Atmospheric Turbulence Modeling and Shock Positioning Control … · 2009-12-15 · Atmospheric Turbulence – Power Spectral Solution Challenges-- Atmospheric disturbances are fractional

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National Aeronautics and Space Administration

Atmospheric Turbulence Modeling and Shock Positioning Control for a Supersonic Inlet

G K ki

Fundamental Aeronautics – Supersonics ProjectAeroPropulsoServoElasticity Task

George Kopasakis

NASA Glenn Research CenterCl l d OhiCleveland, Ohio

www.nasa.gov 11

Propulsion Controls and Diagnostics (PCD) WorkshopCleveland OH, Dec. 8-10, 2009


Atmospheric Turbulence Modeling for High Speed Vehicles

Outline

Motivation/BackgroundMotivation/Background

Atmospheric Turbulence Model Development

-- Approach

-- Formulations

-- Examples (Spectral Densities & Time Domain)

Concluding Remarks

www.nasa.gov 22


Atmospheric Turbulence Modeling for High Speed Vehicles

Motivation

-- Atmospheric turbulence modeling needed for both propulsion and flight control designs

-- Atmospheric Turbulence is fractional order (5/3Atmospheric Turbulence is fractional order (5/3 order)-- Current 2nd order model approximation used

d i t ( d ti t ) t 7dB/d d (ideviates (underestimates) up to 7dB/decade (i.e. 20db x 2 vs. 20dB x 5/3)

www.nasa.gov 3


-- Atmospheric models primarily based on the “Kolmogorov Spectral”

Atmospheric Turbulence – Power Spectral-- Atmospheric models primarily based on the Kolmogorov Spectral , developed by Taraski, 1961, based partially on studies by Kolmogorov, 1941.

3532 //tt k)k(S −= εα

α – constant for the type of disturbanceε – eddy dissipation rate (energy/(mass * time))k b ( d/ )

tt

k – wave number (rad/m)

Figure – Wind and PotentialTemperature Spectra as reported byNastrom (1985). Note: for clarity, themeridional wind and temperature spectrahave been shifted one and two decades to

www.nasa.gov 4

the right, respectively.


-- Kolmogorov Spectral has infinite energy – increases in magnitude with

Atmospheric Turbulence – Power Spectral-- Kolmogorov Spectral has infinite energy increases in magnitude with decreasing frequency

-- Tank, 1994 scaled the von Karman spectrum to fit the Kolmogorov model

longitudinal disturbance6523532

233911272 /

//VK,l ])Lk)(.([

L.)k(Sπ

ε+

=

transverse disturbance6112

2

3532

233911

23391381

72/

//VK,v

])Lk)(.([

)Lk)(.(L.)k(S

π

πε

+

+=

40 Kolmogorov longitudinal

20

30sp

ectra

l, dB

(m/s

ec/H

z)

g gKolmogorov transversevon Karman longitudinalvon Karman transverse

Figure – Acoustic wave velocity spectralcomparisons for the Kolmogorov and Von -10

0

10

acou

stic

wav

e ve

loci

ty s

www.nasa.gov 5

comparisons for the Kolmogorov and VonKarman spectral

10-2 10-1 100 101 102

frequency , Hz


Atmospheric Turbulence – Power Spectral Solution Challenges

-- Atmospheric disturbances are fractional order

g

-- Solution of fractional order derivatives are difficult abbey the law of non-locality state transition matrix is a convolution integral

-- To get around this problem Hoblit, 1998 introduced the Dryden model

2

2

)(112

)(Ωπ

σΩΦ u

uL

L+

=

-- This model is 2nd order instead of 5/3 order, increasingly deviates with frequency (by 7db/decade)

)(1 Ωπ uL+

-- Based on that the idea was born to develop our own fractional order model

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Atmospheric Turbulence – Fractional Order Model Developmentp

Rtq Wt,VKt

Rtq Wt,VKt

1) 6523532

233911272 /

//VK,l ])Lk)(.([

L.)k(Sπ

ε+

=

3/1

⎟⎞

⎜⎛

1/(Cts)qW 1/(Cts)qWW6/52

3/53/2,

])2

339.1(1[

27.2)(

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

+=

oMaf

LLkS VKl π

ε

3/1Circuit Equivalent of Atmospheric Disturbances

2) Formulate circuit parameters in terms of vehicle speed (f= kMa) and atmospheric

