Feedbacks for Fluid Flows and Fusion Miroslav Krstic Department of Mechanical and Aerospace...
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Transcript of Feedbacks for Fluid Flows and Fusion Miroslav Krstic Department of Mechanical and Aerospace...
Feedbacks for Fluid Flows and Fusion
Miroslav KrsticDepartment of Mechanical and Aerospace Engineering
Feedbacks for Fluid Flows and Fusion
2
MAE Control Program
Control of Flows and Propulsion Systems:
• Tom Bewley• Bob Bitmead• Miroslav Krstic
Control of Structures:
• Bob Skelton (macro-structures, e.g., satellite
antennas)• Raymond de Callafon (micro-structures, HDD positioning)
Command and Control for Unmanned Aerial Vehicles:
• Bill McEneaney
3
Bluff Body Flow Control
Controlled
Uncontrolled
Ole Morten Aamo
4
Mixing Control in Channels and Pipes
ControlledControlled
UncontrolledUncontrolled
xPxPkxVxV P wallbottom walltop walltop wallbottom )()( Control law:
Pressure distribution
Andras Baloghand
Ole Morten Aamo
5
Jet Flow Control
tpKtUtU ,0)()( 21Controller:
Lawrence Yuan
6
Particle mixing with control
Controlled - heavy particles
Controlled - light particlesUncontrolled
Diffusive mixing
7
Tailored Fuel Injection for Pulsed Detonation Engines
(Aliseda, Ariyur, Lasheras, Krstic, and Williams)
Laser measurement of water droplets sprayed into a glass tube
1 2 3 4 5-0.06
-0.05
-0.04
-0.03
-0.02
1 2 3 4 51
2
3
4
5
6
7
8
time (PDE cycles)
α
u (control)
*α (desired equiv. ratio distribution)
Multivariable PI controller
Actuator valve array
COMBUSTION INSTABILITY CONTROLvia Extremum Seeking
EXTREMUM SEEKER
• Rayleigh criterion-based controllers, which use phase-shifted pressure measurements and fuel modulation, have emerged as prevalent
• The length of the phase needed varies with operating conditions. The tuning method must be non-model based.
phas
e
sin wt
Pressure
s
1 washout
filter
COMBUSTOR
Phase-ShiftingController
Frequency/amplitudeobserver
fuel
Problem Statement
• Tuning allows operation with minimum oscillations at lean conditions
• Reduced engine size, fuel consumption and NOx emissions
Impact
time
ext. seeking suppresses oscillations
Experimental Results (4MW combustor)
with UTRC
AXIAL FLOW COMPRESSOR CONTROLby Extremum Seeking
Problem Statement• Active controls for
rotating stall only reduce the stall oscillations but they do not bring them to zero nor do they maximize pressure rise.
• Extremum seeking to optimize compressor operating point.
CaltechCOMPRESSOR
Air Injection Stall Controller
Pressure rise
s
1 washoutfilter
sin wt
EXTREMUMSEEKER
bleed valve
• Smaller, lighter compressors; higher payload in aircraft
• Patent issued (August 2000)
Impact
H.-H. Wang
timeP
ress
ure
Ris
e
Experimental ResultsExtremum seeking stabilizes the maximum pressure rise.
10
Tokamak: Plasma electro-magnetically confined in a torus, to obtain nuclear fusion energy.
Densities (~1020 particles/m3) and temperatures (~108 K) must be achieved.
