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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 18, NO. 2, MARCH 2003
Optimized Piezoelectric Energy Harvesting Circuit
Using Step-Down Converter in Discontinuous
Conduction Mode
Geffrey K. Ottman, Member, IEEE, Heath F. Hofmann, Member, IEEE, and George A. Lesieutre
Abstract—An optimized method of harvesting vibrational
energy with a piezoelectric element using a step-down dc–dc
converter is presented. In this configuration, the converter regulates the power flow from the piezoelectric element to the desired
electronic load. Analysis of the converter in discontinuous current
conduction mode results in an expression for the duty cycle-power
relationship. Using parameters of the mechanical system, the
piezoelectric element, and the converter; the “optimal” duty
cycle can be determined where the harvested power is maximized
for the level of mechanical excitation. It is shown that, as the
magnitude of the mechanical excitation increases, the optimal
duty cycle becomes essentially constant, greatly simplifying the
control of the step-down converter. The expression is validated
with experimental data showing that the optimal duty cycle
can be accurately determined and maximum energy harvesting
attained. A circuit is proposed which implements this relationship,
and experimental results show that the converter increases the
harvested power by approximately 325%.
Index Terms—DC–DC, discontinuous conduction mode, energy
harvesting, piezoelectric devices.
I. INTRODUCTION
T
HE need for a remote electrical power supply has spurred
an interest in energy harvesting, or the extraction of electrical energy from a vibrating piezoelectric device. A power
supply of this type would be suitable for systems such as an actively tuned vibration absorber [1], a foot powered radio “tag”
[2], [3], or a PicoRadio [4]. Currently, piezoelectric elements
are being investigated for this purpose due to their small size
and their noninvasive harvesting method.
A vibrating piezoelectric device differs from a typical electrical power source in that its internal impedance is capacitive
rather than inductive in nature, and that it may be driven by mechanical vibrations of varying amplitude and frequency. While
there have been previous approaches to harvesting energy with
a piezoelectric device [2], [3], [5], [6], there has not been an at-
Manuscript received May 22, 2002; revised November 1, 2002. This paper
was presented at the 33rd Annual IEEE Power Electronics Specialists Conference, Cairns Convention Centre, Queensland, Australia, June 23–27, 2002. Recommended by Associate Editor J. D. van Wyk.
G. K. Ottman is with the Applied Physics Laboratory, Johns Hopkins University, Laurel, MD 20723-6099 USA.
H. Hofmann, is with the Department of Electrical Engineering, Pennsylvania State University, University Park, PA 16802 USA (e-mail:
hofmann@engr.psu.edu).
G. A. Lesieutre, is with the Department of Aerospace Engineering, Pennsylvania State University, University Park, PA 16802 USA.
Digital Object Identifier 10.1109/TPEL.2003.809379
tempt to develop a circuit that maximizes power output. Earlier
analysis by the authors contained in [7] introduced a piezoelectric element model and developed analytical expressions for its
power production characteristics when used in conjunction with
an ac–dc rectifier. Using this relationship, a DSP-controlled,
adaptive dc–dc converter was used to maximize the power harvested from the piezoelectric device. Results showed that use of
the converter increased the power to the energy storage element,
an electrochemical battery, by 400% as compared to when the
battery was directly charged with a piezoelectric element-rectifier circuit. The relatively low power levels of a single piezoelectric element, however, prohibited a circuit implementation
that could power the adaptive control circuitry while providing
enough power for an additional electronic load.
Building upon these results, a simpler circuit design using a
step-down converter was pursued and is presented in this paper.
Through analysis of the piezoelectric element’s interaction with
a step-down converter operating in discontinuous current conduction mode (DCM), an optimal duty cycle can be determined
where power flow from the piezoelectric device is maximized.
Based on this result, a simplified control scheme for the converter is introduced, a complete energy harvesting circuit is presented to implement the maximum power transfer theory, and
experimental results are shown to verify the effectiveness of the
circuit.
II. THEORY
Background and validation for the piezoelectric power flow
theory is contained in [7] and a brief summation is presented
here. The electrical characteristics of a vibrating piezoelectric
element can be modeled as a sinusoidal current source i (t) in
parallel with its electrode capacitance C . The magnitude of
the polarization current I depends on the mechanical excitation
level of the piezoelectric element (as characterized by the piezoelectric element’s unloaded or open-circuit voltage V ), but is
assumed to be independent of the external loading conditions.