3/13/53/2)( ⎟

⎟⎠

⎞⎜⎜⎝

⎛=

−

MafkS tt εα

disturbance parametersL)a)((.R x//

tt13223391 επ=

tt

nf CR

Kωω =, , ,

),( LfKt ε=)2()(

1/13/2

ox

tt Maa

Cπε

=

3) Develop von Karman temperature, pressure and density spectral by scaling the respective Kolmogorov spectral to fit the von Karman spectrum for wind gusts.

4) Pl t K S t l d i i it f l ti f l t i f fi t d

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4) Plot von Karman Spectral and using circuit formulations, formulate a series of first order pole-zero TF to approximate fractional order TF.


Atmospheric Turbulence – Fractional Order Model Development

Step 3. scaling for temperature

p

3/13/5 ⎞⎛

140

3/13/53/2)( ⎟

⎟⎠

⎞⎜⎜⎝

⎛=

−

MafkS tt εα

80

100

120

Tem

p. s

pect

ral,

dB Kolmogorov longitudinalKolmogorov temperaturevon Karman longitudinalscaled von Karman temp

20

40

60

Kar

man

vel

ocity

& T

-40

-20

0

Kol

mog

orov

/Von

K

www.nasa.gov 8

10-2 10-1 100 101 102

frequency, Hz


Atmospheric Turbulence – Fractional Order Model Development

Step 4. formulation of pole-zero TF approachp

Fractional order TF

1st order pole-zero TF approximation

mpl

itude

, dB

1 order pole zero TF approximation

d1d2

freq

am

ωH 1

ωHp2ω

ωHp3 ωHp4ω

-- Formulate 1st order pole-zero TF approximation subject to

(a) ωpi zi=f(ωp1..ωpi-1,ωz1..ωzi-1)

freq.ωp1ωz1 ωp2ωz2 ωp3ωz3 ωp4ωHz1 ωHz2 ωHz3

( ) pi, zi ( p1 pi 1, z1 zi 1)

(b) Equal distance: d1=d2=..(symmetry) ωpi, zi=f(ωp1..ωpi-1, ωz1..ωzi-1, ωHpi, ωHzi)

(c) ω=f(circuit parameters)

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( ) ( p )

(d) TF also function of desirable pole-zero density per decade closer approximation



mz

-- Based on this approach the following formulations are derived

tm

pi

zi

fit,to,t W)/s(

)/s(KW

p

z

∏ +

∏ +≅

1

1

1

1

ω

ω

1−i

Generalized atmospheric disturbance TF

1)1/(10

)1/(

1

1

*)12(

1

1

−∏ +

∏ +=

−

=−

−

=−

i

jjziHpi

qi

i

jjpiHpiHpipi

pi

K

ωω

ωωωω

η

ω

Pole-zero frequency computations

qiqfH pi

/1)12( )110( −= −ηωω’

1)1/(10

)1/(

1

*2

1

1

−∏ +

∏ +=

=

−

−

=−

i

jpiHzi

qi

i

jjziHziHzizi

zi

K

ωω

ωωωω

η

ω qqifHzi

/12 )110( −= ηωω’

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-- Example fit using equations with certain atmospheric parameters:

10

15

l, dB

(m/s

ec/H

z)

Von Karman

TF fit

-5

0

5

wav

e ve

loci

ty s

pect

ral

-15

-10

5

long

itudi

nal a

cous

tic w

10-2

10-1

100

101

102

frequency, Hz

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National Aeronautics and Space AdministrationAtmospheric Turbulence – Fractional Order Model

DevelopmentE l fit i th E / dj t t

20

30

40

ral,

dB((m

/sec

/Hz)

c/H

z)

von Karman

-- Example fits using these Eqs. w/ adjustments:

0

10

oust

ic w

ave

velo

city

spe

ctr

von Karman, eddy dissap.=5e-4TF fit, eddy dissap.=5e-4von Karman eddy dissap =8 5e-5

5

10

15

loci

ty s

pect

ral,

dB(m

/sec TF fit

10-2 10-1 100 101 102

-10

frequency, Hz

aco

von Karman, eddy dissap. 8.5e 5TF fit, eddy dissap.=8.5e-5

40)15

-10

-5

0

tudi

nal a

cous

tic w

ave

ve

10

20

30ity

spe

ctra

l, dB

((m/s

ec/H

z10-2 10-1 100 101 102

-15

frequency, Hz

long

it

Longitudinal Acoustic wave velocity spectral

-10

0

10

acou

stic

wav

e ve

loci

von Karman, integral scale length=1500mTF fit, integral scale length=1500mvon Karman, integral scale length=762mTF fit, integral scale length=762m

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Acoustic wave velocity spectral due to temperature gust and its TF fits10-2 10-1 100 101 102

frequency, Hz



-- TF fits with L=765, ε=8.6e-5):(complete equation set takes into account these adjustments)

)11.1593/)(17.85/)(11.30/)(146.1/()15.335/)(10.55/)(12.9/(74.8)(

+++++++

=ssss

ssssGLALongitudinal Acoustic Wave Velocity (m/sec)

)13.816/)(18.109/)(11.25/)(11.1/()14.602/)(16.45/)(10.33/(75.41)(++++

+++=

ssssssssGT Temperature (K)

)13.816/)(18.109/)(11.25/)(11.1/()14.602/)(16.45/)(10.33/(88.20)(++++

+++=

sssssss

aRMsG

oTA

γAcoustic Wave due to Temperature (m/sec)

)13.816/)(18.109/)(11.25/)(11.1/()14.602/)(16.45/)(10.33/(96.37)(++++

+++=

ssssssssGP Pressure (Pa)

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-- Simulating atmospheric Disturbances:a) Construct a time domain unit amplitude sinusoids distributed in frequencyb) Use this time domain sinusoids as input to atmospheric disturbance TFs b) Use this time domain sinusoids as input to atmospheric disturbance TFs

8

12

tinal vel d

ist,

m/sec

40

dist

urba

nce,

o K

Atmospheric DistPres.

0 0.5 1 1.5 2 2.5

0

4

atm

osph

eric lo

ngitu

t

time sec0 0.5 1 1.5 2 2.5

0

20

atm

osph

eric te

mp.

ti

GP(s)

GT(s)

Dist Freqes.

Temp.

Vel. Due

40

60

80

p long

it ve

l dist, m

/sec

20

30

40

sure

distu

rban

ce, P

a

time, sec time, sec GTA(s)

GLA(s)

to Temp.

Vel.

0 0.5 1 1.5 2 2.50

20

atm

osph

eric te

mp

time, sec0 0.5 1 1.5 2 2.5

0

10

atm

osph

eric p

res

time, sec

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Atmospheric Disturbances w/ frequencies from sub Hz to 200 Hz, w/ ε=8.6e-5, L=765 m (11km turbulence patch)



-- Atmospheric wind gust turbulence considering: -- Vehicle Mach=2.35 -- Smallest eddy dissipation scales of 25m (from literature)Smallest eddy dissipation scales of 25m (from literature)-- ~180 mph top wind speeds-- Eddy dissipation rate

R lt i l t f i t 30 H-- Results in cluster frequencies up to 30 Hz

100 150

Moderate to Severe Turbulence (ε=1.7e-3)Light to Moderate Turbulence (ε=8.6e-5)

0

50

d gu

st, m

/sec

50

100

150

g gu

st, m

/sec

-100

-50

atm

osph

eric

win

d

-100

-50

0

atm

osph

eric

win

g

www.nasa.gov 15

0 1 2 3 4 5-150

time, sec0 1 2 3 4 5

-150

time, sec

a


Future Work

C ith id ti f t h i di t b ifi ti f hi h d-- Come up with considerations for atmospheric disturbance specifications for high speed vehicles

-- Integrated Propulsion system studies utilizing atmospheric disturbancesg p y g p

-- Integrated Vehicle (Aero-Propulso-Servo-Elastic) studies utilizing atmospheric and other disturbances

Publications:

1. Kopasakis, “Atmospheric Turbulence Modeling for Aero Vehicles – Fractional Order Fits,” NASA TM, in f bli hiprocess of publishing.

