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Model-Based Test of a WingFlutter Suppression System
MathWorks
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Model-Based Test of a Wi-
ng Flutter Suppression System
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Model-Based Test of a Wing Flutter Suppression System:MathWorks
Publication date 04-Dec-2013 15:13:53
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iii
Table of Contents
1. Introduction ............................................... ........................................................ ............. 1
2. Test Summary ................................................ ........................................................ ......... 2
3. Test Procedure ................................................ ....................................................... ......... 4
4. Results for each flight condition ..... ...... ...... ..... ...... ..... ...... ...... ..... ...... ..... ...... ...... ..... ...... .... 5
Flight Condition 1 ....................................................... ................................................ 5Flight Condition 2 ....................................................... ................................................ 6
Flight Condition 3 ....................................................... ................................................ 7
Flight Condition 4 ....................................................... ................................................ 8
Flight Condition 5 ....................................................... ................................................ 9
Flight Condition 6 ................................................. .................................................... 10
Flight Condition 7 ................................................. .................................................... 11
Flight Condition 8 ................................................. .................................................... 12
Flight Condition 9 ................................................. .................................................... 13
Flight Condition 10 .................................................................................................... 14
Flight Condition 11 .................................................................................................... 15
Flight Condition 12 .................................................................................................... 16
Flight Condition 13 .................................................................................................... 17
Flight Condition 14 .................................................................................................... 18
Flight Condition 15 .................................................................................................... 19
Flight Condition 16 .................................................................................................... 20
5. Model Description ......... ........................................................ ........................................ 22
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List of Figures
2.1. System Damping Ratio Versus Flight Condition ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. 3
4.1. Plot of Pitch vs time for Flight condition 1 ...... ...... ..... ..... ...... ..... ...... ..... ...... ...... ..... ...... ..... 6
4.2. Plot of Pitch vs time for Flight condition 2 ...... ...... ..... ..... ...... ..... ...... ..... ...... ...... ..... ...... ..... 7
4.3. Plot of Pitch vs time for Flight condition 3 ...... ...... ..... ..... ...... ..... ...... ..... ...... ...... ..... ...... ..... 8
4.4. Plot of Pitch vs time for Flight condition 4 ...... ...... ..... ..... ...... ..... ...... ..... ...... ...... ..... ...... ..... 94.5. Plot of Pitch vs time for Flight condition 5 ...... ...... ..... ...... ..... ..... ...... ..... ...... ..... ...... ...... ... 10
4.6. Plot of Pitch vs time for Flight condition 6 ...... ...... ..... ...... ..... ..... ...... ..... ...... ..... ...... ...... ... 11
4.7. Plot of Pitch vs time for Flight condition 7 ...... ...... ..... ...... ..... ..... ...... ..... ...... ..... ...... ...... ... 12
4.8. Plot of Pitch vs time for Flight condition 8 ...... ...... ..... ...... ..... ..... ...... ..... ...... ..... ...... ...... ... 13
4.9. Plot of Pitch vs time for Flight condition 9 ...... ...... ..... ...... ..... ..... ...... ..... ...... ..... ...... ...... ... 14
4.10. Plot of Pitch vs time for Flight condition 10 ................................................................... 15
4.11. Plot of Pitch vs time for Flight condition 11 ................................................................... 16
4.12. Plot of Pitch vs time for Flight condition 12 ................................................................... 17
4.13. Plot of Pitch vs time for Flight condition 13 ................................................................... 18
4.14. Plot of Pitch vs time for Flight condition 14 ................................................................... 19
4.15. Plot of Pitch vs time for Flight condition 15 ................................................................... 20
4.16. Plot of Pitch vs time for Flight condition 16 ................................................................... 21
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List of Tables
1.1. Report Version Information ...... ..... ...... ..... ...... ...... ..... ...... ..... ...... ...... ..... ...... ..... ...... ...... .. 1
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Chapter 1. IntroductionThis document reports the results of model-based functional testing of an active aircraft wing flutter supp-
ression system design developed by NASA Langley Research Center (see Model Description [22]).
The report includes a summary of the test results, a description of the test procedure, and detailed test
results.
