System and method for hysteresis compensation

Abstract

System and method for hysteresis compensation. To compensate for hysteresis of an actuator, a path between a first position and a second position can be selected, and a drive signal including a hysteresis compensation portion can be applied to an actuator element to move an object along the selected path.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to systems and methods for controlling an actuator, such as a piezoelectric actuator, to compensate for hysteresis. BACKGROUND

[0002] Piezoelectric actuators are well 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 obstacle 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. Accordingly, there is a need for improved systems and methods for controlling piezoelectric actuators. SUMMARY

[0003] The present disclosure relates to control systems and methods for controlling an actuator, such as a piezoelectric actuator, to compensate for hysteresis. In representative embodiments, 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.

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

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

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

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

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

[0009] In any and 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 and all of the disclosed embodiments, the method further includes determining a hysteresis model of the actuator element.

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

[0012] In any and all disclosed embodiments, the motion of the object along the selected path is linear or rotational.

[0013] In any and all disclosed embodiments, the actuator element comprises a piezoelectric material, and the drive signal comprises 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 the object along the path.

[0015] In any and all 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 the hysteresis-compensated drive signal based on the hysteresis model of the actuator element.

[0016] In any and all 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-compensated signal, and the processor configured to generate the hysteresis-compensated drive signal based on the hysteresis-compensated signal.

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

[0018] In any and all disclosed embodiments, the control system further comprises a signal generator configured to generate a drive signal for the actuator element, and 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.

[0019] In any and all disclosed embodiments, the control system further comprises a lookup table containing a plurality of predetermined hysteresis-compensated drive signals.

[0020] In any and all 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 a carrier element configured to hold the object, the mover element being engaged with and movable relative to the drive unit to position the object along the path.

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

[0022] In another embodiment, the method includes applying a drive signal to move the actuator element 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, 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 the object along the selected path.

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

[0024] In another representative embodiment, the 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, the 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 be more readily understood upon consideration of the following detailed description with reference to the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 A representative embodiment of a multi-beam system is illustrated.

[0027] Figure 2A A schematic cross-sectional side view of a representative embodiment of a positioning system mounted to a side of an electron microscope system is illustrated.

[0028] Figure 2B A system in which a workpiece is displaced along a z-axis is illustrated. Figure 2A A system in which a workpiece is displaced along a z-axis is illustrated.

[0029] Figure 3 A schematic diagram of a position encoder is illustrated in accordance with one embodiment.

[0030] Figure 4A A schematic diagram of an elevation view of a drive unit engaged with a mover element is illustrated in accordance with one embodiment.

[0031] Figure 4B A schematic diagram of a side view of a drive unit is illustrated. Figure 4B A schematic diagram of a side view of a drive unit is illustrated.

[0032] Figures 5A-5BThis is a perspective view of a representative embodiment of a longitudinal piezoelectric element.

[0033] Figures 6A-6B This is a perspective view of a representative embodiment of a shear piezoelectric element.

[0034] Figures 7A-7D An exemplary drive cycle is described in an embodiment of a drive unit coupled to a motion element.

[0035] Figure 8A for Figures 7A-7D A diagram showing representative drive signals for the clamping elements of the drive unit.

[0036] Figure 8B for Figures 7A-7D A diagram showing representative drive signals of the shearing element in the drive unit.

[0037] Figure 9 A schematic block diagram illustrating a representative embodiment of the control system.

[0038] Figure 10 This is a perspective view of a representative embodiment of a longitudinal piezoelectric element.

[0039] Figure 11 For being in the extended position Figure 10 A perspective view of a longitudinal piezoelectric element.

[0040] Figure 12 This is a perspective view of a representative embodiment of a shear piezoelectric element that is deformed into a parallelogram shape by applying an electric field.

[0041] Figure 13A When applied Figure 13B The diagram shows the displacement of the shear piezoelectric element when a voltage signal is applied.

[0042] Figure 13B This is a diagram of one embodiment of a voltage signal.

[0043] Figure 14 for Figure 13B A graph showing the displacement of the shear piezoelectric element on the y-axis and the displacement of the applied voltage on the x-axis.

[0044] Figure 15 for Figure 14 The displacement versus voltage graph includes two curves approximating the displacement of the piezoelectric element as the voltage increases and decreases.

[0045] Figure 16 A graph is shown to illustrate the approximate values ​​between the scaled voltage and the scaled displacement, where the scaled voltage is on the horizontal axis and the scaled displacement is on the vertical axis.

[0046] Figure 17A graph of a representative parabolic curve that can be used for hysteresis compensation according to the methods described herein.

[0047] Figure 18A A graph of a sawtooth drive signal, and Figure 18B A graph showing the displacement behavior of a piezoelectric element driven by a drive signal without hysteresis compensation.

[0048] Figure 19A A graph showing the voltage signal modified according to the algorithms described herein. Figure 18A and Figure 19B A graph showing the linear extension and contraction of a piezoelectric element between changes in direction of the voltage signal without hysteresis.

[0049] Figure 20A A graph of a representative embodiment of a voltage signal input to a clamping element of a drive unit. Figures 7A-7D

[0050] Figure 20B A graph of a shear element voltage signal that is unmodified according to one embodiment, superimposed on a shear element voltage signal modified according to the methods described herein.

[0051] Figure 21 A graph of the position of a mover element over time when the shear element of a drive unit is driven with a modified voltage signal and an unmodified voltage signal.

[0052] Figure 22 A graph of the velocity of a mover element over time when the shear element of a drive unit is driven with a modified voltage signal and an unmodified voltage signal.

[0053] Figure 23 A representative computer control system for implementing the disclosed methods and apparatus is described.

[0054] Figure 24 A schematic block diagram of a representative control system for implementing the hysteresis compensation systems and methods described herein.

[0055] Figure 25 A schematic block diagram of another embodiment of a control system for implementing the hysteresis compensation systems and methods described herein.

[0056] Figure 26 A schematic block diagram of another embodiment of a control system for implementing hysteresis compensation using a reference capacitor.

[0057] Figure 27 A schematic block diagram of another embodiment of a control system for implementing hysteresis compensation using a reference capacitor. DETAILED DESCRIPTION ​

[0058] This disclosure relates to positioning systems for precisely positioning workpieces relative to instruments and control methods for such systems. The systems described herein allow for precise positioning of workpieces (semiconductor wafers or biological samples) relative to one or more tools (e.g., scanning electron microscopes (SEM), transmission electron microscopes (TEM), ion columns, laser beams, etc.) within a processing chamber, wherein the tools and / or workpieces can be positioned at various angles depending on system limitations. More specifically, the systems and methods provided herein allow for compensation of hysteresis in actuator elements, such as piezoelectric actuators or other actuators having components that move along an axis. By approaching, the positional hysteresis due to the hysteresis of the actuator element can be modified to compensate for the hysteresis. For example, in some embodiments, when hysteresis compensation is not applied, the drive signal of the actuator element can be modified at least in part based on the path traced by the actuator element. As used herein, the “inverse” of an equation or function refers to the function… Mathematical inverse The inverse function Function The image is mirrored or reversed about the axis. Using this method, it is possible to repeatedly operate the piezoelectric actuator in a stepping or walking drive unit to move the moving element driven by the drive unit at approximately 10... -9 The system provides precise positioning accuracy (m). It can also reduce or eliminate disturbances in the position and velocity of the moving parts during operation.

[0059] The systems and methods described below are set in the context of semiconductor processing or the preparation and analysis of biological samples. However, the positioning systems, methods, actuators, and actuator controls described herein can be used in other fields requiring precise positioning and / or velocity control.

[0060] Example 1: Multi-beam system with hysteresis compensation

[0061] refer to Figure 1 In a representative embodiment, the multi-beam system may be configured as a dual-beam system 100 comprising a scanning electron microscope (SEM), generally indicated by 102, and an ion beam column, generally indicated by 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 specifically, 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.

[0062] SEM 102 and ion beam column 104 can be mounted to a vacuum chamber 108 that houses a positioning system 110 for holding and moving workpiece W as desired. Vacuum chamber 108 can be evacuated using a vacuum pump (not shown). As discussed in further detail below, positioning system 110 can move workpiece W along X, Y, and / or Z axes as shown with respect to coordinate system 150, where Y axis is perpendicular to the plane of the page, or rotate workpiece W about one or more axes. In many practical instances, linear motion of workpiece W in a direction orthogonal to the ion beam axis or electron beam axis is desired, and at least the actuator associated with such translation is provided with hysteresis compensation.

[0063] In some embodiments, SEM 102 can be arranged vertically above workpiece W and can be used to image workpiece W, and ion beam column 104 can be arranged at an angle and can be used to machine and / or treat workpiece W. Figure 1 An exemplary orientation of SEM 102 and ion beam column 104 is shown.

