Reduced Order Modeling Enables System Level Simulation of ... · Reduced Order Modeling Enables System Level Simulation of a MEMS Piezoelectric Energy Harvester with a Self-Supplied

Reduced Order Modeling Enables System Level Simulation of a MEMS Piezoelectric Energy Harvester

with a Self-Supplied SSHI-Scheme

F. Sayed1, D. Hohlfeld², T. Bechtold1

1Institute for Microsystems Engineering, Freiburg University, Germany²Reutlingen University, Germany

- 2 -

Outline

Introduction

MEMS Piezoelectric Energy Harvester

Finite Element Model

Reduced Order Model

Power Extraction Techniques

Results and Discussion

Conclusion and Future Work

- 3 -

Outline

Introduction



Reduced Order Model




How to supply all these sensors with energy ?

4

plant monitoring

buildingautomation

© Honeywell

automotive

© Khulsey

deep space probes

Just wire them ...?

You need to install power plugs wiring retrofit cost 100 $ / meter

Wiring complexity

© FlightCommander

© Porsche AG

3 km cables 500+ km cables

- 5 -

Use batteries, but ...

Limited lifetime

Maintenance costsReplacement, recharging, recycling

Environmental effects

© Prof. Woias

thou

sand

tons

only 30 % recycled

remaining 70 % get dumped or burned

- 6 -

Wireless Autonomous Transducer Solution (WATS)

7

thermal, RF, vibrational, light harvesting

Radio20 µW

µ-Contr.20 µW

DSP20 µW

Sensor frontend(ASIC) 20 µW

Sensor20 µW

Micropower module -100 µW

ElectrostaticElectro-magneticPiezoelectric

Thermal PhotovoltaicRF Vibration

use MEMS to provide 100 µW / cm2

to power wireless autonomous systemsVision:

- 8 -

Piezoelectric Material

- 9 -

Coupling modes

Transversal

Piezoelectric Energy Harvester

Transformer represent mechanical and electrical coupling

vibration acceleration

L internal mass

C mechanical stiffness

R the energy lost

09.04.2013 - 10 -

Circuit model of a piezoelectric harvester

Outline

Introduction


1st and 2nd generation designs


Reduced Order Model

Power Enhancement Techniques



09.04.2013 - 11 -

Outline

Energy harvesting context - The vision

Piezoelectric harvestingFabrication, results, applicationModeling

Multifrequency harvestingMotivation for frequency agilityDesign implementations

- 12 -

Piezoelectric energy harvester 1st generation design (single mode)

harvester fabrication on silicon wafer with glass cappingMicromechanical resonatorDRIE-based structuring of SOI substratesAlN and PZT as piezoelectric material

seismicmass

beam

harvestingcapacitor

vibration

- 13 -

Power delivery results1st generation design (non-packaged)

40 µW @ 1.65 kHz 60 µW @ 572 Hz60

50

40

30

20

10

0

585580575570565frequency / Hz

2.0 g 1.0 g 0.5 g 0.25 g

60

50

40

30

20

10

0

1022 4 6

1032 4 6

1042 4 6

105

load resistance /

2.0 g 1.0 g 0.50 g 0.25 g

beam width: 5 mm, device length: 6 mm, mass: 34 mg, load ~ 400 k , Q ~ 150JMM 19(9), (2009)

2005

PZT (lead circonate titanate)

fabricated by sol-gel

2008

AlN (aluminum nitride)

sputtered

- 14 -

Wafer-scale fabrication and packaging

150 mm SOI substrates

Wafer-scale encapsulation between glass substrates

Hermeticity to be improved

- 15 -

Power delivery results1st generation design (packaged)

Vacuum packaged

Max. excitation 1.8 g (mass impact on cap)

device width: 7 mm, mass length: 7 mm, mass: 75 mg, load ~ 500 k , Q ~ 400, max. displ. 600 um @ 1.8 g

