explicit model predictive control of a fuel celldrgona/files/presentation/eucco_fuell_cell.pdf ·...

Explicit Model Predictive Control of a Fuel Cell

Deepak Ingole, Jan Drgona, Martin Kaluz, Martin Klauco,Monika Bakosova, Michal Kvasnica

Faculty of Chemical and Food TechnologySlovak University of Technology in Bratislava

Slovakia

September 12, 2016

Acknowledgment: The research leading to these results has received funding from the People Programme (Marie CurieActions) of the EU’s Seventh Framework Programme under REA grant agreement no 607957 (TEMPO). The Authors gratefullyacknowledge the contribution of the Slovak Research and Development Agency under the project APVV 0551-11.

Deepak Ingole (STU) September 12, 2016 1 / 22

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

Fuel Cell

A device which converts the chemical energy from the fuel intoelectric 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

Day Night

Solar Energy

Wind Energy

Battery Bank

Electrolyzer

Water

Hydrogen

Oxygen

Consumers

FuelCell


Applications of a PEM Fuel Cell


Motivation

Properties of fuel cells

Renewable source of energySilent operationNo pollutionHigh EfficiencyConsumer market


Motivation

Properties of fuel cells

Renewable source of energySilent operationNo pollutionHigh EfficiencyConsumer market

Control of electrolyzer and fuel cell


Principle of a Fuel Cell

,

Fuel In

Anode CathodeElectrolyte

Load

Oxidant In

Water Out

H2

H+

H+

H+

e− e−

O2

H2O


Principle of a Fuel Cell

,

Fuel In

Anode CathodeElectrolyte

Load

Oxidant In

Water Out

H2

H+

H+

H+

e− e−

O2

H2O

H2 −−→ 2H+ + 2 e

−

1

2O2 + 2H

+ + 2 e−

−−→ H2O


Components of a Fuel Cell System

FuelFuel

ProcessorHydrogen

Fuel CellStack

Air

DC AC

Electricity

Clean Exhaust

Heat and Water

PowerConverter


Experimental Set-up of a PEM Fuel Cell

Host PC

Electrolyzer

Input DataMonitor

Tank Load

FC Stack

Output DataMonitor

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 theelectrolyzers input voltage limits

Challenges

Electrolyzer and fuel cell dynamicsTemperature and air flowHigh resistance at load sideSmall operating range of electrolyzers

Control

Model predictive controlDisturbance 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


Plant Model Real-time MPC



Plant Model Plant/Model Mismatch Real-time MPC



Plant Model Plant/Model Mismatch MPC Design Real-time MPC


PEM Fuel Cell Modeling

VOUT

VoltageRegulator

VIN

FC Stack LoadElectrolyzerCanister

+

−

Fuel Cell Plant

Hydrogen

Input: Input voltage (VIN)

Output: Output voltage (VOUT)

Input Constraints: 1.8-2.12 V


Model Identification

0 100 200 300 400 500 600 700 800 900

1.86

1.88

1.9

1.92

Time [s]

InputVoltage

[V]

0 100 200 300 400 500 600 700 800 900

1.2

1.4

1.6

1.8

2

Time [s]

OutputVoltage

[V]


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


Disturbance Modeling

Sources of model/plant mismatch

Temperature and air flowData monitor

Augmented design model

xk+1 = Axk + Buk

dk+1 = dk

yk = Cxk + dk

Luenberger observer

[

x

d

]

k+1

=

[

A 00 I

] [

x

d

]

k

+

[

B

0

]

uk + L (ym,k − yk)

yk =[

C I]

[

x

d

]

k


MPC Problem

minu0,...,uN−1

N−1∑

k=0

(yk − yr )TQ(yk − yr ) + ∆uTk 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)


MPC Problem

minu0,...,uN−1

N−1∑

k=0

(yk − yr )TQ(yk − yr ) + ∆uTk 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 = x(t)

d0 = d(t)


Explicit MPC

Optimization

Problem (mpQP)


Explicit MPC

Optimization

Problem (mpQP)

Explicit Solution

(Look-Up Table)

Estimation

Off-line

On-line

Plant

u⋆(t)

y(t)

x(t), d(t)


Sequential Search

u⋆(x)

x

R3 R4 R5 R6 R7R2R1

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


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


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

Experimental Results

100 200 300 400 500

1.7

1.75

1.8

1.85

OutputVoltage

[V]

Reference

100 200 300 400 5001.8

1.9

2

2.1

Time [s]

InputVoltage

[V]

Lb/Ub


Experimental Results

100 200 300 400 500

1.7

1.75

1.8

1.85

OutputVoltage

[V]

ReferenceOutput

100 200 300 400 5001.8

1.9

2

2.1

Time [s]

InputVoltage

[V]

Lb/UbInput


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

explicit model predictive control of a fuel celldrgona/files/presentation/eucco_fuell_cell.pdf ·...

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