Model-Predictive Control (MPC) of an Experimental SOFC Stack:
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G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a PowerPoint PPT Presentation


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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

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

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

  • The System

  • Basic MPC Theory

  • Our “HC-MPC” Formulation

  • Experimental Validation

  • Concluding Remarks


The system

The System

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 fluxI: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency


Outline of the talk1

Outline of the Talk

  • The System

  • Basic MPC Theory

  • Our “HC-MPC” Formulation

  • Experimental Validation

  • Concluding Remarks

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

πel: power demand η: efficiency


Basic mpc principles

Basic MPC Principles

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 fluxI: 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

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 fluxI: 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

  • MPC objective function

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

QP Transformation

nH2: H2 flux nO2: O2 fluxI: 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

  • 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 fluxI: 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

  • The System

  • Basic MPC Theory

  • Our “HC-MPC” Formulation

  • Experimental Validation

  • Concluding Remarks

nH2: H2 flux nO2: O2 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

ν=0.75

Ucell=0.79V

λ =4

λ =7

nH2: H2 flux nO2: O2 fluxI: 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

ν=0.75

Ucell=0.79V

λ =4

λ =7

nH2: H2 flux nO2: O2 fluxI: 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

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 fluxI: 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

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 fluxI: 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

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 fluxI: 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

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 fluxI: 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

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 fluxI: 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

ν=0.75

Ucell=0.79V

λ =4

λ =7

nH2: H2 flux nO2: O2 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

  • 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 fluxI: 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

  • The System

  • Basic MPC Theory

  • Our “HC-MPC” Formulation

  • Experimental Validation

  • Concluding Remarks

nH2: H2 flux nO2: O2 fluxI: 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

Standard MPC

HC-MPC

η≈ 38%

η≈ 42%

η≈ 42%

standard

HC

nH2: H2 flux nO2: O2 fluxI: 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

HC-MPC

η≈ 38%

η≈ 42%

η≈ 42%

standard

input region

expansion

input region

contraction

HC

nH2: H2 flux nO2: O2 fluxI: 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

  • The System

  • Basic MPC Theory

  • Our “HC-MPC” Formulation

  • Experimental Validation

  • Concluding Remarks

nH2: H2 flux nO2: O2 fluxI: 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

  • 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!

Questions?


Extra slides

Extra Slides


Experimental validation1

Experimental Validation

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

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


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