The use of an AD 100 computer and the ADSIM language in the six-degree-of-freedom digital simulation of an air-to-ground missile is illustrated. The missile is launched from a moving platform, typically a helicopter, and is capable of striking a mobile target up to 10 kilometers away. The missile could be any tactical missile. The performance numbers of the AD 100 show that it is possible to implement a high performance missile model in a real-time simulation without the problems associated with an implementation on a general purpose computer using FORTRAN

Zwaanenburg, Koos

English

NASA Technical Reports Server

N90-23068
Six-Degree-of-Freedom Missile Simulation
Using the ADI AD 100 Digital Computer and
ADSIM Simulation Language
Koos Zwaanenburg
Applied Dynamics International
Ann Arbor, Michigan
Abstract
This paper illustrates the use of an AD 100
computer and the ADSIM language in the six-
degree-of-fieedom digital simulation of an air-
to-ground missile. The missile is launched
from a moving platform, typically a helicopter
and is capable of striking a mobile taxget up
to 10 kilometers away. The missile could be
any tactical missile.
Introduction
Real-time simulation with hardware in the
loop is used extensively in the missile devel-
opment business. It is used primarily to val-
idate designs prior to the actual flight, to
avoid experiments with actual flight hardware,
and to reduce costs of flight trials by simu-
lating a large variety of scenarios and con-
ditions instead of performing these tests in
real life. Missile manufacturing companies are
an important section of Applied Dynamics'
customer base. Therefore, Applied Dynamics
International(ADI) developed this particular
missile model so that it can function as a real-
istic example of the type of models that most
of our customers work with.
Six-Del_ree-of-Preedom Missile Model
The missile is controlled by four fins mounted
in cruciform configuration at the rear of the
missile. The fins are independently controlled
by pneumatic servos. The servos are activated
by commands from the autopilot, which pro-
cesses the sensor and seeker guidance outputs
before issuing these commands. The missile
roll, pitch, and yaw attitudes axe sensed using
two-degree-of-freedom gyros. Two such gyros
are required. The target is tracked using an
inertially stabilised seeker (laser or RF/IR)
mounted at the front end of the missile in-
side a radome. Imperfect attitude sensing and
target tracking axe included in the simulation.
The user can exclude, include or amplify these
extraneous effects by selecting the proper op-
tions switches.
The missile is thrusting during part of the
flight. Thrust is a prespecifled function of
time. Burnout occurs about five seconds from
launch time. As the missile burns the pro-
pellant, the rotational inertias of the vehicle
change and the center of gravity moves for-
ward along the missile longitudinal axis. The
missile aerodynamic center remains aft of the
missile center of gravity at all times. Imperfect
c.g. location, thrust offset, and misalignment
are also modeled in the simulation. Atmo-
spheric wind velocity is modeled as the sum of
a steady state and a gusting component. The
gusting component is assumed to be a sero-
mean, uniformiy distributed random variable
in all directions. Vehicle translational equa-
tions of motion are expressed in earth axes,
while the missile body axes are used for the
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https://ntrs.nasa.gov/search.jsp?R=19900013752 2020-03-19T22:16:01+00:00Z
rotationaldynamicequations.
Aerodynamiccoefficientsare described as mul-
tivariable functions of typically the missile an-
gle of attack, angle of sideslip, control sur-
face displacements and Much number. Fur-
thermore, rotor downwash (the effects of which
a_e confined to the neighborhood of the heli-
copter), instantaneous thrust, gyro drift an-
gles, and seeker tracking errors sue described
as nonlinear functions.
The simulation is terminated when one of the
following conditions occurs: when the simula-
tion end time exceeds the user-specified end
time, when the missile crashes, when the mis-
sile Maeh number exceeds a specified limit, or
when the relative position component along
the relative velocity vector z,. changes sign.
When z,¢ changes sign, the miss distance is
computed by linearly interpolating the sepa-
ration between the missile and the target to
the point where zrt is zero.
The complete system of equations has been
partitioned into different modules for simplic-
ity. These modules can be looked upon as vari-
ous "generic" subsystems of the missile model.
They can be used separately for other missile
simulations.
The missile coordinate conversion module
(MCC) describes the various inertial and body
axes coordinate transformations required for
every tactical missile model, the missile atti-
tude, quaternions, direction cosines, the effect
of steady and gusting wind components, the
rotor downwash, the velocity components, and
angle of attack and sideslip.
The line-of-sight module (LOS) describes the
missile-target geometry and velocities in abso-
lute and relative terms and describes the tar-
get tracking errors, rsdome aberrations, and
glint.
The seeker module describes the tracking er-
rors in azimuth and elevation and the seeker
dynamics. Furthermore, it describes the guid-
