Post on 19-Jan-2016
Model-Predictive Control (MPC) of an Experimental SOFC Stack:
A Robust and Simple Controller for Safer Load Tracking
G.A. Bunina, Z. Wuilleminb, G. Françoisa,
S. Diethelmb, A. Nakajob, and D. Bonvina
a Laboratoire d’Automatique, EPFLb Laboratoire d’Énergétique Industrielle, EPFL
The Goal of This Talk
To demonstrate that the transient SOFC control problem can be handled very simply, yet robustly, while requiring little control knowledge and only a very basic model of the process.
The Goal of This Talk
To demonstrate that the transient SOFC control problem can be handled very simply, yet robustly, while requiring little control knowledge and only a very basic model of the process.
Outline of the Talk
The System
Basic MPC Theory
Our “HC-MPC” Formulation
Experimental Validation
Concluding Remarks
The System Inputs nH2: H2 flux
nO2: O2 flux I: current
Safety Constraints Ucell: cell potential ν: fuel utilization λ: air excess ratio
Performance πel: power demand η: electrical efficiency
FuelAir79% N2 21% O2
Power
Current
97% H2 3% H2O
Furnace
6-cellSOFCStack
2 2 2
Reaction:
1
2H O H O
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency
Control Objective
Track the specified power demand while maximizing the efficiency and honoring the safety constraints.
Outline of the Talk
The System
Basic MPC Theory
Our “HC-MPC” Formulation
Experimental Validation
Concluding Remarks
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency
Basic MPC Principles
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
πel (old)
πel (new)
t0
I = 0 A
I = 30 A
t0 Δt
a1a2
a3a4 a5 a6 a7 a8 ap
t0+pΔt
B = f(a1,…,ap)
Basic MPC Principles
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
πel (old)
πel (new)
t0
I = 0 A
I = 30 A
t0 Δt
t0+pΔt
B = f(a1,…,ap)
t0+mΔt
implement! (…then do it all again)
πel = πel ,0 + BΔI + d
πel,0
d
MPC with Optimization MPC objective function
Constraints: Ucell ≥ 0.79V, ν ≤ 0.75, 4 ≤ λ ≤ 7
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
2 2
2 22 2 2 2( ) ( ) ( )
el cell H OU n n IJ w w w w w w 2 2
newel el cell H Oπ π U .79 ν .75 Δn Δn ΔI
QP Transformation
2
2
2
T T
[ ]
, 2
,
,
1min
2NmL
s.t.: 3.14 1,...,min cm
4 2 7 1,...,
0A 30A
H i
O i
H i
i
n i p
ni p
n
I
H O2 2Δu Δn Δn ΔI
Δu HΔu c Δu
1,...,i p
MPC with Optimization MPC objective function
Constraints: Ucell ≥ 0.79V, ν ≤ 0.75, 4 ≤ λ ≤ 7
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
2 2
2 22 2 2 2( ) ( ) ( )
el cell H OU n n IJ w w w w w w 2 2
newel el cell H Oπ π U .79 ν .75 Δn Δn ΔI
πel (low)
πel (high)
efficiency limited by ν
efficiency limited by Ucell
0cellUw
0w πel (mid)
Outline of the Talk
The System
Basic MPC Theory
Our “HC-MPC” Formulation
Experimental Validation
Concluding Remarks
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
The HC-MPC Formulation HC = “Hard Constraint”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
nH20
InH2 = 3.14mL
nH2 = 10.0mL
I = 30A
Ucell = 0.79Vν = 0.75
The HC-MPC Formulation HC = “Hard Constraint”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
nH20
InH2 = 3.14mL
nH2 = 10.0mL
I = 30A
Ucell = 0.79Vν = 0.75
The HC-MPC Formulation HC = “Hard Constraint”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
nH20
InH2 = 3.14mL
nH2 = 10.0mL
I = 30A
Ucell = 0.79Vν = 0.75
The HC-MPC Formulation HC = “Hard Constraint”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
nH20
InH2 = 3.14mL
nH2 = 10.0mL
I = 30A
Ucell = 0.79Vν = 0.75
The HC-MPC Formulation HC = “Hard Constraint”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
nH20
InH2 = 3.14mL
nH2 = 10.0mL
I = 30A
Ucell = 0.79Vν = 0.75
The HC-MPC Formulation HC = “Hard Constraint”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
nH20
InH2 = 3.14mL
nH2 = 10.0mL
