Flow Control: TD4-2 Overview

- General issues, passive vs active…- Control issues: optimality and learning vs robustness and rough model- Model-based control: linear model, nonlinear control

- Linear model, identification- Sliding Mode Control- Delay effect- Time-delay systems

- Introduction to delay systems- Examples- Much a do about delay? Some special features + a bit of maths- Time-varying delay

- Model-based control: nonlinear model, nonlinear control- Overview of MF’s PhD: Sliding Mode Control- Application to the airfoil- Application to the Ahmed body (MF and CC’PhDs)

…- Machine Learning and model-free control: + 4h with Thomas Gomez

Camila Chovet ¹

Maxime Feingesicht ²

Baptiste Plumejeau 1,4

Marc Lippert ¹

Laurent Keirsbulck ¹

Franck Kerhervé ³

Andrey Polyakov ²

Jean-Pierre Richard ²

Jean-Marc Foucaut 5

¹ LAMIH, ² CRIStAL, INRIA, ³ pPRIME, 4 IPSA, 5 LMFL.

Rear face

PROBLEM

1/27

Flow configuration

𝐹𝐷 = 𝑆𝑤

𝑃𝑡∞ − 𝑃𝑡𝑠𝑤 𝑑𝜎 +1

2𝜌𝑉∞

2 𝑆𝑤

𝑉𝑧2

𝑉∞2 +

𝑉𝑧2

𝑉∞2 𝑑𝜎 −

1

2𝜌𝑉∞

2 𝑆𝑤

1 −𝑉𝑥𝑉∞

2

𝑑𝜎

3

PROBLEM

2/27

Active control (Injection of momentum)

Methods of flow control

Passive control(Small variation in the geometric configuration)

Limitations of design requirements

C_AIR LOUNGE

4

3/27

PROBLEM

Physical system: Case I – Ahmed body

Physical system: Case II – Vehicle

4/27

Characteristics:

Closed-loop wind tunnel

Max. velocity 60m/s 200km/h)

Optimal test section:

2m x 2m, length 10m

5

5/27

𝐻 = 0.135𝑚

𝑊 = 0.170𝑚

𝐿 = 0.370𝑚

𝑟 = 0.05𝑚

𝒈 = 𝟎. 𝟎𝟑𝟓𝒎

𝑈∞ = 10𝑚/𝑠

𝑅𝑒ℎ𝐻 = 9𝑥1046

6/27

W

H

L

PIV

7

7/27

W

H

L

2000 double frame pictures7Hz repetition rate

Interrogation window 16x16𝑝𝑖𝑥𝑒𝑙𝑠2

50% overlapping

PIV domain3.7H x 1.8H

6

Jet velocity𝑉𝑗

Steady jet velocity𝑉𝑗0 = 16𝑚/𝑠

8

8/27

9/27

18

10/27

𝑠 𝑡 = 𝑓 𝑠, 𝑡 + 𝑔 𝑠, 𝑡 . 𝑏(𝑡)Actuation

𝑏(𝑡)

Experimental plant

Controller

Sensor

𝑠 𝑡 = 𝐹𝑑(𝑡)

ref

𝑠∗

19Feingesicht et al. (2017) Int. J. Robust Nonlinear Control

11/27

Experimental plantControl law

𝑃(𝑡)

𝐹𝑑(𝑡)

Sensors

𝑈∞

𝑏 𝑡 =1 𝑖𝑓 𝜎 𝑡 − 𝜎∗ < 0

0 𝑖𝑓 𝜎 𝑡 − 𝜎∗ > 0

𝑆∗ = 𝐹𝑑

20

12/27

Choose 𝑠∗ Reaching phase

• Wait for s(t) to arrive to s*

Sliding phase

• Keep s(t) at s*

21

13/27

Sensors

22

𝑃(𝑡)

𝐹𝑑(𝑡)

𝑈∞

𝑏 𝑡 =1 𝑖𝑓 𝜎 𝑡 − 𝜎∗ < 0

0 𝑖𝑓 𝜎 𝑡 − 𝜎∗ > 0

𝑆∗ = 𝐹𝑑

14/27

Reaching phase Sliding phase

𝑠 𝑡 = 𝑓 𝑠, 𝑡 + 𝑔 𝑠, 𝑡 . 𝑏(𝑡)

23

Choose 𝑠∗ Reaching phase

• Wait for s(t) to arrive to s*

Sliding phase

• Keep s(t) at s*

Feingesicht et al. (2017) Int. J. Robust Nonlinear Control

15/27

t

𝑠 𝑡 = 𝛼𝑠(𝑡) + 𝛽𝑏(𝑡)

𝜎∗ = 𝑠(𝑡)𝑏 𝑡 =

1 𝑖𝑓 𝜎 𝑡 − 𝜎∗ < 0

0 𝑖𝑓 𝜎 𝑡 − 𝜎∗ > 0

𝑠 𝑡 = 𝑓 𝑠, 𝑡 + 𝑔 𝑠, 𝑡 . 𝑏(𝑡) 𝑠 𝑡 = 𝛼𝑠(𝑡) + 𝛽𝑏(𝑡)

24

16/27

t

𝑏 𝑡 =

1 𝑖𝑓 𝜎 𝑡 − 𝜎∗ < 0

0 𝑖𝑓 𝜎 𝑡 − 𝜎∗ > 0

𝑠 𝑡 = 𝛼𝑠(𝑡) + 𝛽𝑏(𝑡 − ℎ)

𝜎∗ = 𝑠(𝑡)

25

17/27

𝑠 𝑡 = 𝑓 𝑠, 𝑡 + 𝑔 𝑠, 𝑡 . 𝑏(𝑡) 𝑠 𝑡 = 𝛼𝑠(𝑡) + 𝛽𝑏(𝑡)

t

𝑏 𝑡 =

1 𝑖𝑓 𝜎 𝑡 − 𝜎∗ < 0

0 𝑖𝑓 𝜎 𝑡 − 𝜎∗ > 0

𝑠 𝑡 = 𝛼𝑠(𝑡) + 𝛽𝑏(𝑡 − ℎ)

𝜎∗ = 𝑠 𝑡 + 𝛽 𝑡−ℎ

𝑡

𝑏 𝑝 𝑑𝑝

26

18/27

𝑠 𝑡 = 𝑓 𝑠, 𝑡 + 𝑔 𝑠, 𝑡 . 𝑏(𝑡) 𝑠 𝑡 = 𝛼𝑠(𝑡) + 𝛽𝑏(𝑡)

t

Sensor with delay

Identification

𝑠 𝑡 = 𝛼1𝑠 𝑡 − ℎ − 𝛼2𝑠 𝑡 + (𝛽 − 𝛾𝑠 𝑡 − ℎ + 𝛾 𝑡 − 𝜏 )𝑏(𝑡 − ℎ)

Sensor without delay

𝐹𝐼𝑇 % = 1 −𝑆𝑒𝑥𝑝 − 𝑆𝑠𝑖𝑚 𝐿2

𝑆𝑒𝑥𝑝 − 𝑆𝑒𝑥𝑝 𝐿2

𝑥 100% = 53%

𝛼1 = 27.37 𝛼2 = 32.70 𝛽 = 1.97 𝛾 = 1.92 𝜏 = 0.18 ℎ = 0.01

Feingesicht et al. (2017) Int. J. Robust Nonlinear Control

19/27

𝑠 𝑡 = 𝛼𝑠(𝑡) + 𝛽𝑏(𝑡 − ℎ)

𝜎∗ = 𝑠 𝑡 + 𝛾 𝑡−𝜏+ℎ

𝑡

𝑠 𝑝 𝑑𝑝 + 𝑡−ℎ

𝑡

𝛼1𝑠 𝑝 + (𝛽 − 𝛾𝑠 𝑝 + 𝛾𝑠 𝑝 − 𝜏 + ℎ 𝑏(𝑝))𝑑𝑝

𝑏 𝑡 =

1 𝑖𝑓 𝜎 𝑡 − 𝜎∗ < 0

0 𝑖𝑓 𝜎 𝑡 − 𝜎∗ > 0

Sliding mode control

28

20/27

𝑡+ = 𝑡 𝑈∞/𝐻

21/27

21/27

https://www.youtube.com/watch?v=ZZ0qxbEBm8s

PROBLEM

Physical system: Case I – Ahmed body

Physical system: Case II – Vehicle

22/27

6

Race track located at

Clastres (North of France)

Measurement mechanisms

23/27

𝐹𝐷 =

𝑆𝑤

𝑃𝑡∞ − 𝑃𝑡

𝑆𝑤 𝑑𝜎 −𝜌𝑈∞

2

2

𝑆𝑤

𝑈𝑦2

𝑈 ∞

2

+𝑈𝑧2

𝑈 ∞

2

𝑑𝜎 +𝜌𝑈∞

2

2

𝑆𝑤

1 −𝑈𝑥2

𝑈 ∞

2

𝑑𝜎

Onorato’s relation

Onorato, M. et al (1984) SAE, SP-569,International congress and

Exposition, Detroit: pp. 85-93

Measurement mechanisms

24/27

𝐹𝐷 =

𝑆𝑤

𝑃𝑡∞ − 𝑃𝑡

𝑆𝑤 𝑑𝜎

Onorato’s relation

25/27

Direction I: departure to arrival

Direction II: arrival to departure

26/27

27/27

Flow ControlOverview

- General issues, passive vs active…- Control issues: optimality and learning vs robustness and rough model- Model-based control: linear model, nonlinear control

- Linear model, identification- Sliding Mode Control- Delay effect- Time-delay systems

- Introduction to delay systems- Examples- Much a do about delay? Some special features + a bit of maths- Time-varying delay

- Model-based control: nonlinear model, nonlinear control- Overview of MF’s PhD: Sliding Mode Control- Application to the airfoil- Application to the Ahmed body (MF and CC’PhDs)

…- Machine Learning and model-free control: + 4h with Thomas Gomez

Journal:

SISO model-based control of separated flows, Internat. Journal of Robust & Nonlinear Control, 2017M. Feingesicht, A. Polyakov, F. Kerherve and J. P. Richard,

Conferences:

Nonlinear Control for Turbulent Flows, IFAC 2017 World Congress, Toulouse, July 2017M. Feingesicht, A. Polyakov, F. Kerherve and J. P. Richard

Model-Based Feedforward Optimal Control Applied to a Turbulent Separated Flow, IFAC 2017 M. Feingesicht, A. Polyakov, F. Kerherve and J. P. Richard

A bilinear input-output model with state-dependent delay for separated flow ctrl, ECC 2016 Aalborg M. Feingesicht, C. Raibaudo, A. Polyakov, F. Kerherve and J. P. Richard

Reducing Car Consumption by Means of a Closed-loop Drag ControlC. Chovet, M. Feingesicht et al., VEHICULAR 2018, Venice

Patent:

Dispositif de contrôle actif du recollement d’un écoulement sur un profil. M. Feingesicht, A. Polyakov, F. Kerherve and J. P. Richard

Book:

Mathématiques pour l’ingénieur (chap.6: Systèmes à retard) https://hal.archives-ouvertes.fr/hal-00519555

J. P. Richard et al., 2009 (available online)

References

What’s next?

Spotter Twingo GThttps://youtu.be/V1BQaCjO7to

Dreams…