Background• Interest is in maximizing the maneuverability of flight

vehicles changing lift vector– but it takes time for forces (lift) to change, even in incompressible

flow

• How fast will the lift on a wing respond to an actuator (aileron or active flow control)?A) Attached flow – e.g., transient forces associated with changing the flap angle

• Wagner (1925),Theodorsen (1935), Leishman (1997)

B) Separated flow – transient AFC actuation• 2D airfoils and flaps – Amitay & Glezer(2002, 2006), Darabi &

Wygnanski(2004), Woo et al.(2008, 2010)• 3D wings - IIT-experiments

Summary of main points • Quasi-steady approach to flow control limited to very low

frequencies – to increase bandwidth Active Flow Control (AFC) in unsteady flows requires – models for the unsteady aerodynamics – and the flow response to actuation

• Both 2-D and 3-D Separated flows demonstrate time delays or lift reversals (RHP-zeros) in response to actuation– Response scales with the convective time and dynamic pressure– Lift reversals are connected with the LEV vortex formation and

convection over the wing surface

• Bandwidth limitations in closed loop control are set by fluid dynamic time delays, hence– Actuator performance characteristics can be determined– Different control architectures may be needed to achieve faster control,

such as, predictive controllers

Outline of presentation• Active Flow Control in Unsteady Flows

– Example Application: ‘gust’ suppression in unsteady freestream– Experimental set up, models, actuators – Steady state lift response

• Quasi-steady and ad-hoc phase matching controller• Requirements for high(er)-bandwidth control

– Unsteady aerodynamics model– Dynamic response to actuation

• Robust controllers– CL-based– L-based

• Role of time delays & rhp zeros• Useful for actuator design

4

Example application of AFC: u’-gust, L’ suppression

Use AFC to suppress L’. Compare the performance of different control architectures

Time varying flow conditions will require time-varying AFC

Unsteady flow wind tunnel & 2 wings

5

•Semi-circular planform (AR=2.54)

•Angle of attack fixed at α=19o-20o

•Wing I - 16 Micro-Valves Pulsed at 29Hz (St=0.84) – t63% const = 2.2 tconv

•Wing II - piezoelectric actuators - t63% const= 0.2 tconv

•6 component force balance – ATI Nano-17

•Shutters at downstream end of test section produce longitudinal flow oscillations – 0.10Uo

•dSPACE® Real-Time-Hardware and software

6

Response to continuous actuation

Uncontrolled flow – CL=0.75 Continuous forcing at 29Hz pjet=34.5kPa CL=1.2

Steady state lift curves & dominant lift/wake frequencies

– Continuous pulsing at 29 Hz produced largest lift increment (StF-J = 0.4)

With ‘dynamic’ AFC we are working between these two states.

With ‘dynamic’ AFC we are working between these two states.

Steady state lift response to actuator supply pressure

Static lift coefficient map dependence on

pjC

Build a controller based on quasi-steady fluid dynamics

= 20o f = 29 Hz St=1.2

U

uconst

U

ppC actuatoratmactuatorpj

2/1

22/1

pjC

Actuation range

Control architectures

• Quasi-steady– Feed forward controller – Ad-hoc time delay and gain matching controller

• Feed forward compensates for unsteady aero

• Berlin robust control approach– CL tracking, robust feedback control

• No unsteady aerodynamics model

– L’ disturbance rejection, robust feedback control• Includes unsteady aerodynamics model • Comparison of slow and fast actuators

Quasi-steady feed-forward control

• Assume

• Subtract mean lift

• Find CL’ for L’ = 0 => Actuator duty cycle controls CL’

• Required CL’

U∞

From hotwireFF controller SCW Plant

CL’Lift

Valvecontrol

Quasi-steady control L’ suppression

-10 dB

U

ck

2

Effective only at low frequencies, k<0.03, because model does not account for plant dynamics and unsteady aerodynamic effects

Lift phase response to actuation frequency steady flow, = 20o

3m/s

5m/s

dφ/df

dφ/dk

td_3m/s = .35 s

td_5m/s = .24 s

+ = td/tconv=5.8±0.5

td_3m/s = .35 s

td_5m/s = .24 s

+ = td/tconv=5.8±0.5

13

Single point, feed forward control with harmonic freestream oscillation

Compensate for time delays: 1) between lift response and actuation2) between lift response and unsteady flow

Increased controller speed 5x (k=0.15), but not the bandwidth

Only works at a specific frequency

Ad-hoc phase & gain matching

Requirements for high-bandwidth control

• A model of the unsteady aerodynamic effects on the instantaneous lift

• A model of the dynamic response of the wing to actuation (plant)– Pulse response provides insight into flow physics– Black-box models obtained using pseudo-random

binary inputs and prediction error method of system identification

Pulse response is ‘common’ to many flows scales with t+ =tU/c, uj /U

Pulsed combustion actuator - Woo, et al. (2008) - 2D airfoilPulsed-jet actuator – Kerstens, et al. (2010) – 3D wingSynthetic jet actuator – Quach, et al. (2010)

See also:2D Flap, Darabi & Wygnanski (JFM 2004)2D Airfoil, Amitay & Glezer (2002, 2006)3D Wing, Bres, Williams, & Colonius (APS-2010)

saturationMax increment at t+=3

Pulse input, 3-D wingFlow physics behind the time delay

Flow behind the time delay

• Vien’s piv movieA

C

B ΔCLmin

ΔCLmax

Flow behind the time delay - 2D

E

System Identification used to obtain a model of the dynamic response of the

wing Randomized step input experiments

– Fixed supply pressure ( ), time intervals between step changes varied

– Vary the flow speed– Vary the supply pressure

Prediction error method of system identification– Measurements repeated at different supply pressures and

different flow speeds to obtain 33 models– Averaged the models to obtain a 1st order (PT1) nominal

model of the flow system, Gn(s)

pjC

Example of pseudo-random input data• used to obtain a ‘black box’ model of the wing’s lift response

Input to actuator, Cpj

0.5

Input to actuator, Cpj

0.5

Output ΔCL response

Output ΔCL response

Bode plots and nominal system model• Input = Cpj

0.5 Output = CL

• PEM and pseudo-random square wave inputs used to obtain 33 models• Nominal first order model obtained from an average of family of models

1)(

,)()(1)()(:

14519.0

008241.0)(

j

sswsGsG

ssG

I

IInpI

n

Nominal model Gn(s) is used to design both the feed forward and the feedback controllers

Nominal model Gn(s) is used to design both the feed forward and the feedback controllers

Control architectures

• Quasi-steady– Feed forward controller – Ad-hoc time delay and gain matching controller

• Feed forward compensates for unsteady aero

• ‘Berlin’ robust control approach– CL tracking, robust feedback control

• No unsteady aerodynamics model

– L’ disturbance rejection, robust feedback control• Includes unsteady aerodynamics model • Comparison of slow and fast actuators

CL-based controller for U’-gust suppression

Lref

(1/2ρU(t)2)S

r = CLref(t)

Kff=F(s)Gn(s)-1Predicted, u*

(Cpj)0.5

f-1(u*)Plant

y = CL

(1/2ρU(t)2)S

x

L

F(s) K(s)

Feed Forward PathFeed Forward Path

CL Feedback PathCL Feedback PathHot-wire measurement of unsteady freestream converts Lref to CLref

Hot-wire measurement of unsteady freestream converts Lref to CLref

Pre-compensator (squared input)

H∞

24

Robust closed loop control of CL

Lift coefficient closed loop control

Better performance than quasi-steady, but still only effective at low frequencies, k<0.04,

Capable of suppressing “random” gusts (not only harmonics)

25

Unsteady aerodynamic effectsFrequency Response Measurements

Lifts leads velocity in steady state sinusoidal forcing Lift lags the fluid acceleration