An ac–dc rectifier is connected to the output of the piezoelectric
device and the dc component of the output current of the device
was shown to be
(1)
is the voltage of the rectifier capacitor and is the
Where V
resonant frequency of the mechanical host structure. The output
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power of the piezoelectric element is the product of the output
current and the rectifier capacitor voltage
(2)
It is then apparent that the peak output power occurs when the
rectifier voltage is maintained at
(3)
or one-half the open-circuit voltage of the piezoelectric element.
The magnitude of the polarization current I generated by the
piezoelectric element, and hence the optimal rectifier voltage,
may not be constant as it depends upon the level and frequency
of the mechanical vibrations. This creates the need for flexibility in the circuit, i.e., the ability to change the output voltage
of the rectifier as the mechanical excitation changes to achieve
and maintain the maximum power flow. To accomplish this, a
dc–dc step-down converter is placed between the rectifier and
the electronic load as shown in Fig. 1. A battery is used at the
output of the converter to provide energy storage and a “stiff”
voltage to power the electronic load. Control of the converter is
designed to maximize the power flow out of the converter and,
if effective, results in the piezoelectric element being at its point
of maximum power flow as described above.
The step-down converter is a natural choice for this application, where the piezoelectric voltage can be very high and
reducing it to a level that is lower is required for the battery
and the electronic load. The analysis of the interaction between
the piezoelectric element and the step-down converter reveals a
simplified control scheme to achieve maximum power flow, allowing the circuit to be self-powering while harvesting enough
energy for additional low-power electronic loads.
Fig. 1. Energy harvesting circuitry.
where
is the time period that the transistor is off and current
flows through the free-wheeling diode. (4) can be used to provide an expression for
(6)
and substituted into (5)
(7)
By conservation of power for the converter (assuming losses are
minimal), the output current can be expressed as a function of
the input voltage and current and output voltage
(8)
The input current of the converter can now be determined by
equating (7) and (8)
(9)
Substituting the output current of the piezoelectric device, (1),
as the input current to the converter and the rectifier capacitor
voltage as the voltage into the converter, (9) becomes
(10)
III. STEP-DOWN CONVERTER ANALYSIS
The maximum power transfer theory developed for the piezoelectric element-rectifier circuit produced an expression for the
optimal rectifier voltage, (3). Regulation of this voltage, and
thereby the power flow from the piezoelectric element, is implemented through adjustment of the step-down converter’s duty
cycle. The following analysis reveals that the power flow from
the piezoelectric element is maximized at an optimal duty cycle
and, as it departs from this optimal value, the output power drops
significantly.
Converter operation in DCM has been assumed in the following analysis and this reasoning will be discussed later in this
section. From [8], expressions for a step-down converter operating in DCM for the input—output voltage relationship and
output current are
Solving (10) for the rectifier voltage
(11)
The input current to the converter can be determined as a function of the duty cycle by substituting (11) into (1)
(12)
Power produced by the piezoelectric element as regulated by the
converter can now be expressed as the product of the rectifier
voltage (converter input voltage) and the input current, (11) and
(12)
(4)
(5)
(13)
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 18, NO. 2, MARCH 2003
Which reduces to
(14)
The rectifier voltage and power flow from the piezoelectric element as regulated by the step-down converter for any excitation
level, as specified by the magnitude of polarization current I ,
can now be determined.
For this circuit, the maximization of the power flow from
the piezoelectric element is considered as a function of the
step-down converter’s duty cycle. Solving (10) for the duty
cycle:
(15)
At peak power, the piezoelectric polarization current can be
found as a function of the optimal rectifier voltage from (3) as
(16)
Substituting into (15) and fixing the output voltage by the bat, the optimal duty cycle which results in maximum
tery V
power can be determined as
Fig. 2. Optimal duty cycle for maximum power transfer, step-down converter.
to avoid the reverse recovery problem of the diode [9], so the
power levels ( 50 mW) generated by the piezoelectric device
and the simplified control method justify this approach. We
also note that the above theory focused on the maximization of
input power rather than output power of the converter, which
would be more appropriate. Maximization of output power of
the converter, however, would require accurate loss models for
the converter components, and was not attempted in this work.
