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

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

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Explicit Model Predictive Control of a Fuel Cell Deepak Ingole, J na , Martin Kal uz, Martin Klau co, an Drgo Monika Bako sov a, Michal Kvasnica Faculty of Chemical and Food Technology Slovak University of Technology in

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SLIDE 1

Explicit Model Predictive Control of a Fuel Cell

Deepak Ingole, J´ an Drgoˇ na, Martin Kal´ uz, Martin Klauˇ co, 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

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SLIDE 2

Outline

1

Fuel Cell

2

Experimental Set-up

3

PEM Fuel Cell Control

4

Fuel Cell Modeling

5

Experimental Results

6

Conclusions

Deepak Ingole (STU) eMPC of Fuel Cell September 12, 2016 2 / 22

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SLIDE 3

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

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SLIDE 4

Fuel Cell Power System

Day Night Solar Energy Wind Energy Battery Bank Electrolyzer Water Hydrogen Oxygen Consumers Fuel Cell

Deepak Ingole (STU) Fuel Cell September 12, 2016 4 / 22

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SLIDE 5

Applications of a PEM Fuel Cell

Deepak Ingole (STU) Fuel Cell September 12, 2016 5 / 22

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SLIDE 6

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

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SLIDE 7

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

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SLIDE 8

Principle of a Fuel Cell

,

Fuel In Anode Cathode Electrolyte Load Oxidant In Water Out

H2 H+ H+ H+ e− e− O2 H2O Deepak Ingole (STU) Fuel Cell September 12, 2016 7 / 22

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SLIDE 9

Principle of a Fuel Cell

,

Fuel In Anode Cathode Electrolyte Load Oxidant In Water Out

H2 H+ H+ H+ e− e− O2 H2O

H2 − − → 2 H+ + 2 e− 1 2O2 + 2 H+ + 2 e− − − → H2O

Deepak Ingole (STU) Fuel Cell September 12, 2016 7 / 22

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SLIDE 10

Components of a Fuel Cell System

Fuel Fuel Processor Hydrogen Fuel Cell Stack Air DC AC Electricity Clean Exhaust Heat and Water Power Converter

Deepak Ingole (STU) Fuel Cell September 12, 2016 8 / 22

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SLIDE 11

Experimental Set-up of a PEM Fuel Cell

Host PC Electrolyzer Input Data Monitor Tank Load FC Stack Output Data Monitor

Deepak Ingole (STU) Experimental Set-up September 12, 2016 9 / 22

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SLIDE 12

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

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SLIDE 13

Implementation of a Real-time MPC

Real-time MPC

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 11 / 22

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SLIDE 14

Implementation of a Real-time MPC

Plant Model Real-time MPC

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 11 / 22

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SLIDE 15

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

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SLIDE 16

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

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SLIDE 17

PEM Fuel Cell Modeling

VOUT Voltage Regulator VIN FC Stack Load Electrolyzer Canister + − Fuel Cell Plant Hydrogen

Input: Input voltage (VIN) Output: Output voltage (VOUT) Input Constraints: 1.8-2.12 V

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 12 / 22

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SLIDE 18

Model Identification

100 200 300 400 500 600 700 800 900 1.86 1.88 1.9 1.92 Time [s] Input Voltage [V] 100 200 300 400 500 600 700 800 900 1.2 1.4 1.6 1.8 2 Time [s] Output Voltage [V]

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 13 / 22

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SLIDE 19

Model Identification

100 200 300 400 500 600 700 800 900 1.86 1.88 1.9 1.92 Time [s] Input Voltage [V] 100 200 300 400 500 600 700 800 900 1.2 1.4 1.6 1.8 2 Time [s] Output Voltage [V]

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 13 / 22

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SLIDE 20

Model Validation

Model Order Fit To Estimated Data FPE MSE 1 95.6 % 3.9×10−5 3.9×10−5 2 96.5 % 2.4×10−5 2.3×10−5 3 96.6 % 2.3×10−5 2.2×10−5 4 96.7 % 2.2×10−5 2.1×10−5 5 96.8 % 2.1×10−5 2.0×10−5 Identified fuel cell model: xk+1 = Axk + Buk yk = Cxk

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 14 / 22

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SLIDE 21

Disturbance Modeling

Sources of model/plant mismatch

Temperature and air flow Data monitor

Augmented design model xk+1 = Axk + Buk dk+1 = dk yk = Cxk + dk Luenberger observer ˆ x ˆ d

