System and method for hysteresis compensation - Patents.com

Abstract

To provide a method capable of selecting a path between a first position and a second position to compensate for hysteresis of an actuator, and applying a drive signal to an actuator element including a hysteresis compensation portion to move an object along the selected path.SOLUTION: A method includes: selecting a path between a first position and a second position; and applying a drive signal including a hysteresis compensation portion to an actuator element to move an object along the selected path. The method further includes identifying at least one change in a direction of the actuator element along the selected path, and the hysteresis compensation portion is partially based on the change of the direction.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present disclosure relates to systems and methods for controlling actuators, such as piezoelectric actuators, to compensate for hysteresis. [Background technology]

[0002] Piezoelectric actuators are ideally suited for applications requiring high stiffness, low drift, fast response times, and the ability to generate relatively large forces. However, piezoelectric materials are known to exhibit a significant amount of hysteresis. This can pose a significant barrier to the use of piezoelectric actuators in applications such as semiconductor processing and electron microscopy, where samples and / or tools must be moved and positioned with high precision and minimal disturbance. Thus, there is a need for improved systems and methods for controlling piezoelectric actuators. Summary of the Invention

[0003] The present disclosure relates to a control system and method for controlling an actuator, such as a piezoelectric actuator, to compensate for hysteresis. In an exemplary embodiment, the method includes selecting a path between a first position and a second position, and applying a drive signal to an actuator element, the drive signal including a hysteresis compensation portion, to move an object along the selected path.

[0004] In any or all of the disclosed embodiments, the method further includes identifying at least one change in orientation of the actuator element along the selected path, the hysteresis compensation portion being based in part on the change in orientation.

[0005] In any or all of the disclosed embodiments, a change in direction is identified based on the sign of the rate of change of the drive signal.

[0006] In any or all of the disclosed embodiments, the drive signal varies between a first value and a second value to move the object along a selected path, and a hysteresis compensation portion of the drive signal varies as the sign of the rate of change of the drive signal changes.

[0007] In any or all of the disclosed embodiments, the hysteresis compensation portion is based on a hysteresis model of the actuator element.

[0008] In any or all of the disclosed embodiments, the hysteresis model of the actuator element includes an equation for the position of the actuator element when actuated between a first position and a second position by an uncompensated drive signal.

[0009] In any or all of the disclosed embodiments, the method further includes determining an inverse equation of the hysteresis model, wherein the hysteresis compensation portion of the drive signal is based at least in part on the inverse equation.

[0010] In any or all of the disclosed embodiments, the method further includes determining a hysteresis model for the actuator element.

[0011] In any or all of the disclosed embodiments, determining the hysteresis model further includes determining a high order polynomial based at least in part on a predetermined hysteresis parameter of the actuator element.

[0012] In any or all of the disclosed embodiments, the movement of the object along the selected path may be linear or rotational.

[0013] In any or all of the disclosed embodiments, the actuator element includes a piezoelectric material and the drive signal includes a voltage signal.

[0014] In another representative embodiment, a positioning system comprises a drive unit including an actuator element and a control system configured to select a path between a first position and a second position, generate a hysteresis-compensated drive signal, and apply the hysteresis-compensated drive signal to the actuator element to move an object along the path.

[0015] In any or all of the disclosed embodiments, the control system further comprises a processor and a memory unit in communication with the processor, the memory unit storing data of a hysteresis model of the actuator element, and the processor configured to generate a hysteresis compensated drive signal based on the hysteresis model of the actuator element.

[0016] In any or all of the disclosed embodiments, the control system further includes a processor and a memory unit in communication with the processor, the memory unit storing data of the hysteresis compensation signal, and the processor configured to generate a hysteresis compensation drive signal based on the hysteresis compensation signal.

[0017] In any or all of the disclosed embodiments, the processor is configured to identify at least one change in orientation of the actuator element along the selected path, select a hysteresis compensation signal from the memory unit based on the at least one change in orientation, and generate a hysteresis compensation drive signal based on the selected hysteresis compensation signal.

[0018] In any or all of the disclosed embodiments, the control system further includes a signal generator configured to generate a drive signal for the actuator element, and the processor is configured to identify at least one directional change based on a sign of a rate of change of the drive signal.

[0019] In any or all of the disclosed embodiments, the control system further comprises a look-up table containing a plurality of pre-defined hysteresis-compensated drive signals.

[0020] In any or all of the disclosed embodiments, the actuator element is a piezoelectric shear element, the drive unit further comprises a piezoelectric clamping element, and the positioning system further comprises a mover element coupled to the carrier element configured to hold the object, the mover element engaging the drive unit and movable relative to the drive unit to position the object along the path.

[0021] In another exemplary embodiment, a scanning transmission electron microscope includes the positioning system of any of the disclosed embodiments.

[0022] In another embodiment, the method includes applying a drive signal to move an actuator element between a first position and a second position, determining a hysteresis model for the actuator element based on movement of the actuator element between the first position and the second position, determining a hysteresis compensation signal based on the hysteresis model, applying the hysteresis compensation signal to the drive signal to generate a hysteresis compensated drive signal, and applying the hysteresis compensated drive signal to the actuator element to move an object along a selected path.

[0023] In any or all of the disclosed embodiments, determining the hysteresis model further includes determining a high order polynomial based at least in part on a predetermined hysteresis parameter of the actuator element.

[0024] In another representative embodiment, a system includes a scanning transmission electron microscope, a positioning system including a mover element and a drive unit configured to engage the mover element and move the mover element relative to the drive unit to position a workpiece relative to the scanning transmission electron microscope, a drive unit including an actuator element, and a processor configured to select a path between a first position and a second position and apply a hysteresis-compensated drive signal to the actuator element to move the mover element along the selected path.

[0025] The foregoing and other objects, features, and advantages of the disclosed technology will become more apparent with reference to the following detailed description and accompanying drawings. [Brief description of the drawings]

[0026] [Figure 1] 1 illustrates an exemplary embodiment of a multi-beam system. [Figure 2A] FIG. 1 shows a schematic cross-sectional side view of an exemplary embodiment of a positioning system mounted to the side of an electron microscope system. [Figure 2B] 2B shows the system of FIG. 2A with the workpiece displaced along the z-axis. [Diagram 3] 1 shows a schematic diagram of a position encoder according to one embodiment; [Figure 4A] FIG. 1 is a schematic diagram illustrating a front view of a drive unit engaging with a mover element according to one embodiment. [Figure 4B] FIG. 4B is a schematic diagram showing a side view of the drive unit of FIG. 4A. [Figure 5A] FIG. 2 is a perspective view of an exemplary embodiment of a longitudinal piezo element. [Figure 5B] FIG. 2 is a perspective view of an exemplary embodiment of a longitudinal piezo element. [Figure 6A] FIG. 2 is a perspective view of an exemplary embodiment of a shear piezo element. [Figure 6B] FIG. 2 is a perspective view of an exemplary embodiment of a shear piezo element. [Figure 7A]1 illustrates an exemplary drive cycle of one embodiment of a drive unit engaging with a moving element. [Figure 7B] 1 illustrates an exemplary drive cycle of one embodiment of a drive unit engaging with a moving element. [Figure 7C] 1 illustrates an exemplary drive cycle of one embodiment of a drive unit engaging with a moving element. [Figure 7D] 1 illustrates an exemplary drive cycle of one embodiment of a drive unit engaging with a moving element. [Figure 8A] 7A-7D are graphs of representative drive signals for clamping elements of the drive units of FIGS. [Figure 8B] 7A-7D are graphs of representative drive signals for shear elements of the drive units of FIGS. [Figure 9] FIG. 1 is a schematic block diagram illustrating an exemplary embodiment of a control system. [Figure 10] FIG. 2 is a perspective view of an exemplary embodiment of a longitudinal piezo element. [Figure 11] FIG. 11 is a perspective view of the longitudinal piezo element of FIG. 10 viewed from an extended position. [Figure 12] FIG. 1 is a perspective view of an exemplary embodiment of a shear piezo element deformed into a parallelogram by application of an electric field. [Figure 13A] 13C is a graph of the displacement of a shear piezo element upon application of the voltage signal of FIG. 13B. [Figure 13B] 1 is a graph of one embodiment of a voltage signal. [Figure 14] The voltage signal in FIG. 13B is plotted with the displacement of the shear piezo element on the y-axis and the voltage signal on the x-axis. [Figure 15] 15 is a graph of displacement versus voltage from FIG. 14 including two curves approximating the displacement of a piezo element for increasing and decreasing voltage. [Figure 16] 1 is a graph showing approximate values ​​of scaled voltage and scaled displacement, with scaled voltage on the horizontal axis and scaled displacement on the vertical axis. [Figure 17] 1 is a graph illustrating a representative parabola that can be used for hysteresis compensation according to the methods described herein. [Figure 18A] 1 is a graph showing a sawtooth drive signal. [Figure 18B] 4 shows the displacement behavior of a piezo element driven by a drive signal without hysteresis compensation. [Figure 19A] 18B shows the voltage signal of FIG. 18A modified according to the algorithm described herein. [Figure 19B] 1 shows the linear expansion and contraction of a piezo element during a change in direction of a voltage signal without hysteresis. [Figure 20A] 8 is a graph of an exemplary embodiment of a voltage signal input to a clamp unit of the drive unit of FIGS. 7A-7D. [Figure 20B] 1 is a graph of an unmodified shear element voltage signal according to one embodiment superimposed on a shear element voltage signal modified according to the methods described herein. [Figure 21] 11 is a graph of the position of a mover element over time when a shear element of a driver unit is driven with a modified and an unmodified voltage signal. [Figure 22] 11 is a graph of the velocity of a mover element over time when a shear element of a driver unit is driven with a modified and unmodified voltage signal. [Diagram 23] 1 illustrates a representative computer control system for use in implementing the disclosed methods and apparatus. [Figure 24] FIG. 1 is a schematic block diagram of an exemplary control system for implementing the hysteresis compensation systems and methods described herein. [Diagram 25] FIG. 2 is a schematic block diagram of another embodiment of a control system for implementing the hysteresis compensation systems and methods described herein. [Figure 26] FIG. 4 is a schematic block diagram of another embodiment of a control system for implementing hysteresis compensation using a reference capacitor. [Figure 27] FIG. 4 is a schematic block diagram of another embodiment of a control system for implementing hysteresis compensation using a reference capacitor. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0027] The present disclosure relates to a positioning system for precisely positioning a workpiece relative to an instrument, and a method for controlling such a system. The system described herein is described to enable a workpiece (semiconductor wafer or biological sample) to be precisely positioned relative to one or more tools (e.g., scanning electron microscope (SEM), transmission electron microscope (TEM), ion column, laser beam, etc.) in a process chamber where the tools and / or workpiece may be positioned at various angles, subject to the constraints of the system. More specifically, systems and methods are provided herein that enable compensation for hysteresis of actuator elements, such as piezo actuators or other actuators with components that move along an axis. By approximating the position delay due to hysteresis of the actuator element, a drive signal applied to the actuator element can be modified to compensate for the hysteresis. For example, in certain embodiments, the drive signal of the actuator element can be modified based at least in part on the inverse of the path traced by the actuator element when no hysteresis compensation is applied. As used herein, the "inverse" of an equation or function refers to the mathematical inverse f of a function f(x). -1 (f(x)), where the inverse function f -1 (f(x)) is a function of the rotational speed of the piezoelectric actuator, or the inversion of a graph of a function f(x) around an axis. Such a process can be used to repeatedly manipulate a piezo actuator in a stepping or walking drive unit to move a moving element driven by the drive unit in a 10-step fashion. -9 It is possible to position the moving element with an accuracy of about 100 mm. It is also possible to reduce or eliminate perturbations in the position and velocity of the moving element during operation.

