Ultra-precision Positioning Research Articles

Design and control of redundant-actuated Six-DOF micropositioning stage with magnetic gravity compensation

Abstract The performance of ultra-precision positioning stages is particularly critical in the field of ultra-precision manufacturing. This paper presents the design of an eight-actuator redundant six-degree-of-freedom micropositioning stage with magnetic suspension gravity compensation (6-DOF RDMS). All drives are electromagnetic direct-drive systems based on voice coil motors (VCMs). The vertical motors incorporate a Halbach array and a magnetic suspension gravity compensation structure. A mathematical model and a finite element model are established for the designed positioning stage. The models are utilized for magnetic field and magnetic force analysis, thermal analysis, and analysis of the dynamic force-induced deformation of stator to ensure operational stability. A decoupling control system for the six-degree-of-freedom micropositioning stage is developed, mapping the six degrees of freedom to the control loops of the eight actuators to achieve high-precision positioning. Finally, a prototype was constructed, validating the effectiveness and feasibility of the structural design and the decoupling control system.

A novel photonic skin sensor based on tapered micro nano fiber structure coated with sodium polyacrylate film

Biomimetic skin sensing devices play an important role in next-generation healthcare, robotics, and bioelectronics. In recent years, biomimetic skin-sensing technologies have gained significant attention due to their broad-ranging utility in the fields of healthcare and automation, and future wearable devices designed for health monitoring, robotic applications, and ultra-precise industrial positioning will necessitate the incorporation of flexible optical systems. A novel photonic skin flexible sensor (PSFS) based on partially neutralized sodium polyacrylate (PAS-50) is reported for the first time in this paper. In this study, a novel wearable sensor was designed for real-time detection of temperature and humidity. A single-mode tapered fiber (SMTF) structure based on the principle of evanescent wave is proposed for fast response and real-time monitoring of humidity and temperature. The sensor incorporates an optical micro/nanofiber (MNF) as the core sensing node, while a hydrophilic and ductile Sodium Polyacrylate (PAS) is chosen as the humidity-sensitive material that overcomes the limitation of commonly reported electrical, optical, and material-based flexible devices. Due to the strain amplification effect of the MNF, the sensitivity of the material to relative humidity (RH) is significantly improved, reaching 0.1411 dB/%. In addition, the temperature response exhibits outstanding sensitivity (0.4 dB/°C) in the human skin surface temperature range (30 ∼ 48 °C). Notably, the sensor exhibits a rapid response with a remarkable response time of 170 ms. The proposed PSFS presents novel opportunities for the advancement of future biomimetic skin devices, thus playing a pivotal role in the advancement of next-generation robotics and medical monitoring technologies.

공간형 위치 결정 스테이지를 위한 타원형 및 포물선형 2 자유도 플렉셔 힌지에 대한 해석

With advancements in semiconductor manufacturing processes and the development of precision processing technology, flexure hinge-based ultra-precision positioning stages are widely used. In the flexure hinge, axial and bending stiffness properties greatly influence positioning performance. This study examined the stiffness properties of elliptic and parabolic 2-degrees-of-freedom (DOF) hinges, which have not been extensively discussed. The Timoshenko beam theory was applied to derive the stiffness equations for the axial and bending directions of each hinge. The stiffness properties were examined in several design conditions by comparing theoretical and finite element analyses. Based on the results of the analyses, an empirical formula in exponential form for the design of an elliptic hinge was constructed through surface-fitting. The elliptic hinge was found to be a better alternative to a circular hinge under certain design conditions by adjusting two design parameters. In the future, we will develop sophisticatedly designed hinges with improved axial and bending stiffness properties compared to the existing circular and elliptic hinges.

Controller design for high-speed, ultra-precision positioning of a linear motion stage on a vibrating machine base stage control on a vibrating base

This paper presents a high-speed, ultra-precision point-to-point position control system design. It addresses precision stages with unknown characteristics, affected by machine base vibration and system effectiveness. The design is based on the nominal characteristic trajectory following (NCTF) control method, which can provide ultra-precision position control performance for the precision stages without accurate dynamic models. However, conventional NCTF control systems neither provide sufficient vibration suppression nor exhibit suitable vibration suppression characteristics. The position control performance is deteriorated by the machine base vibration. To overcome this problem, a procedure for incorporating a bandpass filter and derivative compensator in the NCTF control system is proposed and designed. These compensators exhibit high vibration suppression ability when combined, rather than when used individually. Additionally, they can be easily designed without any accurate dynamic model. The effectiveness of the compensator combination was first investigated using a linear model and subsequently experimentally verified. Using the proposed procedure, a control system was designed for the precision stage with friction characteristics on the vibrating machine base. The designed control system suppresses the residual vibration immediately after the target value becomes constant, and the error converges below 50 nm within 80 ms.

