Actuator pub - Stevens Institute of Technology

J. Micro-Nano Mech.
DOI 10.1007/s12213-009-0017-2
RESEARCH PAPER
Hybrid linear microactuators and their control models
for mirror shape correction
Kirill Shcheglov & Xiaoning Jiang & Risaku Toda &
Zensheu Chang & Eui-Hyeok Yang
Received: 16 January 2009 / Revised: 11 May 2009 / Accepted: 20 May 2009
# Springer-Verlag 2009
Abstract Future space-based imaging systems demand
ultra-lightweight mirrors, which would involve a large
number of actuators to provide the needed surface
correction. These lightweight actuators are required to be
integrated with the mirrors to avoid a significant increase in
overall areal mass density. This paper presents the
fabrication and testing of a linear microactuator and the
modeling of an actuated mirror composed of such lightweight actuators. The linear microactuator is driven by a
combination of a piezoelectric actuator block and electrostatic comb drive units. A full nonlinear optimization model
of a mirror lattice was developed to simulate a lightweight
primary with embedded microactuators, which allows for
an arbitrarily connected lattice with connector elements
having an arbitrary stiffness and actuation response. The
modeling yielded a high precision estimation of the mirror
shape correction.
K. Shcheglov
Sensors in Motion Inc.,
4858 Lincoln Ave #3,
Los Angeles, CA 90042, USA
X. Jiang
TRS Technologies, Inc.,
State College, PA, USA
R. Toda : Z. Chang
Jet Propulsion Laboratory, California Institute of Technology,
4800 Oak Grove Drive,
Pasadena, CA 91109, USA
E.-H. Yang (*)
Stevens Institute of Technology, Castle Point on the Hudson,
Hoboken, NJ 07030, USA
e-mail: [email protected]
Keywords Linear actuator . Adaptive optics . Large stroke .
Bulk-micromachining . Active shape correction .
Segmented mirror
1 Introduction
The application of lightweight (<1 kg/m2) apertures to
space-based imaging will enable substantial performance
gains for future space missions [1]. Previously, inflatable
structures using flexible polymeric membranes [2] and
nanolaminate-based rigid-shell mirrors [3] were investigated. Practical aperture systems could involve segmented
mirrors whose large surface errors are actively corrected
by embedded actuators [1]. A key element of the success
of this technology relies heavily on the ability to develop
actuators that are lightweight and small to be integrated
with the mirrors, in order to reduce the overall areal mass
density of the telescope system. Several MEMS-based
linear actuators with electrostatic [4–8] and thermo-elastic
links [5] were reported. While these previously reported
MEMS actuators represent a significant improvement in
the area, electrostatic clutching requires continuously
supplied voltage to hold actuator position, and if
ambient heating or cooling occurs, thermal actuators
links may be randomly activated. Presented in this paper
is an updated version of the authors’ recently developed
self-latched microactuator [9], which contains further
modeling and analysis of the actuator characteristics to
determine the feasibility for the active mirror application.
Also presented is the modeling of the mirror shape
correction using these embedded microactuators. A mirror
model for general actuated lattice structures was formulated using a direct numerical optimization method.
J. Micro-Nano Mech.
2 Microactuator: modeling, fabrication
and characterization
The actuator consists of two comb drive units, a slider, a
rail substrate and a miniaturized PMN-PT (lead magnesium
niobate-lead titanate, or Pb(Mg1/3Nb2/3)(1−x)TixO3) single
crystal piezoelectric actuator-block. A schematic of the
linear actuator is shown in Fig. 1. The actuator is driven by
a combination of electrostatic comb drive actuator units and
a laterally placed PMN-PT actuator block (Fig. 2). The
dimensions of the PMN-PT actuator block are about
2 mm×0.5 mm×4 mm, and the maximum stroke can be
obtained along the 4 mm direction. The intertwining U-
a
Rail substrate
Lid (glass)
Au wires
Slider
Driver Unit
PMN-PT actuator-block
b
Clutch
Comb drive
Tether
beam
Fig. 1 Actuator schematic. The actuator is driven by a combination of
the electrostatic comb drive and piezoelectric actuators. The comb
drive unit is fabricated on an SOI wafer with a 100-µm-thick device
layer to increase both the stiffness and the electrostatic force. By
applying voltage to the comb drive, the clamps are electrostatically
pulled away to release the slider. a Overall structure b Driver unit
letter shaped comb drive unit design is intended to enhance
stability of the slider motion [9]. During the operation
cycle, the slider is gripped by at least four clutches at a
time; also, the slider is confined to linear motions only,
mitigating undesired slider tilt and drag friction. The slider
is gripped and its position is maintained when power is
turned off, which is made possible by pre-stressing tether
beams during the assembly. Figure 3 illustrates the
operation sequence of the actuator [9]. In this figure, in
step (1), unit A is released by actuating the comb drive
while the unit B remains clutched, whereas in step (2), the
unit B and the slider is laterally pulled toward the right by a
PMN-PT stack actuator. The unit A is clutched while the
unit B is released in step (3), and subsequently, the unit B is
pushed back by the PMN-PT in step (4). By repeating the
actuation sequence for many times, large cumulative stroke
is achieved. The detailed fabrication process is previously
reported [9]. The comb drive structure is designed “initially
unengaged” as shown in Fig. 4(a), and then engaged by the
slider insertion, thereby narrowing the comb-tooth-gap to
approximately 1 µm (Fig. 4(b)) [9]. Once the slider is
inserted, tethers are displaced by approximately 10 µm and,
therefore, grip the slider without external power since they
are pre-stressed. The clamps are electrostatically pulled
away to release the slider by applying voltage to the comb
drive.
