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 – C L -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=19 o -20 o Wing I - 16 Micro-Valves Pulsed at 29Hz (St=0.84) – t 63% const = 2.2 t conv Wing II - piezoelectric actuators - t 63% const = 0.2 t conv 6 component force balance – ATI Nano-17 Shutters at downstream end of test section produce longitudinal flow oscillations – 0.10U o dSPACE ® Real-Time-Hardware and software

6 Response to continuous actuation Uncontrolled flow – C L =0.75 Continuous forcing at 29Hz p jet =34.5kPa C L =1.2

Steady state lift curves & dominant lift/wake frequencies – Continuous pulsing at 29 Hz produced largest lift increment (St F-J = 0.4) With dynamic AFC we are working between these two states.

Steady state lift response to actuator supply pressure Static lift coefficient map dependence on Build a controller based on quasi-steady fluid dynamics = 20 o f = 29 Hz St=1.2 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 Berlin robust control approach – C L tracking, robust feedback control No unsteady aerodynamics model No unsteady aerodynamics model – L disturbance rejection, robust feedback control Includes unsteady aerodynamics model Includes unsteady aerodynamics model Comparison of slow and fast actuators Comparison of slow and fast actuators

Quasi-steady feed-forward control U From hotwire FF controller SCW Plant C L Lift Valve control

Quasi-steady control L suppression -10 dB 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 s teady flow, = 20 o 3m/s 5m/s dφ/df dφ/dk t d_3m/s =.35 s t d_5m/s =.24 s + = t d /t conv =5.8±0.5 t d_3m/s =.35 s t d_5m/s =.24 s + = t d /t conv =5.8±0.5

13 Single point, feed forward control with harmonic freestream oscillation Compensate for time delays: 1) between lift response and actuation 2) 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, u j /U Pulsed combustion actuator - Woo, et al. (2008) - 2D airfoil Pulsed-jet actuator – Kerstens, et al. (2010) – 3D wing Synthetic 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) saturation Max increment at t + =3

Pulse input, 3-D wing Flow physics behind the time delay

Flow behind the time delay Viens piv movie A C B ΔC Lmin ΔC Lmax

Flow behind the time delay - 2 D 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 1 st order (PT1) nominal model of the flow system, G n (s)

Example of pseudo-random input data used to obtain a black box model of the wings lift response Input to actuator, C pj 0.5 Output ΔC L response

Bode plots and nominal system model Input = C pj 0.5 Output = C L PEM and pseudo-random square wave inputs used to obtain 33 models Nominal first order model obtained from an average of family of models Nominal model G n (s) is used to design both the feed forward and the feedback controllers

Control architectures Quasi-steady Quasi-steady – Feed forward controller – Ad-hoc time delay and gain matching controller Feed forward compensates for unsteady aero Feed forward compensates for unsteady aero Berlin robust control approach – C L tracking, robust feedback control No unsteady aerodynamics model – L disturbance rejection, robust feedback control Includes unsteady aerodynamics model Comparison of slow and fast actuators

C L -based controller for U-gust suppression L ref (1/2ρU(t) 2 )S r = C Lref (t) K ff =F(s)G n (s) -1 Predicted, u* (C pj ) 0.5 f -1 (u*) y = C L (1/2ρU(t) 2 )S x L F(s)K(s) Feed Forward Path C L Feedback Path Hot-wire measurement of unsteady freestream converts L ref to C Lref Pre-compensator (squared input) H

24 Robust closed loop control of C L 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 effects Frequency 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 = p j - r = L ref G d (s) G(s) K d (s) K(s) d = U G D – Unsteady aerodynamic (disturbance) model K D – Feedforward disturbance compensation G n – Pressure actuation model K – H controller to correct for uncertainties/errors in modeling Williams, et al. (AFC-II Berlin 2010), Kerstens, et al. AIAA (Chicago 2010) Hot wire measurement Force balance measurement

27 Dynamic response to pulsed-blowing actuation 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 ω c <1/θ. θ=0.157s for pulsed blowing wing, f c < 1.0 Hz – with RHP real zero, for |S|<2 ω B <0.5z Z=19.2 for piezo-actuator wing, f B < 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/L max

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 ω c =1/θ or ω B =z/2 - higher bandwidth has little effect Rise time < 1.5 c/U 0 – faster rise time produces same lift response Amplitude U jet 2U 0 – lift increment saturates