Simulation and Flight Control of an Aeroelastic Fixed Wing Micro Aerial Vehicle

12 Pages·2002·0.86 MB·English

by  Waszak, Martin

AIAA 2002-4875
Simulation and Flight Control
of an Aeroelastic Fixed Wing
Micro Aerial Vehicle
Martin R. Waszak and John B. Davidson
NASA Langley Research Center
Hampton, VA 23681-2199
Peter G. Ifju
University of Florida
Gainesville, Florida 32611-6250
AIAA Atmospheric Flight Mechanics Conference
5-8 August 2002
Monterey, CA
For permission to copy or to republish, contact the copyright owner named on the first page.
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SIMULATION AND FLIGHT CONTROL OF AN AEROELASTIC FIXED WING
MICRO AERIAL VEHICLE
Martin R. Waszak* and John B. Davidson ?
NASA Langley Research Center, Hampton, Virginia
Peter G. Ifju_
University of Florida, Gainesville, Florida
Abstract
Micro aerial vehicles have been the subject of continued interest and
development over the last several years. The majority of current vehicle
concepts rely on rigid fixed wings or rotors. An alternate design based on an
aeroelastic membrane wing has also been developed that exhibits desired
characteristics in flight test demonstrations, competition, and in prior
aerodynamics studies. This paper presents a simulation model and an
assessment of flight control characteristics of the vehicle. Linear state space
models of the vehicle associated with typical trimmed level flight conditions
and which are suitable for control system design are presented as well. The
simulation is used as the basis for the design of a measurement based nonlinear
dynamic inversion control system and outer loop guidance system. The
vehicle/controller system is the subject of ongoing investigations of
autonomous and collaborative control schemes. The results indicate that the
design represents a good basis for further development of the micro aerial
vehicle for autonomous and collaborative controls research.
Introduction battlefield surveillance or mapping the extent of
chemical/radiation spills or viral outbreaks. Other
Micro aerial vehicles, or "MAVs", are typically
applications include use in search and rescue
designated as a class of aircraft with a maximum
operations, traffic/news coverage, and crop or wildlife
dimension of 6 inches that are capable of operating at
monitoring. Many potential uses would require
speeds of 25 mph or less. Ell Developments in
cooperative and collaborative control capabilities so
miniaturized digital electronics, communications, and
that large numbers of MAVs could be used to cover a
computer technologies and strong support by DARPA
large operational area. In these types of applications
have moved the prospect of very small autonomous
MAVs could be coordinated from a central base
flight vehicles from the realm of science fiction to station or used in collaborative swarms to collect and
science fact. The goal is for these vehicles to provide
transmit data.
inexpensive and expendable platforms for surveillance
The research and development required for
and data collection in situations where larger vehicles
developing MAVs and related systems is technically
are not practical. For example, they can be used for
challenging and requires a number of technological
advances that may benefit a broad range of aerospace
applications. The development of avehicle could also
Senior Research Engineer, Dynamics and Control
Branch. Senior Member AIAA. foster development of component technologies and
_ Senior Research Engineer, Dynamics and Control help to support an emerging growth market for micro
Branch. Senior Member AIAA. aerial vehicles.
$ Associate Professor, Department of Aerospace, An aeroelastic fixed wing micro aerial vehicle
Mechanics, and Engineering Sciences. concept has been developed by ateam at the University
of Florida with a goal to design a vehicle that could
Copyright © 2002 by the American Institute of
win the ISSMO (International Society of Structural
Aeronautics and Astronautics, Inc. No copyright is
asserted in the United States under Title 17, U.S. Code. and Multidisciplinary Optimization) Micro Aerial
The U.S. Government has a royalty-free license to Vehicle Competition; a goal that has been
exercise all rights under the copyright claimed herein for accomplished each of the last four years. [2'31
Governmental purposes. All other rights are reserved by The vehicle exploits an innovative aeroelastic wing
the copyright owner.
with the ability to adapt to atmospheric disturbances
1
American Institute of Aeronautics and Astronautics
Table 1 UFMAV geometric and mass properties.