Provided the converter has reasonable efficiency, the optimal
operating points for maximizing input and output power of
the converter should be fairly close.
IV. CIRCUIT IMPLEMENTATION
(17)
This relationship, the optimal duty cycle and piezoelectric
element excitation level, is depicted in Fig. 2. For maximum
power transfer, the rectifier voltage is maintained at one-half the
open-circuit voltage (V being dependent on the mechanical
excitation); and as this voltage becomes much larger than the
output battery voltage, the optimal duty cycle approaches a
constant value. It is emphasized that this excitation/duty-cycle
relationship is for a step-down converter in DCM, and other
topologies or operating conditions would require different
analysis.
By assuming a sufficiently large converter input-to-output
voltage difference, the optimal duty cycle becomes relatively
constant and can be approximated as
(18)
The optimal duty cycle of the converter is thus dependent upon
its inductance and switching frequency, the piezoelectric element’s capacitance, and the frequency of mechanical excitation
of the piezoelectric device.
Although the assumption of discontinuous conduction mode
yields the convenient conclusion of a relatively constant optimal
duty cycle at high excitation, the choice of this mode of
operation bears some discussion. Designing a converter to
always run in discontinuous conduction mode is questionable,
as the large ratio of RMS current to dc current in the inductor
and MOSFET will significantly increase conduction losses
as opposed to continuous conduction mode. However, for
low-power applications, DCM is often used even at full load
Building upon the relationship between the optimal duty
cycle and the mechanical excitation, a dual method of energy
harvesting is proposed. At higher excitation levels of the piezoelectric device, when the optimal duty cycle is nearly constant,
the step-down converter will operate at the fixed duty cycle
specified by (18). This allows for a simple controller consisting
of a fixed-duty-cycle pulse-width-modulated signal to drive the
switching MOSFET. Because the converter is only operated at
high excitations, two advantages are realized: first, the optimal
duty cycle is relatively fixed, so operation at the optimal power
point is ensured; and secondly, the higher excitations provide
sufficient energy to offset converter and control circuitry losses.
At lower excitations, the optimal duty cycle is still varying
substantially with the excitation, requiring a more complex,
adaptive control circuit with higher power consumption. An
initial study of the power levels in this range suggests harvesting would be marginal given even the lowest power control
circuitry [7]. Therefore, at lower excitations, the battery will
be charged by a pulse-charging circuit connected to the piezoelectric element-rectifier circuit with the step-down converter
bypassed. The threshold level of mechanical excitation that
divides these two modes of operation will depend on several
criteria: the power produced by the piezoelectric element, the
losses of the step-down converter, the power consumption of
the control circuitry, and the optimal duty cycle stabilization at
higher excitations.
V. CIRCUIT DESIGN
A schematic of the step-down converter and the accompanying control circuitry is shown in Fig. 3. The sub-circuits:
OTTMAN et al.: OPTIMIZED PIEZOELECTRIC ENERGY HARVESTING CIRCUIT
Fig. 3.
699
Energy harvesting circuit.
pulse-charger, threshold control, PWM generator, and gate
drive are noted in the figure. The piezoelectric device’s voltage
is first rectified with a full-bridge rectifier with a high blocking
voltage, D1, and rectifier capacitor, C1. The pulse-charging
circuit used at lower mechanical excitation levels follows the
rectifier circuit. The pulse-charger is actually a secondary
step-down switching scheme consisting of a depletion-mode
n-channel MOSFET, M1, and an enhancement-mode p-channel
MOSFET, M3. The depletion MOSFET allows an intermediate
charging capacitor, C2, of 1 F to be maintained at a relatively
constant 3.4 V by a comparator, U1, which regulates the
charging pulses to the battery through the p-channel device.
The pulse-charger is nonadaptive, with the frequency of the
charging pulses dependent upon the level of mechanical
excitation, so it does not regulate the rectifier voltage at
its optimal point. It is extremely low power and allows the
circuit to operate even if the battery becomes fully discharged
during a prolonged discharge period. Upon transition to the
main step-down converter, the depletion mode MOSFET is
biased “off” by M2 turning “on”. The charging capacitor is
then maintained at the battery voltage disabling the effective
“switching” action of the comparator.