[0064] SEM 102 can include an electron source 112 and can be configured to manipulate a "raw" beam of radiation from electron source 112 and perform operations such as focusing, aberration mitigation, cropping (using an aperture), filtering, etc. SEM 102 can produce an input charged particle beam 114 (e.g., an electron beam) that propagates along a particle optical axis 115. SEM 102 can generally include one or more lenses (e.g., CPB lenses) that focus beam 114 onto workpiece W, such as condenser lens 116 and objective lens 106. In some embodiments, SEM 102 can be provided with a deflection unit 118 that can be configured to manipulate beam 114. For example, beam 114 can be manipulated in a scan motion (e.g., raster or vector scanning) across a sample under investigation or workpiece to be treated.

[0065] Dual beam system 100 can further include a computer processing device and / or controller 128 for controlling, among other things, deflection unit 118, charged particle beam (CPB) lenses 106, 116, positioning system 110, and a detector (not shown), and for displaying information collected from the detector on a display unit, such as images of the workpiece or portions thereof, position information, or system control data. In some cases, a control computer 130 is provided to establish various excitations, record imaging data, and generally control the operation of both the SEM and FIB.

[0066] Still referring to Figure 1The ion beam column 104 can include an ion source (e.g., a plasma source 120) and ion beam optics 122. In the illustrated embodiment, the ion beam column 104 is a plasma focused ion beam (PFIB), however, in other embodiments, the ion beam column 104 can be a standard focused ion beam (FIB) with a liquid metal ion source (LMIS) or any 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 noted above, the ion column 104 can be used to perform imaging, processing, and / or machining operations, such as cutting, milling, etching, deposition, etc. on a workpiece. The hysteresis-compensated positioning system can include one or more compensation actuators to provide precise positioning and velocity for imaging or processing.

[0067] In embodiments in which the ion beam is a PFIB, the ion source 120 can be fluidically coupled to a variety of gases via a gas manifold 165 including gas sources coupled to the ion source 120 by respective valves. During operation of the ion source 120, a gas can be introduced, where the gas becomes charged or ionized, thereby forming a plasma. Ions extracted from the plasma can then be accelerated through the ion beam column 104, becoming an ion beam. In other embodiments, the system 100 can include one or more lasers, or other types of milling or diagnostic tools.

[0068] As noted above, such multi-beam systems can include a hysteresis-compensated positioning system (e.g., a stage) configured to hold and position a workpiece W. The positioning system can position / move the carrier element in multiple degrees of freedom, including linear movement (e.g., to select a particular region for analysis of the workpiece) and / or angular or rotational motion (e.g., to achieve a selected angle of the workpiece relative to the instrument). Typically, the positioning system (e.g., the positioning system 110) includes one or more hysteresis-compensated piezoelectric actuators as discussed below. In some instances, a controller (e.g., the controller 128) is configured to provide hysteresis-compensated drive signals.

[0069] Example 2: Charged particle beam system with hysteresis compensation

[0070] Figures 2A-2B A cross-sectional view of an exemplary positioning system 200 coupled to a beam system configured as a charged particle microscope (CPM) generally indicated at 208 is shown. The positioning system 200 can include one or more drive units. For example, in the illustrated embodiment, the system can include three drive units, two of which, 202 and 204, are visible in the cross-sectional view. The positioning system 200 can be configured to position a workpiece W in a plurality of degrees of freedom, including linear movement (e.g., to select a particular region for analysis of the workpiece) and / or angular or rotational motion (e.g., to achieve a selected angle of the workpiece relative to the instrument). Typically, the positioning system (e.g., the positioning system 110) includes one or more hysteresis-compensated piezoelectric actuators as discussed below. In some instances, a controller (e.g., the controller 128) is configured to provide hysteresis-compensated drive signals. Figure 2AIn the illustrated embodiment, the drive units 202, 204 are configured to walk or step piezoelectric drive units, such as the piezoelectric stepper (HMPS) actuators available from Heinmade BV. However, in other embodiments, the drive units can include other types of actuators, such as other types of piezoelectric actuators, voice coil motors, rack and pinion systems, linear motors, etc.

[0071] 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 the coordinate system 206 defined relative to the beam system 208. As noted above, the positioning system can include three or more drive units, allowing the workpiece to be moved along the X, Y, and Z axes or rotated about one or more axes. In some particular embodiments, the positioning system can include three drive units oriented such that each drive unit is offset 120 degrees from the others.

[0072] As noted above, the positioning system 200 can be used with a multi-beam system, such as a CPM 208. The CPM 208 can be, for example, a scanning electron microscope (SEM), a transmission electron microscope (TEM), or a combination of scanning and transmission electron microscopes (STEM). The CPM 208 can include a beam source 210, an upper pole objective 212, a lower pole objective 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 photovoltaic cell, etc.). The components can be positioned at least partially within a vacuum chamber 218. The workpiece W is positioned on a carrier element 220 shown extending from the positioning system 200 into the vacuum chamber 218.

[0073] The positioning system 200 can include a frame or housing 222 mounted on an outer surface 224 of the CPM 208 (e.g., an outer surface of the vacuum chamber 218). One or more bearings 226 can be used to mount the housing 222 to the surface 224, which allows the housing 222 to be tilted or rotated (e.g., about the x-axis) relative to the surface 224. In some embodiments, as shown in FIG. 2, the bearings 226 can be coupled to a mounting element 228 disposed on the surface 224 of the CPM 208.

[0074] The housing 222 can be disposed 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 carrier element 220, and thus the workpiece W relative to the charged particle beam 230, by using the drive units (e.g., the first and second drive units 202, 204), as described in more detail below.

[0075] 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, a knuckle joint, a spherical joint, etc.). The strut 238 can be pivotably coupled at a pivot joint 239 to a mover element or member 242, and the strut 240 can be pivotably coupled at a pivot joint 241 to a mover element or member 244. 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 stepwise motions, as described in greater detail below. The drive unit 204 can be configured to move the mover element 244 along its axis toward and away from a rear wall 245 of the housing 222, similar to the mover element 242. The struts 238, 240 (and mover elements and drive units) can be positioned at an angle relative to each other such that movement of the mover element 242 away from the rear wall 243, and movement of the mover element 244 toward the rear wall 245, can cause the carrier element 220 to tilt away from the X-Y plane, as shown in Figure 2B The simultaneous movement of the mover elements 242 and 244 away from the walls 243 and 245 and 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 a 90° angle. In certain embodiments, three drive units and corresponding mover elements can be arranged at 120° angles around the axis of the carrier element 220. As discussed below, the drive units 202, 204 can include piezoelectric actuators provided with hysteresis-compensated drive signals.

[0076] Each mover element 242, 244 can include a respective encoder scale 246. First and second position encoders 248 and 250 (e.g., optical encoders) mounted to the housing 222 can be configured to determine the position of each mover element 242, 244 based on the encoder scale 246, respectively. The encoder scale 246 can be coupled to or integrally formed with the mover 242, 244.

[0077] Figure 3 A schematic diagram illustrating an example position encoder 300 is shown. An encoder scale 302 is mounted to a mover, which can be positioned between a light source 304 and a detector 306. In certain embodiments, the light source and detector can be mounted to a housing of the positioning system.

[0078] As shown, the beam 308 produced by the 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 into the detector 306.

[0079] Referring again to Figure 2A Each encoder 248, 250 can be configured to determine the position of the respective mover element 242, 244. The position data produced 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 selected positions, as described in greater detail below. The positioning system can include one or more piezoelectric actuators, where the disclosed hysteresis compensation system and method can be used, and an encoder, such as the exemplary position encoder 300, can be used to characterize the actuator hysteresis and provide position data for compensation and control of the hysteresis.

[0080] Example 3: Actuator drive system with hysteresis compensation

[0081] Figure 4A And 4B An exemplary drive unit 400 is illustrated in greater detail, which can be configured for use with a positioning system as drive unit 202 or 204. The drive unit 400 can engage a mover member or element 402. As described above, the mover element 402 can be coupled to a load element, and thus can position the workpiece W in the vacuum chamber 218 relative to the CPM 208 or other instrument. In the illustrated embodiment, the drive unit 400 can be a piezoelectric drive unit including two sets of actuators 404, 406 housed within first and second frames or housing portions 408, 410. For example, in the illustrated embodiment, each set of actuators can include three movable members, referred to herein as actuators. Each actuator in turn can include one or more actuator elements, such as shear elements, clamping elements, or various combinations thereof. Each of the actuator elements can be independently movable and / or controllable. In other embodiments, a set of actuators can include a greater or lesser number of actuators. Further, although in the illustrated embodiment each set of actuators includes an equal number of actuators, in other embodiments one set of actuators can include more or fewer actuators than the other set. For example, the first set of actuators can include three actuators, while the second set of actuators can include four actuators, etc. One or more (or all) of the actuators can be provided with hysteresis compensation.

[0082] Returning Figure 4AThe first set of actuators 404 can 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 clamping element 422 and a shear element 420, and the second and third actuators 404b, 404c include shear elements. The clamping and / or shear elements can frictionally engage the mover element 402 to move the mover element 402 in a selected direction, as described in greater detail below.