Empty Weight 0.12 lbs
Wing Area 19.8 in2
Span 6in
MeanChord 3.3 in
Moments of Inertia:
Ixx 0.086 lb-in2
Iyy 0.23 lb-in2
Izz 0.21 lb-in 2
2
Ixz 0.037 lb-in
Figure 1 photograph of Univ. of Florida MAV.
Vehicle Description
and provide smoother flight thereby providing a better
The University of Florida MAV (UFMAV)
surveillance platform and making the vehicle easier to
incorporates a high mounted flexible membrane wing
fly. This is accomplished via a passive adaptive
and low mounted cruciform tail attached to atapered
washout mechanism.
fuselage with rectangular cross section (see figure 1).
The adaptive washout technique has been taken from
The fuselage is a truss-like design constructed of a
sailing vessels which use sail twist to greatly extends
carbon fiber/epoxy material covered with a thin
the wind range of the sail and produce more constant
transparent monofilm membrane. A more detailed
thrust (lift) in gusty wind conditions. Adaptive
description of the vehicle and its construction can be
washout isproduced inthe MAV by deformation of the
found in reference 3. Table 1summarizes the pertinent
membrane wing in response to changes in speed and
geometric and mass properties of the vehicle.
vehicle attitude. The result produces changes in wing
A unique aspect of the vehicle is its flexible
camber and angle of attack along the span. The effect is
membrane wing. The cambered wing structure is
to reduce the sensitivity of the vehicle to disturbances.
constructed of unidirectional carbon fiber prepreg
NASA is collaborating with the University of
laminate forming a leading edge spar and chordwise
Florida to develop an understanding of the underlying
ribs or battens. A membrane material is bonded to the
physical phenomena associated with the vehicle
spar and batten. The wing membrane material is a 4
concept with a goal of enhancing the vehicle design
mil thick flexible latex membrane.
and developing a capability for investigating
The maximum dimension (including length and
autonomous and collaborative control technologies.
wing span) of the vehicle is six inches. The wing area
Reference 4 documents the results of a wind tunnel
is approximately 19.8 square inches. The root chord is
test in which aerodynamic data was collected to provide
4.25 inches and the mean chord is 3.3 inches. The
a database to support the development of a dynamic
camber of the unloaded wing is approximately 6.5
simulation of the University of Florida MAV
percent of the root chord with the maximum camber
(UFMAV) concept. In that paper the flexible
occurring at approximately 30 percent chord and is
membrane wing was shown to significantly increase
uniform across the span. The wing is mounted at an
the stall angle of the vehicle without sacrificing L/D
incidence of approximately nine degrees with wing
ratio. The vehicle was also determined to be statically
incidence defined as the angle between the root chord
stable in all axes.
line and the longitudinal axis of the fuselage.
This paper describes the development of a dynamic
Control is accomplished using two independently
simulation and flight control assessment based on the
controlled elevons that are actuated symmetrically and
aerodynamic data described in reference 4. A
antisymmetrically using small rotary servos. A small
control/guidance system design is also presented. The
gas engine normally provides propulsion with a three
inner loop controller design uses measurement-based
inch diameter propeller with apitch of 1.25. However,
nonlinear dynamic inversion. The structure of the
an electric motor was used during wind tunnel tests to
guidance system allows the vehicle to be integrated
more accurately control propeller rpm and is used in
into an existing multiple vehicle collaborative control
the simulation model as well.
scheme .[5]
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American Institute ofAeronautics andAstronautics
SimulationModel
Thesimulationmodeils basedon theaircraft The longitudinal and lateral-directional subsystems
consist of additional subsystems that systematically
equationosfmotionpresenteindReferenc6e. The
equationsof motion were coded using build up the equations of motion as derived in
Matlab/SimuliNnkT.hestructuroefthesimulatioins reference 6. The equations represent the six degree-of-
freedom motion of a rigid aircraft relative to a flat,
depicteindFigure2. Thesimulatioins structured
non-rotating earth. The atmosphere is represented using
usingsubsystemrespresentinagctuatodrynamics,
the 1976 Standard Atmosphere model. [6]
equationosfmotion(EOMsa),ndsensodrynamicAs.
UFMAV Aero Model
moredetailebdlockdiagraamppeairnstheAppendix.