[0028] In the following, the systems and methods are described in the context of semiconductor processing or biological sample preparation and analysis, however, the positioning systems, methods, actuators, and actuator controls described herein can be used in other fields where precise positioning and / or velocity control is required.

[0029] Example 1: Multi-beam system with hysteresis compensation 1, in an exemplary embodiment, the multi-beam system may be configured as a dual beam system 100 including a scanning electron microscope (SEM), generally designated 102, and an ion beam column, generally designated 104. The SEM 102 may include one or more charged particle beam (CPB) lenses, such as a condenser lens 116 and an objective lens 106. In some embodiments, the one or more CPB lenses may be magnetic lenses, and in particular, the objective lens 106 may be a magnetic objective lens. The ion beam column is arranged to provide a focused ion beam (FIB) to a workpiece W, and the SEM 102 is positioned to generate an image of the workpiece W.

[0030] The SEM 102 and ion beam column 104 may be mounted in a vacuum chamber 108 that houses a positioning system 110 for holding and moving the workpiece W as required. The vacuum chamber 108 may be evacuated using a vacuum pump (not shown). As discussed in more detail below, the positioning system 110 may translate the workpiece W along an X-axis, a Y-axis, and / or a Z-axis, as shown with respect to a coordinate system 150, with the Y-axis being perpendicular to the plane of the page, or rotate the workpiece W about one or more axes. In many practical examples, linear motion of the workpiece W in a direction orthogonal to the ion beam axis or electron beam axis is required, and hysteresis compensation is provided to at least the actuators associated with such translation.

[0031] In some embodiments, the SEM 102 may be disposed vertically above the workpiece W and may be used to image the workpiece W, and the ion beam column 104 may be disposed at an angle and may be used to machine and / or treat the workpiece W. Figure 1 shows an exemplary orientation of the SEM 102 and the ion beam column 104.

[0032] The SEM 102 may include an electron source 112 and may be configured to manipulate a "raw" radiation beam from the electron source 112 and perform operations thereon, such as focusing, aberration reduction, trimming (using an aperture), filtering, etc. The SEM 102 may generate a beam 114 of input charged particles (e.g., an electron beam) propagating along a particle-optical axis 115. The SEM 102 may generally include one or more lenses, such as a condenser lens 116 and an objective lens 106 (e.g., a CPB lens), for focusing the beam 114 onto a workpiece W. In some embodiments, the SEM 102 may include a deflection unit 118 that may be configured to steer the beam 114. For example, the beam 114 may be steered in a scanning motion (e.g., a raster or vector scan) across a sample being investigated or a workpiece to be processed.

[0033] The dual beam system 100 further comprises a computer processor and / or controller 128 for controlling, among other things, the deflection unit 118, the charged particle beam (CPB) lenses 106, 116, the positioning system 110, and the detector (not shown), and for displaying information collected from the detector, such as images of the workpiece or portions thereof, position information, system control data, etc. Optionally, a control computer 130 is provided for establishing various excitations, recording image data, and generally controlling the operation of both the SEM and the FIB.

[0034] With further reference to FIG. 1 , the ion beam column 104 can include an ion source (e.g., plasma source 120) and ion beam optics 122. In the illustrated embodiment, the ion beam column 104 is a plasma focused ion beam (PFIB), but in other embodiments, the ion beam column 104 can be a standard focused ion beam (FIB) with a liquid metal ion source (LMIS) or other ion source compatible with a focused ion beam column. The ion beam column 104 can generate and / or direct an ion beam 124 along an ion optical axis 125. As described above, the ion column 104 can be used to perform imaging, processing, and / or machining operations on a workpiece, such as cutting, milling, etching, deposition, etc. The hysteresis compensation positioning system can include one or more compensation actuators to provide precise positioning and velocity for imaging or processing.

[0035] In embodiments in which the ion beam is a PFIB, the ion source 120 may be fluidly coupled to multiple gases via a gas manifold 165 that includes gas sources coupled to the ion source 120 by respective valves. During operation of the ion source 120, gases may be introduced where they are charged or ionized, thereby forming a plasma. Ions extracted from the plasma may then be accelerated through the ion beam column 104 and become an ion beam. In other embodiments, the system 100 may include one or more lasers, or other types of milling or diagnostic tools.

[0036] As described above, such a multi-beam system may include a hysteresis-compensated positioning system (e.g., a stage) configured to hold and position the workpiece W. The positioning system may position / move the carrier element in multiple degrees of freedom, including linear motion (e.g., to select a particular area of ​​the workpiece for analysis) and / or angular or rotational motion (e.g., to achieve a selected angle of the workpiece relative to the instrument). Typically, a positioning system, such as positioning system 110, includes one or more hysteresis-compensated piezo actuators, as discussed below. In some examples, a controller, such as controller 128, is configured to provide a hysteresis-compensated drive signal.

[0037] Example 2: Charged particle beam system with hysteresis compensation 2A-2B show a cross-sectional view of an exemplary positioning system 200 coupled to a beam system configured as a charged particle microscope (CPM), generally designated 208. The positioning system 200 may comprise one or more drive units. For example, in the illustrated embodiment, the system may comprise three drive units, two of which, drive units 202 and 204, can be seen in FIG. 2A. In the illustrated embodiment, the drive units 202, 204 are configured as walking or stepping piezo drive units, such as Hainmade Piezo Stepper (HMPS) actuators available from Hainmade BV. However, in other embodiments, the drive units may comprise other types of actuators, such as other types of piezo actuators, voice coil motors, rack and pinion systems, linear motors, etc.

[0038] The first and second drive units 202, 204 can be configured to position the workpiece W along at least the X and Z axes of a coordinate system 206 defined with respect to the beam system 208. As noted above, the positioning system can include three or more drive units, enabling movement of the workpiece along the X, Y, and Z axes, or rotation about one or more axes. In some specific embodiments, the positioning system can include three drive units oriented such that each drive unit is offset 120 degrees from the other drive units.

[0039] As mentioned above, the positioning system 200 can be used with a multi-beam system, such as the CPM 208. The CPM 208 can be, for example, a combination of a scanning electron microscope (SEM), a transmission electron microscope (TEM), or a scanning transmission electron microscope (STEM). The CPM 208 can include a beam source 210, an upper pole objective lens 212, a lower pole objective lens 214, an optical or charged particle beam detector 216 (e.g., a camera, a photomultiplier tube, a photodiode, a CMOS detector, a CCD detector, a photocell, etc.). The components can be positioned at least partially within a vacuum chamber 218. The workpiece W is positioned on a carrier element 220, which is shown extending from the positioning system 200 into the vacuum chamber 218.

[0040] The positioning system 200 may include a frame or housing 222 attached to an exterior surface 224 of the CPM 208 (e.g., an exterior surface of the vacuum chamber 218). The housing 222 may be attached to the surface 224 using one or more bearings 226, which allows the housing 222 to tilt or rotate (e.g., about the x-axis) relative to the surface 224. In some embodiments, the bearings 226 may be coupled to a mounting element 228 disposed on the surface 224 of the CPM 208, as shown in FIG.

[0041] The housing 222 can be positioned such that a portion of the housing, including the carrier element 220 for holding the workpiece W, can extend through an opening in a side of the CPM 208 and at least partially into the vacuum chamber 218. The positioning system 200 can be configured to adjust the position of the workpiece W relative to the charged particle beam 230 by adjusting the position of the carrier element 220 using drive units (e.g., first and second drive units 202, 204), as described in more detail below.

[0042] The carrier element 220 can be coupled to first and second guides 232, 234. Each guide 232, 234 can be further coupled to a respective strut 238, 240 via a respective joint 236 (e.g., a hinge, knuckle joint, ball joint, etc.). The strut 238 can be pivotally coupled to a mover element or member 242 at a pivot joint 239, and the strut 240 can be pivotally coupled to a mover element or member 244 at a pivot joint 241. The first and second drive units 202, 204 can be configured to engage the mover elements 242 and 244, respectively. The drive unit 202 can be configured to move the mover element 242 along its axis toward and away from a rear wall 243 of the housing 222 (e.g., between a first position and a second position) in a series of step movements, as described in more detail below. The drive unit 204, like the mover element 242, can be configured to move the mover element 244 along its axis toward and away from the rear wall 245 of the housing 222. The struts 238, 240 (together with the mover elements and drive units) can be positioned at an angle relative to one another such that movement of the mover element 242 away from the rear wall 243, along with movement of the mover element 244 toward the rear wall 245, can tilt the carrier element 220 out of the XY plane, as shown in FIG. 2B. Simultaneous movement of the mover elements 242 and 244 away from the walls 243 and 245 toward the CPM 208 can move the carrier element 200 along the X-axis. In the illustrated embodiment, the mover elements 242 and 244 are positioned at an angle of 90°. In a particular embodiment, three drive units and corresponding mover elements can be arranged around the axis of the carrier element 220 at angular intervals of 120°. As discussed below, the drive units 202, 204 may include piezo actuators with hysteresis-compensated drive signals.

[0043] Each mover element 242, 244 may include a respective encoder scale 246. First and second position encoders 248 and 250 (e.g., optical encoders) mounted to the housing 222 may be configured to determine the position of each mover element 242, 244, respectively, based on the encoder scale 246. The encoder scale 246 may be coupled to or integrally formed with the movers 242, 244.

[0044] 3 shows a schematic diagram of an exemplary position encoder 300. An encoder scale 302 is attached to a moving body that may be positioned between a light source 304 and a detector 306. In certain embodiments, the light source and detector may be mounted to a housing of the positioning system.

[0045] As shown, a beam 308 produced by a light source 304 is split into two beams 310, 312 as it passes through the encoder scale 302. Two mirrors 314, 316 are used to recombine the beams and direct the combined beam 318 towards the detector 306.

[0046] 2A, each encoder 248, 250 can be configured to determine a position of the respective mover element 242, 244. The location data generated by the encoders 248, 250 can be used by the controller 252 to operate the actuators 202, 204 to position the mover elements 242, 244 at selected positions, thereby positioning the workpiece W at a selected position, as described in more detail below. The positioning system can include one or more piezo actuators that can employ the disclosed hysteresis compensation systems and methods, and an encoder such as the exemplary position encoder 300 can be used to characterize actuator hysteresis and provide position data for hysteresis compensation and control.

[0047] Example 3: Actuator drive system with hysteresis compensation 4A and 4B show an exemplary drive unit 400 in more detail, which may be configured for use with a positioning system as either drive unit 202 or 204. Drive unit 400 may engage a mover member or element 402. As described above, mover element 402 may be coupled to a carrier element and thus position a workpiece W relative to a CPM 208 or other instrument within vacuum chamber 218. In the illustrated embodiment, drive unit 400 may be a piezo drive unit comprising two sets of actuators 404, 406 housed within first and second frame or housing portions 408, 410. For example, in the illustrated embodiment, each actuator set may comprise three moveable members, referred to herein as actuators. Each actuator may then comprise one or more actuator elements, such as shear elements, clamping elements, or various combinations thereof. Each of the actuator elements may be independently moveable and / or controllable. In other embodiments, actuator sets may comprise a greater or lesser number of actuators. Additionally, while in the illustrated embodiment, each set of actuators includes the same number of actuators, in other embodiments, one set of actuators includes more or fewer actuators than the other. For example, a first set of actuators may include three actuators, a second set of actuators may include four actuators, etc. One or more (or all) of the actuators may be provided with hysteresis compensation.

[0048] 4A , the first set of actuators 404 may include a first actuator 404a disposed adjacent a first surface 412 of the mover element 402, and second and third actuators 404b, 404c disposed on opposite sides of the mover element 402 adjacent a second surface 414 of the mover element. In the illustrated embodiment, the first actuator 404a includes a shear element 420 and a clamp element 422, and the second and third actuators 404b, 404c include shear elements. As described in more detail below, the clamp and / or shear elements may frictionally engage the mover element 402 to move the mover element 402 in a selected direction.

[0049] The second set of actuators 406 may include a first actuator 406a disposed adjacent to the second surface 414 of the mover element 402, and second and third actuators 406b, 406c disposed adjacent to the first surface 412 of the mover element 402. In the illustrated embodiment, the first actuator 406a includes a shear element 424 and a clamp element 426, and the second and third actuators 406b, 406c include shear elements.

[0050] The two sets of actuators 404, 406 can be operated in an alternating, stepping, or "walking" motion such that when the first set of actuators 404 engages and applies a force to the moving body elements 402, the second set of elements 406 releases and vice versa. There can be a short period between steps when both sets of actuators 404 and 406 are in contact with the moving body 402. This is referred to as a "handover" state when one set of actuators "takes over" from the other set of actuators. This configuration, where one actuator of the set engages a first surface of the moving body elements and the second and third actuators of the set engage a second surface of the moving body elements, can help reduce distortion during operation and provide smoother movement of the moving body elements. The alternating handover action between the two sets of actuators advantageously minimizes slippage between the actuators and the moving body elements. Furthermore, this configuration allows the stroke length of the drive unit to be extended without affecting stiffness or operational performance.

[0051] When actuated, the shear elements can be displaced along the Z axis, as shown with respect to coordinate system 416, which is perpendicular to the plane of the page in Fig. 4A and parallel to the plane of the page in Fig. 4B. The clamping elements can be displaced along the Y axis. By alternating actuation of sets of actuators, large travel strokes can be achieved.

[0052] In some embodiments, the first frame portion 408 can be coupled to a biasing member 418 (e.g., a spring) that allows the first frame portion 408 to move relative to the mover element 402. In use, when the actuator element is energized in an extended position (e.g., clamp element 420 of FIG. 4A), the first frame portion 408 moves relative to the mover element 402, thereby compressing the biasing member 418. In some embodiments, the biasing member 418 can be biased to the extended position to maintain frictional contact between the actuator housed in the first portion of the frame 408 and the mover element 402.

[0053] In some embodiments, the ends of the actuators (e.g., the portions adjacent the mover elements) can be coated with aluminum oxide to reduce wear on the actuators and extend the life of the drive unit. In other embodiments, each of the clamps and / or shear elements can include a wear resistant plate configured to reduce damage to the clamps and / or shear elements due to frictional engagement with the mover.

[0054] Example 4: Clamp and shear element with hysteresis compensation 5A-5B show an exemplary embodiment of a piezo device configured as a clamping element 500, and FIGS. 6A-6B show an exemplary embodiment of a piezo device configured as a shear element 600. In the illustrated embodiment, the clamping element and the shear element comprise piezoelectric elements, one or more of which are hysteresis compensated. Other arrangements of piezo devices can be used, and the examples of FIGS. 5A-6B have been selected for convenience of illustration. In practice, piezo elements may include other components, such as housings, supports, mounts, electrical contacts, metallizations, coatings, etc., in addition to the piezoelectric material not shown in FIGS. 5A-5B and 6A-6B. For ease of illustration, such features are not described herein.

[0055] In certain embodiments, the clamping element 500 can be a longitudinal piezo element and the shearing element 600 can be a shearing piezo element. As described in more detail below, the longitudinal piezo element 500 can be configured to deform or elongate axially when a voltage is applied, and the shearing piezo element 600 can be configured to displace one end laterally relative to the opposite end when a voltage is applied. As shown in Figures 5B and 6B, in some embodiments, each element 500, 600 can comprise multiple piezoelectric members 502, 602 disposed adjacent to one another. In other embodiments, the clamping and shearing elements 500, 600 can be single layer piezo elements or monolithic multi-layer piezo elements, also referred to as monolithic co-fired piezo elements. In certain embodiments, the displacement of the clamping and / or shearing elements can be linearly related to the applied voltage. Depending on how the piezo member 502, 602 is polarized, it can be considered a longitudinal element or a shearing element. The clamping element can move between a first, or neutral, configuration, a second, elongated configuration (e.g., when energized by applying a positive voltage), and / or a third, shortened configuration (e.g., when energized by applying a negative voltage).

[0056] For example, as shown in FIG. 5A, an electric field (indicated by arrow 506) may be applied parallel to the direction of polarization (indicated by arrow 504). In some embodiments, as shown in FIG. 5B, the clamping element may include eight piezo layers, although in other embodiments, the clamping element may include a greater or lesser number of layers. In some specific embodiments, the clamping element may include three piezo layers. In some embodiments, the voltage applied to the clamping element may be, for example, between −30V and 60V.

[0057] When energized (e.g., by applying a positive or negative voltage), the clamping element 500 can expand and / or contract longitudinally, i.e., in the direction indicated by arrow 508. With reference to FIG. 5A, the clamping element 500 has a first or natural length L when no voltage is applied to the clamping element.1 and a first or neutral configuration having a second or third length L when a first or positive power is applied to the element. 2 and a second or extended configuration having a third length L when a second or negative voltage is applied to the element. 3 The second length L may have a third or contracted configuration. 2 is the first length L 1 The first length L1 can be greater than the third length L 3 The length can be based at least in part on the magnitude of the applied voltage.

[0058] 6A and 6B show an exemplary shear piezo element 600. As shown in FIG. 6A, an electric field (indicated by arrow 606) is applied orthogonal to the direction of polarization (indicated by arrow 604). In some embodiments, as shown in FIG. 6B, the shear element 600 may comprise eight layers of piezo members. However, in other embodiments, the shear element may comprise a greater or lesser number of layers. In some particular embodiments, the shear element 600 may comprise four layers of piezo members. In some embodiments, the voltage applied to the shear actuator may be between -250V and 250V, for example.

[0059] When energized (e.g., by applying a positive or negative voltage), a portion of the shear element 600 can shear or move laterally in a selected direction, as indicated by arrow 608. For example, the shearing motion causes a displacement of a first surface 610 of the shearing piezo element relative to an opposing second surface 612 of the shear element. The shear element is configured such that the first surface moves a first displacement length D when a positive voltage is applied. 1 A first surface is displaced from the second surface in the first direction by 1の The offset position and the displacement length D of the second when the first surface is subjected to a negative voltage 2 The second offset position may be displaced from the second surface in a second direction (e.g., opposite the first direction) by a displacement length D 1and D. 2 can be based at least in part on the magnitude of the applied voltage.

[0060] The piezoelectric members 502 and 602 may include, but are not limited to, ceramics (including natural and synthetic ceramics), crystals (including natural and synthetic crystals), Group III-V and II-VI semiconductors, polymers, organic nanostructures, or any combination thereof. In some particular embodiments, the piezoelectric elements may include lead zirconate titanate (PZT). Such piezoelectric elements may expand when a positive voltage is applied and contract when a negative voltage is applied. The magnitude and rate of contraction, expansion, and / or shear displacement may depend on the magnitude of the voltage applied to the piezoelectric members.

[0061] Example 5: Hysteresis Compensation Drive Unit 7A-7D show the positions of actuators of an exemplary drive unit 700 (which may be configured similarly to drive unit 400) throughout a drive cycle. Drive unit 700 is configured to engage mover element 702. Drive unit 700 includes two sets of actuators 704 and 706. Each actuator set may include three actuators. For example, actuator set 704 may include actuators 704a, 704b, and 704c, and actuator set 706 may include actuators 706a, 706b, and 706c. The actuators may include shear elements, clamp elements, and / or combinations thereof. For example, in the illustrated embodiment, actuators 704b, 704c, 706b, and 706c include shear elements. Actuator 704a may include shear element 714 and clamp element 716, and actuator 706a may include shear element 718 and clamp element 720. The actuators can be housed in first and second frame portions 708, 710. In certain embodiments, the displacement of the actuators can be linearly related to the applied voltage. Because there are two sets of actuators 704, 706, and each set can comprise two types of elements (clamp and shear), four drive signals can be used to move the sets of actuators 704, 706 in alternating fashion. In some embodiments, the drive signals can be configured as periodic waveforms (e.g., voltage waveforms) for the repetitive nature of the alternating or walking motion, although in other examples, the motion need not be periodic. For periodic or non-periodic motion, hysteresis compensation can be used, as discussed below.

[0062] In this example, actuators 704a and 706a have equal lengths, but in other examples, actuators 704a and 706a can have different lengths. In this example, there are two clamping elements 716 and 720, and six shearing elements 704b, 704c, 714, 706b, 706c, 718. However, in other examples, the drive unit can include a greater or lesser number of clamping and shearing elements.

[0063] 8A and 8B show periodic drive signals for the drive cycles shown in FIGS. 7A-7D. These drive signals are described with reference to a commutation angle α and a period of 2π radians for purposes of illustration, but may also be described as a function of time and / or position. For convenience in describing the drive cycles, the drive signals are shown without compensation. Compensated drive signals are explicitly shown in later examples. Furthermore, while the drive signals discussed herein are periodic for convenience, in other embodiments the drive signals may also be non-periodic. The commutation angle α may be defined as follows:

number

[0064] FIG. 8A illustrates an example drive or voltage signal for the clamping elements of the first and second sets of actuators, and FIG. 8B illustrates an example drive or voltage signal for the shear elements of the first and second sets of actuators. Referring now to FIG. 8A, a first voltage signal 800 can be applied to the clamping elements 716 of the first actuator set 704, and a second voltage signal 802 can be applied to the clamping elements 720 of the second actuator set 706. The voltage signals in FIG. 8A rise and fall at a constant rate between −30V and 60V. The drive signal for the clamping elements 716 can be πrad out of phase with the drive signal for the clamping elements 720, such that the voltage applied to the clamping elements 716 is 60V and the voltage applied to the clamping elements 720 is −30V, and vice versa. The period, maximum, and minimum values ​​of both signals are the same. However, in other embodiments, the drive signal for the clamping elements 716 can be different from the drive signal for the clamping elements 720.

[0065] The voltage signals 804 and 806 in Figure 8B can increase or rise from -250V to 250V at a first rate through an angle of 3π / 2 rad and decrease or rise from 250V to -250V at a second rate at an angle of π / 2 rad as in a sawtooth waveform. The signals in Figure 8B can also be out of phase or phase shifted by πrad.

[0066] Figure 7A shows the drive unit 700 in a first or starting position of the drive cycle where the commutation angle is zero. This position corresponds to the drive signal value at a commutation angle of 0 rad in Figures 8A and 8B, indicated by reference letter a. In Figures 7A-7D, the displacement of the mover element 702 is out of the plane of the page. As shown in Figure 8A, the voltages applied to the clamping elements 716 and 720 of actuators 704a and 706a are equal in length L 17A , and engage and clamp the mover element 702 between them. Referring to FIG. 8B , the voltages applied to the shear elements of actuators 704b and 704c, and to the shear element 714 of actuator 704a, may be −200V. The voltages applied to the shear elements 706b and 706c, and to the shear element 720 of actuator 706a, may be 200V. Actuators 704b, 704c, 706b, and 706c are also in contact with the mover element 702. The actuator positions in FIG. 7A may correspond to a take-over motion in which all elements of both sets of actuators 704, 706 are in equilibrium with each other and in contact with the mover 702, and actuator set 706 is not engaged with the mover 702. The derivatives of the shear voltages of the shear elements of both shear groups with respect to the commutation angle may be equal. Thus, both shear groups may move at the same speed.

[0067] 7B illustrates the drive unit in a second exemplary position in the drive cycle, corresponding to the portion of the drive signal indicated by reference letters b-c in FIGS. 8A and 8B. The clamping element 716 of the actuator 704a of the first set of actuators 704 is energized with a positive voltage, thus clamping the actuator 704a to a first length L 1 From L 1 Extended length L is greater than 2に 8A, the voltage applied to the clamping element 716 of the actuator 704a may be 60 V, and the voltage applied to the clamping element 720 of the actuator 706a may be −30 V. The expanded length L of the actuator 704a 27 moves the first frame portion 708 relative to the mover element 702 such that the actuators 706b and 706c no longer engage the mover element 702. The first frame portion 708 can be coupled to a biasing element 712. As the shear element drive signal 804 rises between 0 rad and 5π / 4 rad, the shear elements 714, 704b, and 704c displace the mover element 702 relative to the drive unit in a direction out of the page. Meanwhile, between π / 4 rad and 3π / 4 rad, the shear elements 718, 706b, and 706c are repositioned to take over from the first actuator set 704 and continue the movement of the mover element out of the plane of the page.

[0068] The biasing element 712 (e.g., a spring) can compress to allow movement of the first frame portion 708 relative to the mover element 702. Meanwhile, the clamping element 720 of the actuator 706a is energized with a negative voltage (e.g., −30V), thus clamping the actuator 706a to the first length L 1 From the length L 1 Length smaller than L 3 8B , actuator 706a moves mover element 702 to a retracted configuration having a positive bias and actuator 706b no longer engages mover element 702. Actuators 706b and 706c are in position for the next "takeover" movement, while actuators 704b, 704c, and 714 move, displace, or drive mover element 702 relative to drive unit 700 under the influence of increasing drive voltages in FIG. 8B . As shown in FIG. 8B , the voltage applied to shear elements 718, 706b, and 706c can be reduced from 250V to -250V, and the voltage applied to shear elements 714, 704b, and 704c can be increased from -50V to 50V.

[0069] Figure 7C shows the actuators in a third exemplary position in the drive cycle, corresponding to the portion of the drive signal indicated by reference letter d in Figures 8A and 8B. The third exemplary position is a second "handover" motion similar to the handover motion described above with respect to Figure 7A, where all of the actuators are in contact with mover element 702. As shown in Figure 8A, the voltages applied to clamp elements 716 and 720 of actuators 704a and 706a cause both actuators to clamp to equal lengths L 1を 8B, the voltage applied to the shear elements of actuators 704b and 704c and shear element 714 of actuator 704a may be 200V. The voltage applied to shear actuators 706b and 706c and shear element 718 of actuator 706a may be -200V.

[0070] Figure 7D shows the actuators in a fourth exemplary position in the drive cycle, corresponding to the portion of the drive signal indicated by reference letters ef in Figures 8A and 8B. This position is similar to the position shown in Figure 7B, except that the second set of actuators 706 are engaged with the mover elements 702 and the first set of actuators 704 are disengaged. The clamping element 720 of actuator 706a is energized with a positive voltage, thus clamping actuator 706a to a length L 1 From L 1 Length greater than L 28A, the voltage applied to the clamp element 720 of actuator 706a can be 60V and the voltage applied to the clamp element 716 of actuator 704a can be −30V. The extended configuration of actuator 706a can move mover element 702 (and thereby elements 704a, 706b, 706c and first frame portion 708) relative to (e.g., away from) the second frame portion 710 such that actuators 704b and 704c no longer engage mover element 702. Clamp element 716 is energized with a negative voltage (e.g., −30V), thus moving actuator 704a to an extended configuration having a first length L 1 From the length L 1 Length smaller than L 3 8B , the voltage applied to shear elements 718, 706b, and 706c can be increased from −50V to 50V, and the voltage applied to shear elements 714, 704b, and 704c can be decreased from 250V to −250V.

[0071] Because the selected drive signals of the actuator sets are periodic, the configuration of the drive unit corresponding to the portion of the drive signal indicated by reference letter g in Figures 8A and 8B is the same as the configuration shown in Figure 7A. This combination of piezo elements and drive signals enables the drive unit to move the mover element 702 in a series of steps reminiscent of a walking motion. This drive cycle can be repeated as necessary to move the mover element 702 to a selected position. The direction of the drive signal can also be reversed to move the mover element in the opposite direction.

[0072] Example 6: Exemplary Control System As mentioned above, the drive unit(s) can be used to move the mover(s) so that the workpiece W can be positioned relative to a charged particle microscope (CPM), such as a scanning transmission electron microscope (STEM). Disturbances in the position and velocity of the workpiece W can be undesirable for tracking the point-to-point movement of the workpiece W moving at a constant velocity. For example, the disturbances can cause the guidance system to lose track of the position of the workpiece and / or the selected area of ​​the workpiece that is intended to be imaged. In some embodiments, the CPM can be configured to image the workpiece W while the workpiece is moving. In such embodiments, it is particularly advantageous to have a smooth and consistent movement of the workpiece W.

[0073] An exemplary control system 808 for generating the drive signals and operating the drive units in the above sequence is shown in FIG. 9. The control system 808 may include an integrator tool or module 810 and a signal generator module 812. A piezo drive system 814 is coupled to the signal generator module 812 to adjust the drive signal for application to the piezo actuator, typically by adjusting the magnitude of the drive signal as needed. In the illustrated embodiment, a drive frequency f α A clock signal from a clock signal generator 813 or drive frequency can be provided to the integrator module 810 to establish the commutation angle α. In some cases, a digital or other representation of the drive frequency is provided, or alternatively, a periodic signal of the drive frequency is provided and used to determine the commutation angle. In other examples, a signal related to movement to a particular position or a particular speed is provided, as shown at 811. In some examples, a fixed frequency drive is used, and the commutation angle as a function of time can be pre-determined and stored in memory, such as a look-up table. As shown in FIG. 9, the integrator module 810 can output the commutation angle α to a signal generator 812, which in turn generates a corresponding signal U generated by the piezo drive system 814 when the shear and clamp elements are driven. iIn response to a position change x m 8. The piezo drive system 814 is driven by a plurality of (e.g., four) output voltage signals u i These signals can be obtained based on digital representations applied at selected frequencies and generated using one or more digital-to-analog converters. For example, there may be two types of piezo elements (e.g., shear and clamp) grouped into two sets of piezo actuators, so the signal generator in this example generates four signals or voltage functions u i to cause the drive unit to move in a selected manner. The waveform generator 812 can be configured to output any of the voltage signals described herein. Although the control system 808 shown in FIG. 9 is in a feed-forward configuration, in certain embodiments, any of a number of variables, such as the positions of the actuator elements, their velocities, etc., can be determined and fed back to those components and / or one or more other control units not shown.

[0074] The hysteresis compensation module 830 is coupled to the waveform generator 812 to provide hysteresis compensation adjustments for driving the signal from the waveform generator 812. Alternatively, such functionality may be included in the waveform generator 812. The change in direction may be provided based on the commutation angle α received from the integrator 810, or a waveform provided to the piezo drive system 814. In some cases, the control system 808 generates the drive signal based on a digital signal representation that may be stored in memory or generated as needed, using a digital-to-analog converter. For walking-type piezo positioners, a series of steps is typically required to move the workpiece to the desired location, and the drive signal from the waveform generator is periodic and provides multiple steps, with each step being associated with a different hysteresis compensation value.

[0075] Example 7: Representative Piezo Actuator The piezoelectric actuators described herein have the formula ABO3 The piezoelectric drive unit may include any of a variety of piezoelectric materials, such as ceramic materials of the perovskite family having a piezoelectric constant R, R, R, and R. For example, in certain embodiments, the piezoelectric material may include titanium zirconate titanate (PZT). In certain embodiments, the piezoelectric drive unit described herein may be a stepper motor.

[0076] Figures 10-11 show cross section A, length l 0 , and s 3 9 shows an exemplary actuator 900 having a polarization in the s direction. 3 FIG. 12 shows a cross section A and a length L O , and s 2 10 shows a representative shear piezo element 1000 with polarization in the γ direction. Unlike piezo stack elements such as clamping element 900, whose change in length is in the same direction as the applied electric field, the deformation of the shear element 1000 is orthogonal to the applied electric field. As a result, the S shear piezo element 1000 can deform from a square to a parallelogram, with the sides of the element being γ 12 Only axis S 1 and is displaced from its natural position by an amount ΔS.

[0077] Example 8: Hysteresis compensation In certain embodiments, hysteresis in a piezoelectric element can be a significant contributing factor to perturbations observed in the position and / or velocity of the mover element during operation of the drive unit. The following discussion presents control systems and methods that can be used to reduce or eliminate hysteresis in actuators that include piezoelectric elements or other types of actuators that have a stroke extending along an axis.

[0078] In certain embodiments, it is possible to at least partially compensate for the hysteresis of the piezoelectric element by modifying the voltage waveform input to the piezoelectric element. For example, the drive signal waveform can be modified with a function corresponding to the inverse of the observed displacement of the piezoelectric element to modify the displacement of the piezoelectric element. The following discussion proceeds with reference to a shear element for purposes of illustration. However, the systems and methods described herein can also be used to compensate for hysteresis in a clamping element.

[0079] In certain embodiments, the displacement of the piezo actuator element can be measured for a given drive voltage or signal. Such measurements can be performed on the actuator element in an assembled drive unit to determine the effect of the element's position on its stroke and / or displacement. For example, FIG. 13B shows an example of a drive signal in the form of a sawtooth input voltage that alternates between maximum values ​​of -250V and 250V at a constant rate or ramp. FIG. 13A shows the displacement of a shear piezo element that occurs when an alternating voltage is applied as an electrical input. For example, in the illustrated embodiment, the position plot of the shear piezo element is curved between changes in direction (corresponding to the change in direction of the voltage ramp signal). The graph in FIG. 13A shows that there can be substantial nonlinear effects caused by hysteresis in the piezoelectric material of the shear element. In certain embodiments, the displacement of the shear piezo element can be measured using a position sensor, such as the encoder embodiments described above.

[0080] FIG. 14 shows, as an example, the position or displacement of a shear piezo element on the y-axis and the applied voltage on the x-axis. It illustrates the looping effect of the displacement while the applied voltage alternates or ramps between -250V and 250V. In the ideal case, the displacement of the shear element when excited with such a waveform would extend in a straight line between -250V and 250V, regardless of the direction of the voltage ramp. Thus, hysteresis in a piezo element can result in a nonlinear displacement curve that depends on the direction of the time-varying voltage signal applied to the element.

[0081] Referring to FIG. 15, the voltage and displacement in FIG. 14 are set to 250V and 10 -6 M. The slope of the scaled voltage can also be compensated. Superimposed on FIG. 15 are two curves 1202 and 1204, where the upper curve 1202 is outlined with circle symbols and the lower curve 1204 is outlined with diamond symbols. In the example shown, the upper and lower curves are parabolas and can be approximated as follows: y 1202 =0.4(1-x 2 ) y 1204 =0.4(x 2 -1) (1)

[0082] As can be seen in the plot of Figure 15, a parabola thus defined approximates the outer displacement loop. This can be used to provide a piezo control system and method that modifies the applied voltage based on an inverse or inverse parabolic compensation to compensate for the hysteresis of the piezo element. In certain embodiments, such a modified voltage signal can provide a linear or near-linear relationship between the input voltage and the output displacement of the piezo element.

[0083] Figure 16 shows that the scaled voltage (x) is P 1 From P 2 , P 3 and P 4 , P 5 This shows how an approximation of scaled voltage and scaled displacement can be achieved when the horizontal axis is varied in 1 From P 5 indicates where the voltage signal changes direction in time. The dashed line 1400 represents the ideal displacement behavior of a piezo element. 4 and P 3 , P 5 A concave up curve 1402 extending between 2 and P 1The concave up curve 1404 extending between shows the actual displacement with increasing voltage when the signal shown in FIG. 13B is applied. 1 and P 2 A concave down curve 1406 extending between 3 , P 5 and P 4 The concave down curve 1408 extending between represents the actual displacement of the voltage down when the signal shown in FIG. 13B is applied.

[0084] The displacement as a function of applied signal for both increases and decreases in the known applied signal can be used to create a curve that extends between each pair of points and approximates the curvature of the displacement plot versus the applied voltage signal. The equation that describes the movement of the actuator element when driven by a drive signal without hysteresis compensation is referred to herein as a hysteresis model. The plot of actuator element position versus voltage in this example is curved, but in other embodiments the plot can be linear or have other shapes. In this example, the pairs are expressed as {P 1 , P 2}, {P 2 , P 3}, {P 3 , P 4} and {P 4 , P 5}. In the illustrated example, the curve may be defined by a second order polynomial such that the curve is a parabola. However, in other embodiments, the curve may be approximated by any degree of higher order polynomial. In certain embodiments, the input condition may be that all of the resulting parabolas have a constant curvature. However, in other embodiments, the curvature of one or more of the parabolas may be different. In certain embodiments, when the voltage signal changes direction (e.g., from rising to falling), a new parabola may be determined. The new parabola may be defined between a first point or voltage value at which the voltage signal changes direction and the next voltage value (e.g., a second voltage value) at which the voltage signal changes direction again. Thus, in certain embodiments, the curve may be pre-determined for a selected voltage drive signal having a predetermined waveform (e.g., calibrated to result in a selected movement of the piezo element).

[0085] A parabola can be described as a polynomial in terms of vertices and foci. v and focal point P f Equation 2 shows a representative parabola that includes: Equation 2 is a representative example of a hysteresis model that describes a parabola that can be used for hysteresis compensation in terms of its apex and focus.

number

[0086] In Equation 2, Δy f is the focus P f :(x f , v f ) and vertex P v :(x v , y v ) is the perpendicular distance between the term x f , y f represent the voltage value at the focus and the displacement value at the focus, respectively. The terms x v , y v represent the voltage and displacement at the vertex, respectively.

number

number

[0087] In certain embodiments, Δy 0 The amount of curvature, represented by , may be equal to the amount of hysteresis of the piezoelectric material, referred to herein as the hysteresis parameter. The hysteresis parameter may be expressed as a coefficient between 0 and 1, where 0 means the material exhibits no hysteresis and 1 means the displacement of the material lags the voltage by 100% of the expected displacement. However, in certain embodiments, the displacement may lag more than 100% of the expected displacement for a given applied voltage, such as by 125% or more. The displacement may also be increased by 1.25×10 to 300 V before it begins to decrease, for example, with reference to FIG. 14, application of a voltage decreasing from 250 V to 0 V may increase by 1.25×10 to 300 V before it begins to decrease. -6 M, 1×10 -6 In one exemplary embodiment, for a four-layer shear piezo element, the hysteresis parameter Δy 0 can be about 40% (0.4), which means: ΔY 0 =0.4 (4)

[0088] In certain embodiments, the hysteresis parameter Δy 0 can be determined based on measurements. In another embodiment, the hysteresis parameter Δy 0 can be determined based at least in part on variables such as the piezoelectric material(s) of a given piezoelectric actuator, the dimensions and / or shape of the piezoelectric actuator, constraints on motion imposed by the environment, or a combination thereof. When a piezoelectric actuator comprises multiple piezoelectric elements in a stacked arrangement, the hysteresis parameter Δy 0may also be determined based at least in part on the number and / or shape, thickness, etc. of stacked piezo elements. The hysteresis parameter may be the same or different for different piezo actuators in the drive unit. For example, the hysteresis parameter may be different for shear elements compared to clamp elements and / or different shear elements or different clamp elements. In certain embodiments, the hysteresis parameter(s) may be stored in a look-up table or other data structure and referenced by the controller when determining the hysteresis compensation for the selected actuator element. In some embodiments, the hysteresis parameter of the piezo element may be measured or re-evaluated periodically, such as during maintenance. In certain embodiments, according to the above equation, the hysteresis parameter Δy 0 is the focal point P f can be inversely proportional to four times the y coordinate of, but the parameters may vary depending on the function or polynomial chosen.

[0089] curve c 1、2 To define 1 , P 2}, P 1 :(x 1 , y 1 ), and P 2 :(x 2 , y 2 ), and P 1 and 2 is a point on the curve that is assumed to be known, and Equation 3 is v and y v It can be solved in terms of Y 1 and Y 2 The formula for is given below in Equation 5. y 1 =Δy 0 (x 1 -x v ) 2 +y v y 2 =Δy 0 (x 2 -x v )2 +y v (5)

[0090] x v can be solved by subtracting the two equations in Equation 5, v can be solved by adding the two equations together.

number

[0091] One exemplary method for canceling hysteresis in a piezoelectric element is to determine a function or equation that is the inverse of the hysteresis model given in Equation 3. This can be done by solving the equation for x and substituting y for x and x for y.

number

number

[0092] In certain embodiments, the voltage applied to the piezo elements in the drive unit varies over time. In certain embodiments, when the scaled voltage (x) changes direction, which may be equivalent to the voltage signal derivative with respect to time changing sign, dx / dt, y(x) can be recalculated. In certain embodiments, the algorithm can be updated for each step k, and the time between each step k is T s In such an embodiment, the procedure may be as shown in Table 2 below. [Table 1]

[0093] Referring to Table 2 above, in the first step, at time t k-1 The time derivative of the voltage x at time t kIf the absolute value of the voltage at point P is not equal to the time derivative at point P (for example, because the direction of the voltage signal has changed in a particular case), the variable d is assigned the sign of (dx / dt). 1 x in 1 If it is greater than P 2 x in 2 and y 2 can assign the value of d1; otherwise 、2 =X 1、X and Y 2 =Y 1 In certain embodiments, the point P 1 and P 2 can be predetermined based on the selected voltage waveform and can be scaled between −1 and 1. In the third step, d=1 and x is smaller than x 2 If it is greater than 1 , y 1 , x 2 and y 2 can be assigned a value corresponding to step 3 of Table 2. If d=-1 and x is x 2 If it is less than the variable x 1 , y 1 , x 2 , and y 2 can be assigned a value corresponding to step 3 of Table 2. In the fourth step, the coordinate of the apex of the hysteresis model curve (e.g., a parabola) that approximates the displacement of the piezo element for a given drive voltage signal is determined as x v and y v The point P can be calculated using the formula given in step 4 of Table 2. 1 and P 2 Since a quadratic function that approximates or represents the displacement path of the actuator element between t and t is known from Equation 3, the inverse of the path is then given in Step 4 of Table 2 (referred to herein as the inverse function or equation) y(t k ) (e.g., Equation 7). As used herein, the functions and inverse functions describing the displacement path of an actuator element can be calculated using the voltage, position, and hysteresis parameter Δy 0, and the like. The output of Equation 7 may be used as a hysteresis compensation signal. The voltage signal may then be modified according to the curve given in Equation 7 to provide the hysteresis compensation signal. Here, the output of Equation 7 is the hysteresis compensation portion of the overall drive signal. A parabola (or other curve) is fitted to the displacement versus voltage curve and the slope is compensated (e.g., P 1 is (1, 0), and P 2 If is (-1, 0), the voltage waveform given by Equation 7 can be superimposed on the initial voltage waveform. A hysteresis compensation signal can then be applied to the piezo element to compensate for the hysteresis. In other words, the curvature of the actuator element's displacement path due to hysteresis can be at least partially reversed or compensated for by modifying the drive signal with the inverse of the expected (e.g., uncompensated) path.

[0094] 18A-18B and 19A-19B show the results of a time simulation of the above algorithm. FIG. 18A shows a sawtooth drive signal, and FIG. 18B shows the displacement behavior of a piezo element driven by the drive signal without hysteresis compensation. The piezo element exhibits a curved displacement behavior characteristic of hysteresis as the voltage signal changes over time. FIG. 19A-19B show the results when the voltage signal is altered according to the above algorithm. FIG. 19A shows a voltage signal modified to exhibit curved or parabolic upward and downward slopes, and FIG. 19B shows a linear extension and contraction of the piezo element during a change in the direction of the voltage signal. As can be seen in FIG. 19A, the modified voltage signal is the inverse of the displacement plot of FIG. 18B. When the actuator element is driven with this modified voltage signal, hysteresis is almost completely eliminated, and the position plot of the actuator element traces a series of nearly unperturbed sawtooth waves.

[0095] FIG. 20A shows the drive signals of the clamp elements 716 and 720 of the drive unit of FIGS. 7A-7D. FIG. 20B shows the modified drive signals of the shear elements 714, 704b, 704c of the first group 704 and the shear elements 718, 706b, 706c of the second group 706 in dashed lines superimposed on the drive signals of the unmodified shear elements. FIG. 21 shows the measured positions of the mover elements (shown in solid lines) and the positions of the mover elements when the shear element(s) of the driver unit are driven with modified voltage signals (shown in dashed lines) as described herein. As can be seen in FIG. 21, the position perturbations can be largely eliminated by compensating for the hysteresis of the shear elements.

[0096] 22 shows the measured velocity of the mover element (shown in solid line) and the velocity of the mover element with the shear element(s) of the driver unit driven with a modified voltage signal, as described herein. As shown in FIG. 22, perturbations in the velocity of the mover element can be substantially eliminated.

[0097] In certain embodiments, the methods described herein may be implemented by a controller or processor, such as a proportional-integral-derivative (PID) controller in a control system similar to that of Figure 9. In certain embodiments, one or more measured parameters (e.g., position, velocity, etc.) may be fed back to the controller, which may modify the voltage signal based at least in part on the measured parameters.

[0098] Although the above examples are described with reference to functions relating to hysteresis, in some implementations a suitable approximation is based on stored values ​​that characterize the hysteresis of a particular actuator. These values ​​can be stored in a memory or a look-up table, or can be conveniently generated based on the functional relationships described above.

[0099] Example 9: Example of a Computing Environment FIG. 23 and the following discussion are intended to provide a brief, general description of an exemplary computing environment in which the disclosed technology may be implemented. For example, the methods and processes described herein may be executed by a controller or processor configured similarly to the computing environments described below. Additionally, the disclosed technology may be implemented in other computer system configurations, including handheld devices, digital signal processors (DSPs), multiprocessor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, and the like. The disclosed technology may also be implemented in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network.

[0100] 23, an exemplary system implementing the disclosed technology includes a general purpose controller in the form of an exemplary general purpose PC 1500, including one or more processing units 1502, a system memory 1504, and a system bus 1506 coupling various system components including the system memory 1504 to the one or more processing units 1502. The system bus 1506 may be any of several bus structures including a memory bus or memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures. The exemplary system memory 1504 includes a read only memory (ROM) 1508 and a random access memory (RAM) 1510. The ROM 1508 contains a basic input / output system (BIOS) 1512 containing the basic routines that help to transfer information between elements within the PC 1500. In the example of FIG. 20, data and processor-executable instructions for controlling positioning system movement, hysteresis control, imaging, processing, and STEM and / or FIB operating modes are stored in memory 1510A, and data and processor-executable instructions for identifying and providing drive signals to actuator elements and / or identifying and quantifying beam components are stored in memory 1510B.

[0101] The exemplary PC 1500 further includes one or more storage devices 1530, such as a hard disk drive for reading from and writing to a hard disk, a magnetic disk drive for reading from and writing to a removable magnetic disk, and an optical disk drive. Such storage devices may be connected to the system bus 1506 by a hard disk drive interface, a magnetic disk drive interface, and an optical drive interface, respectively. The drives and associated computer-readable media provide non-volatile storage of computer-readable instructions, data structures, program modules, and other data for the PC 1500. Other types of computer-readable media may store data accessible by a PC, such as magnetic cassettes, flash memory cards, digital video disks, etc.

[0102] A number of program modules may be stored on storage device 1530, including an operating system, one or more application programs, other program modules, and program data. A user may enter commands and information into PC 1500 through one or more input devices 1540, such as a keyboard, and a pointing device, such as a mouse. A monitor 1546 or other type of display device is also connected to system bus 1506 via an interface, such as a video adapter. Output, such as commands, drive signals, etc., may be transmitted via one or more output devices 1545.