  • k+1

= A I ˆ x ˆ d

  • k

+ B

  • uk + L (ym,k − ˆ

yk) ˆ yk =

  • C

I ˆ x ˆ d

  • k

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 15 / 22

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SLIDE 22

MPC Problem

min

u0,...,uN−1 N−1

  • k=0

(yk − yr)TQ(yk − yr) + ∆uT

k R∆uk

s.t. xk+1 = Axk + Buk k = 0, . . . , N − 1 yk = Cxk k = 0, . . . , N − 1 ∆uk = uk − uk−1 k = 0, . . . , N − 1 uk ∈ U k = 0, . . . , N − 1 x0 = x(t)

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 16 / 22

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SLIDE 23

MPC Problem

min

u0,...,uN−1 N−1

  • k=0

(yk − yr)TQ(yk − yr) + ∆uT

k R∆uk

s.t. xk+1 = Axk + Buk k = 0, . . . , N − 1 yk = Cxk + dk k = 0, . . . , N − 1 ∆uk = uk − uk−1 k = 0, . . . , N − 1 uk ∈ U k = 0, . . . , N − 1 dk+1 = dk k = 0, . . . , N − 1 x0 = ˆ x(t) d0 = ˆ d(t)

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 16 / 22

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SLIDE 24

Explicit MPC

Optimization Problem (mpQP)

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 17 / 22

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Explicit MPC

Optimization Problem (mpQP) Explicit Solution (Look-Up Table) Estimation Off-line On-line Plant u⋆(t) y(t) ˆ x(t), ˆ d(t)

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 17 / 22

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SLIDE 26

Sequential Search

u⋆(x) x R3 R4 R5 R6 R7 R2 R1 A1x ≤ b1 A2x ≤ b2 A3x ≤ b3 A4x ≤ b4 A5x ≤ b5 A6x ≤ b6 A7x ≤ b7

u⋆(x) =        F1x0 + g1 if x0 ∈ R1 . . . F7x0 + g7 if x0 ∈ R7

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 18 / 22

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SLIDE 27

Sequential Search

u⋆(x) x R3 R4 R5 R6 R7 R2 R1 A1x ≤ b1 A2x ≤ b2 A3x ≤ b3 A4x ≤ b4 A5x ≤ b5 A6x ≤ b6 A7x ≤ b7

u⋆(x) =        F1x0 + g1 if x0 ∈ R1 . . . F7x0 + g7 if x0 ∈ R7

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 18 / 22

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SLIDE 28

Sequential Search

u⋆(x) x R3 R4 R5 R6 R7 R2 R1 A1x ≤ b1 A2x ≤ b2 A3x ≤ b3 A4x ≤ b4 A5x ≤ b5 A6x ≤ b6 A7x ≤ b7

u⋆(x) =        F1x0 + g1 if x0 ∈ R1 . . . F7x0 + g7 if x0 ∈ R7

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 18 / 22

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SLIDE 29

Sequential Search

u⋆(x) x R3 R4 R5 R6 R7 R2 R1 A1x ≤ b1 A2x ≤ b2 A3x ≤ b3 A4x ≤ b4 A5x ≤ b5 A6x ≤ b6 A7x ≤ b7

u⋆(x) =        F1x0 + g1 if x0 ∈ R1 . . . F7x0 + g7 if x0 ∈ R7

Deepak Ingole (STU) Fuel Cell Modeling September 12, 2016 18 / 22

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SLIDE 30

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

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SLIDE 31

Implementation of a Explicit MPC

Prediction horizon: 10 Number of regions: 519 Computational time: 3.58 s

u⋆(x) x2 x1

Deepak Ingole (STU) Experimental Results September 12, 2016 20 / 22

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SLIDE 32

Experimental Results

100 200 300 400 500 1.7 1.75 1.8 1.85 Output Voltage [V] Reference 100 200 300 400 500 1.8 1.9 2 2.1 Time [s] Input Voltage [V] Lb/Ub

Deepak Ingole (STU) Experimental Results September 12, 2016 21 / 22

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SLIDE 33

Experimental Results

100 200 300 400 500 1.7 1.75 1.8 1.85 Output Voltage [V] Reference Output 100 200 300 400 500 1.8 1.9 2 2.1 Time [s] Input Voltage [V] Lb/Ub Input

Deepak Ingole (STU) Experimental Results September 12, 2016 21 / 22

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SLIDE 34

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