0.01

0.1

1

10

100

1000

585580575570565560frequency / Hz

excitation / g 1.80 1.28 0.64 0.32 0.16 0.08

0.01

0.1

1

10

100

1000

585580575570565560frequency / Hz

excitation / g 1.80 1.28 0.64 0.32 0.16 0.08

0.01

0.1

1

10

100

1000

585580575570565560frequency / Hz

excitation / g 1.80 1.28 0.64 0.32 0.16 0.08

0.01

0.1

1

10

100

1000

585580575570565560frequency / Hz

excitation / g 1.80 1.28 0.64 0.32 0.16 0.08

0.01

0.1

1

10

100

1000

585580575570565560frequency / Hz

excitation / g 1.80 1.28 0.64 0.32 0.16 0.08

0.01

0.1

1

10

100

1000

585580575570565560frequency / Hz

excitation / g 1.80 1.28 0.64 0.32 0.16 0.08

140 µW @ 572 Hz

Proc. IEDM (2011)

year 2011:record power of 489 µW

mass dim.: 3×3 mm2, beam length: 1.7 mm, max. displ. 600 um @ 4.5 g,

frequency = 1012 Hz

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Autonomous operation of wireless system

vibration powered at 300 Hz & fully autonomous

15 s duty-cycle for radio transmissions of temperature reading

5

4

3

2

1

0

-1

curr

ent /

mA

-20 -10 0 10 20time / s

5

4

3

2

1

0

curr

ent /

mA

120100806040200-20time / ms

15 s duty-cycle

µ-controller

radio active(800 µs)

standby current2.2 µA

Proc. IEDM (2009)

� Energy harvester

� TI MSP430 µC

� Nordic nRF2401

- 17 -

18

Lumped element modeling1st generation design

Equivalent circuit models electro-mechanical behavior

Coupling factor describes energy conversion

222

2

111

21

piezommm.max,load CRR

FP2221 piezomm

m.opt,load

CRRR

mechanical electrical

Lm = m / 2

Cm = 2 / k

Rm = d / 2

Cpiezo Rload

F /

Inf. Syst. Frontiers 11, 7�18 (2009) - 18 -

Lm = m / 2

Cm = 2 / k

Rm = d / 2

Cpiezo Rload

F /

19




222

2

111

21


FP2221 piezomm

m.opt,load

CRRR

Inf. Syst. Frontiers 11, 7�18 (2009)

at resonance under vacuum

- 19 -

20




Inf. Syst. Frontiers 11, 7�18 (2009)

Lm = m / 2

Cm = 2 / k

Rm = d / 2

Cpiezo Rload

F /

222

2

111

21


FP2221 piezomm

m.opt,load

CRRR

at resonance under vacuum

piezomoptload C

R 1.,

Cpiezo Rload

I0

- 20 -

Numerical (finite element) modeling1st generation design

Model is based on actual geometry

Includes circuit elements

Yields resonance frequency, displacements, strain, power, �

21

output power

FEM displacement

FEM

Model verification: results & experiments

resonance frequency

FEM

- 22 -

Piezoelectric energy harvester 2nd generation design (multi-mode)

Two coupled resonators

Closely spaced resonance frequencies

Subject to design optimization

1st resonance

2nd resonance

IEEE Micro Electro Mechanical Systems, pp. 1201�1204, 2012.- 23 -

Piezoelectric energy harvester 2nd generation design (multi-mode)

Harvested power of 20µW with 1.2g @ 694Hz

Tuning range of 3Hz by varying DC voltage between ± 30V

09.04.2013 Fatma Sayed - 24 -

Top view of the fabricated harvester using MEMS process with multiple masses and

beams (Pt, AlN and Al layers)

Two sets of capacitors denoted by (+) and (-)

IEEE Micro Electro Mechanical Systems, pp. 1201�1204, 2012.- 24 -

Finite Element Model of the Harvester

Geometry and mesh view of the piezoelectric energy harvester with 47.800 nodes (145.000 DOF)implemented in ANSYS V.14.5

09.04.2013 Fatma Sayed - 25 -

2nd resonance3.755,6 Hz

1st resonance1.966,2 Hz

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Outline

Introduction



Reduced Order Model




09.04.2013

Model Order Reduction (1)

Goal: consider interaction between device and electrical circuit,

MOR: algorithms that transform large (sparse) ODE systems intomuch smaller (full) systems

09.04.2013 - 27 -

= +.

. = .

= +. = .

A B

user input system output

original:

reduced:

A

Ar Br

C

Cr.

Model Order Reduction (2)

system matrices are reduced using a Krylov subspace-based Arnoldialgorithm (MIMO setup, expansion around f = 0 Hz).

Advantages :Maintains the accuracy of the original numerical modelReduces the transient simulation time by several orders of magnitudeAllows for multi-physical compact modeling (stability issues have to be considered)

09.04.2013 - 28 -

26.06.2013 - 29 -

Reduced Order Model of the Harvester

Model stabilization [2]

Schur complement

[2] T. Aftab et al., Proc. Micromechanics and Microsystems Europe, 2012.