[0083] The second set of actuators 406 can include a first actuator 406a disposed adjacent the second surface 414 of the mover element 402, and second and third actuators 406b, 406c disposed adjacent the first surface 412 of the mover element 402. In the illustrated embodiment, the first actuator 406a includes a clamping element 426 and a shear element 424, and the second and third actuators 406b, 406c include shear elements.

[0084] The two sets of actuators 404, 406 can be actuated in an alternating, step or "walk" motion, such that when the first set of actuators 404 is engaged with and applying a force to the mover element 402, the second set of elements 406 is disengaged or released from the mover element, and vice versa. There can be a brief period of time between steps when both sets of actuators 404 and 406 are in contact with the mover 402. When one set of actuators "takes over" from the other set of actuators, this is referred to as a "takeover" condition. This configuration, in which one actuator of a set engages a first surface of the mover element, and the second and third actuators of a set engage a second surface of the mover element, helps to mitigate distortion during operation, and can provide smoother motion of the mover element. The alternating takeover movement between the two sets of actuators advantageously minimizes slippage between the actuators and the mover element. In addition, this configuration allows the stroke length of the drive unit to be extended without impacting stiffness or motion performance.

[0085] When actuated, the shear elements can displace along the Z-axis, as shown with respect to coordinate system 416, where the Z-axis is perpendicular to the page plane in Figure 4A and parallel to the page plane in Figure 4B The clamping elements can displace along the Y-axis. Large movement strokes can be achieved through alternating actuation of the sets of actuators.

[0086] 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 elements are energized to an extended position (e.g., as shown in FIG. 4), the biasing member 418 is compressed. When the actuator elements are de-energized, the biasing member 418 expands and moves the first frame portion 408 relative to the mover element 402. This allows the first frame portion 408 to move relative to the mover element 402, which can help to reduce distortion and improve motion performance. Figure 4AThe first frame portion 408 is moved relative to the mover element 402, thereby compressing the biasing member 418. In some embodiments, the biasing member 418 can be biased to an extended position in order to maintain a frictional contact between the actuator housed in the first portion of the frame 408 and the mover element 402.

[0087] In some embodiments, the end portion of the actuator (e.g., the portion proximate to the mover element) can be coated with aluminum oxide to mitigate wear on the actuator and prolong the life of the drive unit. In other embodiments, each of the clamping and / or shearing elements can include a wear plate configured to mitigate damage to the clamping and / or shearing elements that are in frictional contact with the mover.

[0088] Example 4: Clamping and shearing elements with hysteresis compensation

[0089] Figures 5A-5B An exemplary embodiment of a piezoelectric device configured as a clamping element 500 is shown, and Figures 6A-6B An exemplary embodiment of a piezoelectric device configured as a shearing element 600 is shown. In the illustrated embodiment, the clamping and shearing elements include piezoelectric elements, one or more of which are hysteresis compensated. Other arrangements of piezoelectric devices can be used, and for ease of illustration, the example of Figures 5A-6B In practice, the piezoelectric elements can include other components in addition to the piezoelectric material not shown in Figures 5A-5B and 6A-6B, such as housings, supports, mounts, electrical contacts, metallized portions, coatings, etc. For ease of illustration, these features are not shown here.

[0090] In certain embodiments, the clamping element 500 can be a longitudinal piezoelectric element, and the shearing element 600 can be a shear piezoelectric element. The longitudinal piezoelectric element 500 can be configured to axially deform or elongate when a voltage is applied, and the shear piezoelectric element 600 can be configured so that one end is displaced laterally relative to the opposite end when a voltage is applied, as explained in detail below. As Figure 5B and 6B In some embodiments, each element 500, 600 can include a plurality of piezoelectric members 502, 602 disposed adjacent to one another, as shown in

[0091] For example, as shown in FIG. 6, an electric field (shown by arrow 606) can be applied perpendicular to the direction of polarization (shown by arrow 604). In some embodiments, as shown in FIG. 6, the clamping element can include eight layers of piezoelectric material. However, in other embodiments, the clamping element can include a greater or fewer number of layers. In some specific embodiments, the clamping element can include four layers of piezoelectric material. In some embodiments, the voltage applied to the clamping element can be, for example, between -250 V and 250 V. Figure 5A Figure 5B

[0092] 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 shown by arrow 508). Referring to FIG. 5, the clamping element 500 can have a first or neutral configuration having a first or natural length LI when no voltage is applied to the clamping element, a second or expanded configuration having a second length L2 when a first or positive voltage is applied to the element, and a third or contracted configuration having a third length L3 when a second or negative voltage is applied to the element. The second length L2 can be greater than the first length LI, which can be greater than the third length L3. The lengths can be based at least in part on the magnitude of the applied voltage. Figure 5A

[0093] Figure 6A and 6B An exemplary shear piezoelectric element 600 is illustrated. As shown in FIG. 6, an electric field (shown by arrow 606) is applied perpendicular to the direction of polarization (shown by arrow 604). In some embodiments, as shown in FIG. 6, the shear element 600 can include eight layers of piezoelectric material. However, in other embodiments, the shear element can include a greater or fewer number of layers. In some specific embodiments, the shear element 600 can include four layers of piezoelectric material. In some embodiments, the voltage applied to the shear actuator can be, for example, between -250 V and 250 V. Figure 6A Figure 6B

[0094] 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 shown by arrow 608. For example, the shearing motion causes a first surface 610 of the shear piezoelectric element to displace relative to a second surface 612 on an opposite side of the shear element. The shear element can have a first displacement position in which the first surface displaces from the second surface a first displacement length Dl in a first direction when a positive voltage is applied, and a second displacement position in which the first surface displaces from the second surface a second displacement length D2 in a second direction (e.g., opposite the first direction) when a negative voltage is applied. The displacement lengths Dl and D2 can be based at least in part on the magnitude of the applied voltage.

[0095] ​​​​​The piezoelectric members 502 and 602 can include, but are not limited to, ceramics (including naturally occurring and synthetic ceramics), crystals (including naturally occurring and synthetic crystals), III-V and II-VI semiconductors, polymers, organic nanostructures, or any combination thereof. In some embodiments, the piezoelectric elements can include lead zirconium titanate (PZT). Such piezoelectric elements can expand when a positive voltage is applied and contract when a negative voltage is applied. The magnitude and speed of the contraction, expansion, and / or shear displacement can depend on the magnitude of the voltage applied to the piezoelectric member.

[0096] Example 5: Hysteresis compensation drive unit

[0097] Figures 7A-7D The positions of the actuators of an exemplary drive unit 700 (which can be configured similarly to drive unit 400) are shown throughout a drive cycle. Drive unit 700 is configured to engage a mover element 702. Drive unit 700 includes two sets of actuators 704 and 706. Each set of actuators can include three actuators. For example, set of actuators 704 can include actuators 704a, 704b, and 704c, and set of actuators 706 can include actuators 706a, 706b, and 706c. The actuators can 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 can include a shear element 714 and a clamp element 716, and actuator 706a can include a shear element 718 and a 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. Since there are two sets of actuators 704, 706, and each set can include two types of elements (clamp and shear), four drive signals can be used to move a set of actuators 704, 706 in an alternating fashion. In some embodiments, the drive signals can be configured as periodic waveforms (e.g., voltage waveforms) due to the repetitive nature of the alternating or walking movement, although in other instances the movement need not be periodic. For periodic or non-periodic movement, hysteresis compensation as discussed below can be used.

[0098] In this example, actuators 704a and 706a have equal lengths, however, in other examples, actuators 704a and 706a can have different lengths. In this example, there are two clamp elements 716 and 720 and six shear elements 704b, 704c, 714, 706b, 706c, 718. However, in other examples, a drive unit can include a greater or lesser number of clamp and shear elements.

[0099] Figure 8A and 8B illustrated in Figures 7A-7DThe periodic drive signals of the drive cycle are shown in the diagram. For illustrative purposes, these drive signals are described with reference to the commutation angle α and the periodic radians of 2π, but they can also be described as functions of time and / or position. For ease of illustration of the drive cycle, an uncompensated drive signal is shown. Compensated drive signals will be explicitly shown in later examples. Furthermore, although the drive signals discussed herein are periodic for ease of description, in other embodiments, the drive signals may also be aperiodic. The commutation angle α can be defined as:

[0100]

[0101] in f α The driving frequency of the driving signal. t For time. In this example, the initial value of the commutation angle α is 0.

[0102] Figure 8A Exemplary drive or voltage signals are shown for the clamping elements of the first and second sets of actuators, and Figure 8B An exemplary drive or voltage signal is shown for the shear element of the first and second sets of actuators. Now refer to... Figure 8A A first voltage signal 800 can be applied to the clamping element 716 of the first actuator group 704, and a second voltage signal 802 can be applied to the clamping element 720 of the second actuator group 706. Figure 8A The voltage signal in the clamping element 716 ramps up and down at a constant rate between -30 V and 60 V. The drive signal of clamping element 716 may be out of phase with the drive signal π rad of clamping element 720, such that when the voltage applied to clamping element 716 is 60 V, the voltage applied to clamping element 720 is −30 V, and vice versa. Both signals have the same period, maximum value, and minimum value. However, in other embodiments, the drive signal of clamping element 716 may be different from the drive signal of clamping element 720.