A Finite Element Model (FEM) analysis was performed
on the tethers in the clamp structure to estimate the
clamping force. The commercially available ANSYS
Workbench finite element tool was used to create the
FEM model. The tethers and clamp structure were
constructed by using hexahedral (brick) elements. Figure 5
shows a modeled geometry for the bending of the actuator
tether. The estimated bending force on the tethers caused by
10 μm displacement of the clamp during the slider insertion
process is approximately 25 mN. On the other hand, the
repulsion of the 10-µm wide tether perpetually pushes the
slider with the force of 25 mN. Before the slider insertion,
the comb gap is approximately 5 µm and the electrostatic
force is negligible. Once the slider is inserted, the comb gap
narrows to approximately 1 µm (1.2 µm was used in the
calculation) and the electrostatic force is significantly
increased. For example, the estimated electrostatic force is
approximately 35 mN, by applying 200 V to the comb
drive, which exceeds the estimated tether bending force of
25 mN.
Individual parts were fabricated separately and manually
assembled. The PMN-PT single crystal actuator block was
fabricated by stacking ~20 layers of of 6.5 mm×2 mm×
0.15 mm PMN-PT plates and metal shims using epoxy.
Figure 2(a) and (b) show images of a 6.5 mm×2 mm×
4 mm PMN-PT stack. Figure 2(c) is a cross-section of a
miniaturized stack right after dicing, where the PMN-PT
J. Micro-Nano Mech.
Fig. 2 PMN-PT single crystal
stacks. a and b 6.5 mm×2 mm×
4 mm stacks c Cross-section
of a miniaturized actuator after
dicing d Miniaturized actuators.
e Displacement vs. driving
voltage
4.50
4.00
Displacement (um)
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
0
50
100
150
200
Driving Voltage (V)
(e)
layer and metal shim can be clearly observed without
bonding defects between layers. Shim tabs were soldered
for lead wires attachment. The stack was then mounted onto
a dicing substrate using low temperature wax and subsequently diced using a Computer Numerical Control (CNC)
machine tool to form six 2 mm×0.5 mm×4 mm PMN-PT
actuator blocks (Fig. 2(d)). Displacement of all actuatorblocks was measured using a Linear Variable Displacement
Transducer (LVDT) system under a driving voltage of 0–
150 V at room temperature (Fig. 2(e)). The curved line
represents the measured results with a fitted straight line,
from which the average effective d33 (piezoelectric coefficient) of the piezo material used in miniaturized actuators
was calculated approximately to be 1500 pC/N, which is
slightly lower than that of bulk PMN-PT crystal resulting
from the epoxy clamping effect. The hysteresis observed
was about 10%, which is comparible to that of normal
piezoelectric actuators (10%–20%). The average stroke of
the actuator-blocks composed of 19–21 layers of PMN-PT
thin plates (0.15 mm thick) is about 4 µm. The stroke
resolution is depending on the minimum applied driving
voltage. For example, a 26 nm stroke can be obtained by
applying 1 V.
The finished PMN-PT actuator-blocks were bonded to
the finished silicon components for final characterization. The fabrication process of the silicon components
J. Micro-Nano Mech.
Unit B
Unit A
(3) Unit A clutched
(0) Unpowered latching mode
(4) Unit B released; 1-cycle actuation completed
Fig. 3 (continued)
(1) Unit A release
Actuator operation was tested using a LabVIEW-based
setup consisting of interfaced power relays and power
supplies; the voltages applied to the comb drive and the
piezoelectric-stack actuators were 200 V and 20 V, respec-
a
Comb
drive
arrays
(2) Unit B laterally moved
Fig. 3 Operation principle of the microactuator. By repeating the
individual actuation sequences, a large cumulative stroke is achieved.
The step increment resolution can be adjusted by controlling the
voltage applied to the actuator block. This actuator is capable of zero
power latching; the slider is clutched and its position is maintained
when power is turned off
Clutch
Tethers
b
Stopper
Engaged comb
has been reported previously [9]. A rail substrate was
made by attaching side-rails to the base plate by epoxy
adhesive. The slider was fabricated by slicing the silicon
wafer using a dicing saw. After completing the fabrication
of the actuator components, the driver units were mounted
on the rail substrate. The slider was manually inserted
between clamps using a probe needle. Finally, a PMN-PT
actuator-block and a lid were attached using epoxy
adhesive, and the assembled structure was wire-bonded.
Figure 6 shows the finished device, assembled and
mounted.
Fig. 4 Microscope images of clamp structures and comb drive arrays.
a Before slider insertion b Engaged comb teeth after slider insertion
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tively. The cumulative stroke after 200-cycle actuation was
178 µm, with an operation speed of approximately 1 cycle per
second. Table 1 summarizes the linear actuator performance.
Clamp
3 Structure model of actuated mirror
The design of a segmented large aperture adaptive mirror is a
challenging task. A number of system requirements must be
met, such as the actuation rate, the best achievable surface
figure, performance over temperature and vibration, existence
of persistent structure vibration modes, controllability and
influence functions, and other important system parameters.
The ability to meet such requirements can be investigated
using a lumped element model described below relating the
structure response to the actuation of individual actuator
elements. The model describes an arbitrarily connected
mechanical structure containing microactuators, mirrors, and
flexure beams. Such a structure is quite general and can
describe the bulk of real world implementations of a large
aperture segmented adaptive mirror.
The model can be used to determine the mirror
configuration for an arbitrary input set of microactuator
displacements, as well as determine the micro-actuator
control parameters required for achieving the desired mirror
configuration. Dynamic behavior of the primary mirror
such as resonance frequencies and response functions can
be investigated as well. In the current effort, an exemplary
lattice structure envisioned to support the mirror segments
was built and analyzed to investigate the use of the above
Tethers
Boundary Conditions:
The ends of the four
tethers were fixed
Fig. 5 FEM model of a clamp structures and four tethers attached.
The contour plot shows the results of analysis for bending and rotation
of tethers. Location of the maximum stress is clearly indicated. The
deformed shape of the tethers was exaggerated for clarity
Table 1 Measured actuator performance
Max. Freq.
Stroke
Driver A
Driver B
Au wires
Comb unit
Slider
Clutch
Resolution
Force
Power
Size
Mass
Target
Demonstrated
~1 kHz
>1 mm
20-cycle/s a
178 µm @ 200-cycle
<30
>30
100
~10
nm
mN
µW
mm3
b
c
50 nm
48 mN d
0 W when latched
14×7×0.6
100 mg
a
The higher-speed actuation (>20 Hz/cycle) could not be demonstrated due to the frequency limit of the mechanical relay used for
supplying electrical AC signal to actuators. In principle, the actuator
structure with PMN-PT and comb units can move at frequencies
exceeding 1 kHz.
b
The stroke of our actuator is limited only by the slier length and
imposed force.
c
Fig. 6 Image of a fabricated inner component of a linear actuator after
assembly and wire bonding
The measured resolution was limited by the image quality for image
processing. Actual resolution (minimum step size) is expected to be
better.
d
The clamping force was modeled using ANSYS.
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described actuator in such an application. Of particular
concern was the limited maximum actuation force that the
actuator was able to provide as well as the limited
“holding” force (tens of mN). The modeling has shown
the with the stiff lattice structure we have described it is
possible to achieve large displacements while not exceeding
the maximum load on any particular actuator.
The model contains two types of elements: nodes and
connectors. Nodes are conceptual points in space and/or
infinitely stiff junction elements attached to connectors.