I = 30A
Ucell = 0.79Vν = 0.75
The HC-MPC Formulation HC = “Hard Constraint”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
nH20
InH2 = 3.14mL
nH2 = 10.0mL
I = 30A
Ucell = 0.79Vν = 0.75
The HC-MPC Formulation HC = “Hard Constraint”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
nH20
InH2 = 3.14mL
nH2 = 10.0mL
I = 30A
Ucell = 0.79Vν = 0.75
The HC-MPC Formulation HC = “Hard Constraint”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
nH20
InH2 = 3.14mL
nH2 = 10.0mL
I = 30A
Ucell = 0.79Vν = 0.75
The HC-MPC Formulation HC = “Hard Constraint”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
nH20
InH2 = 3.14mL
nH2 = 10.0mL
I = 30A
Ucell = 0.79Vν = 0.75
The HC-MPC Formulation HC = “Hard Constraint”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
nH20
InH2 = 3.14mL
nH2 = 10.0mL
I = 30A
Ucell = 0.79Vν = 0.75
The HC-MPC Formulation HC = “Hard Constraint”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
nH20
InH2 = 3.14mL
nH2 = 10.0mL
I = 30A
Ucell = 0.79Vν = 0.75
The HC-MPC Formulation HC = “Hard Constraint”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
nH20
InH2 = 3.14mL
nH2 = 10.0mL
I = 30A
Ucell = 0.79Vν = 0.75
The HC-MPC Formulation
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
4
6
8
10
510
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
Ucell = 0.79V
The HC-MPC Formulation
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
4
6
8
10
510
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
Ucell = 0.79V
The HC-MPC Formulation
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
4
6
8
10
510
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
The HC-MPC Formulation
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
4
6
8
10
510
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
The HC-MPC Formulation
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
4
6
8
10
510
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
The HC-MPC Formulation
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
4
6
8
10
510
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
The HC-MPC Formulation
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
4
6
8
10
510
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
The HC-MPC Formulation
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
4
6
8
10
510
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
Ucell = 0.79V
Side-by-Side Standard MPC Issues
Weight Tuning Only partially intuitive Requires a good model Need validation
Active Constraint? Must know πel (mid) Degradation!
πel (mid) changes
Violations Norms are directionless Constraints are “soft”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
HC-MPC Solutions Weight Tuning
Completely intuitive Practically no tuning Minimal validation
Active Constraint? ν kept active Degradation?
Doesn’t matter
Violations Inequalities have direction Constraints are “hard”
Intuitive Weight Scheme Sufficient to normalize
weights into 3 categories High Priority (w = 10)
e.g.: power demand Standard Priority (w = 1.0)
e.g.: efficiency (tracking active constraint)
Low Priority (w = 0.1) e.g.: penalties on input
moves (controller behavior)
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
Bias Filter α
1 (1 )
: convergence
criterion (0 to 1)
: sampling time
: time to converge
c
t
t
c
c
c
t
t
Side-by-Side Standard MPC Issues
Weight Tuning Only partially intuitive Requires a good model Need validation
Active Constraint? Must know πel (mid) Degradation!
πel (mid) changes
Violations Norms are directionless Constraints are “soft”
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
HC-MPC Solutions Weight Tuning
Completely intuitive Practically no tuning Minimal validation
Active Constraint? ν kept active Degradation?