[0103] exist Figure 8B Voltage signals 804 and 806 in the first rate can pass through The rad angle is increased from −250 V or ramped up to 250 V, and can be transmitted in a sawtooth wave manner at a second rate. The angle of the rad decreases from 250 V or slopes back to −250 V. In Figure 8B The signal in the signal can also be out of phase or phase-shifted by π rad.

[0104] Figure 7A The diagram shows a drive unit 700 in the first or starting position during a drive cycle in which the commutation angle is zero. This position is related to... Figure 8A and 8BThe drive signal value at the commutation angle of 0 rad corresponds to the reference letter. a Instructions. In Figures 7A-7D In this case, the displacement of the mover element 702 leaves the plane of the page. For example... Figure 8A As shown, the voltages applied to the clamping elements 716 and 720 of actuators 704a and 706a are equal at 0 rad, such that the two actuators have equal lengths L1, and engage and clamp the mover element 702 between them. Reference Figure 8B The voltage applied to the shear elements of actuators 704b and 704c and the shear element 714 of actuator 704a can be −200 V. The voltage applied to the shear elements 706b and 706c and the shear element 720 of actuator 706a can be 200 V. Actuators 704b, 704c, 706b, and 706c are also in contact with the mover element 702. Figure 7A The position of the actuators in the actuator assembly corresponds to the movement of the "pipeline," where all elements of the two sets of actuators 704 and 706 are balanced with each other and in contact with the mover 702, and before the actuator assembly 706 disengages from the mover 702. In both shear groups, the derivatives of the commutation angles of the shear voltages with respect to the shear elements can be equal. Therefore, the two shear groups can move at the same speed.

[0105] Figure 7B This illustrates a drive unit in a second exemplary position during a drive cycle, corresponding to... Figure 8A and 8B The middle is composed of reference letters b-c The driving signal shown is a portion thereof. The clamping element 716 of the actuator 704a in the first group of actuators 704 is positively voltage-energized, thereby moving the actuator 704a from a first length L1 to an extended length L2 greater than L1. As... Figure 8A As shown, the voltage applied to the clamping element 716 of actuator 704a can be 60 V, and the voltage applied to the clamping element 720 of actuator 706a can be -30 V. The extended length L2 of actuator 704a moves the first frame portion 708 relative to the mover element 702, such that actuators 706b and 706c are no longer engaged with the mover element 702. The first frame portion 708 can be coupled to the bias element 712. When the shear element drive signal 804 is at 0 rad and... When the speed increases by rad, shear elements 714, 704b, and 704c displace the actuator element 702 relative to the drive unit in the direction away from the page. Simultaneously, in rad and Between rad, shear elements 718, 706b, and 706c are repositioned to take over from the first actuator group 704, and the mover elements continue to move away from the plane of the page.

[0106] A compressible biasing element 712 (e.g., a spring) allows the first frame portion 708 to move relative to the mover element 702. Simultaneously, a negative voltage (e.g., -30 V) actuates the clamping element 720 of actuator 706a, thereby moving actuator 706a from a first length L1 to a retracted configuration with a length L3 less than length L1, such that actuator 706a no longer engages mover element 702. Actuators 706b and 706c are in the next "pivot" movement position, while... Figure 8B Under the influence of the increased driving voltage, actuators 704b, 704c, and 714 move, displace, or drive the actuator element 702 relative to the drive unit 700. For example... Figure 8B As shown, the voltage applied to shear elements 718, 706b and 706c can drop from 250 V to -250 V, and the voltage applied to shear elements 714, 704b and 704c can rise from -50 V to 50 V.

[0107] Figure 7C The actuator is shown in the third exemplary position during the drive cycle, corresponding to the position in Figure 8A and 8B The middle is composed of reference letters d The indicated drive signal portion. The third exemplary position is the second "controller" movement, similar to the above regarding... Figure 7A The described control unit movement involves all actuators contacting the actuator element 702. (As follows) Figure 8A As shown, the voltages applied to the clamping elements 716 and 720 of actuators 704a and 706a are equal at 0 rad, such that the two actuators have equal lengths L1, and engage and clamp the mover element 702 between them. Reference Figure 8B The voltage applied to the shear elements of actuators 704b and 704c and the shear element 714 of actuator 704a can be 200 V. The voltage applied to the shear element 718 of shear actuators 706b and 706c and actuator 706a can be -200 V.

[0108] Figure 7D The actuator is shown in the fourth exemplary position during the drive cycle, corresponding to the position in Figure 8A and 8B The middle is composed of reference letters e-f The portion of the drive signal shown. This location is similar to... Figure 7B The positions shown are exceptions, except that the second set of actuators 706 engages with the mover element 702 and the first set of actuators 704 disengages. The clamping element 720 of actuator 706a is actuated with a positive voltage, thereby moving actuator 706a from length L1 to an extended configuration having a length L2 greater than L1. Figure 8AAs shown, the voltage applied to the clamping element 720 of actuator 706a can be 60 V, and the voltage applied to the clamping element 716 of actuator 704a can be -30 V. The extended configuration of actuator 706a can move the 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 are no longer engaged with the mover element 702. Actuator 704a is energized with a negative voltage (e.g., -30 V), thereby moving actuator 704a from the first length LI to a retracted configuration having a length L3 that is less than length LI, such that actuator 704a is not engaged with the mover element 702. Actuators 704b and 704c are in position for the next "hand-off" movement, while actuator 706b and 706c drive or displace the mover element 702 due to the increase in drive voltage in Figure 8B As shown, the voltage applied to the clamping element 720 of actuator 706a can be 60 V, and the voltage applied to the clamping element 716 of actuator 704a can be -30 V. The extended configuration of actuator 706a can move the 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 are no longer engaged with the mover element 702. Actuator 704a is energized with a negative voltage (e.g., -30 V), thereby moving actuator 704a from the first length LI to a retracted configuration having a length L3 that is less than length LI, such that actuator 704a is not engaged with the mover element 702. Actuators 704b and 704c are in position for the next "hand-off" movement, while actuator 706b and 706c drive or displace the mover element 702 due to the increase in drive voltage in Figure 8B As shown, the voltage applied to the clamping element 720 of actuator 706a can be 60 V, and the voltage applied to the clamping element 716 of actuator 704a can be -30 V. The extended configuration of actuator 706a can move the 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 are no longer engaged with the mover element 702. Actuator 704a is energized with a negative voltage (e.g., -30 V), thereby moving actuator 704a from the first length LI to a retracted configuration having a length L3 that is less than length LI, such that actuator 704a is not engaged with the mover element 702. Actuators 704b and 704c are in position for the next "hand-off" movement, while actuator 706b and 706c drive or displace the mover element 702 due to the increase in drive voltage in

[0109] Because the selected drive signals of the actuator set are periodic, the configuration of the drive cells corresponding to the portions of the drive signals indicated by reference letter g in Figure 8A and 8B are the same as the configuration shown in Figure 7A This combination of piezoelectric elements and drive signals enables the drive cells to move the mover element 702 in a series of steps reminiscent of a walking motion. This drive cycle can be repeated as needed in order to move the mover element 702 to a selected position. The direction of the drive signals can also be reversed in order to move the mover element in the opposite direction.

[0110] Example 6: Exemplary control system

[0111] As previously described, the drive cell(s) can be used to move the mover(s), thereby positioning the workpiece W relative to a charged particle microscope (CPM), such as a scanning transmission electron microscope (STEM). In order to track a point-to-point motion of the workpiece W traveling at a constant speed, perturbations in the position and speed of the workpiece W can be undesirable. For example, the perturbations can cause the guidance system to lose track of the positioning of the workpiece and / or the selected region of the workpiece to be imaged. In some embodiments, the CPM can be configured to image the workpiece W while the workpiece is in motion. In such embodiments, it is particularly advantageous to have smooth and consistent movement of the workpiece W.