ance commands for the autopilot module.
This module allows insertion of specifics for
laser, RF, or IR seekers.
The autopilot module describes an analog au-
topilot that accepts guidance commands from
the seeker module and body attitude informa-
tion from the MCC module to implement a
proportional navigation scheme that will guide
the missile to the target. The autopilot mod-
ule features separate autopilot channels for
roll, pitch, and yaw. Gyro drift is modeled
as well. The autopilot module generates four
fin position commands for the four actuators.
The actuator module will be used four times
for this particular missile simulation. The ac-
tuators are described as nonlinear fourth-order
systems with nonlinearities like running and
breakaway friction, torque limiting, and fin an-
gular traveling limiting.
The aerodynamics module describes all aero-
dynamic force and moment coefficients acting
on the missile airframe as multivariable func-
tions. Inputs to the functions are typically
the missile angle of attack, angle of sideslip,
control surface displacements and Much num-
ber. This module is dependant on the types
of wind-tunnel measurements performed on
the missile; therefore, this module is the least
"generic _ of all missile modules. For this par.
ticular missile there are 14 functions of one
variable, 17 functions of two variables and 9
functions of three variables that describe the
aerodynamics. Furthermore, some functions
are included to represent thrust and mass vari-
ations due to propellant burn.
The missile equations of motion module com-
bines the aerodynamic coefficients with air
density, dynamic pressure, and gravity to form
the total forces and moments acting on the aiI-
frame. Dividing these forces and moments by
mass or moments of inertia provides the mis-
sile translational and rotational accelerations.
T25
SYSTEM 100 Architecture
Applied Dynamics International has been in-
volved in solving time-crltical simulation of
continuous dynamic systems since its found-
ing in 1957. The SYSTEM 100 simulation
computer system was introduced by ADI in
1984. It consists of an AD 100, a high-speed,
floating-point compute engine; a host con-
troller, a general-purpose digital computer of
the VAX family; and ADSIM, a user-friendly
simulation language designed specifically for
the AD 100. The SYSTEM 100 hardware and
software work together to form a complete
simulation environment.
The AD 100
The AD 100, a synchronous, bus-oriented mul-
tiprocessor compute engine designed for time-
critical digital simulation, is the basic funda-
mental building block of the SYSTEM 100.
The AD 100 is s single-user system without
an operating system. It is controlled by a mul-
tiprocessing VAX host computer running the
VMS operating system. Acting as the con-
troller and user interface, the host computer
relieves the AD 100 of these interrupt-based
tasks. The compute engine needs to be iso-
lated from the overheads and restrictions as-
sociated with an operatin 8 system in order to
achieve and maintain its optimum computa-
tion speed or frame rate.
The AD 100 is capable of 20 million fioatin 8-
point operations per second. The basic system
consists of four processors and a host interface
tied to a common bus, the PLUSBUS. The
PLUSBUS is 105 bits wide, 65 bits of data
and 40 bits of address and control. Emitter-
Coupled Logic (ECL) devices are used to ob-
tain high computational speed. The four basic
processors axe the Communication and Con-
trol Processor (COM), the Arithmetic Logic
Unit (ALU), the Multiplier (MUL), and the
Storage Processor (STO). Each processorhas
itsown program memory, program counter,
and instructiondecoder. Each processor has
a 64-bitinstruction.The COM Processor has
a 64K program memory, and the other proces-
sors have 4K program memories. Timings in
the AD 100 are expressed interms ofa master
clock period of 25 nanoseconds. The instruc-
tion cycle of the AD 100 consistsof four of
these phases or periods.
Every arithmeticoperation performed on the
AD 100 is done in floating-pointarithmetic.
Calculationsare performed using eithera 53-
bit short-word format or a 65-bitlong-word
format. Both formats contain 1 sign bit,12
exponent bits,and either40 or 53 significand
bits.The long-word format isused where ad-
ditionalaccuracy isneeded, such asin the case
ofnumerical integrationto minimize roundoff
and truncationerrors.
The STO Processor provides 64K of 65-bit
high-speeddata storage.Memory accessesand
address arithmeticcan take place two per in-
structioncycle. Some simulation tasks such
as functiongenerationand memory buffersre-
quire large amounts of data storage. It is
for thesepurposes that an optionalprocessor,
the Function Memory Unit (FMU), was intro-
duced, which has data memory of 2 million
words by 64 bits.
ADSIM Environment
With a specific application area in mind,
namely reai-time simulation, ADI was able to
design the AD 100's hardware and ADSIM to
handle the necessities of the simulation envi-
ronment. ADSIM is made up of a high-level
simulation language and a run-time interactive
control environment.
The ADSIM language is mathematically ori-
ented. Many key elements of a typical simu-
lation are built into the language, such as in-
tegration techniques, function generation, and
726
control-system nonlinearity functions. A con-
trol executive consisting of two programs, one
