Bang-Bang Optimal Control Method with Plasma …Bang-Bang Optimal Control Method with Plasma....

.Bang-Bang Optimal Control Method with PlasmaActuators in Airfoil Roll Control

Qingkai Wei,1 Zhongguo Niu,2 Bao Chen,2 Xun Huang1

1College of Engineering, Peking University2Aerodynamics Research Institute, Aviation Industry Corporation of China

The project is supported by NFS Grant of China (90916003), Aviation Science FoundationProject (20090771001) and the Scientific Research Foundation for the Returned Overseas

Chinese Scholars.

Qingkai Wei (LNA) College of Engineering, Peking University 2012 CCC, Hefei 1 / 23

.

Outline

.. .1 Background of Plasma Actuators

.. .2 Description of Model and Wind-tunnel ExperimentModel descriptionExperimental apparatus

.. .3 Bang-bang Controller Design

.. .4 Numerical Simulation

.. .5 Summary and Vision


.

Background of Plasma Actuators

Introduction of plasma actuators

.concept..

.. ..

.

.What is? What for?

Huang, X., Zhang, X., and Li, Y., “Broadband Flow-induced Sound Control using PlasmaActuators”, Journal of Sound and Vibration, Vol. 329, No. 13, 2010, pp. 2477.


.


Introduction of plasma actuators.application.... ..

.

.examples of application.

flow control:

Moreau E., “Airflow control by non-thermal plasma actuators”, Journal of Physics D:Applied Physics, Vol. 40, No. 3, 2007, pp. 605-632.Qingkai Wei (LNA) College of Engineering, Peking University 2012 CCC, Hefei 4 / 23

.



.


cavity noise control:

Huang, X., Chan, S., Zhang, X., and Gabriel, S., “Variable Structure Model forFlow-induced Tonal Noise Control with Plasma Actuators”, AIAA Journal, Vol. 46, No. 1,2008, pp. 241-250.Qingkai Wei (LNA) College of Engineering, Peking University 2012 CCC, Hefei 5 / 23

.



.


wake flow control:

Li, Y., Zhang, X., Huang, X.,“The Use of Plasma Actuators for Bluff Body BroadbandNoise Control”, Experiments in Fluids, Vol 49, No 2, 2010, pp. 367-377Qingkai Wei (LNA) College of Engineering, Peking University 2012 CCC, Hefei 6 / 23

.

Description of Model and Wind-tunnel Experiment Model description

What we doNot only flow control, use flow control to realize flight control;

Advantages toward traditional mechanical part: no moving part, easeof application;Asymmetric Cz to roll the airfoil.

Figure 1: The schematic of the NACA 0015 airfoil and the layout of plasmaactuators (mm).


.


What we doNot only flow control, use flow control to realize flight control;Advantages toward traditional mechanical part: no moving part, easeof application;

Asymmetric Cz to roll the airfoil.



.


What we doNot only flow control, use flow control to realize flight control;Advantages toward traditional mechanical part: no moving part, easeof application;Asymmetric Cz to roll the airfoil.



.

Description of Model and Wind-tunnel Experiment Experimental apparatus

Experimental apparatusExperiment conducted in FL-5 (1.5m diameter round and 1.95m long, windspeed range from 0m/s to 53m/s).

(a) Setup in wind tunnel. (b) Layout of DBDs.

Figure 2: Experimental apparatus.


.


Experiment resultsStall angle increases by about 2deg;Increasement of Cz is small.

α (deg)

Cz

-20 -10 0 10 20-1

-0.5

0

0.5

1Cz (plasma on)Cz (plasma off)

Figure 3: Cz at 15m/s (Re = 3 × 105).


.


Experiment resultsActuators in the left airfoil are on and the right ones are off;The arm of force: 3Ws/8 from the center of plasma area to symmetric axis.

α (deg)

Clp

-20 -10 0 10 20

0

0.1

0.2

0.3

0.4

0.5

Figure 4: Plasma-induced roll moment coefficient Clp .


.

Bang-bang Controller Design

Bang-bang control methodTwo discrete input;Minimum-time optimal feedback control method;

.Why bang-bang?..

.. ..

.

.Plasma-induced velocities oscillate at high voltage input.

time (s)

velo

city

(m/s

)

1 2 3 4 5 6

0

2

4

6

8

Vpp = 22 kVVpp = 12.5 kVVpp = 10 kV

Figure 5: Measurements of plasma-induced velocities.Qingkai Wei (LNA) College of Engineering, Peking University 2012 CCC, Hefei 11 / 23

.


Mathematic roll model

.mathematic roll model..

.. ..

.

.

L = Ixp − (Iy − Iz)qr + Ixy(pr − q) − Ixz(pq + r) + Iyz(r2 − q2),L = L0 + Lp,

p = ϕ− (sinθ)ψ.

.reduction conditions..

.. ..

.

.Ixy = Iyz = 0, q ≡ 0, r ≡ 0, ψ ≡ 0, θ ≡ 0.

.reduced model..

.. ..

.

.

Lp = M or −Mϕ = ±M/Ix.


.


Bang-bang controller design

.state space equation..

.. ..

.

.

[ϕ

ϕ

]=

[0 10 0

] [ϕ

ϕ

]+

[0M/Ix

]u, u = ±1.

.phase line..

.. ..

.

.

[ϕ(0), ϕ(0)] = [0, 0]→[ϕ(T), ϕ(T)] = [ϕT, 0]

ϕ =

MIx

t

ϕ =M2Ix

t2 + C1

for u = 1;

ϕ = −M

Ixt

ϕ = − M2Ix

t2 + C1

for u = −1.

(1)


.


Bang-bang controller design

..O

.ϕ

.ϕ

.u = +1.u = −1 . .ϕ

.ϕ

.O

.A

.B(ϕT, 0)

.on-off line.

.

.

.on-off line and control input..

.. ..

.

.

ϕ = − 12M/Ix ϕ|ϕ| + ϕT.

u =

8

>

<

>

:

+1; (ϕ +1

2M/Ixϕ|ϕ| − ϕT < 0) or (ϕ +

1

2M/Ixϕ|ϕ| − ϕT = 0, ϕ < 0)

−1; (ϕ +1

2M/Ixϕ|ϕ| − ϕT > 0) or (ϕ +

1

2M/Ixϕ|ϕ| − ϕT = 0, ϕ > 0)

.


.

Numerical Simulation

Parameters for simulation.parameters..

.

. ..

.

.

Wingspan Ws = 3m, chord d = 0.3m, force arm 3Ws/8, wing density 200kg/m3,moment of inertial Ix = 4.05kgm2, dynamic pressure q = ρU2

∞/2 = 137.8Pa.



.


Simulation case

Figure 7: The simulation case in MATLAB.


.


Nominal numerical results

[ϕ(0), ϕ(0)] = [0, 0]→[ϕ(T), ϕ(T)] = [ϕT, 0]

0 1 2 3 4

0

2

4

6

8

10

time (s)

φ (d

eg)

(a)

0 2 4 6 8 10

0

2

4

6

8

10

12

φ (deg)

p (d

eg/s

)(b)

Figure 8: Dynamics during the airfoil rolls from 0deg to 10deg at α=12deg andU∞=15m/s, where (a) roll angle dynamics and (b) phase line.


.


Monte-Carlo simulation. ..instability of plasma velocity

..aerodynamic coefficients fluctuation

..a 20% disturbance Cz

Plasma-induced velocities oscillate, ±20% of Clp is considered.

0 1 2 30

2

4

6

8

10

12

time (s)

φ (d

eg)

(a)

0 5 10−5

0

5

10

φ (deg)

p (d

eg/s

)

(b)

Figure 9: Monte-Carlo simulation results of roll control from 0deg to 10deg.Qingkai Wei (LNA) College of Engineering, Peking University 2012 CCC, Hefei 18 / 23

.


Simulation with disturbance

Plasma-induced velocities oscillate, ±20% of Clp is consideredtime-invariant.

0 1 2 30.8

0.9

1

1.1

1.2

time (s)

dist

urba

nce

0 1 2 3

0

2

4

6

8

10

time (s)

φ (d

eg)

Nominal solution1Hz perturbation

0 2 4 6 8 10

0

2

4

6

8

10

12

φ (deg)

p (d

eg/s

)


0 1 2 30.8

0.9

1

1.1

1.2

time (s)

dist

urba

nce

0 1 2 3

0

2

4

6

8

10

time (s)

φ (d

eg)


0 2 4 6 8 10

0

2

4

6

8

10

12

φ (deg)

p (d

eg/s

)



.


Time-variant roll command

0 2 4 6 8 10−15

−10

−5

0

5

10

15

time (s)

φ (d

eg)

Roll commandNominal roll anglePerturbed roll angle

Figure 10: Roll angle in a time-variance roll command.


.


More realistic

More realistic with α changes over time.

0 1 2 3 40

5

10

15

20

time (s)

α (d

eg)

0 1 2 3 4

0

2

4

6

8

10

time (s)

φ (d

eg)

0 1 2 3 4

0

2

4

6

8

10

12

time (s)

p (d

eg/s

)

0 2 4 6 8 10

0

2

4

6

8

10

12

φ (deg)

p (d

eg/s

)


.

Summary and Vision

Summary and Vision

Wind tunnel experiment to verify the effect of DBDs.

Bang-bang controller design for fight control with DBDs.Numerical simulation of bang-bang controller in roll motion control.Roll control validation in wind tunnel, more realistic flight control.


.

Summary and Vision

Summary and Vision

Wind tunnel experiment to verify the effect of DBDs.Bang-bang controller design for fight control with DBDs.

Numerical simulation of bang-bang controller in roll motion control.Roll control validation in wind tunnel, more realistic flight control.


.

Summary and Vision

Summary and Vision

Wind tunnel experiment to verify the effect of DBDs.Bang-bang controller design for fight control with DBDs.Numerical simulation of bang-bang controller in roll motion control.

Roll control validation in wind tunnel, more realistic flight control.


.

Summary and Vision

Summary and Vision

Wind tunnel experiment to verify the effect of DBDs.Bang-bang controller design for fight control with DBDs.Numerical simulation of bang-bang controller in roll motion control.Roll control validation in wind tunnel, more realistic flight control.


.

Summary and Vision

Thanks!Discussion!


Bang-Bang Optimal Control Method with Plasma …Bang-Bang Optimal Control Method with Plasma....

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