[0112] In Figure 9An exemplary control system 808 for producing drive signals and operating drive units in the sequence described above is shown in FIG. 8. Control system 808 can include an integrator tool or module 810 and a signal generator module 812. A piezoelectric drive system 814 is coupled to signal generator module 812 to condition drive signals for application to piezoelectric actuators, typically by conditioning the drive signal size as needed. In the illustrated embodiment, a drive frequency faor a clock signal from a clock signal generator 813 at the drive frequency can be provided to integrator module 810 to establish a commutation angle a. In some cases, a digital or other representation of the drive frequency is provided; alternatively, a periodic signal at the drive frequency is provided and used to determine the commutation angle. In other examples, as shown at 811, a signal associated with moving to a specified position or a particular velocity is provided. In some examples, a fixed frequency drive is used, and the commutation angle as a function of time can be predetermined and stored in memory, such as in a lookup table. As Figure 9 shown, integrator module 810 can output the commutation angle a to signal generator 812, which can generate a plurality (e.g., four) of output voltage signals u i for the shear and clamp elements to produce position changes U i x m in response to corresponding signals u i generated by piezoelectric drive system 814. These signals can be obtained based on digital representations applied at a selected frequency and generated using one or more digital-to-analog converters. Because two types of piezoelectric elements (e.g., shear and clamp) can be grouped into, for example, two sets of piezoelectric actuators, the signal generator in this example can output four signals or voltage functions Figure 9 i to move the drive units in a selected manner. Waveform generator 812 can be configured to output any of the voltage signals described herein. Although control system 808 shown in

[0113] Hysteresis compensation module 830 is coupled to waveform generator 812. It provides hysteresis compensation adjustments to the drive signal from waveform generator 812. Alternatively, such functionality can be included in waveform generator 812. The direction change can be provided based on commutation angle a received from integrator 810 or the waveform provided to piezoelectric drive system 814. In some cases, control system 808 is based on digital signal representations that can be stored in memory or generated as needed, with digital to analog converters used to generate the drive signals. For walking type piezoelectric positioners, a series of steps is typically required to move a workpiece to a desired position, and the drive signal from the waveform generator is periodic to provide the multiple steps, and each step can be associated with a different hysteresis correction value.

[0114] Example 7: Representative piezoelectric actuator

[0115] The piezoelectric actuators described herein can include any of a variety of piezoelectric materials, such as ceramic materials of the perovskite family having the formula ABO3. For example, in certain embodiments the piezoelectric material can include lead zirconate titanate (PZT). In particular embodiments, the piezoelectric drive units described herein can be stepper motors.

[0116] Figures 10-11 A representative example of a shear piezoelectric element 1000 is shown having a cross section , a length , and polarized in the direction. Thus, the actuator 900 can extend and contract in the direction. Figure 12 A representative example of a shear piezoelectric element 1000 is shown having a cross section , a length , and polarized in the direction. Thus, the actuator 900 can extend and contract in the direction. Figure 12 As a result, the shear piezoelectric element 1000 can be deformed from a square shape to a parallelogram shape, with the side surfaces of the element rotated by an angle γ12about the axis S1and the upper surface displaced by an amount ΔSfrom its natural position.

[0117] Example 8: Hysteresis compensation

[0118] In certain embodiments, the hysteresis of a piezoelectric element can be an important contributor to the perturbations in the position and / or velocity of a mover element observed during operation of a 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 that extends along an axis.

[0119] In some embodiments, the hysteresis of a piezoelectric element can be at least partially compensated by modifying the voltage waveform input to the piezoelectric element. For example, the drive signal waveform can be modified as a function corresponding to the inverse of the observed displacement of the piezoelectric element, thereby modifying the displacement of the piezoelectric element. For illustrative purposes, reference is made to a shearing element in the following discussion. However, the systems and methods described herein can also be used to compensate for the hysteresis of clamping elements.

[0120] In some embodiments, for a given drive voltage or signal, the displacement of the piezoelectric actuator element can be measured. This can be done for actuator elements in an assembled drive unit to determine the effect of the element's position on its stroke and / or displacement. For example, Figure 13B This illustrates an example of a drive signal in the form of a sawtooth input voltage that alternates at a constant rate or ramp between the maximum value of -250 V and 250 V and values ​​in between. Figure 13A This describes the displacement generated by the shear piezoelectric element when alternating voltages are applied as an electrical input. For example, in the illustrated embodiment, the positional pattern of the shear piezoelectric element bends between changes in direction (corresponding to changes in the direction of the voltage ramp signal). Figure 13A The figure illustrates the substantially nonlinear effect caused by the hysteresis of the piezoelectric material of the shear element. In some embodiments, the displacement of the shear piezoelectric element can be measured using a position sensor, such as the encoder embodiment described above.

[0121] Figure 14 This diagram illustrates the position or displacement of a shear piezoelectric element on the y-axis and the applied voltage on the x-axis. It demonstrates the loop effect of the displacement when the applied voltage alternates or sags between -250V and 250V. Ideally, when a shear element is excited by such a waveform, its displacement would produce a straight line extending between -250V and 250V, independent of the direction of the voltage sag. Therefore, the hysteresis of the piezoelectric element can lead to a nonlinear displacement curve that depends on the direction of the time-varying voltage signal applied to the element.

[0122] refer to Figure 15 ,exist Figure 14 The voltage and displacement in the middle are 250 V and 10 respectively. -6 m-scaling is used to account for displacement errors. It can also compensate for the slope of the scaled voltage. Superimposed on... Figure 15 The figures above show two curves, 1202 and 1204, where the upper curve 1202 is outlined with a circle and the lower curve 1204 with a diamond. In the illustrated example, the upper and lower curves are parabolas, which can be approximated as:

[0123]

[0124] If available Figure 15As shown in the figure, the parabola defined in this way approximates an external displacement loop. This can be used to provide piezoelectric control systems and methods that modify the applied voltage based on inverse or parabolic compensation to compensate for the hysteresis of the piezoelectric element. In some embodiments, such modified voltage signals can result in a linear or nearly linear relationship between the input voltage and output displacement of the piezoelectric element.

[0125] Figure 16 Showing the voltage when scaled ( How can an approximation between scaling voltage and scaling displacement be achieved when the voltage signal varies from P1 to P2 to P3 to P4 to P5 on a horizontal axis? In the illustrated example, points P1 to P5 indicate the locations where the voltage signal changes direction over time. The dashed line 140° represents the ideal displacement behavior of the piezoelectric element. When applied... Figure 13B The concave curve 1402 extending between P4 and P3, P5, and the concave curve 1404 extending between P2 and P1, as shown in the signal diagram, illustrate the actual displacement as the voltage increases. When applied to... Figure 13B When the signal is shown, the concave curve 1406 extending between P1 and P2 and the concave curve 1408 extending between P3, P5 and P4 illustrate the actual displacement as the voltage decreases.

[0126] For known increases and decreases in the applied signal, the displacement changes with the applied signal, and a curve extending between each pair of points can be constructed that approximates the curvature of the displacement map with respect to the applied voltage signal. The equations describing the motion of the actuator element when driven by a drive signal without hysteresis compensation are referred to herein as the hysteresis model. Although in this example the curve of the actuator element's position versus voltage is curved, in other embodiments the curve may be linear or may have other shapes. In this example, these pairs may be {P1, P2}, {P2, P3}, {P3, P4}, and {P4, P5}. In the illustrated example, the curve may be defined by a quadratic polynomial such that the curve is parabolic. However, in other embodiments, the curve may be approximated by higher-order polynomial equations of any degree. In some embodiments, the input condition may be that all generated parabolas have a constant curvature. However, in other embodiments, the curvature of one or more of the parabolas may be different. In some embodiments, a new parabola may be determined when the voltage signal changes direction (e.g., from ramping to descent). A new parabola can be defined between a first point where the voltage signal changes direction or between a voltage value and a next voltage value where the voltage signal changes direction again (e.g., a second voltage value). Therefore, in some embodiments, a curve can be predetermined for a selected voltage drive signal having a predetermined waveform (e.g., calibrated to result in selective movement of the piezoelectric element).

[0127] A parabola can be described as a polynomial based on its vertex and focus. Figure 17The equation describes a representative parabola including a vertex P v and a focus P f Equation 2 is a representative example of a hysteresis model describing a parabola in terms of the vertex and focus that can be used for hysteresis compensation:

[0128]

[0129] In Equation 2, is the vertical distance between the focus and the vertex The terms represent the voltage value at the focus and the displacement value at the focus, respectively. The terms represent the voltage and displacement at the vertex, respectively. By substituting for the measured value of curvature, the equation becomes:

[0130]

[0131] In certain embodiments, the amount of curvature represented by may also equal the amount of hysteresis of the piezoelectric material, referred to herein as a hysteresis parameter. The hysteresis parameter can be represented as a coefficient between 0 and 1, where 0 means that the material exhibits no hysteresis, and 1 means that the material's displacement hysteresis the expected displacement for 100% of the applied voltage. However, in certain embodiments, the displacement can hysteresis more than 100% of the expected displacement, such as 125% or more, for a given applied voltage. For example, with reference to Figure 14 , an applied voltage decreasing from 250 V to 0 V can produce a brief positive displacement of more than 1 x 10 -6 m, such as 1.25 x 10 -6 m, before the displacement also begins to decrease. In one exemplary embodiment, for a four-layer shear piezoelectric element, the hysteresis parameter Ay0may be approximately 40% ( Thus, this means that:

[0132]

[0133] In certain embodiments, the hysteresis parameter Ay0may be determined based on the measured values. In other embodiments, the hysteresis parameter Ay0may be determined based at least in part on variables such as the piezoelectric material(s) of a given piezoelectric actuator, the size and / or shape of the piezoelectric actuator, the limits on motion imposed on the environment, or combinations thereof. In cases where the piezoelectric actuator includes multiple piezoelectric elements in a stacked arrangement, the hysteresis parameter Ay0may also be determined based at least in part on the number and / or shape, thickness, etc. of the stacked piezoelectric elements. The hysteresis parameters can be the same or different for different piezoelectric actuators in a drive unit. For example, the hysteresis parameter can be different for a shear element compared to a clamping element, and / or the hysteresis parameter can be different for different shear elements or different clamping elements. In certain embodiments, the hysteresis parameter(s) can be stored in a lookup table or other data structure and referenced by the controller when determining hysteresis compensation for a selected actuator element. In some embodiments, the hysteresis parameter of a piezoelectric element can be periodically measured or reevaluated as in maintenance. In certain embodiments, the hysteresis parameter Ay0may be inversely proportional to the fourth power of the y coordinate of the focus point P f but the parameters can differ according to a selected function or polynomial.

[0134] To define the curve where and and P 1 and P 2 are points on the curve and are assumed to be known, equation 3 can be solved with respect to and y 1 and y 2 The expression for

[0135]

[0136] can be solved by subtracting the two equations in equation 5, and can be solved by adding the two equations:

[0137]

[0138] One example method of canceling the hysteresis of 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 with respect to and substituting for and for :​

[0139]

[0140] and

[0141]

[0142] In certain embodiments, the voltage applied to the piezoelectric element in the drive unit will vary with time. In certain embodiments, when the scaled voltage (V) changes direction, this can be equivalent to the derivative of the voltage signal with respect to time (dV / dt) changing sign. The variable may be recalculated. In certain embodiments, assuming that for each step the algorithm can be updated, and at each step the time between steps is equal to In such embodiments, the procedure can be as given in Table 2 below. k Table 2 - Procedure for determining hysteresis compensation curve

[0143] Table 2 - Procedure for determining hysteresis compensation curve

[0144] .

[0145] Referring to Table 2 above, if the time derivative of the voltage k-1 at time t x is not equal to the time derivative at time t k (e.g., in the particular case because the direction of the voltage signal has changed), then the variable is assigned the sign of d in the first step. In the second step, if the absolute value of the voltage is greater than the voltage at point P 1 then x 1 at point P 2 is assigned the value x 2 and y 2 Otherwise, and In certain embodiments, the points P 1 and P 2 may be predetermined based on the chosen voltage waveform, and can be scaled between -1 and 1. In the third step, if d = 1 and x is greater than x 2 then the variable x may be assigned the value in step 3 of Table 2.​1 、 y 1 、 x 2 and y 2 corresponding values. If d = -1 and x is less than x 2 , then the variable x 1 、 y 1 、 x 2 and y 2 is assigned a corresponding value. In the fourth step, the coordinates of the vertex of the hysteresis model curve (e.g., a parabola) of the approximate displacement of the piezoelectric element for a given drive voltage signal can be calculated using the equation given in Table 2, Step 4 for x v and y v . Since the approximate or indicative displacement path of the actuator element between points P 1 and P 2 is a quadratic function, the inverse of the path (referred to herein as an inverse function or equation) can be calculated using the equation given in Table 2, Step 4 y(t k ) (e.g., Equation 7). As used herein, a function and inverse function indicative of a displacement path of an actuator element are a relationship or expression including one or more variables, such as voltage, position, hysteresis parameter Ay0, etc. The result of Equation 7 can be used as a hysteresis compensation signal. The voltage signal can then be modified according to the curve given by Equation 7 to provide a hysteresis compensation signal, where the result of Equation 7 is the hysteresis compensation portion of the overall drive signal. In embodiments where the parabola (or other curve) is fit to a curve of displacement versus voltage whose slope is compensated (e.g., where P 1 is (1, 0) and P 2 is (-1, 0)), the voltage waveform given by Equation 7 can be superimposed on the initial voltage waveform. The hysteresis compensation signal can then be applied to the piezoelectric element to compensate for hysteresis. In other words, by modifying the drive signal to be the inverse of the expected (e.g., uncompensated) path, the curvature of the displacement path of the actuator element due to hysteresis can be at least partially reversed or compensated.

[0146] Figures 18A-18B and 19A-19B show the results of a time simulation of the above algorithm. Figure 18AThe sawtooth drive signal is illustrated, and Figure 18B The displacement behavior of a piezoelectric element driven by a drive signal without hysteresis compensation is shown. The piezoelectric element exhibits a hysteresis characteristic of the bending displacement behavior as the voltage signal changes over time. Figures 19A-19B The result when the voltage signal is modified according to the algorithm described above is illustrated. Figure 19A The voltage signal modified to exhibit a bending or parabolic curve that ramps up and down is shown, and Figure 19B The linear extension and contraction of the piezoelectric element between changes in the direction of the voltage signal is shown. As can be seen from Figure 19A It can be seen that the modified voltage signal is the inverse of the displacement plot of Figure 18B When the actuator element is driven with this modified voltage signal, the hysteresis is almost completely eliminated, and the position plot of the actuator element tracks a series of almost undisturbed sawtooth waves.

[0147] Figure 20A The drive signal for the clamping elements 716 and 720 of the drive unit of Figures 7A-7D is illustrated. Figure 20B The modified drive signal for the shear elements 714, 704b, 704c of the first set 704 and for the shear elements 718, 706b, 706c of the second set 706 is illustrated in dashed lines superimposed on the unmodified shear element drive signal. Figure 21 The measured position of the mover element (shown in solid lines) and the position of the mover element when the shear element(s) of the drive unit are driven with the modified voltage signal as described herein (shown in dashed lines) is illustrated. As can be seen in Figure 21 By compensating for the hysteresis of the shear element, the disturbance of the position can be greatly eliminated.

[0148] Figure 22 The measured velocity of the mover element (shown in solid lines) and the velocity of the mover element when the shear element(s) of the drive unit are driven with the modified voltage signal as described herein is illustrated. As Figure 22 The disturbance of the velocity of the mover element can be substantially eliminated, as shown.

[0149] In certain embodiments, the methods described herein can be implemented by a controller or processor, such as a proportional-integral-derivative (PID) controller in a control system similar to Figure 9 In certain embodiments, one or more measured parameters (e.g., position, velocity, etc.) can be fed back to the controller, which can modify the voltage signal based at least in part on the measured parameters.

[0150] Although the above examples refer to functions associated with hysteresis, in some embodiments, a suitable approximation is based on stored values characterizing the hysteresis of a particular actuator. These values can be stored in memory or a lookup table, or can be conveniently generated based on the above function relationships.

[0151] Example 9: Example computing environment

[0152] Figure 23 The following discussion is intended to provide a brief, general description of an example computing environment in which the disclosed technology can be implemented. The method and program described herein can be implemented by a controller or processor configured similarly to the computing environment described below, for example. Furthermore, the disclosed technology can be implemented with other computer system configurations, including hand-held devices, digital signal processors (DSPs), multi-processor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, and the like. The disclosed technology can also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network.

[0153] Reference Figure 23 An example system for implementing the disclosed technology includes a general-purpose controller in the form of an example conventional PC 1500, including one or more processing units 1502, a system memory 1504, and a system bus 1506 coupling the various system components including the system memory 1504 to the one or more processing units 1502. The system bus 1506 can be any of several types of 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 example system memory 1504 includes read-only memory (ROM) 1508 and random access memory (RAM) 1510. A basic input / output system (BIOS) 1512 containing the basic routines that help to transfer information between elements within the PC 1500, such as during startup, is stored in ROM 1508. In the example of FIG. 20, data and processor-executable instructions for controlling the motion of the positioning system, hysteresis control, imaging, processing, and operating modes of STEM and / or FIB 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.

[0154] The exemplary PC 1500 also includes one or more input devices 1540 such as a keyboard, mouse, pen, etc. One or more output devices 1545 such as a monitor, printer, etc. also can be included. All these devices are connected to the bus 1506 by interface devices (e.g., adapter, etc.). The system 1500 also can include a communication interface 1550 taking the form of modem, a network interface card, etc. to enable the PC 1500 to communicate with other devices.

[0155] A number of program modules can be stored on the storage devices 1530, including an operating system, one or more application programs, other program modules, and program data. A user can enter commands and information into the 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 the system bus 1506 via an interface, such as a video adapter. Output to, such as commands, drive signals, etc. can be transmitted via one or more output devices 1545.

[0156] The PC 1500 can operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 1560, by way of a logical connections 1550, in some examples, the logical connections 1550 include a network or a communication link. The remote computer 1560 can 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 relative to the PC 1500, although only a memory storage device 1562 has been illustrated in Figure 23 The personal computer 1500 and / or the remote computer 1560 can be connected to a logical local area network (LAN) and a wide area network (WAN). In certain embodiments, the remote computer 1560 can include a virtual processor implemented in a remote server environment or a cloud computing environment.

[0157] Example 10: Control system for hysteresis compensation

[0158] Figure 24 A representative embodiment of a control system 1600 for implementing the previously described methods is shown. 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.

