data,
slosh parameters, and structural modes at ?xed times called
“time-slices.” The ?ight vehicle data is obtained from point
mass trajectory simulations, fuel slosh models, Wind tunnel
data, mass properties, and ?nite element structural models
(such as Nastran.)
occur at rates signi?cantly loWer than the time constants
a feW seconds), and the time constant associated With the rate
of change of the coef?cients is usually large in comparison
With the time constants associated With the vehicle short
period dynamics. The most common approach in ?ight con
trol design is to derive control laWs using linear models at
?xed ?ight conditions and interpolate the control laWs in
betWeen. The assumption is that, if the ?ight control system
can provide an acceptable performance and robustness to
uncertainties at many individual ?ight conditions along a
trajectory this Will obviously be a good indication that the
vehicle canbe successfully guided Without deviating from the
trajectory due to instability or due to its inability to respond to
guidance signals. The linear model, hoWever, is only useful
for preliminary design and analysis. The ?nal ?ight control
system must also be evaluated using a detailed 6-DOF non
linear simulation.
[0111] The rigid-body equations used in this ?ight vehicle
modeling program 100 comprise three rotational (roll, pitch
and yaW), and three translational equations along x, y and Z
axes. The vehicle forces and moments generated in this model
are computed With respect to the body axes system. The x axis
robustness against uncertainties, and system performance in
is aligned along the fuselage reference line and its direction is
positive along the velocity vector, the Z axis is de?nedpositive
doWnWard toWards the ?oor, and the y axis right hand per
response to commands and Wind gusts disturbances. Launch
vehicles are usually controlled by small de?ections of the
Wing. The Euler angles ((1), 6, 1p) de?ne the vehicle attitude
[0109] Linear vehicle models are used to analyZe the short
period dynamic behavior of a vehicle in terms of stability,
pendicular to the x and Z axes and positive toWards the right
May 16,2013
US 2013/0124177 A1
With respect to the inertial reference axes. In a launch vehicle
coupling coe?icients or “h-parameters.” It provides a more
the attitude reference is usually measured With respect to the
degrees, 0 degrees) respectively. Coupling betWeen the pitch
accurate representation of the dynamics involved because it
at-tempts to capture the coupling betWeen the vehicle struc
tural ?exibility and the aerodynamic forces and moments
and lateral axes is also included in the equations of motion.
This coupling can occur in several places due to lack of
created by the vehicle motion (0t, [3, p, q, r) and the control
surface de?ections. The GAFD approach captures also the
launch pad With the Euler angles initially set at (0 degrees, 90
vehicle symmetry. For example, in the TVC, thrust mismatch,
effect of vehicle acceleration (including ?exibility) on the
products of inertia, a non-symmetrical structure, or due to the
presence of cross coupling terms in the aerodynamic coe?i
cients, for example, Cm[3, Cnot, ?ying in a circle at a constant
([3), etc. The x, y, Z coordinates at various vehicle locations,
such as: the engine gimbals, the control surface hinges, the
IMU, gyros, accelerometers, CG, slosh masses, the moment
reference center MRC, etc, are de?ned With respect to the
vehicle reference axes. Sometimes the trajectory model, the
control surface hinge moments. Both approaches require the
folloWing conditions: (a) the Nastran model must be “free
free,” (b) the gimbaling engines and the slosh masses should
not be included in the FEM model because they are coupled
via the equations, (c) When the GAFD method is used to
model the aero-surface/?ex coupling, the control surfaces
must be included in the FEM model and rigidly attached at the
hinges. The surfaces are released in the equations via the
mass properties, and the ?nite element model are de?ned in a
h-parameters.
different coordinate axes, units, and directions. The appropri
ate axes transformations and unit conversions in the mass
properties, aero data, trajectory, and modal data is necessary
When setting up the vehicle input data.