100
101
102
103
10-27
10-26
10-25
10-24
10-23
10-22
10-21
Energy (keV)
Rea
ctio
n R
ate
(m3 /s
ec)
D-T
Reactivity rate , vs T, for D-T mixturev Quenching P T
Excursion Thermal P T
Low Temperature – High Density Regime(economically attractive)
Reaction rate increases with temperature
Thermally Unstable
Eugenio Schuster, coadvised w/ George Tynan
Burn Instability Control in Tokamaks
11
Burn Instability
0 20 40 60 80 100 120 140 160 180 2000
5
10
15x 10
19
Time [sec]
Den
siti
es [
1/m
3 ]
n
nDT
nn
ne
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
30
35
Time [sec]
[%
] -
Tem
pera
ture
[ke
V]
T
Open loop desired equilibrium is unstable MHD stability conditions are violated
Active control is required for stabilization
Our approach: Nonlinear Model-Based Control
12
Model
Total Density
Electron Density enn
Reactivity Rate
Delay Confinement Time
D-T Confinement Time
Alpha Confinement Time
Energy Confinement Time EDTd
vIImpurity Confinement Time
vnn
dt
dn DT
2
2
Alpha Particles Balance Equation
Sn
dt
dn
nv
nn
dt
dn
d
nn
d
nDT
DT
DTDT
2
22
D-T and Neutral Particles Balance Equations
II
II Sn
dt
dn
Impurity Particles Balance Equation
auxradDT
E
PPQvnE
dt
dE
2
2
Energy Balance Equation
eIDTeiIIDTe nnnnnnnnTEnZnnn ,2
3 ,2
Impurity Density In
Fueling Rate
Auxiliary Power
Energy
Neutral Density
Deuterium-Tritium Density
Alpha Density
auxPE
nnDTnn
Impurity Injection ISS
13
Model
EIIEddEDTDTE
auxradDT
iPHITERE
kkkk
PPQvn
P
kPPABRIf
, , ,
2
082.02
47.047.019.05.015.06.102.190ITER Scaling:
Beta Limit
Delay Scaling Constant
Plasma Volume
D-T Scaling Constant
Elongation at
Alpha Scaling Constant
Magnetic Field
Minor Radius
Major Radius
Plasma Current
Impurity Scaling Constant
7k3DTk
1dk
%3.5
5.2lim
aBI
10Ik
MA 22Im 6R
m 15.2aT 85.4B
2.2k3m 1100V
4
63
52
4321exp TaTaTaTaa
T
av rDT Reactivity:
Radiation Losses: Bremsstrahlung (Ab) – Line (Al) – Recombination (Ar)
eIIrIIlIIDTbrad nTnZnATnZnATnZnnAP
23
621
421
2 64164
14
Simulation Results—Region of Stability
0 2 4 6 8 10 12 14 160
0.5
1
1.5
2
2.5
3
3.5
4x 10
20
T [keV]
n e [
m-3
]
Stab ilit y
Linear Pole PlacementLinear Rob ust Nonlinear Eq uilib rium Limit
15
Control of Temperature and Density Profiles
Goal: make the temperature and density converge to desired radial profiles.
• Burn Control• MHD Instability Avoidance• High-beta and High-confinement mode access • Confinement Time Improvement• Transport Reduction
Why control kinetic profiles?
Eugenio Schuster
16
Model
Density Balance Equation
SnVr
nDr
rrt
np
1
Energy Equation
auxbrem PPr
ErD
rrt
E
1
,5.0 ,
sec
0
3
2 2
r
T
T
DV
m
rn
nD p
1 , 22
e
iiieffeeffbbrem nZnZTnZAP
Boundary Conditions and Controls:
),( ,00
),( ,00
tank(a,t)r
n,t)(
r
n
taEk(a,t)r
E,t)(
r
E
n
E
rn
rE
17
Simulation Results
Closed Loop: Energy Profile Evolution Closed Loop: Density Profile Evolution
18
Control of Tokamak Vertical Stability
•Objective: plasma shape control and vertical stability control
•Actuators: poloidal coils
Eugenio Schuster, with Mike Walker and Dave Humphreys (General Atomics)
19
Saturation Anti-Windup Design
Experimental tests at GA
this year
DIII-DTOKAMAK
GA design
Loss of stability due to saturation!
20
Control of Magnetohydrodynamic Flows
•For drag management in hypersonic flight (re-entry vehicles and SCRAMJET propulsion).
•For liquid metal blankets in fusion reactors.
•Control possible using purely electrical actuators and sensors (rather than MicroElectroMechanicalSystems).
Eugenio Schuster
21
MHD Governing Equations
0
0
1
11
2
2
B
v
vBBBvB
BBvvvv
t
Pt
Navier-Stokes Equation
Incompressibility Condition
Magnetic Field Equation
Faraday’s Law
Ampere’s Law
Ohm’s Law
Magnetic Induction Equation
BEj
Bj
EB
v
t
ty conductivi electric:
ty permeabili magnetic:
viscositykinematic:
density mass:
22
Hartmann Flow
Actuators and sensors on the wall.0 0.1 0.2 0.3 0.4 0.5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
u
y
Velocity Profile - Perfectly Insulating Walls
Ha=0 Ha=2 Ha=5 Ha=10 Ha=100
23
Control Approach
Goal: minimize/maximize the cost functional
t
tdmtE
0 )(lim
Energy functional: dxdybbvuEd vu ,
1
1
0
2222 Bv
dxdy bbbb
R
R
dxdy vvuum
d vy
vx
uy
ux
m
d
yxyx
1
1
0
2222
1
1
0
2222
, BvDissipation functional:
mR
R Reynolds number Magnetic Re number
0
0
2wall ),(
LdxdttxB
Using the minimal amount of control energy
0
0
2wall ),(
Ldxdttxj
0
0
2wall ),(
LdxdttxV
24
Control Results (preliminary)
Pressure or electric potential distribution
Vwall or jwall
wall
zoom out
Velocity or current vectors
Inspired by: