G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a
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Transcript of G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a
![Page 1: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/1.jpg)
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
![Page 2: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/2.jpg)
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.
![Page 3: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/3.jpg)
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.
![Page 4: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/4.jpg)
Outline of the Talk The System
Basic MPC Theory
Our “HC-MPC” Formulation
Experimental Validation
Concluding Remarks
![Page 5: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/5.jpg)
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:12
H 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.
![Page 6: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/6.jpg)
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
![Page 7: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/7.jpg)
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)
![Page 8: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/8.jpg)
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
![Page 9: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/9.jpg)
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 2
NmL 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 ΔIΔu HΔu c Δu
1,...,i p
![Page 10: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/10.jpg)
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)
![Page 11: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/11.jpg)
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
![Page 12: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/12.jpg)
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
![Page 13: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/13.jpg)
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
![Page 14: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/14.jpg)
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
![Page 15: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/15.jpg)
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
![Page 16: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/16.jpg)
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
![Page 17: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/17.jpg)
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
![Page 18: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/18.jpg)
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
![Page 19: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/19.jpg)
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
![Page 20: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/20.jpg)
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
![Page 21: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/21.jpg)
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
![Page 22: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/22.jpg)
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
![Page 23: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/23.jpg)
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
![Page 24: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/24.jpg)
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
![Page 25: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/25.jpg)
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
152025
3035
0
5
10
15
20
25
30
nO2nH2
I
λ = 4λ =
7
ν = 0.75
Ucell = 0.79V
![Page 26: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/26.jpg)
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
152025
3035
0
5
10
15
20
25
30
nO2nH2
I
λ = 4λ =
7
ν = 0.75
Ucell = 0.79V
![Page 27: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/27.jpg)
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
152025
3035
0
5
10
15
20
25
30
nO2nH2
I
λ = 4λ =
7
ν = 0.75
![Page 28: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/28.jpg)
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
152025
3035
0
5
10
15
20
25
30
nO2nH2
I
λ = 4λ =
7
ν = 0.75
![Page 29: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/29.jpg)
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
152025
3035
0
5
10
15
20
25
30
nO2nH2
I
λ = 4λ =
7
ν = 0.75
![Page 30: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/30.jpg)
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
152025
3035
0
5
10
15
20
25
30
nO2nH2
I
λ = 4λ =
7
ν = 0.75
![Page 31: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/31.jpg)
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
152025
3035
0
5
10
15
20
25
30
nO2nH2
I
λ = 4λ =
7
ν = 0.75
![Page 32: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/32.jpg)
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
152025
3035
0
5
10
15
20
25
30
nO2nH2
I
λ = 4λ =
7
ν = 0.75
Ucell = 0.79V
![Page 33: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/33.jpg)
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”
![Page 34: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/34.jpg)
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
tt
c
cc
tt
![Page 35: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/35.jpg)
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”
![Page 36: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/36.jpg)
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
![Page 37: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/37.jpg)
0 10 20 300.25
0.3
0.35
0.4
0.45
Time (min)
el
(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)
Flux
es (N
mL/
min
/cm
2 )
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)
el
(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)
Flux
es (N
mL/
min
/cm
2 )
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
![Page 38: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/38.jpg)
0 10 20 300.25
0.3
0.35
0.4
0.45
Time (min)
el
(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)
Flux
es (N
mL/
min
/cm
2 )
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)
el
(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)
Flux
es (N
mL/
min
/cm
2 )
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)
U cell (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)
U cell (V
)
input regionexpansion
input regioncontraction
standard
HC
![Page 39: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/39.jpg)
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
![Page 40: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/40.jpg)
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
![Page 41: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/41.jpg)
Thank You!
Questions?
![Page 42: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/42.jpg)
Extra Slides
![Page 43: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/43.jpg)
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)
U cell (V
)
![Page 44: G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a](https://reader035.fdocuments.in/reader035/viewer/2022062815/5681301e550346895d959d79/html5/thumbnails/44.jpg)