Explicit Model Predictive Control of a Fuel Cell Deepak Ingole, J na - PowerPoint PPT Presentation

Explicit Model Predictive Control of a Fuel Cell Deepak Ingole, J´ na , Martin Kal´ uz, Martin Klauˇ co, an Drgoˇ Monika Bakoˇ sov´ a, Michal Kvasnica Faculty of Chemical and Food Technology Slovak University of Technology in Bratislava Slovakia September 12, 2016 Acknowledgment: The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the EU’s Seventh Framework Programme under REA grant agreement no 607957 (TEMPO). The Authors gratefully acknowledge the contribution of the Slovak Research and Development Agency under the project APVV 0551-11. Deepak Ingole (STU) September 12, 2016 1 / 22

Outline Fuel Cell 1 Experimental Set-up 2 PEM Fuel Cell Control 3 Fuel Cell Modeling 4 Experimental Results 5 Conclusions 6 Deepak Ingole (STU) eMPC of Fuel Cell September 12, 2016 2 / 22

Fuel Cell A device which converts the chemical energy from the fuel into electric energy through a chemical reaction Emits heat and pure water Operates like a battery Proton Exchange Membrane (PEM) Deepak Ingole (STU) Fuel Cell September 12, 2016 3 / 22

Fuel Cell Power System Night Day Consumers Solar Energy Battery Bank Oxygen Wind Energy Fuel Electrolyzer Cell Hydrogen Water Deepak Ingole (STU) Fuel Cell September 12, 2016 4 / 22

Applications of a PEM Fuel Cell Deepak Ingole (STU) Fuel Cell September 12, 2016 5 / 22

Motivation Properties of fuel cells Renewable source of energy Silent operation No pollution High Efficiency Consumer market Deepak Ingole (STU) Fuel Cell September 12, 2016 6 / 22

Motivation Properties of fuel cells Renewable source of energy Silent operation No pollution High Efficiency Consumer market Control of electrolyzer and fuel cell Deepak Ingole (STU) Fuel Cell September 12, 2016 6 / 22

Principle of a Fuel Cell , Load e − e − Fuel In Oxidant In H + O 2 H + H 2 H 2 O H + Water Out Anode Cathode Electrolyte Deepak Ingole (STU) Fuel Cell September 12, 2016 7 / 22

Principle of a Fuel Cell , Load e − e − Fuel In Oxidant In H + O 2 H + H 2 H 2 O H + Water Out Anode Cathode Electrolyte → 2 H + + 2 e − H 2 − − 1 2O 2 + 2 H + + 2 e − − → H 2 O − Deepak Ingole (STU) Fuel Cell September 12, 2016 7 / 22

Components of a Fuel Cell System Heat and Water Clean Exhaust Electricity Fuel Fuel Cell Power Hydrogen Fuel DC AC Processor Stack Converter Air Deepak Ingole (STU) Fuel Cell September 12, 2016 8 / 22

Experimental Set-up of a PEM Fuel Cell Host PC Output Data Monitor Electrolyzer FC Stack Input Data Monitor Tank Load Deepak Ingole (STU) Experimental Set-up September 12, 2016 9 / 22

PEM Fuel Cell Control Generate desired voltage from the fuel cell stack without violating the electrolyzers input voltage limits Challenges Electrolyzer and fuel cell dynamics Temperature and air flow High resistance at load side Small operating range of electrolyzers Control Model predictive control Disturbance modeling Deepak Ingole (STU) PEM Fuel Cell Control September 12, 2016 10 / 22

Implementation of a Real-time MPC Real-time MPC Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 11 / 22

Implementation of a Real-time MPC Plant Model Real-time MPC Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 11 / 22

Implementation of a Real-time MPC Plant Model Plant/Model Mismatch Real-time MPC Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 11 / 22

Implementation of a Real-time MPC Plant Model Plant/Model Mismatch MPC Design Real-time MPC Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 11 / 22

PEM Fuel Cell Modeling + V IN V OUT − Voltage Electrolyzer Hydrogen FC Stack Load Regulator Canister Fuel Cell Plant Input: Input voltage ( V IN ) Output: Output voltage ( V OUT ) Input Constraints: 1.8-2 . 12 V Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 12 / 22

Model Identification 1 . 92 Input Voltage [V] 1 . 9 1 . 88 1 . 86 0 100 200 300 400 500 600 700 800 900 Time [s] 2 Output Voltage [V] 1 . 8 1 . 6 1 . 4 1 . 2 0 100 200 300 400 500 600 700 800 900 Time [s] Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 13 / 22

Model Identification 1 . 92 Input Voltage [V] 1 . 9 1 . 88 1 . 86 0 100 200 300 400 500 600 700 800 900 Time [s] 2 Output Voltage [V] 1 . 8 1 . 6 1 . 4 1 . 2 0 100 200 300 400 500 600 700 800 900 Time [s] Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 13 / 22

Model Validation Model Order Fit To Estimated Data FPE MSE 3.9 × 10 − 5 3.9 × 10 − 5 1 95.6 % 2.4 × 10 − 5 2.3 × 10 − 5 2 96.5 % 2.3 × 10 − 5 2.2 × 10 − 5 3 96.6 % 2.2 × 10 − 5 2.1 × 10 − 5 4 96.7 % 2.1 × 10 − 5 2.0 × 10 − 5 5 96.8 % Identified fuel cell model: x k +1 = Ax k + Bu k y k = Cx k Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 14 / 22

Disturbance Modeling Sources of model/plant mismatch Temperature and air flow Data monitor Augmented design model x k +1 = Ax k + Bu k d k +1 = d k y k = Cx k + d k Luenberger observer � ˆ � � A � � ˆ � � B � x 0 x = + u k + L ( y m , k − ˆ y k ) ˆ ˆ d 0 I d 0 k +1 k � � ˆ � x � y k = ˆ C I ˆ d k Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 15 / 22

MPC Problem N − 1 � ( y k − y r ) T Q ( y k − y r ) + ∆ u T min k R ∆ u k u 0 ,..., u N − 1 k =0 s.t. x k +1 = Ax k + Bu k k = 0 , . . . , N − 1 y k = Cx k k = 0 , . . . , N − 1 ∆ u k = u k − u k − 1 k = 0 , . . . , N − 1 u k ∈ U k = 0 , . . . , N − 1 x 0 = x ( t ) Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 16 / 22

MPC Problem N − 1 � ( y k − y r ) T Q ( y k − y r ) + ∆ u T min k R ∆ u k u 0 ,..., u N − 1 k =0 s.t. x k +1 = Ax k + Bu k k = 0 , . . . , N − 1 y k = Cx k + d k k = 0 , . . . , N − 1 ∆ u k = u k − u k − 1 k = 0 , . . . , N − 1 u k ∈ U k = 0 , . . . , N − 1 d k +1 = d k k = 0 , . . . , N − 1 x 0 = ˆ x ( t ) d 0 = ˆ d ( t ) Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 16 / 22

Explicit MPC Optimization Problem (mpQP) Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 17 / 22

Explicit MPC Optimization Problem (mpQP) Off-line On-line Explicit Solution (Look-Up Table) x ( t ) , ˆ ˆ d ( t ) u ⋆ ( t ) Estimation Plant y ( t ) Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 17 / 22

Sequential Search u ⋆ ( x ) A 1 x ≤ b 1 A 2 x ≤ b 2 A 3 x ≤ b 3 A 4 x ≤ b 4 A 5 x ≤ b 5 A 6 x ≤ b 6 A 7 x ≤ b 7 R 1 R 2 R 3 R 4 R 5 R 6 R 7 x  F 1 x 0 + g 1 if x 0 ∈ R 1   .  . u ⋆ ( x ) = .   F 7 x 0 + g 7 if x 0 ∈ R 7  Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 18 / 22

Sequential Search u ⋆ ( x ) A 1 x ≤ b 1 A 2 x ≤ b 2 A 3 x ≤ b 3 A 4 x ≤ b 4 A 5 x ≤ b 5 A 6 x ≤ b 6 A 7 x ≤ b 7 R 1 R 2 R 3 R 4 R 5 R 6 R 7 x  F 1 x 0 + g 1 if x 0 ∈ R 1   .  . u ⋆ ( x ) = .   F 7 x 0 + g 7 if x 0 ∈ R 7  Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 18 / 22

Sequential Search u ⋆ ( x ) A 1 x ≤ b 1 A 2 x ≤ b 2 A 3 x ≤ b 3 A 4 x ≤ b 4 A 5 x ≤ b 5 A 6 x ≤ b 6 A 7 x ≤ b 7 R 1 R 2 R 3 R 4 R 5 R 6 R 7 x  F 1 x 0 + g 1 if x 0 ∈ R 1   .  . u ⋆ ( x ) = .   F 7 x 0 + g 7 if x 0 ∈ R 7  Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 18 / 22

Sequential Search u ⋆ ( x ) A 1 x ≤ b 1 A 2 x ≤ b 2 A 3 x ≤ b 3 A 4 x ≤ b 4 A 5 x ≤ b 5 A 6 x ≤ b 6 A 7 x ≤ b 7 R 1 R 2 R 3 R 4 R 5 R 6 R 7 x  F 1 x 0 + g 1 if x 0 ∈ R 1   .  . u ⋆ ( x ) = .   F 7 x 0 + g 7 if x 0 ∈ R 7  Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 18 / 22

Explicit MPC : Pros and Cons Pros � Simple implementation: small code, division-free � Predictable execution: exact worst-case runtime and memory � Verifiable performance: closed-loop stability, feasibility, and safety Cons � Only for small scale problems � Explicit solutions can be very complex � Reducing complexity requires scarifying performance Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 19 / 22

Implementation of a Explicit MPC Prediction horizon: 10 Number of regions: 519 u ⋆ ( x ) Computational time: 3.58 s x 1 x 2 Deepak Ingole (STU) Experimental Results September 12, 2016 20 / 22

Experimental Results 1 . 85 Output Voltage [V] 1 . 8 1 . 75 1 . 7 Reference 100 200 300 400 500 Lb/Ub 2 . 1 Input Voltage [V] 2 1 . 9 1 . 8 100 200 300 400 500 Time [s] Deepak Ingole (STU) Experimental Results September 12, 2016 21 / 22

Experimental Results 1 . 85 Output Voltage [V] 1 . 8 1 . 75 Reference 1 . 7 Output 100 200 300 400 500 Lb/Ub 2 . 1 Input Input Voltage [V] 2 1 . 9 1 . 8 100 200 300 400 500 Time [s] Deepak Ingole (STU) Experimental Results September 12, 2016 21 / 22

Conclusions Identification of fuel cell model Disturbance modeling Model predictive control design Verification of explicit MPC on fuel cell system Deepak Ingole (STU) Conclusions September 12, 2016 22 / 22