[0103] The PC 1500 can operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 1560 including memory 1562. In some examples, one or more network or communication connections 1550 are included. The remote computer 1560 may be another PC, a server, a router, a network PC, or a peer device or other common network node, and typically includes many or all of the elements described above with respect to the PC 1500, although only the storage device 1562 is illustrated in FIG. 23. The personal computer 1500 and / or the remote computer 1560 can be connected to logical local area networks (LANs) and wide area networks (WANs). In certain embodiments, the remote computer 1560 can comprise a virtual processor implemented in a remote server environment or a cloud computing environment.

[0104] Example 10: Control system with hysteresis compensation 24 illustrates an exemplary embodiment of a control system 1600 for implementing the aforementioned process. The control system 1600 can be configured to compensate for hysteresis of a shear element, a clamp element, or any other actuator element in a linear or rotary actuator. The control system 1600 can include an integrator tool 1610, a clamp signal generator 1602, a shear signal generator 1604, a look-up table (LUT) 1606, and a signal modification tool or module 1608.

[0105] Drive frequency f αOr a clock signal from a clock signal generator (not shown) at the drive frequency can be provided to the integrator tool 1610 to establish the commutation angle α. In some cases, as described above, a digital or other representation of the drive frequency, or a periodic signal at the drive frequency, can be provided and used to determine the commutation angle α. The integrator tool 1610 can output the commutation angle α to the clamp signal generator 1602 and the shear signal generator 1604. The clamp signal generator 1602 can be configured to generate a number of clamp element drive signals, represented generally at 1612, that are applied to one or more clamp elements of the drive unit, represented at 1618. For example, the clamp signal generator 1602 can generate a first clamp element drive signal for a first clamp element (e.g., element 716 of FIGS. 7A-7D ) and a second clamp element drive signal for a second clamp element (e.g., clamp element 720 of FIGS. 7A-7D ). In certain embodiments, the clamp element drive signals are determined based on the commutation angle α, the drive frequency f α , a selected path of a mover element, a selected path of a clamping element (eg, to generate a movement along a selected path), etc.

[0106] The shear signal generator 1604 can be configured to generate a number of shear element drive signals, represented generally at 1616, such as a first shear element drive signal (e.g., for shear elements 714, 704b, and 704c) and a second shear element drive signal (e.g., for shear elements 718, 706b, and 706c). The shear element drive signals can correspond to the clamp element drive signals to generate a selected movement of the mover element, and can have a commutation α, a drive frequency f α , a selected path of a moving element, a selected path of a shear element, etc.

[0107] In some embodiments, the LUT 1606 may include an array of paths of the clamping and / or shearing elements (e.g., configured to effect a selected movement of the mover element). The LUT 1606 may also store a commutation angle α as a function of time. In some embodiments, the lookup table 1606 may store a signal, equation, or function that indicates the position or path of the shearing and / or clamping elements when the drive signal is applied without hysteresis compensation. In some embodiments, the LUT 1606 may include an array of hysteresis compensation signals for various commutation angles, drive frequencies, and / or actuator element paths. In some embodiments, the hysteresis compensation signals may be based on the inverse or reciprocal of a hysteresis model that describes the position or path of the shearing and / or clamping elements when the elements are driven by a selected drive signal, as described above. The hysteresis compensation signals of the LUT 1606 may be pre-calculated and stored in static program storage, calculated as part of an initialization phase of the control system, or stored in application-specific platform hardware. The LUT 1606 may also store hysteresis models for the various actuator elements.

[0108] In some embodiments, a path of an object (e.g., a moving element, a workpiece coupled to the moving element, etc.) moved by a drive unit may be selected and provided to the control system 1600. In some embodiments, the path may be selected by the signal modification tool 1608 or by another control system based on system requirements. In certain embodiments, the signal modification tool 1608 may select a hysteresis compensation signal 1620 from the LUT based on the selected path of the moving element and / or the system requirements (e.g., based on detecting a commutation angle, a sign change in the direction of the actuator element drive signal, etc.). In embodiments in which the hysteresis compensation signal 1620 is based on the path of the actuator element without hysteresis compensation, the signal modification tool 1608 may determine or calculate an inverse of the signal 1620 to obtain an inverse signal of the actuator element. The signal modification tool 1608 combines the hysteresis compensation signal with an appropriate drive signal to obtain modified or hysteresis compensated shear element drive signals 1622 and 1624 and / or hysteresis compensated clamp element drive signals 1614 and 1615. The hysteresis compensation drive signals 1614, 1615, 1622 and 1624 can be sent to a piezo drive system tool 1628, which can scale and / or condition the signals and can convert the signals from digital to analog signals using a digital-to-analog converter (DAC). The hysteresis compensation drive signal can be applied to the drive unit 1618 to move an actuator of the drive unit to generate movement of the mover element relative to the drive unit along a selected path.

[0109] In certain embodiments, the clamping element drive signal and the shear element drive signal are driven by a frequency f α Based on the frequency f α24 is a feedforward control system, in other embodiments, one or more variables, such as mover position, mover velocity, actuator position and / or velocity, voltage, etc., can be measured and fed back to a signal modification tool 1608 that can use such data to select a hysteresis compensation signal.

[0110] Example 11: Control system with hysteresis compensation 25 illustrates another exemplary embodiment of a control system 1700 for implementing the aforementioned process. The control system 1700 can be configured to compensate for hysteresis in a shear element, a clamp element, or any other type of actuator element in a linear or rotary actuator. The control system 1700 can include an integrator tool 1710, a clamp signal generator 1702, a shear signal generator 1704, a processor 1706 including a memory unit 1728, and a signal modification tool 1708.

[0111] Drive frequency f α Or a clock signal from a clock signal generator (not shown) at the drive frequency can be provided to the integrator tool 1710 to establish the commutation angle α. In some cases, as described above, a digital or other representation of the drive frequency, or a periodic signal at the drive frequency, can be provided and used to determine the commutation angle α. The integrator tool 1710 can output the commutation angle α to the clamp signal generator 1702 and the shear signal generator 1704. The clamp signal generator 1702 can be configured to generate a number of clamp element drive signals, represented generally at 1712, that are applied to one or more clamp elements of the drive unit, represented at 1710. For example, the clamp signal generator 1702 can generate a first clamp element drive signal for a first clamp element (e.g., element 716 of FIGS. 7A-7D) and a second clamp element drive signal for a second clamp element (e.g., clamp element 720 of FIGS. 7A-7D).

[0112] The shear signal generator 1704 can be configured to generate a number of shear element drive signals, represented generally at 1716, such as a first shear element drive signal (e.g., for shear elements 714, 704b, and 704c) and a second shear element drive signal (e.g., for shear elements 718, 706b, and 706c).

[0113] In some embodiments, the memory unit 1728 may include data of multiple paths of the clamping elements and / or shear elements between selected positions. In some embodiments, the memory unit 1728 may store hysteresis models of the clamping and / or shear elements. In some embodiments, the hysteresis models may include data of signals, equations, or functions that indicate the position or displacement paths of the shearing and / or clamping elements when the drive signals are applied without hysteresis compensation. In some embodiments, the memory unit 1728 may include multiple pre-calculated hysteresis compensation signals 1720 for various commutation angles, drive frequencies, and / or actuator element paths. In other embodiments, the memory unit 1728 may include data of positions and / or voltage values ​​where the drive signals of the shearing and clamping elements change direction. The data in the memory 1728 may be pre-calculated and stored in the memory 1728, calculated by the processor unit 1706 as part of an initialization phase of the control system, and / or calculated based on information of the shearing and / or clamping element drive signals 1712, 1716.

[0114] In some embodiments, the processor 1706 can calculate or determine the hysteresis compensation signal 1720 based on the drive frequency f, the commutation angle α, the selected actuator element path, and / or a plurality of predefined shear and / or clamp drive signals stored in the memory 1728. In some embodiments, a path of an object (e.g., a mover element, a workpiece coupled to the mover element, etc.) moved by the drive unit can be selected and provided to the control system 1700. In some embodiments, the path can be selected by the processor 1706 or another control system. In certain embodiments, the processor 1706 can determine the hysteresis compensation signal 1720 by identifying a change in direction of the actuator element. Such a change in direction can be identified based on a sign of the rate of change of the drive signals provided by the signal generators 1702 and 1704. In some embodiments, the hysteresis compensation signal 1720 can be based on an actuator element hysteresis model stored in the memory 1728. In certain embodiments, the hysteresis model can be based on the inverse or reciprocal of the position or path of the shear or clamp element when a drive signal is applied to the element without hysteresis compensation, as described above. In some embodiments, the processor 1706 can select a pre-calculated hysteresis compensation signal from the memory 1728.

[0115] The hysteresis compensation signal 1720 can be provided to a signal modification tool 1708, which can combine the signal 1720 with appropriate shear and / or clamp element drive signal(s) to generate hysteresis compensation shear element drive signals 1722 and 1724 and / or hysteresis compensation clamp element drive signals 1714 and 1715. The modified shear element drive signals 1722 and 1724, along with the clamp element drive signals 1714 and 1715, can be scaled and / or adjusted by a piezo drive system 1726, converted to an analog signal by a digital-to-analog converter (DAC) (e.g., part of the piezo drive system 1726), and output to a drive unit 1718 to generate movement of the mover element (e.g., mover element 702) relative to the drive unit.

[0116] In a particular embodiment, the position encoder 1730 measures the displacement x of the moving element. m and / or data for the velocity v of the moving element may be determined and the data may be sent back to the signal modification tool 1708 and / or the processor 1706. The processor 1706 may use the position and / or velocity data to determine or update a hysteresis compensation signal, update hysteresis models of actuator elements, etc.