Theactuatosrsubsystecmurrentlcyonsistosffirst The aerodynamic model was obtained primarily from
orderactuatotrransfefrunctionasndlimitersthat
wind tunnel data collected inthe NASA Langley Basic
boundthepermissibrlaengeofsymmetri8csymand Aerodynamics Research Tunnel (BART). H Linear
antisymmet8riacsycontroslurfacdeeflection(±s25 regression analysis was used to generate functions that
approximate the dependence of the forces and moments
degreeasnd±20degreeres,spectivealyn)dcommanded
on angle of attack, sideslip angle, and propeller rpm.
motorvoltage(0 20volts).Thesensosrubsystem
The functions are inthe form of Taylor series.
currentlcyontainnsodynamicbsutwillpermistensor
The regression analysis was performed using wind
modetlsobeaddeadtalatetrime.
tunnel data that consists of the aerodynamic force and
Theequationosf motionincludethelongitudinal
moment coefficients at various combinations of angle
andlateral-directioenqsuationosfmotionm,odelfsor
of attack, sideslip angle, control surface deflection,
thrustandaerodynamfoicrcesandmomentsa,nda
dynamic pressure, and motor rpm. The range of
standaardtmosphemreodel(seeFigure3 andthe
variation for these parameters correspond to the region
AppendixE).achofthemajorcomponenotsfthe
over which the aerodynamics are linear. HI The main
EOMssubsystewmillbedescribesudbsequently.
implication of this simplification is that the angle of
Equations of Motion attack is limited to values below 20 degrees and
The equations of motion are implemented in two sideslip to values between 5 and 5 degrees. Cross
major subsystems representing the vehicle dynamics in terms between angle of attack, control deflection, and
the longitudinal and lateral-directional axes. There is motor rpm are used to account for the dependence on
coupling between these two subsystems due to inertial propeller slipstream effects and the effect angle of
attack has on control effectiveness. The values of the
and gravitational coupling. There are also several
quantities that are used to determine the aerodynamic coefficients are shown in the tables inthe Appendix.
forces and moments (e.g., body rates, angle of attack, Note that there are three sets of coefficients for lift,
sideslip angle, speed). These quantities are fed back to drag, and pitching moment. Each set corresponds to a
the aero model as necessary. different dynamic pressure. The differences are
attributable to Reynolds number effects. Interpolation
is used in the simulation to determine the coefficient
values at any given dynamic pressure between 1.0 and
2.0 psi. Lack of sufficient lateral-direction force and
[.... [ [ [ [I[.... [ ve°hicl2eses
moment data and higher levels of uncertainty for these
quantities made it impossible to isolate Reynolds
Figure 2 UFMAV simulation structure. number effects for side force, rolling and yawing
moment coefficients. As a result, the values for the
UFe ArVVlateeral-direc tionoal co'effincients °repres'entsan aveerage oever s
dynamic pressure.
LDMT Additional terms were added to the Taylor series in
an ad hoc manner to account for dependence on angular
rates (i.e., dynamic derivatives). Terms associated with
the angle of attack and pitch rates were added for lift
(CLq, CLa) and pitching moment (CMq, CMa).
Terms associated with roll and yaw rates were added for
the side force (Cyp , Cyr ), rolling moment (Clp,
Figure 3 EOMs subsystem structure.
C6) and yawing moment (Cnp,Cn_). The
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coefficienftosrmostofthesetermswerecomputed
where KRPM represents rpm/1000. Note that the
usingPMARCE.sTl woexceptionwserethedynamic
behavior is essentially quadratic in motor voltage
derivativeasssociatwedithrateofchangoefangleof
(Vmotor) with a variable offset which is determined
attack(CLa,CMa)whichwerechosenbasedon
by propeller loading effects expressed through a
"typicalv"aluepsublisheindreferen9ce,page19T. he dynamic pressure (_ ) dependent term and the angle
valuefsorallthedynamdicerivativeasreshowinnthe ofattack dependent terms.
tableisntheAppendix. The function relating thrust to motor rpm is
Theexpressiofonrtotallift forcecoefficienist
showninequatio(n1)asanexampleoftheTaylor
serieesxpansion.
where CT is the thrust coefficient. No attempt was
made to explain the structure of this equation on a
physical basis. Tables of the propulsion model
coefficients are presented inthe Appendix.