Table 1.1. Report Version Information
Model
Name
Model Last Saved Model
Version
Model
Author
Simulink Version Simulink Report
Generator Version
Flutter-
Suppre-
ssionS-
ystem
Wed Oct 24 16:41:12 2012 1.272 Math-
Works
8.3(R2014a Prerelease) 3.16(R2014a Prerelease)
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Chapter 2. Test SummaryThe test reported in this document determines whether the flutter suppression system suppresess rotational
(pitch) flutter over a specified set of operating conditions (desired pitch angle, speed, and altitude). The
system is considered to meet this requirement if pitch oscillations decay exponentially as a function of time,
i.e., the system has a positive damping ratio, at each of the specified operating conditions. The followingtable summarizes the test results for 16 flight conditions for a desired pitch angle of 0 degrees.
Flight
Cond-
ition
Mach Altitu-
de (ft)
Damping
Ratio
Pas-
s/Fa-
il
1
[5]
0.2000 1000 0.0514 Pass
2
[6]
0.2000 21000 0.0281 Pass
3
[7]
0.2000 41000 0.0127 Pass
4
[8]
0.2000 51000 0.0083 Pass
5
[9]
0.4000 1000 0.1262 Pass
6
[10]
0.4000 21000 0.0807 Pass
7
[11]
0.4000 41000 0.0410 Pass
8
[12]
0.4000 51000 0.0267 Pass
9
[13]
0.6000 1000 0.0853 Pass
10
[14]
0.6000 21000 0.1137 Pass
11
[15]
0.6000 41000 0.0806 Pass
12
[16]
0.6000 51000 0.0570 Pass
13
[17]
1 1000 -0.0637 Fail
14 [18]
1 21000 -0.0748 Fail
15
[19]
1 41000 0.1875 Pass
16
[20]
1 51000 0.1298 Pass
Test Statistics. The test passed for 14 of the 16 test cases (87.5000 percent).
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Test Summary
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The following figure plots the system's damping ratio as a function of altitude and Mach number. The
damping ratio is 0 on the blue plane. The system is unstable in the region below the blue plane.
Figure 2.1. System Damping Ratio Versus Flight Condition
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Chapter 3. Test ProcedureThe following procedure was used to produce the test results reported in this report:
1. Read a set of flight conditions from an Excel spreadsheet. The spreadsheet specified 4 Mach values and
4 altitude values, giving 16 flight conditions.2. For each flight condition, simulate the flutter suppression system, using a Simulink model (see Model
Description [22]) that represents a wing controlled by the system and aerodynamic forces acting
on the wing resulting from the flight conditions. The model also represents an initial disturbance in
the wing's pitching moment that causes an oscillation in the wing pitch angle. If effective, the flutter
suppression system should cause this oscillation to decay exponentially with time.
3. Determine the positive peaks of the pitch oscillations from simulation data.
4. Fit an exponential curve to the peak data.
5. Compute the pitch damping ratio as a function of the positive (or negative) decay parameter of the
exponential curve.
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Chapter 4. Results for each flightcondition
Table of Contents
Flight Condition 1 ................................................... ....................................................... ..... 5
Flight Condition 2 ................................................... ....................................................... ..... 6
Flight Condition 3 ................................................... ....................................................... ..... 7
Flight Condition 4 ................................................... ....................................................... ..... 8
Flight Condition 5 ................................................... ....................................................... ..... 9
Flight Condition 6 ...................................................... ....................................................... 10
Flight Condition 7 ...................................................... ....................................................... 11
Flight Condition 8 ...................................................... ....................................................... 12
Flight Condition 9 ...................................................... ....................................................... 13
Flight Condition 10 ............................................................................................................ 14
Flight Condition 11 ............................................................................................................ 15
Flight Condition 12 ............................................................................................................ 16
Flight Condition 13 ............................................................................................................ 17
Flight Condition 14 ............................................................................................................ 18
Flight Condition 15 ............................................................................................................ 19
Flight Condition 16 ............................................................................................................ 20
Below are the results for each of the 16 test cases.
Flight Condition 1
Mach Altitude(in ft) Damping Ratio
0.2000 1000 0.0514
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Results for each flight condition
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Figure 4.1. Plot of Pitch vs time for Flight condition 1
For test case 1, a Mach number of 0.2000 was chosen and the vehicle was flown at an altitude of 1000
feet. Under these flight conditions, the damping ratio was observed to be 0.0514, and since the value was
greater than zero, the model meets the requirement, given this test condition. Hence, passed.
