Progress Report Notes:
T fm
The progress reports are formatted so that
the milestones and major tasks have their status
listed immediately below the heading. For any one
report, only the tasks that actually received effort
during the reporting period will have material in
their corresponding sections. Tasks that have not
been worked on to the current date will be listed at
0% complete. Tasks that have been completed will
be listed at 100% complete. The milestones, major
tasks, dates and planned completion status are taken
from the project-planning summary.
Va ( Vi ) Armature (input) voltage
Torques and moments
Torque correction due to the angular
Tc
acceleration of the connecting rod
Crankshaft inertia torque
Tcs
NOMENCLATURE
Angles and frequencies

Connecting rod axis to cylinder axis
 ,( k ) Crank angle (individual cylinders), referred to
reference-cylinder axis
 L (  m ) Angular displacement of belt drive connected to
motor (crankshaft)
 L ( m ) Crankshaft (motor) angular frequency
Lengths
Center of crankpin to center of piston pin (length of
L
connecting rod)
Belt drive displacement

Center of crankshaft to center of crankpin
R
rL ( rm ) Radius of belt drive at engine (motor) end
xc , xe
Rod lengths to rod cg
xP
Distance of piston pin from cylinder end (exit slot
end)
Masses
Equivalent mass at joint of crankpin with connecting
M2
rod
Equivalent mass of connecting rod at crank pin end
M R2
Mc
Mass of crankpin
M c2
Equivalent mass of crankpin at connecting rod end
M c1
Equivalent mass of crankpin at crankshaft end
MR
Mass of connecting rod
Mp
Idealized mass at piston end (including connecting
M R3
M ps
rod) i.e, reciprocating mass
Equivalent mass of connecting rod at
piston end
Mass of piston, piston rings etc
Motor/input parameters
Viscous damping in motor
Bm
i
Jm
Current through armature
Polar moment of inertia of armature
Ka
Amplifier voltage gain
K e ( KT ) Motor voltage (torque) constant
Armature inductance
Lm
R
Armature resistance
Coulomb friction toque in motor
TL
Load (total engine) torque
Tm
Load (total engine) torque referred to motor shaft
Tp
Torque on crankshaft due to air pressure
Torque due to inertia of the reciprocating part
Tt
Inertias
Mass moment of inertia (actual) of connecting rod
IL
I L'
Mass moment of inertia of idealized connecting rod
J
J cs
Mass moment of inertia (general)
Mass moment of crank shaft
Load mass moment of inertia
JL
Miscellaneous

Load divider constant
A p ( As ) Piston (exit slot) area
cg
Center of gravity

f ( M ) Force (moment) - general
Acceleration due to gravity
g
Pressure at jet exit
Po
Rg
Universal gas constant
T

C
Temperature inside piston cavity
Density of air in/out cavity
Jet momentum coefficient
U
h
U
Jet exit velocity
Width of jet exit
Freestream velocity
C
F xp
Reference or characteristic length
Piston inertial force
1. Development of Compact Reconfigurable SJA’s for Distributed Control:
Planned Status: Start April 15th, 2003 – 100% Complete
Actual Status: 80%
Notes Regarding Milestone:
1.1 Development of Modified Experimental Setups
Planned Status: Start April 15th, 2003 – 100% Complete
Actual Status: 100% Complete
Notes Regarding Tasks:
1.1.1 Design Modifications to Wind-Tunnel Setups
For the pitching moment about the model the single-SJA wing developed was mounted on the free-to-pitch
setup shown in Figure 1. This figure is repeated here from an earlier report. The free-to-pitch setup is being
expanded to also include free-to-plunge capabilities. Design is almost complete. Fabrication is anticipated to
start in two weeks.
1.1.2 Fabricate and Assemble Parts for Modified Setups
Figure 1. Free-to-Pitch wing setup.
For the pitching moment tests the trailing edge of the
wing was restricted from moving with a thin strut,
which was equipped with a Futek in-line force sensor.
This allowed us to perform a range of experiments, in
which, for a variety of angles of attack and actuation
operation parameters (particularly frequency), we
measured the wing pitching moment directly from the
load sensor and not by integrating the wing surface
pressures. The freestream velocity of the experiment
was 20 m/s. Data were obtained at angles from 17
degrees to 25 degrees. The frequency was tested to a
maximum of 100 Hz. The aerodynamic moment was
extracted from the measured forces after removal of
loads due to the wing mass. The moments are
measured about x/c = 0.36. Figure 2 shows the plots of
the pitching moment as a function of angle of attack
and actuation frequency. These data were also reported
in our previous report. New data that were obtained at
man more frequencies are included in Section 3.1. The
results of the test show that the SJA produces a
significant change in aerodynamic moment as the
frequency is increased.
Aerodynamic Moment Coeffecient vs. SJA frequency
0.03
Coeffecient of Moment
0.025
0.02
0.015
AoA=21.2
AoA=23.2
0.01
AoA=24.9
AoA=17.3
0.005
AoA=19.0
0
0
10
20
30
40
50
60
70
80
90
100
-0.005
-0.01
frequency (Hz)
Figure 2. Pitching Moment vs. frequency of actuation
1.2 Control Wing with Single SJA, Form Guidelines for Distributed Actuation
Planned Status: Start June 18th, 2003 – 100% Complete
Actual Status: 70% Complete
Notes Regarding Tasks:
1.2.1 Wind-Tunnel Testing of Modified Setups with Single Actuator
1.2.2 Data Reduction and Analysis for Wing/Flow/Control Characterization
Based on the data gathered in the Phase I effort, we have begun to form guidelines for SJA control and
have made progress in the controlled system identification: SJA-control and system identification progress
report. Tasks accomplished in this area to date are:
1. Further developed mathematical models for representing the aerodynamic behavior using
Radial Basis Function Networks.
2. We have also finalized the hardware for the testing of the closed –loop, free-to-pitch controller
in the wind tunnel. This is quite an elaborate setup that interfaces DSpace and the control
algorithm with the wing and wind-tunnel hardware. Closed-loop pitch control tests are
anticipated to start in two weeks.
1.3 Design, Development and Installation of Reconfigurable and Distributable SJA
Planned Status: Start April 15th, 2003 – 80% Complete
Actual Status: 50% Complete
Notes Regarding Tasks: Because of the inability of the original SJA design to provide control authority at low
angles of attack (for  < 12°), we have made it a priority to develop an SJA actuator that will fill this void. As
discussed in the kick-off meeting presentation, we have decided to focus our initial efforts on designing and
developing a “synthetic Gurney flap”: an actuator that can simulate a Gurney flap and provide the necessary
authority at low angles of attack. New tasks and sections dealing with the synthetic Gurney flap (SGF) have
been added as necessary to document the plans and effort associated with this new development.
1.3.1 Design New SJA Suitable for Distributive Control
In this section, we study the behavior of the SJA by simulation of its nonlinear model under the condition of
motor rotation at a constant angular velocity m   m  m first, and then under a step voltage input. Thus, we
mainly focus on the behavior of the following four equations:
 m  m
(1)
m  