2. Kopasakis, “Modeling of Atmospheric Turbulence as Disturbances for Control Design and Evaluation of High Speed Propulsion Systems,” ASME TurboExpo 2010 to be published

www.nasa.gov 16


Shock Positioning Controls Design for a Supersonics Inlet

Outline

BackgroundBackground

Controls Design Approach

Inlet Shock Positioning Controls Design

-- Plant Transfer Functions

-- Atmospheric Disturbances

-- Controls Design

-- Results

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Concluding Remarks


Shock Positioning Controls Design for a Supersonics InletBackgroundac g ou d

Supersonic Axisymmetric Inlet- Mixed-compression- Single flow path

T l ti / ll i t b d

terminal shock

Throat

- Translating / collapsing centerbody

Internal SubsonicEngine Face

ExternalSupersonic

Compression

Supersonic Diffuser

Subsonic Diffuser

Terminal Shock PositionLow Performance

Engine Center Linep

Normal PerformanceHigh Performance

www.nasa.gov

18


Feedback Controls Loop Shaping Design Approach

Motivation:• Tie controls design to hardware capabilities.

M i i f• Maximize performance-- Better command tracking-- Enabling reduction of design margins to improve propulsion efficiency.

Features of Approach:• Using control system requirements and actuator speed(s) to shape the

feedback controller Closed Loop Gain (CLG)feedback controller Closed Loop Gain (CLG)

• Methodical design w/ quantifiable performance-- Emphasizes how to trade competing requirements p p g q-- Maximize performance (command tracking, disturbance rejection,

stability-- Guaranteed stability by avoiding plant inversion

www.nasa.gov 19

Kopasakis, “Feedback Control Systems Loop Shaping Design with Practical Considerations,” NASA/TM-2007-215007



St S l t CLG b d idthmrlrco /raC=ω

Step a. – Select CLG bandwidth,

St b D i d i d CLG f ifi ti

)11000/)(1100/()125/(13.353)(

+++

=sss

ssL

Step b. – Design desired CLG for specifications(stability, disturbance rejection, etc.)

Feedback Control System Diagram.

)()( sLsC )()( sGsC d )11000/)(1100/( ++ sss)(1

)()()(

sLsR +=

)(1)(

)()(

sLsDd

+=,

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Example of Closed Loop Gain (CLG) Design Step Response



Step c. – Calculate control TF and plot

)(log20)(log20)( 1010 sGsLsG PC −=

))(())(())(( sGsLsG PC φφφ −=

)1/2/) (1/( 22K

Step d. – Fit control TF w/ poles and zeros

)1/2/)......(1/()1/2/)....(1/(

)( 221

221

+++

+++=

pnpnp

znznzC wsss

wssKsG

ωςωωςω

www.nasa.gov 21


Inlet Shock Position Controls Design

-- Control the opening of bypass doors to position the shock against disturbances(atmospheric turbulence, aeroservoelastic, pitch, yaw, and engine)

Atmospheric Dist

+

GPS(s)

Inlet Dist TFsGP(s)

GT(s)

Atmospheric Dist

Dist Freq pressure

temperature

KcrcowlRad

+

Σ+

GTS(s)

GMS(s)1/ao

Vel to Mach

Σ+GTA(s)

GLA(s)

+Vel. Due to Temp

Velocity

GC(s) GBS(s)GA(s)Σ Σ1/Kcr Σ

C

1/cowlRad +

++

++

-

Shock posref pos

Shock Dist

CCmnd Sch

Shock Position Feedback Control Diagram

www.nasa.gov 22


Inlet Shock Position Controls-- Plant TFs:-- Plant TFs:

Bypass door to shock position (Using Large Perturbation Inlet (LAPIN) simulation

*)12513/)(1653/(325.3

)(++ ssK

G cr

)13707/3.13707/)(13519/3.13519/(1

*)13330/3.13330/)(13142/1.13142/)(1911/5.1911/)(1118/(

))(()(

2222

222222

++++

+++++++=

ssss

ssssssssG cr

BS

0

20

de (d

B)

