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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 a , S. Diethelm b , A. Nakajo b , and D. Bonvin a a Laboratoire d’Automatique, EPFL

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G a bunin a z wuillemin b g fran ois a s diethelm b a nakajo b and d bonvin a

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, EPFL

b Laboratoire d’Énergétique Industrielle, EPFL


The goal of this talk
The Goal of This Talk Stack:

To demonstrate that the transient SOFC control problem can be handled very simply, yet robustly, while requiring littlecontrolknowledge and only a very basic model of the process.


The goal of this talk1
The Goal of This Talk Stack:

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
Outline of the Talk Stack:

  • The System

  • Basic MPC Theory

  • Our “HC-MPC” Formulation

  • Experimental Validation

  • Concluding Remarks


The system
The System Stack:

79% N2 21% O2

97% H2 3% H2O

Air

Fuel

  • Inputs

    • nH2: H2 flux

    • nO2: O2 flux

    • I: current

  • Safety Constraints

    • Ucell: cellpotential

    • ν: fuel utilization

    • λ: air excess ratio

  • Performance

    • πel: power demand

    • η: electrical efficiency

Control Objective

Track the specified power demand while maximizing the efficiency and honoring the safety constraints.

6-cell

SOFC

Stack

Power

Furnace

Current

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency


Outline of the talk1
Outline of the Talk Stack:

  • The System

  • Basic MPC Theory

  • Our “HC-MPC” Formulation

  • Experimental Validation

  • Concluding Remarks

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency


Basic mpc principles
Basic MPC Principles Stack:

B = f(a1,…,ap)

πel(new)

a5

a6

a7

a8

ap

a4

a3

a2

a1

πel(old)

t0+pΔt

t0

I = 30 A

I = 0A

t0

Δt

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


Basic mpc principles1
Basic MPC Principles Stack:

πel=πel ,0 + BΔI + d

B = f(a1,…,ap)

πel(new)

d

πel,0

πel(old)

t0+pΔt

t0

I = 30 A

implement! (…then do it all again)

I = 0A

t0+mΔt

t0

Δt

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


Mpc with optimization
MPC with Optimization Stack:

  • MPC objective function

    • Constraints: Ucell ≥ 0.79V, ν≤ 0.75, 4 ≤ λ ≤ 7

QP Transformation

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


Mpc with optimization1
MPC with Optimization Stack:

  • MPC objective function

    • Constraints: Ucell ≥ 0.79V, ν≤ 0.75, 4 ≤ λ ≤ 7

πel(high)

efficiency limited by Ucell

πel(mid)

efficiency limited by ν

πel(low)

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


Outline of the talk2
Outline of the Talk Stack:

  • The System

  • Basic MPC Theory

  • Our “HC-MPC” Formulation

  • Experimental Validation

  • Concluding Remarks

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation
The HC-MPC Formulation Stack:

  • HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation1
The HC-MPC Formulation Stack:

  • HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation2
The HC-MPC Formulation Stack:

  • HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation3
The HC-MPC Formulation Stack:

  • HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation4
The HC-MPC Formulation Stack:

  • HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation5
The HC-MPC Formulation Stack:

  • HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation6
The HC-MPC Formulation Stack:

  • HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation7
The HC-MPC Formulation Stack:

  • HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation8
The HC-MPC Formulation Stack:

  • HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation9
The HC-MPC Formulation Stack:

  • HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation10
The HC-MPC Formulation Stack:

  • HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation11
The HC-MPC Formulation Stack:

  • HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation12
The HC-MPC Formulation Stack:

  • HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation13
The HC-MPC Formulation Stack:

ν=0.75

Ucell=0.79V

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation14
The HC-MPC Formulation Stack:

ν=0.75

Ucell=0.79V

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation15
The HC-MPC Formulation Stack:

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation16
The HC-MPC Formulation Stack:

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation17
The HC-MPC Formulation Stack:

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation18
The HC-MPC Formulation Stack:

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation19
The HC-MPC Formulation Stack:

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


The hc mpc formulation20
The HC-MPC Formulation Stack:

ν=0.75

Ucell=0.79V

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


Side by side
Side-by-Side Stack:

  • 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”

  • 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: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


Intuitive weight scheme
Intuitive Weight Scheme Stack:

  • Bias Filter α

  • 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: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


Side by side1
Side-by-Side Stack:

  • 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”

  • 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: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


Outline of the talk3
Outline of the Talk Stack:

  • The System

  • Basic MPC Theory

  • Our “HC-MPC” Formulation

  • Experimental Validation

  • Concluding Remarks

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


Experimental validation
Experimental Validation Stack:

Standard MPC

HC-MPC

η≈ 38%

η≈ 42%

η≈ 42%

standard

HC

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


G a bunin a z wuillemin b g fran ois a s diethelm b a nakajo b and d bonvin a

Standard MPC Stack:

HC-MPC

η≈ 38%

η≈ 42%

η≈ 42%

standard

input region

expansion

input region

contraction

HC

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


Outline of the talk4
Outline of the Talk Stack:

  • The System

  • Basic MPC Theory

  • Our “HC-MPC” Formulation

  • Experimental Validation

  • Concluding Remarks

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix


Concluding remarks
Concluding Remarks Stack:

  • 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

Thank You! Stack:

Questions?


Extra slides

Extra Slides Stack:


Experimental validation1
Experimental Validation Stack:

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix