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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.

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Presentation on theme: "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."— Presentation transcript:

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 a, S. Diethelm b, A. Nakajo b, and D. Bonvin a 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 little control knowledge 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 Inputs  n H2 : H 2 flux  n O2 : O 2 flux  I: current Safety Constraints  U cell : cell potential  ν : fuel utilization  λ : air excess ratio Performance  π el : power demand  η : electrical efficiency FuelAir 79% N 2 21% O 2 Power Current 97% H 2 3% H 2 O Furnace 6-cell SOFC Stack n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency Control Objective Track the specified power demand while maximizing the efficiency and honoring the safety constraints.

6 Outline of the Talk The System Basic MPC Theory Our “HC-MPC” Formulation Experimental Validation Concluding Remarks n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency

7 Basic MPC Principles n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix π el (old) π el (new) t0t0 I = 0 A I = 30 A t0t0 ΔtΔt a1a1 a2a2 a3a3 a4a4 a5a5 a6a6 a7a7 a8a8 apap t 0 +pΔt B = f(a 1,…,a p )

8 Basic MPC Principles n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix π el (old) π el (new) t0t0 I = 0 A I = 30 A t0t0 ΔtΔt t 0 +pΔt B = f(a 1,…,a p ) t 0 +mΔt implement! (…then do it all again) π el = π el,0 + BΔI + d π el,0 d

9 MPC with Optimization MPC objective function  Constraints: U cell ≥ 0.79V, ν ≤ 0.75, 4 ≤ λ ≤ 7 n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix QP Transformation

10 MPC with Optimization MPC objective function  Constraints: U cell ≥ 0.79V, ν ≤ 0.75, 4 ≤ λ ≤ 7 n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix π el (low) π el (high) efficiency limited by ν efficiency limited by U cell π el (mid)

11 Outline of the Talk The System Basic MPC Theory Our “HC-MPC” Formulation Experimental Validation Concluding Remarks n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

12 The HC-MPC Formulation HC = “Hard Constraint” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix n H2 0 I n H2 = 3.14mL n H2 = 10.0mL I = 30A U cell = 0.79V ν = 0.75

13 The HC-MPC Formulation HC = “Hard Constraint” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix n H2 0 I n H2 = 3.14mL n H2 = 10.0mL I = 30A U cell = 0.79V ν = 0.75

14 The HC-MPC Formulation HC = “Hard Constraint” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix n H2 0 I n H2 = 3.14mL n H2 = 10.0mL I = 30A U cell = 0.79V ν = 0.75

15 The HC-MPC Formulation HC = “Hard Constraint” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix n H2 0 I n H2 = 3.14mL n H2 = 10.0mL I = 30A U cell = 0.79V ν = 0.75

16 The HC-MPC Formulation HC = “Hard Constraint” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix n H2 0 I n H2 = 3.14mL n H2 = 10.0mL I = 30A U cell = 0.79V ν = 0.75

17 The HC-MPC Formulation HC = “Hard Constraint” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix n H2 0 I n H2 = 3.14mL n H2 = 10.0mL I = 30A U cell = 0.79V ν = 0.75

18 The HC-MPC Formulation HC = “Hard Constraint” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix n H2 0 I n H2 = 3.14mL n H2 = 10.0mL I = 30A U cell = 0.79V ν = 0.75

19 The HC-MPC Formulation HC = “Hard Constraint” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix n H2 0 I n H2 = 3.14mL n H2 = 10.0mL I = 30A U cell = 0.79V ν = 0.75

20 The HC-MPC Formulation HC = “Hard Constraint” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix n H2 0 I n H2 = 3.14mL n H2 = 10.0mL I = 30A U cell = 0.79V ν = 0.75

21 The HC-MPC Formulation HC = “Hard Constraint” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix n H2 0 I n H2 = 3.14mL n H2 = 10.0mL I = 30A U cell = 0.79V ν = 0.75

22 The HC-MPC Formulation HC = “Hard Constraint” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix n H2 0 I n H2 = 3.14mL n H2 = 10.0mL I = 30A U cell = 0.79V ν = 0.75

23 The HC-MPC Formulation HC = “Hard Constraint” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix n H2 0 I n H2 = 3.14mL n H2 = 10.0mL I = 30A U cell = 0.79V ν = 0.75

24 The HC-MPC Formulation HC = “Hard Constraint” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix n H2 0 I n H2 = 3.14mL n H2 = 10.0mL I = 30A U cell = 0.79V ν = 0.75

25 The HC-MPC Formulation n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix λ = 4 λ = 7 ν = 0.75 U cell = 0.79V

26 The HC-MPC Formulation n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix λ = 4 λ = 7 ν = 0.75 U cell = 0.79V

27 The HC-MPC Formulation n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix λ = 4 λ = 7 ν = 0.75

28 The HC-MPC Formulation n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix λ = 4 λ = 7 ν = 0.75

29 The HC-MPC Formulation n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix λ = 4 λ = 7 ν = 0.75

30 The HC-MPC Formulation n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix λ = 4 λ = 7 ν = 0.75

31 The HC-MPC Formulation n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix λ = 4 λ = 7 ν = 0.75

32 The HC-MPC Formulation n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix λ = 4 λ = 7 ν = 0.75 U cell = 0.79V

33 Side-by-Side Standard MPC Issues  Weight Tuning Only partially intuitive Requires a good model Need validation  Active Constraint? Must know π el (mid) Degradation!  π el (mid) changes  Violations Norms are directionless Constraints are “soft” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : 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”

34 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) n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix Bias Filter α

35 Side-by-Side Standard MPC Issues  Weight Tuning Only partially intuitive Requires a good model Need validation  Active Constraint? Must know π el (mid) Degradation!  π el (mid) changes  Violations Norms are directionless Constraints are “soft” n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : 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”

36 Outline of the Talk The System Basic MPC Theory Our “HC-MPC” Formulation Experimental Validation Concluding Remarks n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

37 Experimental Validation n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix η ≈ 42% η ≈ 38% Standard MPCHC-MPC standard HC

38 n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix η ≈ 42% η ≈ 38% Standard MPCHC-MPC input region expansion input region contraction standard HC

39 Outline of the Talk The System Basic MPC Theory Our “HC-MPC” Formulation Experimental Validation Concluding Remarks n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : 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 n H2 : H 2 flux n O2 : O 2 flux I: current U cell : potential ν: fuel utilization λ: air ratio π el : power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

44


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