Bm

1
K
m 
2m sin(3rml m ) 
T fm  T i
J mcs
J mcs
J mcs
J mcs
 p1m  p22m sin(3rml m )  p3T fm  p4i
(2)
K
R
K
i   e m  m i  a Vi  q2m  q3i  q1Vi
Lm
Lm
Lm
(3)
3 3
U  rml
m (a1 sin  cos   a2 sin 2 cos 2
a3 sin  cos 2  a4 sin 2 cos )
, and  
, ai , i  1,,4 ,
J mcs  J m  Jcs ,
p1  Bm / J mcs ,
p2   / J mcs ,
q3  Rm / Lm ,   L  rmlm ,
where 
2
 rml
(4)
3
orml
p3  1/ J mcs ,
p4  KT / J mcs ,
q1  Ka / Lm , q2  Ke / Lm ,
(5)
Fig.3 shows the jet exit velocity curves at constant motor frequency f m  m /( 2)  55 , 70 and 40 Hz. These
curves show that the jet exit velocity changes periodically with time, and also changes as the motor rotation
speed changes, i.e., m and f m changes. Furthermore, a simulation of the jet exit velocity surface is generated
for a range of f m ( m ) values. Fig.4 simulates the jet exit velocity for f m from 100Hz to 140Hz around a
nominal value of 120Hz in a 3-D plot. Notice the surface is periodic along the t axis. The 3-D plots in Figs.5-7
are for f m ranges of 60~120, 0~60, and 0~200 Hz. It shows that the velocity increases as f m increases, but the
period decreases. Fig.8 shows the motor rotation frequency f m with oscillations when a constant step voltage
input Vi  5.282 v is applied
15
fm = 70 Hz
Jet Exit Velocity (m/sec)
10
55 Hz
5
30 Hz
0
-5
-10
-15
0
0.01
0.02
0.03
Time (sec)
0.04
0.05
Fig.3. Jet exit velocity curves for three different f m
Fig.4. Jet exit velocity surface for f m of 100 ~ 140 Hz
Fig.5. Jet exit velocity surface for f m of 60 ~ 120 Hz
Fig.6. Jet exit velocity surface for f m of 0 ~ 60 Hz
Fig.7. Jet exit velocity surface for f m of 0 ~ 200 Hz
Motor Rotation Frequency (Hz)
25
20
15
10
5
0
0
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time (sec)
2
Fig 8. Motor rotation frequency f m at a constant Vi
The above graphs provide information on the performance of the jet exit velocity for various motor angular
velocities. These studies are useful for the design of a controller that will command a certain jet exit velocity
time history.
The nonlinear model of a high-power, compact synthetic jet actuator used in open loop flow separation
control has been derived. We developed the state space nonlinear model from the voltage input to the jet exit
velocity. Simulations of the jet exit velocity at various motor rotation frequencies were performed to
demonstrate the results. Furthermore, a simulation was carried out of the motor rotation velocity/frequency
response for a step voltage input. Current research is focused on validating the model via open loop
experiments and subsequently using the model in closed-loop control and the development of robust controllers.
For the dynamic model, we will do further simulations together with the controller development.
1.3.2 Fabricate New SJA with Dynamically Reconfigurable Slot Geometry
1.3.3 Fabricate Distributable SJA (with Dynamically Reconfigurable Slot Geometry)
Task Notes: To this point, we have not fabricated an SJA with an integrated reconfigurable slot (see discussion
of reconfigurable slot, section 1.3.5). We have concentrated our efforts more on the development of the
synthetic Gurney flap. The integration of the new SJA’s and SGF’s require a more compact actuator.
1.3.4 Design and Evaluation of Synthetic Gurney Flap Controller
Although it has been demonstrated that control of flow separation can be used for pitch control at high
angles of attack, this mechanism is neither available nor viable at low angles of attack, where
aerodynamic efficiency would be marred by large-scale flow separation. At low incidence, the most
receptive and effective location for modification to generate pitching moment is the trailing edge.
Obvious modifications are the flap. Moments are generated through flap deflection by movement of
the rear stagnation point yielding increased vertical momentum transfer. Other trailing edge
modifications are pneumatic; either
a virtual jet flap, where a high
velocity jet is issued from the
trailing edge or a blown flap, where
the jet is directed over the flap.
Super-circulation may also be
Gurney flap
achieved by using blowing in
concert with a Coanda type trailing
edge. All these methods are
Fig. 9 Typical Gurney flap installation.
effective but may require significant
quantities of air for operation.
The Gurney flap has been shown to be a highly effective, small-scale (typically 0.75 – 1.5% of the
chord) modification that can achieve significant lift and pitching moment generation. A typical Gurney
flap installation is shown in Fig. 9. The flap functions by essentially increasing the downward
