B ackground
description
Transcript of B ackground
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
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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
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•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
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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.
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
Uuconst
UppC actuatoratmactuator
pj
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’ LiftValvecontrol
Quasi-steady control L’ suppression
-10 dB
Uck2
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
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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
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)()(:
14519.0008241.0)(
j
sswsGsG
ssG
I
IInpI
n
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 Path
CL Feedback PathHot-wire measurement of unsteady freestream converts Lref to CLref
Pre-compensator (squared input)
H∞
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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)
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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
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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) modelKD – Feedforward disturbance compensationGn – Pressure actuation modelK – 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
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Dynamic response to pulsed-blowing actuation
seTsksG
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
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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
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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
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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
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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