[0159] Drive frequencyf α A clock signal, or a clock signal from a clock signal generator (not shown) at the drive frequency, can be provided to 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. Integrator tool 1610 can output the commutation angle α to clamping signal generator 1602 and shearing signal generator 1604. Clamping signal generator 1602 can be configured to generate drive signals for a plurality of clamping elements, schematically represented by 1612, to be applied to one or more clamping elements of the drive unit, represented by 1618. For example, clamping signal generator 1602 can generate drive signals for a first clamping element (e.g., Figures 7A-7D The first clamping element drive signal of element 716) and the second clamping element (e.g., Figures 7A-7D The second clamping element drive signal (of the clamping element 720). In some embodiments, the clamping element drive signal may be based on the commutation angle α and the drive frequency. f α Data generation includes the selection path of the mover element, the selection path of the clamping element (e.g., to generate movement of the mover along the selected path), etc.

[0160] The shear signal generator 1604 can be configured to generate a plurality of shear element drive signals, schematically represented by 1616, such as a first shear element drive signal (e.g., for shear elements 714, 704b, and 704c) and a second shear drive signal (e.g., for shear elements 718, 706b, and 706c). The shear element drive signals may correspond to clamping element drive signals to generate selective motion of the mover elements, and may be based on a commutation angle α, drive frequency, etc. f α The path for selecting mover components, the path for selecting shear components, etc.

[0161] In some embodiments, LUT 1606 can include an array of paths for the clamping elements and / or the shear elements (e.g., configured to implement the selected motion of the mover elements). LUT 1606 can also store the time-varying commutation angle a. In some embodiments, when a drive signal is applied without hysteresis compensation, lookup table 1606 can store a signal, equation, or function indicative of the position or path of the shear and / or clamping elements. In some embodiments, LUT 1606 can include an array of hysteresis-compensated signals for various commutation angles, drive frequencies, and / or actuator element paths. In some embodiments, the hysteresis-compensated signals can be based on an inverse or reciprocal of a hysteresis model that describes the position or path of the shear elements and / or clamping elements when the elements are driven by a selected drive signal, as described above. The hysteresis-compensated signals in LUT 1606 can be pre-computed and stored in static program memory, computed as part of a control system initialization phase, or stored in hardware of a dedicated platform. LUT 1606 can also store hysteresis models for various actuator elements.

[0162] In some embodiments, the path of the object to be moved by the drive unit (e.g., the mover elements, a workpiece coupled to the mover elements, etc.) can be selected and provided to control system 1600. In some embodiments, the path can be selected by signal modification tool 1608 or by another control system based on system requirements. In particular embodiments, signal modification tool 1608 can select a hysteresis-compensated signal 1620 from a LUT based on the selected path of the mover elements and / or based on system requirements (e.g., based on detection of a sign change in the direction of the actuator element drive signal). In embodiments where the hysteresis-compensated signal 1620 is based on the path of the actuator elements without hysteresis compensation, signal modification tool 1608 can determine or compute the inverse of the signal 1620 to obtain an inverse signal for the actuator elements. Signal modification tool 1608 combines the hysteresis-compensated signal with the appropriate drive signal to obtain modified or hysteresis-compensated shear element drive signals 1622 and 1624, and / or hysteresis-compensated clamping element drive signals 1614 and 1615. The hysteresis-compensated drive signals 1614, 1615, 1622, and 1624 can be transmitted to piezoelectric drive system tool 1628, which can scale and / or condition the signals, and can convert the signals from digital to analog using a digital-to-analog converter (DAC). The hysteresis-compensated drive signals can be applied to drive unit 1618 to cause actuation of the drive unit to move the mover elements along the selected path relative to the drive unit.

[0163] In certain embodiments, the clamping element drive signals and the shear element drive signals can be based on a frequency f α , or independent of the frequencyf α Confirmed. Furthermore, although in Figure 24 The system 1600 depicted is a feedforward control system, but in other embodiments, one or more variables, such as mover position, mover speed, actuator position and / or speed, voltage, etc., may be measured and fed back to the signal modification tool 1608, which may use such data to select a hysteresis compensation signal.

[0164] Example 11: Control system for hysteresis compensation

[0165] Figure 25 Another representative embodiment of a control system 1700 for implementing the previously described methods is shown. The control system 1700 may be configured to compensate for hysteresis of a shearing element, clamping element, or any other actuator element in a linear or rotary actuator. The control system 1700 may include an integrator tool 1710, a clamping signal generator 1702, a shearing signal generator 1704, a processor 1706 including a storage unit 1728, and a signal modification tool 1708.

[0166] Drive frequency f α A clock signal, or a clock signal from a clock signal generator (not shown) at the drive frequency, can be provided to 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. Integrator tool 1710 can output the commutation angle α to clamping signal generator 1702 and shearing signal generator 1704. Clamping signal generator 1702 can be configured to generate drive signals for a plurality of clamping elements, schematically represented by 1712, to be applied to one or more clamping elements of the drive unit represented by 1710. For example, clamping signal generator 1702 can generate drive signals for a first clamping element (e.g., Figures 7A-7D The first clamping element drive signal of element 716) and the second clamping element (e.g., Figures 7A-7D The second clamping element drive signal of the clamping element 720.

[0167] The shear signal generator 1704 can be configured to generate a plurality of shear element drive signals, schematically represented by 1716, such as a first shear element drive signal (e.g. for shear elements 714, 704b and 704c) and a second shear drive signal (e.g. for shear elements 718, 706b and 706c).

[0168] In some embodiments, memory unit 1728 can include data for a plurality of paths of the clamping elements and / or shearing elements between selected positions. In some embodiments, memory unit 1728 can store a hysteresis model for the clamping and / or shearing elements. In some embodiments, the hysteresis model can include a signal, equation, or function indicating the position or displacement path of the shearing and / or clamping elements when a drive signal without hysteresis compensation is applied. In some embodiments, memory unit 1728 can include a plurality of pre-computed hysteresis compensation signals 1720 for various commutation angles, drive frequencies, and / or actuator element paths. In other embodiments, memory unit 1728 can include data for position and / or voltage values where the drive signal for the shearing and clamping elements changes direction. The data in memory 1728 can be pre-computed and stored in memory 1728, computed by processor unit 1706 as part of an initialization phase of the control system, and / or computed based on information for the shearing and / or clamping element drive signals 1712, 1716.

[0169] In some embodiments, processor 1706 can compute or determine the hysteresis compensation signal 1720 based on the drive frequency f、 In some embodiments, the hysteresis compensation signal 1720 can be computed or determined based on the commutation angle a, the selected actuator element path, and / or a plurality of predetermined shearing and / or clamping drive signals stored in memory 1728. In some embodiments, a path for an object to be moved by the driven unit (e.g., a mover element, a workpiece coupled to a mover element, etc.) can be selected and provided to the control system 1700. In some embodiments, the path can be selected by processor 1706 or another control system. In certain embodiments, processor 1706 can determine the hysteresis compensation signal 1720 by identifying changes in the direction of the actuator element. Such changes in direction can be identified based on the sign of the rate of change of the drive signals provided by signal generators 1702 and 1704. In some embodiments, the hysteresis compensation signal 1720 can be based on a hysteresis model for the actuator element stored in memory 1728. In certain embodiments, the hysteresis model can be based on the inverse or reciprocal of the position or path of the shearing clamping element when a drive signal without hysteresis compensation is applied to the element, as described above. In some embodiments, processor 1706 can select a pre-computed hysteresis compensation signal from memory 1728.

[0170] 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 signals to produce hysteresis-compensated shear element drive signals 1722 and 1724, and / or hysteresis-compensated clamp element drive signals 1714 and 1715. The modified shear element drive signals 1722 and 1724 and clamp element drive signals 1714 and 1715 can be scaled and / or conditioned by a piezoelectric drive system 1726, converted to analog signals by digital-to-analog converters (DACs) (e.g., part of the piezoelectric drive system 1726), and output to drive units 1718 to produce movement of the mover elements (e.g., mover elements 702) relative to the drive units.

[0171] In certain embodiments, a position encoder 1730 can determine data for displacement x m and / or velocity v of the mover elements, and can transmit the data back to the signal modification tool 1708 and / or the processor 1706. The processor 1706 can use the position and / or velocity data to determine or update the hysteresis compensation signal to update the hysteresis model of the actuator elements, etc.

[0172] Example 12: Hysteresis measurement and compensation using a reference capacitance

[0173] Figure 26 Another control system 1800 is shown, which includes multiple capacitors and is configured to determine and / or correct for hysteresis of a piezoelectric element or set of piezoelectric elements. For illustrative purposes, the following example is with reference to three shear piezoelectric elements 1802, 1804, and 1806, but the system can be configured for use with clamp elements as well. A capacitor 1808 can be associated with the shear element 1802, a capacitor 1810 can be associated with the shear element 1804, and a capacitor 1812 can be associated with the shear element 1806. The capacitors 1808-1812 can be connected in parallel, and the system can include a reference capacitor 1814 connected in series with the three capacitors 1808-1812. A piezoelectric element reference voltage V 压电,REF may be supplied to a control module or tool 1816, described further below. The voltage output by the module 1816 can be converted to an analog signal by a digital-to-analog converter (DAC) 1818 and supplied to an operational amplifier 1820 at a non-inverting input. The voltage V 放大器 output by the amplifier 1820 can be supplied to the capacitors 1808-1812 associated with the shear elements. The voltage drop V REF across the reference capacitor 1814 can be measured, converted to a digital signal by an analog-to-digital (ADC) converter 1822, and subtracted from the reference signal V 压电,REF at a summing point 1824.