deflection of the trailing edge flow, facilitated through the formation of a series of counter-rotating
vortices, similar to those of a von Karman vortex street. A consequent effect is an apparent violation of
the trailing edge Kutta condition. Experimental data show that finite loading is carried to the trailing
edge. For hinge-less flow control the basic tenet of the Gurney flap is attractive, but its implementation
would require moving parts. Consequently, we have suggested the implementation of a “Synthetic”
Gurney flap, where the flap is pseudo-formed using a jet developed by a SJA or continuous pneumatic
supply.
Experimental Details
For initial proof of concept testing, a continuous air supply was implemented using an external high
pressure source. A wing was manufactured from foam and balsa to accommodate the continuous jet or
SJA. The wing was then covered with heat sink to ensure a smooth surface. A NACA 0015 profile was
used. The wing was equipped with end plates to mimic two-dimensional flow. Figure 2 shows the wing
and blowing slot details. The width of the slot was 1mm, giving a slot exit area of 0.0002m 2. The slot
was located 15mm from the wing’s trailing edge. As implemented, the flap is a jet flap, with a large jet
inclination (90 deg) angle.
Geometric details of the model are a chord of 0.71m and a span of 0.235m. The tests were carried out
in Texas A&M University’s 3’ by 4’ closed-loop wind tunnel. A freestream velocity of 15m/s was
used yielding a Reynolds number of 0.7x106. Tunnel turbulence intensity has been measured at less
then 0.5%, assuming isotropic turbulence. Data acquisition was facilitated using a 3-component
Pyramidal balance. Balance output voltages were read using a 16-bit A/D board. A dedicated software
slot exit
side plate
compressed air supply
support strut
Fig. 10 Wind tunnel model details
acquisition code has been written for this facility and was used for acquisition and processing. Prior to
use for these experiments, the Pyramidal balance was re-calibrated. Subsequent balance verification
through application of pure and combined loads suggests accuracies better then 0.6% for lift, drag and
pitching moment. Figures 10 and 11 shows the wing installed in the wind tunnel (nearest end plate
omitted for clarity).
To achieve blowing, shop air was used as
the pneumatic source. Slot exit jet
momentum coefficients were measured
using a British Standard (Part 1042) orifice
plate.
The
orifice
facilitated
the
measurement of the mass flow rate, which in
conjunction with continuity allowed
determination of the jet slot exit velocity.
The measurement technique was verified
using a TSI calibrator which allows accurate
measurement of an air jet exhausting from
Fig. 11 Model tunnel installation
its settling chamber. Air to the calibrator was supplied through the orifice plate. Slot exit velocities
were measured and compared with predictions using the orifice. Agreement was generally within
1.5%.
Lift Coefficient
Lift Augmentation
Ratio
Force Balance Results
In all data, the effects of the jet reaction on lift and pitching moment coefficient have been removed
through tare runs; consequently, pure aerodynamic loading is shown. Results are summarized in Figs.
12 and 13. The effects of the jet momentum coefficient, Cmu on the measured lift are shown in figure
12. Also included is a plot showing the lift augmentation ratio. This ratio is defined as (Cl Cmu≠0ClCmu=0)/Cmu for the present jet configuration. The ratio clearly shows how the effectiveness of the jet
relates to the supplied momentum. A coefficient greater then 1 indicates that augmentation is greater
then if the jet had been used purely for its reactive lift. Also included in the data are results for a 0.75%
of chord Gurney flap, which was positioned at the same location as the jet. This is a typical size for a
Gurney flap, and provides a reference for the lift and moment alteration provided through blowing.
The data in figure 12 show that the jet flap shifts the angle of attack for zero lift to negative values, as
does a conventional flap. A momentum coefficient of 0.0068 is seen to provide similar lift
augmentation to the gurney flap. The
15
magnitudes of the recorded lift also suggest
that the end plates were not large enough to
ensure 2D flow. Notice that all lift curves
appear to have a non-linear increase around
10
4 deg, as seen on low aspect ratio wings.
However, this does not affect the
comparative nature of the data presentation.
The effectiveness of the blowing may be
gauged by examining the lift augmentation