Flight Condition 2
Mach Altitude(in ft) Damping Ratio
0.2000 21000 0.0281
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Results for each flight condition
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Figure 4.2. Plot of Pitch vs time for Flight condition 2
For test case 2, a Mach number of 0.2000 was chosen and the vehicle was flown at an altitude of 21000
feet. Under these flight conditions, the damping ratio was observed to be 0.0281, and since the value was
greater than zero, the model meets the requirement, given this test condition. Hence, passed.
Flight Condition 3
Mach Altitude(in ft) Damping Ratio
0.2000 41000 0.0127
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Results for each flight condition
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Figure 4.3. Plot of Pitch vs time for Flight condition 3
For test case 3, a Mach number of 0.2000 was chosen and the vehicle was flown at an altitude of 41000
feet. Under these flight conditions, the damping ratio was observed to be 0.0127, and since the value was
greater than zero, the model meets the requirement, given this test condition. Hence, passed.
Flight Condition 4
Mach Altitude(in ft) Damping Ratio
0.2000 51000 0.0083
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Results for each flight condition
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Figure 4.4. Plot of Pitch vs time for Flight condition 4
For test case 4, a Mach number of 0.2000 was chosen and the vehicle was flown at an altitude of 51000
feet. Under these flight conditions, the damping ratio was observed to be 0.0083, and since the value was
greater than zero, the model meets the requirement, given this test condition. Hence, passed.
Flight Condition 5
Mach Altitude(in ft) Damping Ratio
0.4000 1000 0.1262
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Results for each flight condition
10
Figure 4.5. Plot of Pitch vs time for Flight condition 5
For test case 5, a Mach number of 0.4000 was chosen and the vehicle was flown at an altitude of 1000
feet. Under these flight conditions, the damping ratio was observed to be 0.1262, and since the value was
greater than zero, the model meets the requirement, given this test condition. Hence, passed.
Flight Condition 6
Mach Altitude(in ft) Damping Ratio
0.4000 21000 0.0807
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Results for each flight condition
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Figure 4.6. Plot of Pitch vs time for Flight condition 6
For test case 6, a Mach number of 0.4000 was chosen and the vehicle was flown at an altitude of 21000
feet. Under these flight conditions, the damping ratio was observed to be 0.0807, and since the value was
greater than zero, the model meets the requirement, given this test condition. Hence, passed.
Flight Condition 7
Mach Altitude(in ft) Damping Ratio
0.4000 41000 0.0410
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Results for each flight condition
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Figure 4.7. Plot of Pitch vs time for Flight condition 7
For test case 7, a Mach number of 0.4000 was chosen and the vehicle was flown at an altitude of 41000
feet. Under these flight conditions, the damping ratio was observed to be 0.0410, and since the value was
greater than zero, the model meets the requirement, given this test condition. Hence, passed.
Flight Condition 8
Mach Altitude(in ft) Damping Ratio
0.4000 51000 0.0267
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Results for each flight condition
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Figure 4.8. Plot of Pitch vs time for Flight condition 8
For test case 8, a Mach number of 0.4000 was chosen and the vehicle was flown at an altitude of 51000
feet. Under these flight conditions, the damping ratio was observed to be 0.0267, and since the value was
greater than zero, the model meets the requirement, given this test condition. Hence, passed.
Flight Condition 9
Mach Altitude(in ft) Damping Ratio
0.6000 1000 0.0853
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Results for each flight condition
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Figure 4.9. Plot of Pitch vs time for Flight condition 9
For test case 9, a Mach number of 0.6000 was chosen and the vehicle was flown at an altitude of 1000
feet. Under these flight conditions, the damping ratio was observed to be 0.0853, and since the value was
greater than zero, the model meets the requirement, given this test condition. Hence, passed.
Flight Condition 10
Mach Altitude(in ft) Damping Ratio
0.6000 21000 0.1137
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Results for each flight condition
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Figure 4.10. Plot of Pitch vs time for Flight condition 10
For test case 10, a Mach number of 0.6000 was chosen and the vehicle was flown at an altitude of 21000
feet. Under these flight conditions, the damping ratio was observed to be 0.1137, and since the value was
greater than zero, the model meets the requirement, given this test condition. Hence, passed.