[0174] The modified or summed voltage signal from summing point 1824 can be input to control module 1816 (e.g., as negative feedback). Control module 1816 can determine the voltage drop V across reference capacitor 1814. REF With the piezoelectric element reference voltage V 压电 , REF The difference between them can be controlled to reduce the difference. In some embodiments, the reference voltage V REF This can be related to the hysteresis of actuator elements 1802-1806. For example, in some embodiments, the voltage V measured across reference capacitor 1814 is... REF However, due to the hysteresis of actuator elements 1802-1806, the indication is similar to Figure 14 Or cyclic or loop-forming behavior of 15. Voltage drop V REF It can also be supplied to the inverting input of amplifier 1820.

[0175] In some embodiments, the controller 1816 can increase the gain. K The voltage signal applied to the summation, as indicated by Equation 9 below, generates the voltage output V to the DAC 1818. 输出 .

[0176]

[0177] In other embodiments, controller 1816 may apply any one or a combination of proportional, integral, and / or derivative control. Control methods may be selected to reduce the hysteresis of piezoelectric elements 1802-1806 (e.g., by reducing VL). REF and V 压电，REF (The difference between them).

[0178] The control system 1800 can be used in combination with any motor and control system described herein. For example, any piezoelectric motor described herein may include a reference capacitor, similar to 1814, for shearing each of two sets of piezoelectric elements and a reference capacitor for clamping each of the piezoelectric elements to reduce hysteresis.

[0179] exist Figure 27 The diagram shows, in another embodiment, the voltage drop V across shear capacitors 1808-1812. 压电 It can be used with the ADC converter 1822.

[0180] Additional details of piezoelectric motors, stages, and beam systems described herein can be found in the application titled "Systems and Methods of Clamp Compensation" filed with this application and also referenced by attorney reference number 9748-102339-01, and in the application titled "Electron Microscope Stage" filed with this application and also referenced by attorney reference number 9748-102714-01, each of which is incorporated herein by reference in its entirety.

[0181] The disclosed embodiments are not limited to include piezoelectric element actuators, and can extend to any other type of actuator that exhibits hysteresis, such as a rotary or linear motor or actuator, a voice coil motor, etc.

[0182] The principles of this disclosure have been described and illustrated with reference to the illustrated embodiments, it will be realized that the illustrated embodiments can be modified in arrangement and detail without departing from such principles. For example, elements of the illustrated embodiments shown in software can be implemented in hardware, and vice versa. Moreover, the techniques from any example can be combined with the techniques described in one or more of any other examples.

[0183] Clause Interpretation

[0184] For the purposes of this description, certain aspects, advantages, and novel features of the embodiments of the disclosure are described. The disclosed methods, devices, and systems should not be construed as limiting in any way. Instead, 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 sub-combinations with one another. The methods, devices, and systems are not limited to any particular aspect, feature, or combination of parts, nor do the disclosed embodiments require the presence of any particular advantage or solve a problem.

[0185] Although the operations of some of the disclosed embodiments are described in a particular, sequential order for convenient presentation, it should be understood that unless otherwise specified, this manner is merely an example. The description could be understood to allow reordering or simultaneous performance of some operations, unless the order of operations is explicitly required by the specific language used in the description. Also, for brevity, some operations that are well known in the art are not described in detail. Furthermore, the accompanying drawings possibly do not illustrate all the ways in which the disclosed methods can be used. Additionally, the description sometimes uses terms like "provide" and "achieve" to describe the disclosed methods. These terms are high-level abstractions of the actual operations that are performed. The actual operations that correspond to these terms can vary depending on the particular implementation and are readily recognizable by one of ordinary skill in the art.

[0186] All features described herein are independent of each other, and can be used in combination with any other feature described herein, unless structurally impossible.

[0187] As used in this application and the appended claims, the singular forms "a," "an," and "the" include plural referents unless the context clearly dictates otherwise. Pursuant to standard dictionary practices, the term "about" is used to indicate that the subsequent reference point is "approximately" or "around" the referenced point. Furthermore, the term "include," as used in this application and the appended claims, means "comprise." Additionally, the terms "coupled" and "associated" generally mean electrically, electromagnetically, and / or physically (e.g., mechanically or chemically) coupled or linked with, and do not exclude the presence of intermediate elements between coupled or associated items absent specific contrary language.

[0188] In the following description, certain terminology will be used that, for example, in the context of the following description, will be used as follows. The terms "above" and "below" refer to a relative position of one object with respect to another. The terms "upper" and "lower" refer to a relative position of one object with respect to another. The terms "horizontal" and "vertical" refer to a relative position of one object with respect to another. The terms "left" and "right" refer to a relative position of one object with respect to another. These terms are used to provide some clear description in treating relative relationships. However, these terms are not intended to imply absolute relationships, positions, and / or orientations. For example, an "upper" surface of one object can become a "lower" surface by simply turning the object over. Nonetheless, it is still the same object.

[0189] In view of the principles disclosed herein, it is recognized that the illustrated embodiments are merely preferred examples and should not be considered limiting the scope of the disclosure. Rather, the scope of the disclosure is at least as broad as the appended claims. We therefore claim all that falls within the scope and spirit of these claims.

Claims

1. A method for hysteresis compensation, comprising: selecting a path between a first position and a second position; and applying a drive signal comprising a hysteresis compensation portion to an actuator element to move an object along the selected path, wherein the hysteresis compensation portion is based on a hysteresis model of the actuator element, wherein the hysteresis model of the actuator element comprises a position equation of the actuator element when actuated between the first position and the second position by an uncompensated drive signal, and the equation is defined by a quadratic polynomial, such that the hysteresis model comprises a parabola; and the method further comprising 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.

2. The method of claim 1, further comprising: identifying at least one change in direction of the actuator element along the selected path, wherein the hysteresis compensation portion is based in part on the change in direction.

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

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

5. The method of claim 1, further comprising determining the hysteresis model of the actuator element.

6. The method of claim 5, wherein determining the hysteresis model further comprises determining a higher order polynomial based at least in part on predetermined hysteresis parameters of the actuator element.

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

8. The method of claim 1, wherein: the actuator element comprises a piezoelectric material; and the drive signal comprises a voltage signal.

9. A positioning system, comprising: a drive unit comprising 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, wherein: 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, wherein the hysteresis model of the actuator element comprises a position equation of the actuator element when actuated between the first position and the second position by an uncompensated drive signal, wherein the equation is defined by a quadratic polynomial, such that the hysteresis model comprises a parabola; and the processor is configured to generate the hysteresis compensated drive signal based on an inverse equation of the hysteresis model of the actuator element.

10. The positioning system of claim 9, wherein: the control system further comprises a processor and a memory unit in communication with the processor, the memory unit storing data of a hysteresis compensation signal; and the processor is configured to generate the hysteresis compensation signal based on an inverse equation of the hysteresis model of the actuator element. ​ The processor is configured to generate the hysteresis compensation drive signal based on the hysteresis compensation signal.

11. The positioning system of claim 10, wherein the processor is configured to: identify at least one change in direction 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 direction; and generate the hysteresis compensation drive signal based on the selected hysteresis compensation signal.

12. The positioning system of claim 11, wherein: the control system further comprises a signal generator configured to generate a drive signal for the actuator element; and 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.

13. The positioning system of claim 9, wherein the control system further comprises a lookup table comprising a plurality of predetermined hysteresis compensation drive signals.

14. The positioning system of claim 9, wherein: 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 a carrier element configured to hold the object, the mover element being engaged with and movable relative to the drive unit to position the object along the path.

15. A scanning transmission electron microscope comprising the positioning system of claim 9.

16. A method for hysteresis compensation, comprising: applying a drive signal to move an actuator element between a first position and a second position; determining a hysteresis model of the actuator element based on motion of the actuator element between the first position and the second position, wherein the hysteresis model of the actuator element comprises a position equation of the actuator element when actuated between the first position and the second position by an uncompensated drive signal, wherein the equation is defined by a quadratic polynomial such that the hysteresis model comprises a parabola; determining a hysteresis compensation signal based on an inverse equation of the hysteresis model; applying the hysteresis compensation signal to the drive signal to generate a hysteresis compensation drive signal; and applying the hysteresis compensation drive signal to the actuator element to move an object along a selected path.

17. The method of claim 16, wherein determining the hysteresis model further comprises determining a higher order polynomial based at least in part on predetermined hysteresis parameters of the actuator element.

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