5
ratio (ClCmu≠0- ClCmu=0)/Cmu) shown in the
top of the multi-part figure (Fig. 12). As
0.8
0.75% Gurney
may be seen, the jet greatly augments the
Cmu = 0
lift compared to the momentum added to the
flow. Greatest augmentation is seen for the
Cmu = 0.0037
lower Cmu’s; increasing the jets momentum
0.6
Cmu = 0.0068
reduces the relative benefit if not the
Cmu = 0.01
magnitude of the augmentation. The
augmentation ratios are of similar
Cmu = 0.029
magnitude to those calculated by Lockwood
0.4
and Vogler (1958).
2% chord
0.2
0.0
0
4
8
12
Angle of Attack, deg
Fig. 12 Effect of Cmu of measured lift
coefficient and lift augmentation ratio
In the present application, the primary
significance of the jet is in its impact on the
pitching moment, so as to be suitable for
hinge-less control. The negative shift of the
pitching moment curve, typical of a trailing
edge flap, is clearly seen, see Fig. 13. As
16 noted for lift, the zero pitching moment
Zero Angle of Attack
Increment
caused by Cmu = 0.0068 is comparable to that generated by a 0.75% chord Gurney flap. The
magnitudes of the moment generated, although towards the low end of what a conventional trailing
edge flap may generate, are sufficient for pitch control at low angles of attack. Additionally, the
required jet momentum coefficients are not excessively large, and are achievable using a SJA (as will
be tested in the next phase). Pitch control would be achieved by locating a jet slot on the upper and
lower surface, allowing control of the vehicles incidence. Also shown in figure 13 are the
dependencies of the zero lift increments of Cm and Cl on the jet momentum coefficient. As may be
seen, the greatest augmentation occurs at the lowest Cmu’s, with the increment appearing to
monotonically approach a bound for increasing Cmu. Analytic expressions due to Spence (1958)
suggest a dependency proportional to Cmu1/2 for Cl.
0.15
0.10
FlowVisualization
Pitching Moment Coefficient
To
gain
an
insight
into
the
similarities/differences of the trailing edge
0.05
flow physics between the Gurney and Jet
Cm
Cl
flap, flow visualization using Titanium
0.00
Dioxide was used. A thin plate was attached
parallel to the side plates. Visualization of
-0.05
the skin friction lines on the stream-wise
plate would then give an indication as to the
-0.10
fluid behavior. Please note that due to the
0.00
0.01
0.02
0.03 effects of gravity on the fluid medium, the
Cmu
results are purely qualitative and no
0.10
inferences should be made as to precise
locations or trajectories of flow features.
Cmu = 0
Figure 14 presents acquired images for the
0.75% Gurney flap and Jet flap (Cmu = 0.01)
Cmu = 0.0037
0.05
at a freestream velocity of 15m/s. The results
Cmu = 0.0068
indicate that despite similar aerodynamic
effects, the flow physics present are
Cmu = 0.01
somewhat dissimilar. The jet flap shows
0.00
Cmu = 0.029
evidence of significant turning of the flow
around the trailing edge such that the jet exit
becomes functionally the rear separation
point. The jet is seen to expand rapidly and
deflect streamwise; initially due to pressure
-0.05
gradients across the jet and later due to
entrainment and absorption of the free stream
axial momentum (Jordinson 1956). The
Gurney flap appears to shed a fairly thick
-0.10
0
4
8
12
16 wake extending from the separation bubble
formed behind the flap. The visualized wake
Angle of Attack, deg
may correspond to the von Karman vortex
Fig. 13 Effect of Cmu on Pitching Moment
street identified by Jeffrey (2000). The
Coefficient and Zero Lift Coefficient Increments
significant turning of the flow seen with the
jet flap is not observed. A line indicating the
approximate trajectory of the shear layer shed from the flap extremity is also observed. Comparison of the skin
friction patterns also suggests that while the jet flap draws the lower surface boundary layer away from the
surface, the Gurney causes deceleration and recompression. It may thus be tentatively inferred that the Gurney
augments lift by violating the Kutta condition while the jet flap increases flow turning and hence effective
camber near the trailing edge.
Jet exit
Gurney flap
Fig. 14 Stream-wise flow patterns
1.3.5 Design and Development of Dynamically Reconfigurable Slot Exit Geometry
Notes: In this section, we reiterate our design for reconfigurable slot geometry. Depending on the
performance of the synthetic Gurney flaps (SGF’s) and SJA’s, and the relative complexity to the
reconfigurable slot, we will maintain slot reconfiguration as a viable option.