The fixed duty cycle control signal for the step-down converter is generated by a CMOS 555 timer, U6, operated in the
astable mode. The signal is inverted and then used by a high
side driver, U9, to control the main switching MOSFET, M4.
A drawback to this chip is the 10 V minimum supply voltage
requirement, so two switched-capacitor voltage converters, U7
and U8, are needed to raise the 3 V battery level to a 10.5 V
supply rail. The step-down converter consists of an n-channel
MOSFET, M4, a custom-wound inductor, L1, with inductance
of 10 mH, a Schottky diode, D7, and a 2200 F filter capacitor,
C4. The optimal switching frequency of the converter should
maximize the overall efficiency of the circuit while ensuring
DCM operation over the expected operating range. Rather than
develop a comprehensive converter model based on the highly
variable piezoelectric-produced power, the switching frequency
will be experimentally determined to achieve the highest output
power for the circuit.
Implementation of the threshold control is based upon two
factors: the state of charge of the battery and the level of
excitation of the piezoelectric device. The excitation is determined by the magnitude of the battery charging current and
is measured by a high-side current shunt monitor, U2. During
both direct charging and step-down converter operation, the
battery charging current is pulsed so an averaging circuit is
used. Internally-referenced comparators, U3 and U4, evaluate
this condition and the battery voltage (3 V minimum). When
both conditions are met, an AND gate, U5, turns the depletion-mode MOSFET “off” and the converter’s control circuitry
“on”, initiating step-down converter harvesting at the set duty
cycle. The excitation is continually monitored and when it
drops below the threshold level, the step-down converter is
turned “off” and pulse-charging of the battery resumes.
The overall power consumption for the control circuitry is
estimated at 5.74 mW from datasheet values and allows the
threshold point between the two harvesting modes to be determined. This point is where the mechanical excitation level is
high enough that the step-down converter harvests more power
than the pulse-charging circuit. As such, the converter will be
used for harvesting at excitations above this point. The excitation level at this point should also be high enough so that the
optimal duty cycle is relatively close to its constant value predicted by (18).
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VI. EXPERIMENTAL SETUP
A Quickpack QP20W, is used in the following experiments as
the piezoelectric energy source. It is a two-layer device designed
for operation as a bimorph, and generates an ac voltage when vibrated in a direction perpendicular to its mid-plane. The dimenin.
sions of the two piezoelectric elements are
This was chosen for the experiments due to its commercial availability and to demonstrate the general operation of the energy
harvesting circuit. Because the equation for the optimal duty
cycle, (18), is a function of the piezoelectric capacitance, any
optimization of the piezoelectric element, i.e. size, form factor,
resonant frequency, etc.; would affect the circuit minimally.
To provide variable mechanical excitation, the piezoelectric
element was secured to an electric-powered shaker. The magnitude of the mechanical excitation of the piezoelectric element
is characterized in this paper by the open-circuit voltage that is
measured across the unloaded rectifier capacitor, V . A small
mass was added to the free tip of the bimorph to enhance the
external stress and increase the tip deflection, thus providing a
higher open-circuit voltage.
Fig. 4. Maximum power harvested vs. converter switching frequency (V
45:0 V).
=
VII. RESULTS
Experimental data were taken to validate the energy harvesting approach presented in this paper and to demonstrate the
operation of the energy harvesting circuitry. For comparison
purposes, direct charging of the battery across the rectifier
circuit represents a simple, nonoptimal method of energy
harvesting that was sought to be improved upon. The available
power of the rectified piezoelectric element is determined by
placing various resistors across the piezoelectric device/rectifier
circuit to determine the “optimal” resistance that results in the
maximum power dissipation.