[0117] Example 12: Hysteresis measurement and compensation using reference capacitance FIG. 26 illustrates another control system 1800 including multiple capacitors and configured to determine and / or correct hysteresis of a piezo element or set of piezo elements. For illustrative purposes, the following example proceeds with reference to three shear piezo elements 1802, 1804, and 1806, but the system may also be configured for use with clamping elements. Capacitor 1808 may be associated with shear element 1802, capacitor 1810 may be associated with shear element 1804, and capacitor 1812 may be associated with shear element 1806. Capacitors 1808-1812 may be wired in parallel, and the system may include a reference capacitor 1814 wired in series with the three capacitors 1808-1812. A reference voltage V of the piezo elements may be determined by the following equation: PIEZO、REF may be provided to a control module or tool 1816, as described further below. The voltage output by the module 1816 may be converted to an analog signal by a digital-to-analog converter (DAC) 1818 and provided at a non-inverting input to an operational amplifier 1820. The voltage V output by the amplifier 1820 may be AMPLIFIER may be provided to capacitors 1808-1812 associated with the shear elements. REF is measured across the reference capacitor 1814, converted to a digital signal by an analog-to-digital (ADC) converter 1822, and output at a summing junction 1824 as a reference signal V PIEZO、REF can be subtracted from

[0118] The modified or summed voltage signal from the summing junction 1824 can be input to the control module 1816 (e.g., as negative feedback). The control module 1816 determines the voltage drop V across the reference capacitor 1814. REF and the piezo element reference voltage V PIEZO、REF A difference between the reference voltage V and the reference voltage V may be determined and a control may be applied to reduce the difference. REF may be correlated to the hysteresis of the actuator elements 1802-1806. For example, in certain embodiments, the voltage V measured across the reference capacitor 1814REF may exhibit periodic or looping behavior similar to that of FIG. 14 or 15 due to hysteresis in the actuator elements 1802-1806. REF may also be provided to the inverting input of amplifier 1820.

[0119] In a particular embodiment, the controller 1816 applies a gain K to the summed voltage signal to produce a voltage output V to the DAC 1818, as shown in Equation 9 below: OUT can be generated. V OUT =K×(V PIEZO、REF -V REF ) (9)

[0120] In other embodiments, the controller 1816 can apply either proportional, integral, and / or derivative control, or a combination thereof. The control method can be selected to reduce hysteresis in the piezo elements 1802-1806 (e.g., V REF and V PIEZO、REF by reducing the difference between the

[0121] Control system 1800 can be used in combination with any of the motors and control systems described herein. For example, any of the piezo motors described herein can include reference capacitors similar to 1814 for each of the two groups of shear piezo elements, and a reference capacitor for each of the clamp piezo elements, which can be used to reduce hysteresis in the piezo elements.

[0122] In another embodiment shown in FIG. 27, the voltage drop V across the shear capacitors 1808-1812 is PIEZO can be provided to the ADC converter 1822.

[0123] Additional details of the piezo motors, stages, and beam systems described herein can be found in applications entitled "Systems and Methods of Clamp Compensation," filed herein and referenced by Attorney Reference Number 9748-102339-01, and in applications entitled "Electron Microscope Stage," filed herein and referenced by Attorney Reference Number 9748-102714-01, each of which is incorporated herein by reference in its entirety.

[0124] The disclosed embodiments are not limited to actuators including piezoelectric elements, but may be extended to any other type of actuator that exhibits hysteresis, such as rotary or linear motors or actuators, voice coil motors, etc.

[0125] Although the principles of the disclosure have been described and illustrated with reference to exemplary embodiments, it will be recognized that the exemplary embodiments may be modified in arrangement and detail without departing from such principles. For example, elements of an exemplary embodiment shown in software may be implemented in hardware and vice versa. Also, techniques from any embodiment may be combined with techniques described in any other one or more embodiments.

[0126] Explanation of terms For the purpose of this description, certain aspects, advantages, and novel features of the disclosed embodiments are described herein. The disclosed methods, devices, and systems should not be construed as limiting in any manner. Rather, the present disclosure is directed to all novel and non-obvious features and aspects of the various disclosed embodiments, alone and in various combinations and subcombinations with each other. The disclosed methods, devices, and systems are not limited to any particular aspect or feature or combination thereof, nor do they require any one or more particular advantages to exist or problems to be solved.

[0127] Although some operations of the disclosed methods are described in a particular order for convenience, it is to be understood that this method of description encompasses reordering, unless a particular order is required by specific language described below. For example, operations described in order may in some cases be reordered or performed simultaneously. Furthermore, for simplicity, the accompanying drawings may not show the various ways in which the disclosed methods may be used with other methods. In addition, the description may use terms such as "provide" and "achieve" to describe the disclosed methods. These terms are high-level abstractions of actual operations that are performed. The actual operations that correspond to these terms may vary depending on the particular implementation and are readily discernible to those skilled in the art.

[0128] All features described herein are independent of one another and can be used in combination with any other feature described herein, except where structurally impossible.

[0129] As used in this application and the claims, the singular forms "a," "an," and "the" include the plural forms unless the context clearly dictates otherwise. Additionally, the term "include" means "comprise." Additionally, the terms "coupled" and "associated" generally mean electrically, electromagnetically, and / or physically (e.g., mechanically or chemically) coupled or linked and do not exclude the presence of intermediate elements between coupled or associated items unless specifically stated to the contrary.

[0130] In the following description, certain terms may be used, such as "up," "down," "upper," "lower," "horizontal," "vertical," "left," and "right." These terms are used for clarity of explanation when dealing with relative relationships, where applicable. However, these terms are not intended to imply absolute relationships, positions, and / or orientations. For example, with respect to an object, a "top" surface can become a "bottom" surface simply by flipping the object over. Nevertheless, it is still the same object.

[0131] In view of the many possible embodiments to which the principles of the disclosed technology may be applied, it should be recognized that the illustrated embodiments are only preferred examples and should not be construed as limiting the scope of the disclosure. Rather, the scope of the disclosure is at least as broad as the following claims. Accordingly, we claim all that comes within the scope and spirit of those claims.

Claims

1. selecting a path between a first location and a second location; applying a drive signal including a hysteresis compensation portion to an actuator element including a piezoelectric material to move an object along the selected path; and identifying at least one change in orientation of the actuator element along the selected path, the hysteresis compensation portion being based in part on the change in orientation; The direction of the actuator element is the direction in which the actuator element is displaced.

2. The method of claim 1 , wherein the change in direction is identified based on a sign of a rate of change of the drive signal.

3. the drive signal varies between a first value and a second value to move the object along the selected path; The method of claim 1 , wherein the hysteresis compensation portion of the drive signal changes when the sign of the rate of change of the drive signal changes.

4. The method of claim 1 , wherein the hysteresis compensation portion is based on a hysteresis model of the actuator element.

5. 5. The method of claim 4, wherein the hysteresis model of the actuator element comprises an equation for a position of the actuator element when actuated between the first position and the second position by an uncompensated drive signal.

6. The method of claim 5 , further comprising determining an inverse equation of the hysteresis model, the hysteresis compensation portion of the drive signal being based at least in part on the inverse equation.

7. The method of claim 4 , further comprising determining the hysteresis model of the actuator element.

8. The method of claim 7 , wherein determining the hysteresis model further comprises determining a high order polynomial based at least in part on a predetermined hysteresis parameter of the actuator element.

9. The method of claim 1 , wherein the movement of the object along the selected path is linear or rotational.

10. The method of claim 1, wherein the drive signal comprises a voltage signal.

11. 1. A positioning system comprising: a drive unit comprising an actuator element; 1. A control system comprising: selecting a path between a first location and a second location; generating a hysteresis compensated drive signal; and a control system configured to apply the hysteresis compensated drive signals to actuator elements to move an object along the path; the control system further comprising a processor and a memory unit in communication with the processor; the processor is configured to generate the hysteresis compensated drive signal based on a hysteresis model; The processor, identifying at least one change in orientation of the actuator element along the selected path; selecting a hysteresis compensation signal from the memory unit based on the at least one change in the direction; generating the hysteresis compensation drive signal based on the selected hysteresis compensation signal; A positioning system, wherein the orientation of the actuator element is a direction in which the actuator element is displaced.

12. The memory unit stores data of a hysteresis model of the actuator element, The positioning system of claim 11 , wherein the processor is further configured to generate the hysteresis compensated drive signal based on the hysteresis model of the actuator element.

13. the control system comprising a signal generator configured to generate a drive signal for the actuator element; The positioning system of claim 11 , wherein the processor is configured to identify the at least one change in direction based on a sign of a rate of change of the drive signal.

14. The positioning system of claim 11 , wherein the control system further comprises a look-up table containing a plurality of predetermined hysteresis compensated drive signals.

15. the actuator elements are piezoelectric shear elements; the drive unit further comprising a piezoelectric clamping element; 12. The positioning system of claim 11, further comprising a mover element coupled to a carrier element configured to hold the object, the mover element engaging the drive unit and movable relative to the drive unit to position the object along the path.

16. A scanning transmission electron microscope comprising a positioning system according to claim 11.

17. applying a drive signal to move an actuator element comprising a piezoelectric material between a first position and a second position; determining a hysteresis model of the actuator element based on movement of the actuator element between the first position and the second position, the determining the hysteresis model further comprising identifying at least one change in orientation of the actuator element; determining a hysteresis compensation signal based on the hysteresis model; applying the hysteresis compensation signal to the drive signal to generate a hysteresis compensation drive signal; applying the hysteresis compensated drive signal to the actuator element to move an object along a selected path; A method, wherein the direction of the actuator element is the direction in which the actuator element is displaced.

18. The method of claim 17 , wherein determining the hysteresis model further comprises determining a high order polynomial based at least in part on a predetermined hysteresis parameter of the actuator element.

19. The method of claim 1, wherein the direction of the actuator element is a direction in which displacement of the actuator element is measured.

20. The positioning system of claim 11, wherein the direction of the actuator element is a measurement direction of displacement of the actuator element.

21. The method of claim 17, wherein the direction of the actuator element is a direction in which displacement of the actuator element is measured.

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