1.3.6 Manufacture/Purchase Instrumentation for Testing/Verification of New SJA
Two 32-channel pressure scanners from Pressure Systems Inc. have been ordered to serve in pressure
data acquisition for the remainder of the project. Aeroprobe has begun manufacturing two fast-response fivehole probes for use in flow diagnostics during the project. The sensors for these probes have a rather long
delivery time, and we are still waiting for these sensors.
1.3.7 Integrate New SJA into NACA-0015 Wing
2. Experimental Data Acquisition with New SJA and/or Feedback Sensors
Planned Status: Start September 24th, 2003 –11% Complete
Actual Status:15% Complete
Notes Regarding Milestone: Our CMOS camera needed for the PIV work is damaged. It has been
shipped to the manufacturer for repairs. What delays us is the need to determine the cause of the damage.
This is a very expensive piece of equipment and we could not afford to risk again damaging it.
2.1 Testing of Synthetic Gurney Flap Controller
Planned Status: Start September 24th, 2003 – 27% Complete
Actual Status: 15% Complete
Notes Regarding Tasks:
We have completed the design of our high-precision, rotary (Wankel type) SJA for use at the wing’s trailing
edge as synthetic gurney flap. The actuator is now being fabricated using our CNC machine.
2.2 Testing/Verification of New SJA/Slot Design in Benchtop Testing
Planned Status: Start September 24th, 2003 – 27% Complete
Actual Status: 0% Complete
Notes Regarding Tasks:
2.3 Perform Time-Resolved PIV on New SJA
Planned Status: Start September 24th, 2003 –20% Complete
Actual Status: 0% Complete
Notes Regarding Tasks:
2.4 Acquire Steady/Unsteady Data During Testing of SJA/Wing System with Feedback
Sensors
Planned Status: Start December 17th, 2003 – 4% Complete
Actual Status: 0% Complete
Notes Regarding Tasks:
3. Development of Aerodynamic Models for Wing with Distributed SJA
Planned Status: Start March 15th, 2004 – 0% Complete
Actual Status: 10% Complete
Notes Regarding Milestone:
3.1 Develop Aerodynamic Models for Distributed Actuation
Planned Status: Start March 15th, 2004 – 0% Complete
Actual Status: 20% Complete
Notes Regarding Tasks:
To develop control laws for closed loop synthetic jet actuation, wherein a desired angle of attack is to be
achieved through hinge-less actuation, static experiments were first conducted to model the pitching moment
coefficient of the wing section. This model is then utilized to design control laws for set point tracking of the
angle of attack. The control law development will be carried out in two phases. The first phase would involve
development of a PID controller for set point tracking. The PID architecture is chosen for the ease of implement
ability and to gain sufficient insight into the control related issues. The second phase involves development of an
adaptive controller to account for uncertainties that could be parametric in nature or un-modeled dynamics.
Objective:
1. To learn the static relationship between angle of attack, jet frequency and moment coefficient.
Free Variables: Angle of attack (  ), Jet Frequency (f), Free Stream Velocity ( U ).
Measurement Variables: Pitching moment coefficient ( cm ).
Experiment Procedure: For a fixed value of angle of attack and free stream velocity (20m/s), we varied the jet
frequency from 30Hz to 100Hz with the interval of 10Hz . Then keeping the free stream velocity same, we
varied the angle of attack from 17 to 27 with the interval of 2 .
Results:
Figure 15 shows the pitching moment variation with angle of attack for various synthetic jet
frequencies. From the Figure it is clear that pitching moment about pivot point always increases with positive
change in angle of attack or jet frequency. The MRAN algorithm mentioned in previous reports was used to
approximate static pitching moment data. As the available experimental data corresponds to static experiments,
we model pitching moment as function of angle of attack and jet frequency.
M  f  , f 
Figure 16 shows the variation of modeled and experimental moment data for zero jet frequency. From the figure
it is clear that we were able to model the static pitching moment data within experimental error tolerances.
Figures 17 and 18 show the modeled and experimental pitching moment data variation with angle of attack for
various jet frequencies. Further, Figure 19 shows the modeled and experimental pitching moment data variation
with jet frequency for different angles of attack. It is important to mention that we required only 8 Gaussian
functions to model the static pitching moment data. It should be noticed that SJA is more effective for   22o .
Pitching Moment vs 
-0.5
-1
Moment (N-m)
-1.5
0Hz
30Hz
40Hz
50Hz
60Hz
70Hz
80Hz
90Hz
100Hz
-2
-2.5
-3
-3.5
17
18
19
20
21
22
23
24
25
26
27
 (deg.)
Figure 15: Static Experiment Moment Data Plots for Different Jet Frequencies.
Jet Freq. 0 Hz
-0.8
Expt. Data
Modeled Data
-1
-1.2
-1.4
Moment (N-m)
-1.6
-1.8
-2
-2.2
-2.4
-2.6
-2.8
17
18
19
20
21
22
23
24
25
26
27
 (deg.)
Figure 16: Pitching Moment vs Angle of Attack (Jet Freq. = 0 Hz.).
Jet Freq. 30 Hz
Jet Freq. 40 Hz
-0.5
-0.5
Expt. Data
Modeled Data
Expt. Data
Modeled Data
-1
Moment (N-m)
Moment (N-m)
-1
-1.5
-2
-2.5
-3
16
-1.5
-2
-2.5
18
20
22
24
26
-3
16
28
18
20
 (deg.)
22
24
Jet Freq. 50 Hz
-1
Expt. Data
Modeled Data
Expt. Data
Modeled Data
-1.5
Moment (N-m)
-1
Moment (N-m)
28
Jet Freq. 60 Hz
-0.5
-1.5
-2
-2.5
-3
16
26
 (deg.)
-2
-2.5
-3
18
20
22
 (deg.)
24
26
28
-3.5
16
18
20
22
24
26
28
 (deg.)
Figure 17: Pitching Moment vs. Angle of Attack for Various Jet Frequencies
Jet Freq. 70 Hz
Jet Freq. 80 Hz
-1
-1.5
Expt. Data
Modeled Data
Expt. Data
Modeled Data
-2
Moment (N-m)
Moment (N-m)
-1.5
-2
-2.5
-2.5
-3
-3
16
18
20
22
24
26
-3.5
16
28
18
20
 (deg.)
22
24
Jet Freq. 90 Hz
28
Jet Freq. 100 Hz
-1.5
-1.5
Expt. Data
Modeled Data
Expt. Data
Modeled Data
-2
Moment (N-m)
-2
Moment (N-m)
26
 (deg.)
-2.5
-2.5
-3
-3
-3.5
16
18
20
22
24
26
28
-3.5
16
18
20
 (deg.)
22
24
26
28
 (deg.)
Figure 18: Pitching Moment vs. Angle of Attack for Various Jet Frequencies
 =21o
 =23o
-1
-0.5
Expt. Data
Modeled Data
Moment (N-m)
Moment (N-m)
-2
-2.5
-3
-3.5
Expt. Data
Modeled Data
-1
-1.5
-1.5
-2
-2.5
-3
0
20
40
60
Jet Frequency (Hz)
80
-3.5
100
0
20
 =25o
100
-0.5
Expt. Data
Modeled Data
-1
Expt. Data
Modeled Data
-1
-1.5
Moment (N-m)
Moment (N-m)
80
 =27o
-0.5
-2
-2.5
-1.5
-2
-2.5
-3
-3.5
40
60
Jet Frequency (Hz)
0
20
40
60
Jet Frequency (Hz)
80
100
-3
0
20
40
60
Jet Frequency (Hz)
80
100
Figure 19: Pitching Moment vs. Jet Frequency for Various Angle of Attacks
We can use this RBFN model to compute the slopes of pitching moment with respect to angle of attack and jet
frequency at different operating points thereby enabling us to do quasi-steady control of the SJA wing.
3.2 Develop Artificial Neural Network (ANN) to Incorporate Aerodynamic Models
Planned Status: Start March 15th, 2004 – 0% Complete
Actual Status: 0% Complete
Notes Regarding Tasks:
4. Development and Verification of Feedback Control Methods for a Wing
with Distributed SJA’s
Planned Status: Start February 18th, 2004 – 0% Complete
Actual Status: 10% Complete
Notes Regarding Milestone:
4.1 Develop Closed-Loop Control Methodologies
Planned Status: Start February 18th, 2004 – 0% Complete
Actual Status: 20% Complete
Notes Regarding Tasks:
The equation of motion for a SJA controlled, free to pitch wing can be represented as:
I  M ( , f )  M 0
where I is the Moment of Inertia of the wing about the pivot point,  is the angle of attack f is the SJA
frequency and M 0 is the static moment acting due to the offset between the centre of gravity of the wing and
the pivot point..
The nonlinear moment function M ( , f ) is unknown and can be learnt online/off-line by RBFN as described
in previous report. But now the control variable f appears in a non-affine way which makes the control problem
more difficult. To be able to characterize these and other nonlinear control effects better, we first investigate the
efficacy of simple PID based fixed/scheduled gain controllers for quasi-steady control of the SJA wing in the
wind tunnel. Further, from Figures 15,16 and 17, it is apparent that the moment variation with respect to angle
of attack and jet frequency is predominantly linear and therefore the moment function can be approximated as
follows:
M ( , f )  M  Cm   Cm f f
Where, Cm and Cm f represents the pitching moment slopes w.r.t. angle of attack, α and jet frequency, f and
approximate values for these slopes can be obtained from RBFN fit of static data.
I  Cm   Cm f f  M 0
Hence,
We mention that M 0 in above equation also includes the effect of M term (pitching moment when
  f  0 ). The control objective is to track a trajectory in terms of  r which is at least twice differentiable
with respect to time (So  r , r can be determined). The reference trajectory can be designed as a step function
from one angle of attack value to another or a smooth 5th order polynomial, so that the jerk is minimized.
Let e be the error between the actual and the reference angle of attack:
e   r
Cm f
Cm
M
f  0  r
Hence e    
I
I
I
Adding and Subtracting
Cm
I
 r on the right hand side, we get:
e
Cm
e
I
Cm f
I
 Cm

