model-predictive control (mpc) of an experimental sofc stack: a robust and simple controller for...
TRANSCRIPT
![Page 1: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/html5/thumbnails/4.jpg)
Outline of the Talk
The System
Basic MPC Theory
Our “HC-MPC” Formulation
Experimental Validation
Concluding Remarks
![Page 5: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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:
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.
![Page 6: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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
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
![Page 10: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
Ucell = 0.79V
![Page 26: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
Ucell = 0.79V
![Page 27: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
![Page 28: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
![Page 29: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
![Page 30: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
![Page 31: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
![Page 32: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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
1520
2530
35
0
5
10
15
20
25
30
nO2
nH2
I
λ = 4λ =
7
ν = 0.75
Ucell = 0.79V
![Page 33: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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
t
t
c
c
c
t
t
![Page 35: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/html5/thumbnails/37.jpg)
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
![Page 38: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/html5/thumbnails/38.jpg)
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
![Page 39: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/html5/thumbnails/41.jpg)
Thank You!
Questions?
![Page 42: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/html5/thumbnails/42.jpg)
Extra Slides
![Page 43: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/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)
Ucell (V
)
![Page 44: Model-Predictive Control (MPC) of an Experimental SOFC Stack: A Robust and Simple Controller for Safer Load Tracking G.A. Bunin a, Z. Wuillemin b, G. François](https://reader035.vdocument.in/reader035/viewer/2022062315/56649c7e5503460f94933739/html5/thumbnails/44.jpg)