Doesn’t matter
Violations Inequalities have direction Constraints are “hard”
Outline of the Talk
The System
Basic MPC Theory
Our “HC-MPC” Formulation
Experimental Validation
Concluding Remarks
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
0 10 20 300.25
0.3
0.35
0.4
0.45
Time (min)
e
l(W/c
m2)
0 10 20 3015
20
25
30
Time (min)
I (A
)
0 10 20 300.6
0.65
0.7
0.75
0.8
Time (min)
0 10 20 300
5
10
15
Time (min)
Flu
xes
(Nm
L/m
in/c
m2)
0 10 20 3035
40
45
50
55
Time (min)
0 10 20 300.75
0.8
0.85
Time (min)
Uce
ll (V)
H2
air
Experimental Validation
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
η ≈ 42%
η ≈ 42%
η ≈ 38%
0 10 20 300.25
0.3
0.35
0.4
0.45
Time (min)
e
l(W/c
m2)
0 10 20 3015
20
25
30
Time (min)
I (A
)
0 10 20 300.6
0.65
0.7
0.75
0.8
Time (min)
0 10 20 300
5
10
15
Time (min)
Flu
xes
(Nm
L/m
in/c
m2)
0 10 20 3035
40
45
50
55
Time (min)
0 10 20 300.75
0.8
0.85
Time (min)
Uce
ll (V)
H2
air
Standard MPC HC-MPC
0 10 20 300.6
0.62
0.64
0.66
0.68
0.7
0.72
0.74
0.76
0.78
0.8
Time (min)
0 10 20 300.6
0.62
0.64
0.66
0.68
0.7
0.72
0.74
0.76
0.78
0.8
Time (min)
standard
HC
0 10 20 300.25
0.3
0.35
0.4
0.45
Time (min)
e
l(W/c
m2)
0 10 20 3015
20
25
30
Time (min)
I (A
)
0 10 20 300.6
0.65
0.7
0.75
0.8
Time (min)
0 10 20 300
5
10
15
Time (min)
Flu
xes
(Nm
L/m
in/c
m2)
0 10 20 3035
40
45
50
55
Time (min)
0 10 20 300.75
0.8
0.85
Time (min)
Uce
ll (V)
H2
air
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
η ≈ 42%
η ≈ 42%
η ≈ 38%
0 10 20 300.25
0.3
0.35
0.4
0.45
Time (min)
e
l(W/c
m2)
0 10 20 3015
20
25
30
Time (min)
I (A
)
0 10 20 300.6
0.65
0.7
0.75
0.8
Time (min)
0 10 20 300
5
10
15
Time (min)
Flu
xes
(Nm
L/m
in/c
m2)
0 10 20 3035
40
45
50
55
Time (min)
0 10 20 300.75
0.8
0.85
Time (min)
Uce
ll (V)
H2
air
Standard MPC HC-MPC
0 10 20 300.6
0.62
0.64
0.66
0.68
0.7
0.72
0.74
0.76
0.78
0.8
Time (min)
0 10 20 300.6
0.62
0.64
0.66
0.68
0.7
0.72
0.74
0.76
0.78
0.8
Time (min)
0 10 20 300.75
0.76
0.77
0.78
0.79
0.8
0.81
0.82
0.83
0.84
0.85
Time (min)
Uce
ll (V
)
0 10 20 300.75
0.76
0.77
0.78
0.79
0.8
0.81
0.82
0.83
0.84
0.85
Time (min)
Uce
ll (V
)
input regionexpansion
input regioncontraction
standard
HC
Outline of the Talk
The System
Basic MPC Theory
Our “HC-MPC” Formulation
Experimental Validation
Concluding Remarks
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
Concluding Remarks The proposed HC-MPC is very effective as it:
does NOT require a good model only four experimental step responses were used here
has only one decision variable for tuning which is very intuitive
minimizes oscillatory behavior and overshoot Potential Applications
The above should hold for more complex systems + gas turbine + steam reforming + heat-load following
Thank You!
Questions?
Extra Slides
Experimental Validation
nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratioπel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix
0 5 10 15 20 25 30 35 40 45 50 55 600.29
0.3
0.31
0.32
0.33
0.34
0.35
0.36
Time (min)
el(W
/cm2
)
0 5 10 15 20 25 30 35 40 45 50 55 600.6
0.62
0.64
0.66
0.68
0.7
0.72
0.74
0.76
0.78
0.8
Time (min)
0 5 10 15 20 25 30 35 40 45 50 55 600.75
0.76
0.77
0.78
0.79
0.8
0.81
0.82
0.83
0.84
0.85
Time (min)
Ucell (V
)