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 mm
20-cycle/s a 178 µm @ 200-cycle
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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