Bypass Door to Shock Position TF

0-60

-40

-20

Mag

nitu

720

-540

-360

-180

Pha

se (d

eg)

www.nasa.gov 23

100

101

102

103

-720

Frequency (Hz)


out1in1 out2

-- Plant TFs: Valve actuator to bypass door position

in1 out21

Out1

1/(2*pi*250)s+1

1/(2*pi*3500)s+1Transfer Fcn4

1/(2*pi*10)s+1


1

s

Transfer Fcn2

1

A.s

Transfer Fcn1

1/Kf

1/Wn^2s +2*Z/Wns+12

Transfer Fcn

10.3

K1

K3

Gain3

K2

Gain2

1In1

2

Valve Actuator Feedback Control Diagram

Kw

Gain4

)14753/6.04753/)(11136/8.01136/)(160/()163/(

)(2222 +++++

+=

ssssss

sGA

0Valve Actuator TF

-50

-40

-30

-20

-10

Mag

nitu

de (d

B)

360

-270

-180

-90

0

Pha

se (d

eg)

www.nasa.gov 24

100

101

102

103

-360

Frequency (Hz)


Inlet Disturbance Transfer FunctionsF t di t b t h k P itiFreestream disturbances to shock PositionUsing Large Perturbation Inlet (LAPIN) simulation

Free Stream TFs

Engine Face

Disturbance

ShockPosition

TFs

1786.61562.81366.11078.1707.1309.31475.81416.21019.8737.5408.255.1)(

23456

2345

esesesesesesesesesesessGPS

++++++

−+−+−=

Pressure:

20

0

20

de (d

B)

g

2443226219941602136910463113832226.62093.21712.11420.21128.1769.5478.189.4)(

2345678

234567 esesesesesesessGTS−−+−+−+−

=

Temperature:-60

-40

-20

Mag

nitu

d

720

Mach No. TF

2447.32265.21997.41602.71369.51046.3751.1387.3 2345678 esesesesesesesesS

++++++++

Mach Number:0

180

360

540

Pha

se (d

eg)

www.nasa.gov 25

2121.11931.11623.21388.31016.2742.1312.32169.41952.11669.21301.1916.9624.3288.4)(

234567

23456

esesesesesesesesesesesesesesGMS

+++++++

+++−+−= 100 101 102 103 104 105

-180

Frequency (rad/sec)


Atmospheric Turbulence“Atmospheric Turbulence Modeling for Aero Vehicles – Fractional Order Fits,”

NASA/TM submitted for publication, George KopasakisApproach:Taking an existing atmospheric wind gust model, also scaling it for temperature and pressure and deriving whole order TF’s to fit the fractional order disturbances (for ε=8 6e-5 L=765)and deriving whole order TF s to fit the fractional order disturbances (for ε 8.6e 5, L 765)

Longitudinal acoustic velocity (m/sec):)15.335/)(10.55/)(12.9/(74.8)( +++

=ssssGLA 20

30

40

tral,

dB((m

/sec

/Hz)

Temperature (oK):

)11.1593/)(17.85/)(11.30/)(146.1/()(

++++ sssssGLA

)14.602/)(16.45/)(10.33/(75.41)( +++ sssG-10

0

10

acou

stic

wav

e ve

loci

ty s

pect

von Karman, integral scale length=1500mTF fit, integral scale length=1500mvon Karman, integral scale length=762mTF fit i t l l l th 762

Acoustic Velocity due to Temperature (m/sec):

)13.816/)(18.109/)(11.25/)(11.1/())()(()(++++

=ssss

sGT

)14602/)(1645/)(1033/(8820 +++RM

10-2 10-1 100 101 102

frequency, Hz

TF fit, integral scale length=762m

30

40

(m/s

ec/H

z)

Pressure (Pa):

)13.816/)(18.109/)(11.25/)(11.1/()14.602/)(16.45/)(10.33/(88.20)(++++

+++=

sssssss

aRMsG

oTA

γ

0

10

20

ic w

ave

velo

city

spe

ctra

l, dB

((

von Karman, eddy dissap.=5e-4TF fit eddy dissap =5e 4

www.nasa.gov 26

)13.816/)(18.109/)(11.25/)(11.1/()14.602/)(16.45/)(10.33/(96.37)(++++

+++=

ssssssssGP

10-2 10-1 100 101 102

-10

frequency, Hz

acou

sti

TF fit, eddy dissap.=5e-4von Karman, eddy dissap.=8.5e-5TF fit, eddy dissap.=8.5e-5