Analysis
Thethrusdtependecnrotstserms The simulation model of the UFMAV was used to
CL(.)r account for
perform a number of analyses to assess the stability
the fact that the effects of thrust are coupled with and control properties of the vehicle. These analyses do
angle of attack and control surface deflection through not, however, constitute a validation or verification of
prop stream effects. The expressions for drag, side the simulation model since there are no static or
force, and pitching, rolling, and yawing moments are dynamic data available for the actual aircraft in flight.
similar in structure but differ in the particular First a trim comparison is made for the vehicle in
coefficients associated with coupling. straight level flight at several dynamic pressures. The
UFMAV Propulsion Model dynamic pressures (1.0, 1.6, and 2.0 psf) correspond to
The propulsion model was obtained from wind conditions at which experimental data are available.
tunnel data collected during the BART test. H Motor These data were obtained during the wind tunnel test in
BAR_If41and are representative of typical flight speeds
thrust was approximated by subtracting the prop-off
ofthe UFMAV.
axial force from the prop-on axial force. Regression
analysis was used to generate generalized Taylor series The results of three longitudinal trim studies are
functions that approximate the dependence of motor shown in table 2. The experimental trim results were
thrust on angle of attack, dynamic pressure, and obtained by achieving trim in the BART tunnel. This
voltage commands. The propulsion model consists of was accomplished by first setting the tunnel speed
two parts: a motor model that characterizes the corresponding to the desired dynamic pressure and then
relationship between motor voltage command and varying the vehicle angle of attack, symmetric elevon
propeller rpm, and a thrust model that characterizes the deflection, and motor voltage (i.e., propeller rpm) until
relationship between propeller rpm and thrust the lift was approximately equal to the gross vehicle
coefficient. This implementation separates the effect of weight and the pitching moment and total axial force
propeller loading on motor rpm from the thrust were both approximately zero.
produced at agiven rpm. The simplified analytical trim was determined using
The regression analysis was performed in an ad hoc the method described in reference 10. Equation (4) is
manner to identify a combination of parameters that the matrix equation that was solved to determine trim
provide a reasonable approximation to experimental angle of attack and symmetric elevon.
data. The function approximating the relationship
between motor voltage and motor rpm is
Mc_
CMs_,ym 8syn_rim [-CMo
KRPM = CMo + CM_t_1+ CMc_ +CMc2 5 2
2 (2)
The lift curve slope, moment curve slope, and lift and
+CMvmotorl:m°t°r +CM 2 Vmotor
moment control sensitivities were obtained from the
12moto F
experimental data for the corresponding dynamic
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American Institute ofAeronautics andAstronautics
Table 2 Experimental, analytical, and simulation Table 4 longitudinal modes.
based lon: ;itudinal trim. Dynamic Short Period Mode Phugoid Mode
Dynamic Propeller Angle of Symmetric Pressure damping freq. damping freq.
Pressure RPM Attack Elevon (psf) ratio (rad/sec) ratio (rad/sec)
(psf) (de_) (de_) 1.0 0.13 23.3 0.44 0.85
Experimental Trim 1.6 0.12 30.2 0.35 0.65
1.0 18,900 10.4 -6.5 2.0 0.12 32.6 -0.56 0.67
1.6 20,600 5.4 -3.5
Table 5 lateral-directional modes.
2.0 21,900 4.0 -2.5
Dynamic Spiral Roll Dutch Roll Mode
Analytical Trim (Simplified) Pressure Mode Mode
1.0 11.2 -5.6 (psf) eigenvaluc eigenvalue damping freq.
1.6 5.4 -2.5 ratio (rad/sec)
2.0 3.5 -1.9 1.0 -1.04 -27.7 0.094 21.1
1.6 -1.04 -37.3 0.065 24.2
Computed Trim (UFMAV)
2.0 -1.02 -42.8 0.050 25.9
1.0 19,600 11.1 -6.8
1.6 21,200 5.6 -4.7 The simulation was also linearized about the above
2.0 22,000 3.5 -1.9 trim conditions to assess the dynamic stability of the
vehicle. Table 4 summarizes the frequency and
Table 3 Computed lateral-directional trim.
damping of the linearized longitudinal modes. Note
Dynamic Sideslip Bank Antisymmetric
that the short period mode is stable for all three
Pressure Angle Angle Elevon
dynamic pressures but lightly damped. Its frequency
(psf) (de_) (de_) (de_)
increases with increasing dynamic pressure but the
Computed Trim (UFMAV) damping is essentially constant. The damping of the
1.0 -0.051 -0.97 -0.59 phugoid mode varies significantly and is unstable at
1.6 0.028 -1.6 -0.54 the higher dynamic pressure.
