flutter suppression system test example

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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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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 6 ................................................. .................................................... 10




Flight Condition 10 .................................................................................................... 14







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



4.4. 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




4.10. Plot of Pitch vs time for Flight condition 10 ................................................................... 15








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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 6 ...................................................... ....................................................... 10




Flight Condition 10 ............................................................................................................ 14







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


0.2000 21000 0.0281


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Flight Condition 3


0.2000 41000 0.0127


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Flight Condition 4


0.2000 51000 0.0083


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Flight Condition 5


0.4000 1000 0.1262


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Flight Condition 6


0.4000 21000 0.0807


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Flight Condition 7


0.4000 41000 0.0410


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Flight Condition 8


0.4000 51000 0.0267


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Flight Condition 9


0.6000 1000 0.0853


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14





Flight Condition 10


0.6000 21000 0.1137


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Flight Condition 11


0.6000 41000 0.0806


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Flight Condition 12


0.6000 51000 0.0570


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Flight Condition 13


1 1000 -0.0637


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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


1 21000 -0.0748


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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


1 41000 0.1875


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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


1 51000 0.1298


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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)

flutter suppression system test example

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