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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…