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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 b Laboratoire d’Énergétique Industrielle, EPFL

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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.

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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.

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

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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.

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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

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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 )

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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

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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

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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)

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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”

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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

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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”

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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

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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

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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

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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

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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

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Thank You! Questions?

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Extra Slides

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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

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