Lift amplitude increases with increasing frequency Dynamic stall vortices formed during deceleration of flow

26

Lift-based controller for U’-gust suppression

y = L-

u = pj-

r = Lref

Gd(s)

G(s)

Kd(s)

K(s)

d = U’

GD – Unsteady aerodynamic (disturbance) model

KD – Feedforward disturbance compensation

Gn – Pressure actuation model

K – H∞ controller to correct for uncertainties/errors in modeling

dnFd GGGK 1~

Williams, et al. (AFC-II Berlin 2010), Kerstens, et al. AIAA -2010-4969 (Chicago 2010)

Hot wire measurement

Force balance measurement

27

Dynamic response to pulsed-blowing actuation

seTs

ksG

1

•Prediction-Error-Method used to model dynamic response to actuation

•First order models with delay fit the measured data better than PT1

θ=0.157s

28

Bode plots of models at different flow speeds and actuator amplitudes

•A nominal model is constructed from a family of 11 models at 7m/s

•All-pass approximation causes deviations in phase at higher frequencies

Closed loop control bandwidth limitations

• Time delays in the plant consist of:– Actuator delays

• i-p regulator, plenum, plumbing for the pulsed-blowing actuator• Modulated pulse of the piezo-actuator

– Time delay in the flow response to actuation• LEV formation and convection

• For an ideal controller (ISE optimal) Skogestad & Postlethwaite (2005)

– with time delay e-θs, the bandwidth is limited to ωc<1/θ. • θ=0.157s for pulsed blowing wing, fc < 1.0 Hz

– with RHP real zero, for |S|<2 ωB<0.5z • Z=19.2 for piezo-actuator wing, fB < 1.5 Hz

30

Fast & slow actuators-step response

•Piezo-actuator rise time is 10X faster than pulsed-blowing actuator.

•Pulsed-blowing actuator has ‘plumbing’ delay

•Faster actuators show initial lift reversal (non-minimum phase behavior)

Hot-wire measurement of

actuator jet velocity

Lift/Lmax

31

Sensitivity functions

•Sensitivity function shows disturbances will be amplified in the range of frequencies between ~0.9Hz to ~4.5Hz

•Bandwidth is comparable for both actuators

Suppression of lift fluctuations

Amplification of lift fluctuations

Uncontrolled plant – blue line

Feedback only – green line

Feedback and feedforward – red line

Piezo- Actuator

Pulsed-blowing Actuator

Pulsed-blowing control is effective with bandwidth of about 1.0 Hz, k=0.15

•Simulation results obtained using experimentally measured velocity and reference lift

Piezo-Actuator Control is Effective, with bandwidth about 0.9 Hz, k = 0.13

•Simulation results obtained using experimentally measured velocity and reference lift

34

Lift suppression spectra

Suppression of lift fluctuations

Amplification of lift fluctuations

Pulsed Blowing Actuator

Piezo-Actuator

Bandwidth is comparable for slow and fast actuators, because fluid dynamic time delays limit controller performance.

Conclusions• Quasi-steady approach to flow control limited to very low frequencies -

to increase bandwidth Active Flow Control (AFC) in unsteady flows requires models for the unsteady aerodynamics and the flow response to actuation– Controller bandwidth improvement was significant when the unsteady aero

model was included

• Both 2-D and 3-D Separated flows demonstrate time delays or lift reversals (RHP-zeros) in response to actuation– Response scales with the convective time and dynamic pressure– Lift reversals are connected with the LEV vortex formation and convection over

the wing surface

• Bandwidth limitations in closed loop control are set by fluid dynamic time delays, hence– Actuator design guidelines

• Bandwidth ≈ ωc =1/θ or ωB=z/2 - higher bandwidth has little effect

• Rise time < 1.5 c/U0 – faster rise time produces same lift response

• Amplitude ≈ Ujet ≥ 2U0 – lift increment saturates