The first experiment considered was to determine the optimal
switching frequency of the converter. Due to the low power
levels expected from the piezoelectric element, overall circuit
efficiency is greatly affected by frequency dependent loss mechanisms, i.e. controller and gate drive, MOSFET switching, and
inductor core losses. Switching frequencies from 0.5 to 50 kHz
were considered and the maximum output power for a fixed
mechanical excitation of 45.0 V was determined (for each
switching frequency the optimal duty cycle was experimentally
determined). Fig. 4. shows that as the switching frequency is increased above 1 kHz, the maximum harvested power decreases,
due largely to the increased power consumption of the gate drive
circuitry. The decrease in the harvested power level with the
0.5 kHz switching frequency is most likely due to the increased
conduction losses that can be a significant problem in converters
designed to operate in DCM. At a switching frequency of 1 kHz,
the harvested power level peaked at 9.73 mW, and so 1 kHz will
be used for the converter switching frequency in the following
experiments.
The next experiment was to validate the optimal duty cycle
expression presented in (17). Fig. 5 shows the theoretical
optimal duty cycle and the experimentally determined optimal duty cycle as a function of the mechanical excitation.
The theoretical duty cycle was calculated using an experimentally-determined device capacitance of 0.184 F and a
Fig. 5. Optimal duty cycle for step-down converter as a function of excitation.
mechanical resonant frequency, 385–400 rad/s, which varies
slightly with the piezoelectric device’s loading condition. The
experimental optimal duty cycle was determined by manually
varying the duty cycle to achieve maximum power flow to the
battery for that level of excitation. Over the range of excitation
considered, up to 100 V , the two curves follow a similar trend,
both becoming nearly constant above excitations of 45 V .
At low excitations, the experimentally determined values are
considerably higher than those theoretically predicted, but both
curves become constant at higher excitations at a duty cycle
of roughly 3.16%. The experimental data converges to within
0.25% in the region of constant optimal duty cycle.
A closer investigation of the optimal duty cycle was then
conducted. Using (18) with a constant mechanical excitation
OTTMAN et al.: OPTIMIZED PIEZOELECTRIC ENERGY HARVESTING CIRCUIT
701
Fig. 6. Power versus excitation for fixed duty cycle control.
frequency of 338 rad/s, the optimal duty cycle is theoretically
determined to be 2.81%
To verify this value, the power harvested over a sufficiently
broad range of excitation was considered and the experiment
repeated with duty cycle values around the theoretical optimal
value. Fig. 6 shows the resulting power for fixed duty cycles of
2.6, 2.8, 3.0, 3.2, and 3.4%. An expanded view of the higher
excitation levels shows the fixed duty cycle of 2.8% outperforms the other values as predicted. At the highest excitation,
67.3 V , the optimal duty cycle improves the power harvested
by 2 mW over the next closest value, the 3.2% duty cycle. At
about 62 V , the power outputs for 3.0% and 3.2% “cross,”
and a significant increase in power occurs for each duty cycle.
This may be due to nonlinear effects that occur at higher excitations, such as saturation of the polarization of the piezoelectric
device.
The waveforms for the step-down converter at peak excitation for the optimal duty cycle, 2.8%, are shown in Fig. 7. The
is maintained at 33.86 V, which
rectifier capacitor voltage V
is approximately one-half the open-circuit voltage. Also shown
are the freewheeling diode voltage V , the current-sense resistor voltage V , and the inductor current I . Discontinuous
current conduction mode of the converter can be seen when the
inductor current goes to zero, reverse-biasing the diode at the
battery voltage.
The final experiment considered shows the performance of
the energy harvesting circuit. The optimal duty cycle is set at
2.8% and the threshold control is disabled, locking the circuit
in the step-down converter harvesting mode. As compared to
direct charging of the battery, the advantages of the simplified
controlled step-down converter can be clearly seen in Fig. 8. At
Fig. 7. Step-down converter waveforms(V
and I .
= 67:3 V): V
,V
,V
,
the peak excitation level, almost 70 V , the harvested power
increased from 9.45 mW by direct charging to 30.66 mW with
the step-down converter operating at a fixed duty cycle, over a
factor of three improvement. The step-down converter outperforms the direct charging of the 3 V battery at all levels of excitation above 25 V despite the power consumption of the control
circuitry and the converter losses. This means the threshold control turn on point for the converter can be set anywhere above
this excitation. Note that with the step-down converter, the harvested power follows the same curve as available power, essentially increasing with the square of the open-circuit excitation
voltage. This makes the circuit even more critical for effective
energy harvesting on systems experiencing higher levels of vibration. With the fixed duty cycle, the converter maintained the
rectifier voltage at approximately 48.7% of the open-circuit excitation voltage, which is very close to the predicted one-half
the open-circuit voltage.