that runs on the host controller and one that
runs on the AD 100, provides the basis for im-
plementing a model. The control structure
built into this executive controls such param-
eters as system time (simulation time), frame
time, and integration step sise. A dynamic
section is provided for the model's differen-
tial equations. ADSIM allows the model to
be implemented as a series of scalar and first-
order differential equations. If conditional
code is included as part of the model, the
controlexecutive takes care of padding the
frame such that each frame isconsistentwith
real time. Sorting of the dynamic equations
and identifyingMgcbralc loops are examples
ofsome ofthe capabilitiesofthe ADSIM com-
piler. Integrationis handled using Runge-
Kutta, Adams-Bashforth, or Adams-Moulton
system-levelroutines.The model development
time ismuch lesswhen a simulationlanguage
such as ADSIM isused since many of these
standard simulation techniquesare builtinto
the language.
ADSIM program development, includingedit-
ing, compiling, and debugging, isperformed
on the host computer. There are two ADSIM
compilers: one that produces code to be ex-
ecuted on the AD 100 for time-criticalwork
and one that produces code to be executed on
the host computer fornon-time-criticalexper-
imentation and debugging. The same ADSIM
sourcecan be processed by eithercompiler.
Running a program on the AD IO0 involves
loading the executable code from the host
computer into the AD 100 at run time. The
user run-time interface consists of a program
called INTERACT running on the host com-
puter. INTERACT provides a user-friendly
interface for debugging and experimentation,
allowing constants to be changed, variables
to be displayed, integration methods changed,
breakpoints to be set, etc. This environment
reduces the time it takes to get the simulation
into a state where it can be integrated into the
design ud testing phase.
FORTRAN
The AD 100 is also able to run FORTRAN
programs. ADI developed FORTRAN/AD, a
subset of the FORTRAN 77 standard, to run
on the AD 100 computer. In general, FOR-
TRAN programs will not be as computation-
ally efficient as ADSIM programs, but they
allow the user to benefit from investments al-
ready made in FORTRAN simulations.
Implementation in ADSIM
The interactive nature of ADSIM, together
with the INTERACT uti]ity, make the task
of implementation, verification, and validation
easier and allows one to develop a feel for the
system being simulated. A rich set of INTER-
ACT commands allows the user to change any
simulation variable or to change the integra-
tion time step and method; an on-line data
logger and graphics package allow the capa-
bility to verify simulation results. Vaxions re-
searchers have estimated that the verification
and validation portion of a simulation can con-
sume 30 to 60 percent of a particular project's
schedule and budget. The implementation of
the missile model in ADSIM, together with
its interactive environment, is very struightfor-
ward. It requires about 1150 lines of ADSIM
source code. The implementation runs on the
AD I00 with a frame time of 444 ps, allowing
the model to run more than four times faster
than real time. The same ADSIM model runs
on VAXcs as well. The frame times on vari-
ous VAXes allow the model to run between 5
and 20 times slower than real time, depend-
ing on the type of VAX. On the AD I00, the
entire model requ_es about 5 percent of the
hardware resources.
727
Implementation in FORTRAN
To compare the accuracy and performance of
the model, ADI also implemented the missile
model in FORTRAN. This FORTRAN code
runs on the AD 100 as well as on many general-
purpose digital computers. The implementa-
tion in FORTRAN requires about 3950 lines
of source code. On the AD 100, the frame
time of the model is about 1100 ps, allowing
the model to run just a bit faster than real
time. On a VAX computer, the same FOR-
TRAN code runs from 10 to 50 times slower
than real time, depending on the type of VAX.
References
[1] Wright, M. System I00 Simulation Com-
puter Architecture. European Simulation
Multiconference, June 1989.
[2] Siz-Degree-of-Freedom Missile Simula-
tion. Applied Dynamics Application Re-
port, March 1989.
Comparing ADSIM and FORTRAN
The implementation in FORTRAN does not
support an interactive environment. As a re-
suit, the development of the FORTRAN ver-
sion of the simulation turned out to be or-
ders of magnitude more tedious than the corre-
sponding ADSIM implementation. Such issues
as functions, models, sorting of the equations,
and optimizing were major hurdles for the
FORTRAN implementation, while they were
trivial for the ADSIM implementation. The
numerical accuracy of the two models is es-
sentially the same. The two implementations
provide answers that are similar up to seven
or eight decimal places. Both models, when
running on the AD 100, can he extended, to
hardware-in-the-loop studies.
(_onelusions
The performance numbers of the AD 100
show that it is possible to implement a high-
performance missile model in a real-time tim-
ulation without the problems associated with
an implementation on a general-purpose com-
puter using FORTRAN.
7"28


Six-degree-of-freedom missile simulation using the ADI AD 100 digital computer and ADSIM simulation language

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