Flight Condition 11
Mach Altitude(in ft) Damping Ratio
0.6000 41000 0.0806
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Results for each flight condition
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Figure 4.11. Plot of Pitch vs time for Flight condition 11
For test case 11, a Mach number of 0.6000 was chosen and the vehicle was flown at an altitude of 41000
feet. Under these flight conditions, the damping ratio was observed to be 0.0806, and since the value was
greater than zero, the model meets the requirement, given this test condition. Hence, passed.
Flight Condition 12
Mach Altitude(in ft) Damping Ratio
0.6000 51000 0.0570
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Results for each flight condition
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Figure 4.12. Plot of Pitch vs time for Flight condition 12
For test case 12, a Mach number of 0.6000 was chosen and the vehicle was flown at an altitude of 51000
feet. Under these flight conditions, the damping ratio was observed to be 0.0570, and since the value was
greater than zero, the model meets the requirement, given this test condition. Hence, passed.
Flight Condition 13
Mach Altitude(in ft) Damping Ratio
1 1000 -0.0637
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Results for each flight condition
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Figure 4.13. Plot of Pitch vs time for Flight condition 13
For test case 13, a Mach number of 1 was chosen and the vehicle was flown at an altitude of 1000 feet.
Under these flight conditions, the damping ratio was observed to be -0.0637, and since the value was less
than zero, the model does not meet the requirement, given this test is condition. Hence, failed.
Flight Condition 14
Mach Altitude(in ft) Damping Ratio
1 21000 -0.0748
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Results for each flight condition
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Figure 4.14. Plot of Pitch vs time for Flight condition 14
For test case 14, a Mach number of 1 was chosen and the vehicle was flown at an altitude of 21000 feet.
Under these flight conditions, the damping ratio was observed to be -0.0748, and since the value was less
than zero, the model does not meet the requirement, given this test is condition. Hence, failed.
Flight Condition 15
Mach Altitude(in ft) Damping Ratio
1 41000 0.1875
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Results for each flight condition
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Figure 4.15. Plot of Pitch vs time for Flight condition 15
For test case 15, a Mach number of 1 was chosen and the vehicle was flown at an altitude of 41000 feet.
Under these flight conditions, the damping ratio was observed to be 0.1875, and since the value was greater
than zero, the model meets the requirement, given this test condition. Hence, passed.
Flight Condition 16
Mach Altitude(in ft) Damping Ratio
1 51000 0.1298
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Results for each flight condition
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Figure 4.16. Plot of Pitch vs time for Flight condition 16
For test case 16, a Mach number of 1 was chosen and the vehicle was flown at an altitude of 51000 feet.
Under these flight conditions, the damping ratio was observed to be 0.1298, and since the value was greater
than zero, the model meets the requirement, given this test condition. Hence, passed.
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Chapter 5. Model DescriptionThe model used to generate the test data used in this report is a Simulink model based on a mathematical
model of a flutter suppression system developed at NASA Langley Research Center (see AIAA_96_-
3437.pdf [matlab:web(fullfile(matlabroot,'toolbox','rptgenext','rptgenextdemos','flutter_suppression','AI-
AA_96_3437.pdf'))]).
The Simulink model represents a physical wing model used for wind tunnel testing, aerodynamic forces on
the wing, and a flutter suppression system for the wing. The model uses Simscape modelling components
to model the wing. It uses Simulink blocks to model the flutter suppression system's controller and sensors.
Model inputs include flight conditions (desired pitch angle, speed (Mach number), and altitude) and an
initial pitch moment disturbance.The model snapshot is below:
Qflutter = 147.1 PSF
Enable/Disable Controller
1
qPSF
161.5
Q (PSF)
Pulse
Generator
Plunge
PitchAileron Pos
States Pi tch
Outputs
6{6}
1
Mach
K-
K-
K-
Qtheta
h
delta
0
Desired angle
Error TE Pos
Controller
TE Pos
Lift
Pitching Moment
Disturbance
states
TE Position (deg)
Lift
Pitching Moment
Initial Disturbance
States
BACT Wing & PAPA Mount
6{6}
51000
Altitude
Mach
Alt (ft)
Lift
Moment
Aero Forces
Wing Plunge (in)
Wing Pitch (deg)
error
angle
Aileron Pos (deg)