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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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slide1

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 flux I: 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 flux I: 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 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

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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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

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

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

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

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

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

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

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

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
  • 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
  • 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
  • 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
  • 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

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

slide38

Standard MPC

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
  • 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
  • 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?

experimental validation1
Experimental Validation

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

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