Inlet Shock Position Controls Design ProcessM lti L C t l D i A hMulti-Loop Controls Design Approach:

1. For Max. Disturbance Attenuation, starting with a high shock controller bandwidth (145 Hz –vs.- 175 Hz bandwidth of the actuator loop)

Shock Dist

GC(s) GBS(s)GA(s)Σ Σ1/Kcr Σ+

+++

+

-

Shock posref posout1in1 out21

Out1

1/(2*pi*250)s+1


1/(2*pi*10)s+1


1

s

Transfer Fcn2

1

A.s

Transfer Fcn1

1/Kf

1/Wn^2s +2*Z/Wns+12

Transfer Fcn

10.3

K1

Kw

Gain4

K3

Gain3

K2

Gain2

1In1 2

GA(s)

2. Design shock CLG (steps a-d) to maximize disturbance attenuation w/ sufficient stability margins (20 db mid-frequency disturbance atten.,

).deg60>Mφ )

3. Lower proportional controller gain until control loops are sufficiently decoupled (bandwidth will proportionally decrease as well)

.deg60>Mφ

4. Repeat Step 2. w/ new shock controller bandwidth

5. If this doesn’t meet design objectives (command tracking, margin reduction, etc) what’s left is to ask for more hardware capability

www.nasa.gov 27

, ) p y

Kopasakis et al. – Shock Positioning Controls Design for a Supersonic Inlet, AIAA-2009-5117


Inlet Shock Position Controls Design Process60

g

)1)52/(( +πs

2. Designed shock controller closed loop gain (CLG):

0

20

40

Mag

nitu

de (d

B)

)1)5.142/(()1)52/((310)(

++

=ππ

ssssL

-20

-70

-60

se (d

eg)

)()()()( sGsGsGsL BSAC=

10-1 100 101 102 103-90

-80

Pha

s

Frequency (Hz)

)()(log20)(log20)( 1010 sGsGsLsG BSAC −=

))()(())(())(( sGsGsLsG BSAC φφφ −=

www.nasa.gov 28


Inlet Shock Position Controls Design Process

)155002/4.1)55002/()(150002/4.1)50002/()(11042/)(15.142/()12502/3.1)2502/()(11452/98.0)1452/()(18.182/)(152/(310

)(2222

2222

++++++

++++++=

ππππππππππππ

sssssssssssss

sGC

Shock Controller from pole/zero TF fit:

)175002/41)75002/()(170002/41)70002/(()16502/60.0)6502/()(15502/0.1)5502/((

)165002/4.1)65002/()(160002/4.1)60002/(()14502/0.1)4502/()(13502/36.1)3502/((

2222

2222

2222

2222

++++

++++

++++

ππππ

ππππππππ

ssss

ssssssss

)175002/4.1)75002/()(170002/4.1)70002/(( 2222 ++++ ππππ ssss

40

50designed loop gaindesired loop gain

Verify CLG designStep Response

4.8

-10

0

10

20

30

Mag

nitu

de (d

B) desired loop gain

4

4.2

4.4

4.6

4.8

ositi

on, i

nc

-90

-60

Pha

se (d

eg)

10

3

3.2

3.4

3.6

3.8

shoc

k po

www.nasa.gov 29

Frequency (Hz)10-1 100 101 102

-120 0.3 0.35 0.4 0.45 0.5time, sec


Inlet Shock Position Controls Design Process

3. Lower controller proportional gain until control loops are decoupled

-- Sufficient decoupling when proportional gain lower to 100 from 310

-- Mid-frequency disturbance attenuation will drop to ~10 dB

-- Shock position control bandwidth falls to 35 Hz

4.6

Step Responses w/ gain of 100

4.6

4.8

Gain of 310 Gain of 100

3.8

4.2

ock

posi

tion,

in3 6

3.8

4

4.2

4.4

k po

sitio

n, in

c

0.3 0.35 0.4 0.45 0.5

3

3.4sho

0 3 0 35 0 4 0 45 0 5

3

3.2

3.4

3.6

shoc

www.nasa.gov 30

time, sec

-- Check shock control system performance with reduced gain0.3 0.35 0.4 0.45 0.5

time, sec


Atmospheric Turbulence

Worst case turbulence at over 20k feet altitude-- combined longitudinal acoustic velocity gust w/ temperature fluctuation (temp + acoustic velocity due to temp), w/ pressure fluctuationfluctuation

8

12

nal v

el dist, m/sec

40

distur

banc

e, o K

0

4

atmos

pher

ic lo

ngitu

tin

20

atmos

pher

ic te

mp. d

60

80

el dist, m/sec

30

40

urba

nce, P

a

0 0.5 1 1.5 2 2.5time, sec

0 0.5 1 1.5 2 2.50

time, sec

20

40

osph

eric te

mp long

it ve

l

10

20

mos

pher

ic pre

sure

distur

www.nasa.gov 31

0 0.5 1 1.5 2 2.50

atmos

time, sec0 0.5 1 1.5 2 2.5

0

atmo

time, sec


Shock Control System Command Tracking PerformanceC t l t ithi b d-- Control parameters within bounds

-- Shock position tracking within approx. 0.15 in

www.nasa.gov 32


Shock Control System Command Tracking Performance

Check Mid-frequency disturbance attenuation

Applying 10 HZ disturbance at the shock position

0.5

1

ce,in

4.2

4.25

,in

0

hock

dis

turb

anc

4.1

4.15

shoc

k po

sitio

n0 0.2 0.4 0.6 0.8 1

-1

-0.5sh

ti0.2 0.4 0.6 0.8 1

4.05

titime, sec time, sec

-- Mid Frequency attenuation of ~ 20 dB instead of 10 db due to lower gain(aided by the actuator control loop)

www.nasa.gov 33

(aided by the actuator control loop)


Integrated Linear Propulsion System ModelI t t d li l i t-- Integrated linear propulsion system

model developed

51015

20

urba

nce,

N

Upstream Flow Field DisturbancesDist TF's

time

time speed to mdot

num(s)

den(s)

mdot to shock

Switch2

-21.6

Shock Ref1

Scope81

Gain2

Display

8.158

CowlRadius

Cl k2

Add1 -10-50

5

Thru

st D

istu

num(s)

den(s)

-K-cowlRadius (in)

12000

Scope6

Scope2

Pos Dist1

In1

In2

Out1

FreeStream Dist

0

Constant1

Clock2

-20-15

5 5.4 5.8 6.2 6.6Time, sec

pres (pa) 1

thrust_cl

thrust

In1

In2

Out2

i f l t d

In2

Out1

Temp&Pres2Speednum(s)

den(s)

Speed to Thrust

Speed Ref

4.13

Shock Ref

Scope7

Scope4

Scope3

Scope1

In3

In1

In2

Out1

Inlet Bypass to shock 1 Add5-K-

1/cowlRadius1pres (pa)

deltaPres_2engine

DeltaTemp_2engine

1

DeltaTrustengine fuel to speed

Controller -63440.25

TrustOffset

In3Switch1

In1

In2

Out1

Out2

Shock Ref

Scope9Scope5

Inlet Bypass to shockcontroller

Gain1

0

Constant2

www.nasa.gov 34

Shock2Temp&Pres


Conclusion

Shock controls design approach developed to maximize command tracking performance in the presence of disturbance

More work needed to include other disturbance, like pitch, yaw, and aeroservoelasticae ose oe ast c

Additional work needed to study integrated propulsion and aeropropulsoservoelastic effectsaeropropulsoservoelastic effects

So far results are encouraging; g gIf tight shock position control can be maintained, reduction in shock control margin and significant propulsion efficiency gains can be realized as well as reduction in thrust transients

www.nasa.gov 35

Documents

Atmospheric Turbulence Modeling and Shock Positioning Control … · 2009-12-15 · Atmospheric Turbulence – Power Spectral Solution Challenges-- Atmospheric disturbances are fractional