2.0 0.070 -2.1 -0.51 Table 5 summarizes the eigenvalues or frequency
and damping of the linearized lateral-directional modes.
pressure. [4]The data was assumed to correspond to a Note that all the modes are stable and that the dutch
propeller rpm near trim. roll mode is lightly damped. This is qualitatively
The computed trim was obtained by using the consistent with behavior of the vehicle in flight. Note
UFMAV simulation model and a constrainted that the spiral mode is relatively unaffected by changes
optimization routine to achieve level trim at a specified in dynamic pressure but that the magnitudes of both
dynamic pressure. Comparison of the three trim the roll and dutch roll modes increase with increasing
analyses shows very good agreement for angle of dynamic pressure.
attack, symmetric elevon deflection, and propeller rpm. Linearized models used to perform this analysis can
This implies that the longitudinal aerodynamic forces be found in the Appendix.
and moments are well approximated in the simulation. Control Design
A straight and level trim analysis using the
A preliminary guidance/control system has been
simulation model was also performed to determine the
developed to enable investigations of autonomous and
lateral-directional quantities: sideslip, bank, and yaw
collaborative control issues. The controller is
angles. Table 3 shows the results of this analysis.
composed of two main parts: an inner-loop
Note that the UFMAV achieves lateral- directional
measurement-based nonlinear dynamic inversion
control via antisymmetric elevon and dihedral
controller for control of angular rates and an outer-loop
coupling. It does not have two independent lateral-
navigation command follower for control of wind-axis
directional controls (such as redder and aileron) and angles. [11'12] An overview of the control system is
cannot be trimmed at zero bank angle (or zero sideslip
given in figure 4. The control system inputs are
angle) as is typical. The results indicate that though
commanded flight-path angle 7, wind-axis heading
the vehicle does have significant asymmetries, all the
angle Z, and total speed Vr These inputs were chosen
trim values are small and within the range of values at
to allow the vehicle to be readily integrated into an
which the aerodynamic data was obtained and are
existing multiple vehicle collaborative control
qualitatively consistent with the vehicle in flight. scheme. E51Controller outputs are commanded symmetric
5
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7_ Letting Xoand 80denote aprevious state and control
_ .g y from the recent past and defining
O (f(x) +g(x,8)) X=Xo
A°=_xx ¢5_° (7)
Figure 4 structure of UFMAV control system. 0
B0= _-_ X=Xo,6=6°
and antisymmetric elevon deflection. A separate
proportional-integral error loop is used to generate F(x, 8) can be written as
motor voltage commands to control total velocity.
F(x,8) =2=2O +Ao(x-xo)+BOA8 (8)
For this preliminary study, the feedback
measurements are assumed to be known perfectly. in the neighborhood of x=xo, 8=8O where
The two main parts of the control system are 8 80+ AS.
discussed in more detail in the following. At this point, this development differs from
reference 11in that the number of controls is less than
Measurement-based Nonlinear Dynamic Inversion the number of controlled variables and so the desired
Given desired values of roll acceleration /), pitch responses cannot be completely achieved. A control law
acceleration +),and yaw acceleration ?, the inner- is obtained by minimizing
loop controller generates symmetric and
J = @d- Y)TQ(2d- Y) (9)
antisymmetric elevon commands to achieve the
desired angular accelerations. The inner-loop where
controller isbased on a modified nonlinear dynamic
inversion approach developed in reference 11. This 2=oO-h-(2-x-)- i = hx(xo +Ao(x-xo) +BOAS) (10)
approach does not require a model of the baseline
vehicle (i.e. no stability derivatives), but does require and Q isa positive-definite diagonal weighting matrix
a model of the vehicle's control effector derivatives
used to emphasize desired system responses. This
and feedback of body-axis angular accelerations and yields
control effector positions. Since this approach uses
acceleration measurements in lieu of acomplete on-
A8 = [(hxBo )r QhxBo]-l( hxBo)r Q.
