Reduced Order Modeling Enables System Level Simulation of ... · Reduced Order Modeling Enables...
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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
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Outline
Introduction
MEMS Piezoelectric Energy Harvester
Finite Element Model
Reduced Order Model
Power Extraction Techniques
Results and Discussion
Conclusion and Future Work
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Outline
Introduction
MEMS Piezoelectric Energy Harvester
Finite Element Model
Reduced Order Model
Power Extraction Techniques
Results and Discussion
Conclusion and Future Work
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How to supply all these sensors with energy ?
4
plant monitoring
buildingautomation
© Honeywell
automotive
© Khulsey
deep space probes
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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
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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
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Wireless Autonomous Transducer Solution (WATS)
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thermal, RF, vibrational, light harvesting
Radio20 µW
µ-Contr.20 µW
DSP20 µW
Sensor frontend(ASIC) 20 µW
Sensor20 µW
Micropower module -100 µW
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ElectrostaticElectro-magneticPiezoelectric
Thermal PhotovoltaicRF Vibration
use MEMS to provide 100 µW / cm2
to power wireless autonomous systemsVision:
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Piezoelectric Material
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Coupling modes
Transversal
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Piezoelectric Energy Harvester
Transformer represent mechanical and electrical coupling
vibration acceleration
L internal mass
C mechanical stiffness
R the energy lost
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Circuit model of a piezoelectric harvester
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Outline
Introduction
MEMS Piezoelectric Energy Harvester
1st and 2nd generation designs
Finite Element Model
Reduced Order Model
Power Enhancement Techniques
Results and Discussion
Conclusion and Future Work
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Outline
Energy harvesting context - The vision
Piezoelectric harvestingFabrication, results, applicationModeling
Multifrequency harvestingMotivation for frequency agilityDesign implementations
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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
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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
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Wafer-scale fabrication and packaging
150 mm SOI substrates
Wafer-scale encapsulation between glass substrates
Hermeticity to be improved
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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
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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 -
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Lm = m / 2
Cm = 2 / k
Rm = d / 2
Cpiezo Rload
F /
19
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
Inf. Syst. Frontiers 11, 7�18 (2009)
at resonance under vacuum
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Lumped element modeling1st generation design
Equivalent circuit models electro-mechanical behavior
Coupling factor describes energy conversion
Inf. Syst. Frontiers 11, 7�18 (2009)
Lm = m / 2
Cm = 2 / k
Rm = d / 2
Cpiezo Rload
F /
222
2
111
21
piezommm.max,load CRR
FP2221 piezomm
m.opt,load
CRRR
at resonance under vacuum
piezomoptload C
R 1.,
Cpiezo Rload
I0
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Numerical (finite element) modeling1st generation design
Model is based on actual geometry
Includes circuit elements
Yields resonance frequency, displacements, strain, power, �
21
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output power
FEM displacement
FEM
Model verification: results & experiments
resonance frequency
FEM
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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 -
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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
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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 -
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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
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2nd resonance3.755,6 Hz
1st resonance1.966,2 Hz
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Outline
Introduction
MEMS Piezoelectric Energy Harvester
Finite Element Model
Reduced Order Model
Power Extraction Techniques
Results and Discussion
Conclusion and Future Work
09.04.2013
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Model Order Reduction (1)
Goal: consider interaction between device and electrical circuit,
MOR: algorithms that transform large (sparse) ODE systems intomuch smaller (full) systems
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= +.
. = .
= +. = .
A B
user input system output
original:
reduced:
A
Ar Br
C
Cr.
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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)
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Reduced Order Model of the Harvester
Model stabilization [2]
Schur complement
[2] T. Aftab et al., Proc. Micromechanics and Microsystems Europe, 2012.
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Reduced Order Model of the Harvester
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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
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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 -
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Outline
Introduction
MEMS Piezoelectric Energy Harvester
Finite Element Model
Reduced Order Model
Power Extraction Techniques
Results and Discussion
Conclusion and Future Work
09.04.2013
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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.
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harvester rectifier capacitiveload
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Power Extraction Techniques
Fatma Sayed - 34 -
Synchronous electric charge extraction (SECE)
Synchronized switch harvesting on inductor (SSHI)
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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.
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Outline
Introduction
MEMS Piezoelectric Energy Harvester
Finite Element Model
Reduced Order Model
Power Extraction Techniques
Results and discussion
Conclusion and Future Work
09.04.2013
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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
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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.
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Results and Discussion Parametrization and Optimization
Parametrization within system-level simulation (Simplorer 11)
output peaks at optimum load resistance value
appr. 70 % power efficiency.
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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
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-2
0
2
-4 -2 0 2 4time (ms)
Vpiezo Vsense
electro-mechanical coupling
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Outline
Introduction
MEMS Piezoelectric Energy Harvester
Finite Element Model
Reduced Order Model
Power Extraction Techniques
Results and Discussion
Conclusion and Future Work
09.04.2013
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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.
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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
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New Book Published at Wiley-VCH
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Thank you very much for your kind attention !
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acknowledgements: Micropower group (IMEC), E. Rudnyi (CADFEM)