Reduced Order Model of the Harvester

Fatma Sayed - 30 -

full model reduced model

computation time (s ) 3.1 GHz with 8 GB RAM 6.269,0 4,71

model dimension 145.517 50

100

80

60

40

20

0

40003000200010000frequency (Hz)

-200

-150

-100

-50

0

50

amplitude phase

full reduced

Transfer functions near fundamental resonance frequency

Comparison between the full and the reduced model

[2] T. Aftab et al., Proc. Micromechanics and Microsystems Europe, 2012.

[3] F. Sayed et al., EuroSimE 2013

26.06.2013

Performance Comparison between Full and Reduced Model

Model order reductionfrom 145.500 (full) 50 (reduced)

Acceleration of computation time for transient simulationfrom 6.300 seconds (full) 4,7 seconds (reduced) !

Accuracy is maintained

09.04.2013

100

80

60

40

20

0

40003000200010000frequency (Hz)

-200

-150

-100

-50

0

50

amplitude phase

full reduced

Proc. Micromechanics and Microsystems Europe, 2012. - 31 -

- 32 -

Outline

Introduction



Reduced Order Model




09.04.2013

Power Extraction TechniquesBridge Rectifier

Low power extraction efficiency

Increasing the conversion ability:Increase the piezoelectric output voltage.Increase the electro-mechanical coupling coefficient.Reduce the time shift between the voltage and the harvester speed.

09.04.2013 - 33 -

harvester rectifier capacitiveload


Fatma Sayed - 34 -

Synchronous electric charge extraction (SECE)

Synchronized switch harvesting on inductor (SSHI)

09.04.2013- 34 -

SSHI Circuit Implementation

MOR of a high dimensional FEM (mechanical port (left) and electrical port (right))

self-supplied comparator

switchable inductive branch for voltage inversion

full-bridge rectifier with flattening capacitor and resistive load09.04.2013 - 35 -

MultiphysicsMOR

pos1

pos2

p

m

F

Bridge rectifierSwitching inductorSelf-supplied comparator

Proc. EurosimE, 2013.

- 36 -

Outline

Introduction



Reduced Order Model


Results and discussion


09.04.2013

Results and Discussion Transient response

Transient response of system-level simulation (Simplorer 11)

output voltage at open circuit condition increased from 3.7V to 5.9V

09.04.2013 - 37 -

26.06.2013 Fatma Sayed - 38 -

comparator switch bridge rectifier load

3% 12 % 25 % 60 %

� The power dissipation through the circuit.

Results and Discussion Parametrization and Optimization

Power drops due to:

The electrical losses in the harvesting stages.

The mechanical re-injection losses due to the damping effect.

Results and Discussion Parametrization and Optimization

Parametrization within system-level simulation (Simplorer 11)

output peaks at optimum load resistance value

appr. 70 % power efficiency.

09.04.2013 - 39 -

Results and Discussion Experimental verification

Voltage inversion event is observed under attached SSHI circuit

Sinusoidal excitation (0.3 g) at resonance frequency

External supply for the comparator

09.04.2013 - 40 -

-2

0

2

-4 -2 0 2 4time (ms)

Vpiezo Vsense

electro-mechanical coupling

- 41 -

Outline

Introduction



Reduced Order Model




09.04.2013

Conclusion

A reduced order model of the harvester was successfully used in a co-simulation with electrical power circuitry.

Enables true system-level simulationReduces the computation timePreserves system dynamics / accuracy of FE modelStability is preserved after the Schur-Complement transformation

Improve harvested voltage using SSHI-scheme with simple self-supplied control circuit.

09.04.2013 - 42 -

Future Work

Consider other power extraction approaches.

Extend reduced order model to multiport form (two electrical ports and one mechanical port)

Stability issues of the reduced order model deserve further research

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0 0

MultiportMOR

disp

p1

m1

centr

northsouth

p2

m2 R1R2

New Book Published at Wiley-VCH

Thank you very much for your kind attention !

- 45 -

acknowledgements: Micropower group (IMEC), E. Rudnyi (CADFEM)

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Reduced Order Modeling Enables System Level Simulation of ... · Reduced Order Modeling Enables System Level Simulation of a MEMS Piezoelectric Energy Harvester with a Self-Supplied