board vehicle model, this approach is less sensitive to
(11)
vehicle model errors and can adapt to vehicle failures (2d-h+ o)
and/or damage. An overview of the approach from
reference 11is given in the following. With a sufficiently fast update rate xtends to Xoand
Given the vehicle equations of motion
equation (11) becomes
2 =F(x,8) = f(x) +g(x,8)
(5) A+=[OxBO)++ ]-i ++
QhxBoj (hxBo) Q(J_d-hx_cO) (12)
Y=[P q r]r=h(x)
where 8 80+ AS. The vehicle's control derivatives
where x is the vehicle state vector, 8 is the vehicle
Bo are generated from the nonlinear aerodynamic
control vector, and y is the vector of control
variables: roll ratep, pitch rate q,and yaw rate r. A control coefficients using a central difference
approximation.
Taylor series expansion of (5) yields the following
first-order approximation to F(x, 8) in the
Navigation Command Follower
neighborhood of [x0,80]
Given desired values of flight path angle 7, wind-
axis heading Z, and total velocity Vtthe navigation
f(x,8) =f(x 0)+g(xo,8 0)+
command follower generates required roll rate, pitch
(x-xo (6) rate, and yaw rate acceleration commands for the
inner-loop controller.
x=x0,8=80
The desired dynamics for the outer-loop were chosen
to be
(8-8o
X=X 0
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and 6b. A stability-axis roll rate doublet was
7d=c%(W.- 7)
(13) commanded (50 deg/sec from 1to 2 seconds and 50
)Cd:%(Xc- X) deg/sec from 2 to 3 seconds) with pitch rate and
stability-axis yaw rate commanded to zero. The effect
where the subscript ddenotes the desired value and the of choice of control variable weighting is demonstrated
subscript c denotes commanded input values. The in these figures. Figure 6a shows responses for a
bandwidths mz and m_ were chosen to be control variable weighting of Q diag([roll
approximately a decade below the bandwidths of the acceleration error weighting, pitch acceleration error
desired inner-loop dynamics and therefore were weighting, yaw acceleration error weighting])
chosen to be 2 rad/sec. diag([1,5,2]). As can be seen, the stability-axis roll rate
Using the wind-axis point mass equations of motion
and assuming sideslip angle and sideforce are small and
that Vt and cos(y) are non-zero, commanded wind- de_/ps_ec *_ ;-. : ...... ... ....
axis bank angle _tocan be determined as a function of ::1_ _...................................-.--_-._ ..................................
Vt"_d and )_d [1B]
2
vt)Cdco<, deg/sec _KIE..............2...................,...............................;.................j..V
tangc Vtj d + gcosy (14)
d_g
The desired dynamics for wind-axis bank angle was
chosen to be
deg iN21_ 2i • _"
_d = mp,(_c -_) (15)
where m, were chosen to be 4 rad/sec.
The wind-axis angular rates [i, "_, and )_ are deg .......
transformed to commanded body-axis rates (assuming _y
sideslip angle is zero) using deg
Time (sec)
qrccj_=/[sin0c_ 10 co0sc_100 -csions,, csoins_gtccoossyYj[n)__j[ (16) Figure 6a inner-loop Pc, qc, and rcangular rate
commands, Q diag([ 1,5,2]).
where c_ is angle of attack. The desired closed-loop
dynamics )?d for the inner-loop were chosen to be
deg/sec ©
hd=m/pc - p) •:_ k........... J :
r_ _'_ ....... : .... :--_
Old= mq (qc - q) (17)
deg/sec ;:_
_d=m_(_.-r)
where the subscript ddenotes the desired value and the
subscript cdenotes commanded values determined by
the outer-loop control law. The inner-loop
bandwidths rap, mq, mr were chosen to be 20, 15 and deg O ....
20 rad/sec, respectively, consistent with the open- •N'5_
loop bandwidth. (_sym
Figure 6 shows time responses for inner-loop po, qc, deg
and rc angular rate commands (i.e. no outer-loop
controller). The initial condition for these time deg &"._
responses is straight and level flight at V, 37 feet/sec.
