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G.A. Bunin a , Z. Wuillemin b , G. François 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. 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. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a

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  1. 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

  2. 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.

  3. 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.

  4. Outline of the Talk • The System • Basic MPC Theory • Our “HC-MPC” Formulation • Experimental Validation • Concluding Remarks

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

  35. 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

  36. 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

  37. 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

  38. 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

  39. 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

  40. 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

  41. Thank You! Questions?

  42. Extra Slides

  43. 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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