System losses, including the power consumption of the controller, can be calculated as the difference between the available
power and that harvested with the converter. The experimental
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 18, NO. 2, MARCH 2003
experimental optimal duty cycle showed excellent agreement
with the theoretical value of 2.81%. Using a simplified control scheme to implement this, the step-down converter harvested energy at over 3 times the rate of direct charging of the
battery. Furthermore, it is expected that this rate would continue to increase as the harvested power increases approximately
with the square of the excitation. Presently, 30.66 mW was harvested, which is more than adequate to meet the power needs of
many electronic systems. Because the system is designed to be
self-powering, no external power supply is needed, making the
system suitable for remote operation.
REFERENCES
Fig. 8. Energy harvesting circuit performance.
Fig. 9.
Energy harvesting circuit efficiency.
efficiency of the step-down converter was between 0 and 70%,
as shown in Fig. 9. The efficiency initially increases with the
excitation due to the lessening proportion of the controller
power consumption. At excitations above 50.0 V , the efficiency begins to degrade as the input-output voltage difference
across the converter increases. At the highest excitation, the
total losses were estimated to be 15.8 mW. At low excitations, below 40 V , the losses account for less than 4.5 mW,
indicating that the controller power consumption is less than
the estimated value of 5.74 mW. The efficiency where the
converter will operate, excitations above 45 V , is about 65%.
VIII. CONCLUSION
This paper presents an approach to “harvesting” electrical
energy from a mechanically excited piezoelectric element that
maximizes the harvested power level. An expression for the optimal duty cycle for a step-down converter operating in discontinuous conduction mode is developed and reveals that, as the
level of mechanical excitation is increased, the optimal duty
cycle becomes relatively constant. In the circuit presented, the
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Geffrey K. Ottman (M’02) received the B.S. degree
in electrical engineering from the U.S. Coast Guard
Academy, New London, CT, in 1995 and the M.S.
degree in electrical engineering from Pennsylvania
State University, University Park, in 2002.
He is currently employed in the Space Systems
Department, Applied Physics Laboratory, Johns
Hopkins University, Laurel, MD. His interests
include power electronics and converter design.
Heath F. Hofmann (M’90) received the B.S. degree
in electrical engineering from the University of
Texas, Austin, in 1992, and the M.S. and Ph.D. degrees in electrical engineering from the University of
California, Berkeley, in 1997 and 1998, respectively.
He recently began his career at Pennsylvania State
University, University Park, as an Assistant Professor
in the Department of Electrical Engineering. His research interests are in power electronics and electromechanical systems. Specific interests are the development and application of sensorless field-oriented
control schemes, quiet electric drives, high-speed machine design, piezoelectric power generation, and the application of advanced numerical methods to
the design and simulation of electromechanical systems, focusing on finite-element analysis techniques. He is the primary co-author on several journal papers
on electric machine design and control.
Dr. Hofmann received the prize paper award from the electric machines committee at the 1998 IEEE lAS Annual Meeting.
OTTMAN et al.: OPTIMIZED PIEZOELECTRIC ENERGY HARVESTING CIRCUIT
George A. Lesieutre received the B.S. degree in
aeronautics and astronautics from the Massachusetts
Institute of Technology, Cambridge, in 1981 and
the Ph.D. degree in aerospace engineering from the
University of California, Los Angeles, in 1989.
From 1977 to 1989, he held positions at Argonne National Laboratory, Allison Gas Turbines,
Rockwell International Satellite Systems Division,
and SPARTA. In 1989, he joined the faculty of the
Department of Aerospace Engineering, Pennsylvania State University, University Park. His research
interests include the dynamics of adaptive aerospace vehicles and composite
structures; vibration control, with emphasis on passive damping; piezoelectric
actuators; and tunable transducers.
Dr. Lesieutre received best paper awards from the American Institute of Aeronautics and Astronautics (AIAA), the American Society of Mechanical Engineers, and the American Helicopter Society. He is an Associate Fellow of the
AIAA, which he presently serves as Chair of the Adaptive Structures Technical
Committee.
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