Reference signals were generated for comparison with
Time (sec)
the achieved responses from equations (13), (15), and
(17) using the specified bandwidths. The commands Figure 6b inner-loop Pc, qc, and rcangular rate
and reference signals are shown respectively as dashed commands, Q diag([1,5,10]).
and dotted lines in the upper two plots of figures 6a
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The simulation was used to assess vehicle trim and
basic stability and control properties. The analysis
7deg __ "_-_--_-_-_,_
indicates that the vehicle has acceptable stability
properties and good controllability.
A control system was designed using a
measurement-based nonlinear dynamic inversion
V,fps approach. The method was extended to accommodate
application to systems with fewer controls than
controlled variables as is the case for the subject
vehicle. A guidance loop was also designed to allow
the simulation model to be integrated into an existing
multiple vehicle collaborative framework.
m voltss_ "...................._ " -..... " Assessment of the control and guidance systems
using the simulation demonstrated satisfactory
Time _sec performance. Additional research is underway to
improve the dynamic response, investigate performance
Figure 7- Figure 3 outer-loop y_, Z _, and robustness, and explore implementation issues.
Vt commands, Q diag([1,5,2]). Acknowledgements
The authors wish to acknowledge Matt Pfenninger,
reference signal is more closely followed than the
Blain Levedahl, Matthew Lackner, and Jonathan Cook
stability-axis yaw rate reference signal with low dutch
for their assistance in developing and documenting the
roll damping as illustrated by the oscillatory sideslip
simulation.
response. Figure 6b shows responses for Q
diag([ 1,5,10]). This results in the stability-axis yaw References
rate reference signal being more closely followed [1] Mueller, T. J. editor, "Proceedings of the
than in figure 6a and a better damped sideslip Conference on Fixed, Flapping and Rotary
response. Wing Vehicles at Very Low Reynolds
Figure 7 shows time responses for outer-loop y_, Numbers," Notre Dame University,
Indiana, June 5-7, 2000.
Z_, and Vt commands. The control variable
[2] Ifju, P.G., Jenkins, D.A., et.al.,
weighting was Q diag([1,5,2]). The commanded and
"Flexible Win_Based Micro Air
reference signal values are shown respectively as dashed
Vehicles," AIAA Paper No. 2002-0705.
and dotted lines inthe top three plots. As can be seen,
AIAA Aerospace Sciences Meeting, Reno,
the vehicle closely follows the reference signal with
NV, January 2002.
reasonable control activity.
[3] Ifju, P.G., Ettinger, S., Jenkins, D.A., and
These preliminary results demonstrate that this is a
Martinez, L.," Society for the Advancement
viable approach for control of systems where the
of Materials and Process Engineering
number of controls is less than the number of control
Annual Conference, Long Beach, CA, May
variables, such as, MAV's. Future efforts will focus on
6-10, 2001.
improvements to this approach, robustness analysis,
[4] Waszak, M.R., Jenkins, L.N., and Ifju,
and use of this method as part of a multiple vehicle
P.J., "Stability and Control Properties of
collaborative control scheme.
an Aeroelastic Fixed Wing Micro Aerial
Concluding Remarks Vehicle." AIAA Paper 2001-4005.
A dynamic simulation model of an aeroelastic fixed Presented at the 2001 AIAA Atmospheric
wing micro aerial vehicle has been developed that is Flight Mechanics Conference. Montreal,
suitable for a wide variety of uses including control Canada. August 2001.
system design, navigation and guidance algorithm [5] Anderson, M.R. and Robbins, A.C.,
development, and their assessment. The simulation is "Formation Flight as a Cooperative
based on a vehicle concept developed at the University Game," AIAA Paper Number AIAA-98-
of Florida and wind-tunnel data collected inthe NASA 4124. Presented at the 1998 AIAA
Langley Basic Aerodynamics Research Tunnel. Guidance, Navigation, and Control
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Taylor series aerodynamic model.
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AIAA Paper 2000-4565 AIAA Guidance.
Navigation and Control Conference,
Denver, CO, August 2000.
Simulation Block Diagram
Long and Lat-Dir EOMs
gamma_tad
UFMAV Aero Model
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