Figure 7(a) shows a lattice structure consisting of these
elements, and a close-up of a small portion of it containing
three adjacent nodes. Such adjacent sets of three nodes in
the top layer are envisioned as being kinematic mount
points for hexagonal mirror segments filling the mirror
Fig. 7 Lattice and mirror structures. a The modeled lattice
structure and a schematic of a
small section showing the node
and connector elements.
b Supporting hexagonal mirror
segments with the modeled
structure
aperture (Fig. 7(b)). Connectors are rod-like elements that
span two nodes. Connectors have an arbitrary stiffness (a 6
DOF spring constant) and an actuation capability which can
either be force-driven or displacement driven. Although the
model supports an arbitrary nonlinear actuator response
(such as piezoelectric), in the present implementation each
connector is assumed to be an actuator with the following
simple energy function Eact ¼ kðjrj þ ΔrÞ2 where k represents the spring constant of the connector in the axial
direction, |r| is the length distance between connector
endpoints, and Δr is the inchworm displacement. The response
of the structure to applied stimulus was calculated by fixing the
“driven” parameters to their prescribed values and minimizing
the total structure energy with respect to the rest of the
parameters. A simple elastic tensile stiffness was assumed for
Actuators
Springs
Connectors
50
50
0
0
X
50
50
(a)
(b)
Y
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each connector. The bending and torsional stiffnesses were set
to zero, corresponding to a frictionless hinged attachment at
each end. The three rotation angles for each node were
therefore not included into the calculation. The energy
minimization method was used to calculate the structure
actuation and response by numerically minimizing the total
structure energy with respect to the sought parameters.
The structure model developed was a stiff lattice
supported at three symmetric points. The dimensions (in
centimeters) were chosen to roughly correspond to a
structure for a segmented mirror with 1 foot segments.
The stiffness of the effective connector spring constant was
chosen to mimic a realistic light rod-like element made of a
typical metal-like material (Elastic modulus in the 100 GPa
range; For reference, 7075 Aluminum has an elastic
modulus of 72 GPa, 6Al-4 V Titanium−115 GP, 304
Stainless−200 GPa), approximately 20 cm in length and
Fig. 8 Response of the structure
to a set of minimum energy
commands calculated for the
same prescribed shape. a
Segment displacement and b
actuator force in dynes
10 mm2 in cross-section. The resulting stiffness was
calculated to be 107 N/m or 1010 dyne/cm. For a nanometer
step, the maximum force on all actuators is around 1 mN.
However if larger step sizes are desired, the stiffness of the
connector must be reduced proportionally, i.e., for a 1 μm
maximum step size the stiffness must be reduced by a factor
of a thousand. This can be done by designing the connector
shape to have a reduced stiffness, such as by machining
flexures into a portion of it. For instance, with the stiffness
of 105 N/m, the actuator with 10 mN force can have a
100 nm maximum step size. The model lends itself both to
computing the structure response to a set of control inputs
(such as actuator displacements or voltages applied to
piezoelectric elements), as well as to computing the
required command inputs to achieve a prescribed shape.
Figure 8 shows the response of the structure to a
calculated set of actuator displacements achieving the same
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structure shape while forces on the actuators are nearly
negligible. Figure 9 shows structure control of the top layer
of the structure to the Zernike modes. A Zernike mode was
constructed on a lattice of top layer structure nodes. The
other nodes were required to remain in place. Actuator
displacement commands were calculated and applied.
Subsequently, the structure response to the commands was
computed. The difference between the target and the
achieved control result is dominated only by the round-off
error. The mirror modeling results described above show
that the microactuators reported in this paper can correct the
curvature and deformation of future segmented mirrors.
4 Conclusions
A self-latched linear actuator has been fabricated and tested,
and a mirror lattice structure actuated using embedded
microactuators has been modeled. The measured cumulative stroke of the actuator after a 200-cycle actuation is
178 µm. Further development is required to analyze the
actuator push force, increase operation speed, improve
linearity and reliability, and improve packaging technique.
A mirror model for general actuated lattice structures has
been built using a direct numerical optimization model. The
model has yielded an arbitrarily connected lattice with
connector elements having an arbitrary stiffness and
actuation response. The tested actuator performance and
the mirror modeling results show that the developed
microactuators can correct the curvature and deformation
of future segmented mirrors. The current form of the linear
microactuator may be susceptible to lateral force and launch
load. For practical applications in the future, the actuator
technology described in this paper has to be further
developed to be more reliable for applications on the mirror
system, consisting of actuators and backing structures.
Fig. 9 Example of structure control: the top layer nodes required to move in the vertical direction to match Zernike modes composed over the
appropriate grid
J. Micro-Nano Mech.
Acknowledgement The research described in this paper was
partially carried out under Research and Technology Development
program at the Jet Propulsion Laboratory, California Institute of
Technology under a contract with the National Aeronautics and Space
Administration.
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