M
f    r  0  r 
I
 I

The control law calculates the control as a summation of two components, such that f  f1  f 2 . The first
component performs PID control on the tracking error:
f1   K1  edt  K 2 e  K3e
and the second component of the control performs dynamic inversion to cancel the known terms
 Cm

M
r  0  r 

I
 I

 Cm

M
I
f2     r  0 
r 
 Cm

Cm f Cm f
 f

So the closed loop error dynamics can be written as:
Cm
Cm f


 K1  edt  K 2e  K 3e
I
I
 Cm K3   Cm f K 2 Cm   Cm f K1

e   f

edt   0
 e  
 e  

I   I
 I   I

e
e

Introducing new state variable z1  edt , z2  e and z3  e , we get:


 z1   0
 
z   z2    0

z   C K
 3
m
1
 f
I

1
0
 Cm K 2 Cm 
 f


 I
I 



0
  z1 
  z   Az
1
 2
Cm f K 3   z3 


I 
The asymptotic stability of the system now corresponds to having the eigenvalues of the closed loop matrix ‘A’,
to lie in the open left half plane which leads us to the following conditions:
Cm f K 3
 Cm f K 2 Cm 

0

  0,
I
I
I
I


 Cm f K 3   Cm f K 2 Cm 
 Cm f K1 



 


  0
I 
 I  I
 I 
Cm f K1
 0,
As Cm f  0 (moment increases with the jet frequency) therefore K1 , K3 should be greater than zero
and K 2  
Cm
Cm f
. Thus by making a judicious choice for various gains, asymptotic tracking of the reference
trajectory can be achieved.
The above control law assumes that Cm and Cm f are known accurately, so that the dynamic inversion
 Cm

M
 r  0   r  . But that is not the case in reality,
I
 I

component of the control law can cancel out the terms 
and hence to handle any disturbance due to modeling errors we can design indirect adaptation laws for Cm
and Cm f as discussed in Subbarao (2001). Further, from figure 3 it is apparent that there are two values for
Cm for α < 22o and α > 22o. To take care of that we will schedule the gains i.e. we need to choose different
values of controller gains for α < 22o and α > 22o. We also mention that the PID controller requires the
knowledge of the rates of angle of attack which are not being measured in the current set up. To obtain estimates
of the rate of change of angle of attack, we will use a first-order lead filter, or a first/second order difference of
the filtered angle of attack measurements as discussed in Singla et al. (2003).


 k 1   k
t
4 k 1  3 k   k  2
2 t
Beside this, the design of control law for non-affine RBFN model is also in progress. We mention that the
control law discussed in this report will be used only to control the SJA wing in quasi-steady manner.
Tentative Schedule:
 Test PID controller discussed is this report by 25th October.
 Complete free to pitch experiment to learn the dynamic model of the wing by first week of
November.
4.2 Verify Closed-Loop Control Methodologies
Planned Status: Start August 8th, 2004 – 0% Complete
Actual Status: 5% Complete
Notes Regarding Tasks:
The controller of the closed-loop simulations for free-to-pitch motions has been developed. It incorporates the
SJA dynamical model, the wing aerodynamics model and the wing dynamics model. Simulations are being run
at present.
5. Demonstration of Distributed Sensing/Actuation/Control
Planned Status: Start October 13th, 2004 – 0% Complete
Actual Status: 0% Complete
Notes Regarding Milestone:
5.1 Demonstration of Distributed Actuation/Sensing and Feedback Control in
Experimental Setup
Planned Status: Start October 13th, 2004 – 0% Complete
Actual Status: 0% Complete
Notes Regarding Tasks:
5.2 In-Flight Demonstration of SJA and Control on UAV Platform
Planned Status: Start October 13th, 2004 – 0% Complete
Actual Status: 0% Complete
Notes Regarding Tasks:
5.2.1 Integrate Distributed Sensing/Actuation Modules into UAV Platform
5.2.2 Flight Test on UAV Platform for Final Verification of Distributed SJA and Controllers
6. References
Jeffrey, D. Zhang, X., and Hurst, D. W., 2000, “Aerodynamics of Gurney Flaps on a Single-Element High-Lift
Wing," Journal of Aircraft, Vol. 37, No. 2, pp. 295-301.
Jordinson, R., 1956, “Flow in a Jet Directed Normal to the Wind,” R&M 3071, London.
Lockwood, V. E., and Vogler, R. D., 1958 “Exploratory Wind-Tunnel Investigation at High Subsonic and
Transonic Speeds of Jet Flaps on Unswept Rectangular Wings,” NACA TN 4353.
Singla,, P., J.L. Crassidis and J.L. Junkins, 2003, “Spacecraft Angular Rate Estimation Algorithms for StarTracker Based Attitude Determination,” Paper # AAS 03-191, AAS/AIAA AIAA space Flight Mechanics
Meeting February 9-13, 2003, Ponce, Puerto-Rico
Spence, D. A., “Some Simple Results for Two-Dimensional Jet-Flap Aerofoils, 1958, ” The Aeronautical
Quartely, pp. 395-406.
Subbarao K., 2001,“Structured Adaptive Model Inversion: Theory and Applications to Trajectory Tracking for
Non-Linear Dynamical Systems,” Ph.D Dissertation, Aerospace Engineering Dept., Texas A&M University.