[01 12] There are also situations Where the analyst may have
to post-process the vehicle quadruple model in order to
remove some undesirable state variables from the model. For
example, to extract a reduced order pitch or lateral model, or
in a launch vehicle With a ?xed thrust and at Zero (ot), the
change in velocity state (6V) along the velocity vector (V0),
and the acceleration output along the x axis are not useful and
they can be removed because they are not controllable from
the TVC input (be). It is a good practice to reduce the vehicle
Tail-Wags-Dog and Hinge Moments
[0113]
The “tail-Wags-dog” (TWD) in launch vehicles
engine gimbals, and at the hinges of the control surfaces of an
aircraft, represent reaction forces and moments on the vehicle
applied at the gimbals or hinges, Which are created by the
sWiveling (accelerations) of the TVC engines or the control
surfaces. The TWD introduces a complex pair of Zeros in the
transfer function “6(s)/6(s).” Assuming a sinusoidal sWivel
ing of an aero-surface about its hinge, the TWD Zero is at the
frequency Where the reaction forces due to the sinusoidal
acceleration of the surface balance the aerodynamic forces at
the hinge, or in the case of a TVC engine the reaction forces
model by removing the non-contributing state-variables, spe
cially When developing models for control synthesis, because
most design algorithms require minimal state-space realiZa
at the gimbal balance the small thrust component, T*sin(6),
perpendicular to the thrusting direction, due to small de?ec
tions. Note, that the state (6V) and the forWard acceleration
are important in regulating the speed of an aircraft or reentry
[0114] The “dog-Wags-tail” (DWT), also knoWn as load
torque feedback, is a loading torque at the TVC actuator
tions (6).
gliders ?ying at high angles of attack, using speed-brake,
created by the sWiveling (accelerations) of the TVC engines.
variable thrust, or alpha control as means to regulate the
speed. In these cases the (6V) variables are used in the control
There is also the equivalent “hinge moments feedback” at the
design and analysis. A large number of ?exible modes can be
used in the model to simulate the structural elasticity of the
vehicle. Each bending mode is represented by a loW damped
second order equation that has a distinct natural frequency
and a mode shape. Each bending equation behaves like a 2nd
order transfer function Which relates the excitation forces and
acceleration. When the vehicle accelerates, mainly in the
torques generated by the engines, the control surfaces, slosh
control surface actuators of an aircraft due to the aircraft
normal or lateral directions, as a result of aero or engine
forces, the vehicle accelerations create an external loading
torque in addition to the commanded actuator torque. The
total torque applied to the engine or control surface is: (a) the
steady-state trim torque due to the steady aero forces, (b) the
torque due to the actuator de?ection commanded (6), and (c)
the external load-torque due to the vehicle acceleration. The
ing, and other disturbances, to the generaliZed modal dis
placements (nj) of each mode (j). The actual bending dis
modeling of tail-Wags-dog and load-torque feedback requires
placement of the structure at a certain location is a
an actuator model for every control surface hinge or engine
combination of the generaliZed modal displacements from all
gimbaling direction that is de?ned in the vehicle model. The
the modes. In most applications 20 to 80 modes is suf?cient to
actuator model has tWo inputs: a 6-command and a load
get an accurate representation of the structural ?exibility.
torque input, and three outputs: engine de?ection, engine rate
and acceleration outputs. When the TWD/load-torque option
Sometimes as many as 400 modes may be included for ?ight
veri?cation. The coef?cients of the bending equations are
obtained from a ?nite elements program (FEM) such as Nas
tran. The aero-elastic coupling betWeen the control surfaces
and the vehicle modes can be implemented using tWo differ
ent approaches. The ?rst approach is easy to implement but
not very accurate and it requires modal shapes at the control
surface hinges. It assumes that the structure is excited only by
the aerodynamic forces and torques at the hinges generated
by the de?ections and accelerations of the control surfaces.
The control surfaces are assumed to be rigid and they are
coupled to the vehicle structure as separate bodies. The sec
ond method is more complex because in addition to the modal
data it requires also GAFD (aero-elastic) data and inertial
is turned on, the vehicle model provides “load-torque” out
puts for every engine direction and for every control surface.
The load-torque feedback dynamics is in general considered
to be a second order effect and it is only included in the ?nal
phase of the FCS analysis. Since the TWD and load-torque
feedback dynamics require detailed actuator models for their
implementation and since these effects can be removed from
the model Whenever necessary, When they are not used and
the vehicle model no longer requires engine acceleration
inputs, the actuator models can be simpli?ed into simple
transfer functions or unity gains. OtherWise, for the TWD/
DWT implementation, a detailed actuator model is needed for
every gimbaling direction (one for pitch and one for yaW
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