Flexible and Wearable Optical System Based on U‐Shaped Cascaded Microfiber Interferometer

AbstractFuture wearable devices for health monitoring, robotics, and ultraprecise industrial positioning necessitate flexible optical systems. Here, an optical microfiber interferometer‐based wearable system is demonstrated with wavelength interrogation that overcomes the limits of commonly reported electrical, optical, and material‐based flexible devices. The microfiber in a finely tuned configuration is enclosed in polydimethylsiloxane (PDMS) thin film to provide a means of controlling interference between fundamental and higher‐order modes. Using this approach, it is possible to create a simple, adaptable, and cost‐effective optical device with a direction recognizable bending sensitivity of up to 1.01 nm per degree, and remarkable temperature sensitivity of −3.07 nm °C−1. The ultrahigh sensitivity, mechanical robustness, and outstanding flexible and biocompatible nature make this sensor system a leading candidate for wearable medical devices for elder‐care facilities, physiological monitoring, athletic training, and rehabilitation programs.

Measurement of sub-fm/Hz1/2 displacement spectral densities in ultrahigh-Q single-crystal microcavities with hertz-level lasers

Tracing a resonance frequency of a high quality factor (Q) optical cavity facilitates subpicometer displacement measurements of the optical cavity via Pound–Drever–Hall (PDH) locking scheme, tightly synchronizing a laser frequency to the optical cavity. Here we present observations of subfemtometer displacements on a ultrahigh-Q single-crystal MgF 2 whispering-gallery-mode microcavity by frequency synchronization between a 1 Hz cavity-stabilized laser and a resonance of the MgF 2 cavity using PDH laser-cavity locking. We characterize not only the displacement spectral density of the microcavity with a sensitivity of 1.5 × 10 − 16 m / Hz 1 / 2 over the Fourier offset frequency ranging from 15 mHz to 100 kHz but also a 1.77 nm displacement fluctuation of the microcavity over 4500 s. Such measurement capability not only supports the analysis of integrated thermodynamical and technical cavity noise but allows for minute displacement measurements using laser-cavity locking for ultraprecise positioning, metrology, and sensing.

Systematic error analysis and parameter design of a vision-based phase estimation method for ultra-precision positioning.

Ultra-precision position measurement is increasingly important in advanced manufacturing such as the semiconductor industry and fiber optics or photonics. A vision-based phase estimation method we proposed previously performs position measurement by imaging a 2D periodic pattern. In this paper, systematic errors of this method are analyzed and derived mathematically, which are classified into two types: spectrum leakage error caused by image truncation and window function modulation, and sub-pixel error resulting from discrete Fourier transform (DFT) intensity interpolation. Key design parameters are concluded including pattern period T, camera pixel size t and resolution N, as well as the type of window function used. Numerical simulations are conducted to investigate the relationship between the phase errors and design parameters. Then an error reduction method is proposed. Finally, the improved performance of parameter optimization is validated by a comparative experiment. Experimental results show the measurement errors of the prototype are within ∼2 nm in X or Y axis, and ∼1µrad in axis, which reaches the sub-pixel accuracy better than 10-3pixel.

A Reflective-Type Heterodyne Grating Interferometer for Three-Degree-of-Freedom Subnanometer Measurement

A heterodyne grating interferometer (HTGI) able to simultaneously measure the three-axis translational displacements of ultra-precision motion stages with a sub-nanometer resolution is demonstrated. The HTGI is composed of two main parts, a reflective planar grating with a uniform micron-scale period in two orthogonal directions, and a reading head. Thanks to the reflective grating, the reading head design manages to make main optical paths common and located on the same side of this compact structure, potentially resulting in low Abbe errors and environmental variations. Relying on a laboratory-made dual-frequency laser source at 780 nm, two heterodyne interferometric measurement modules for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> -/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</i> -direction motions and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -direction motion were realized based on first-order and zeroth-order diffraction, respectively. Experiments show that the proposed HTGI, in all three axes, can distinguish a 0.5 nm step or even better, perform an up to 2.5×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> 10linearity in a range of 80 μm, and hold a 5 nm stability within 300 s. These performances confirm that the proposed HTGI can greatly benefit nanoscience and technology, where multi-axis ultra-precision positioning is required, such as wafer stage in next-generation lithography machine, and so forth.

Positioning Performance of a Sub-Arc-Second Micro-Drive Rotary System.

In the macro/micro dual-drive rotary system, the micro-drive system compensates for the position error of the macro-drive system. To realize the sub-arc-second (i.e., level of 1″–0.1″) positioning of the macro/micro dual-drive rotary system, it is necessary to study the positioning performance of the sub-arc-second micro-drive rotary system. In this paper, we designed a sub-arc-second micro-drive rotary system consisting of a PZT (piezoelectric actuator) and a micro rotary mechanism, and used simulation and experimental methods to study the positioning performance of the system. First, the micro-drive rotary system was developed to provide ultra-precise rotary motion. In this system, the PZT has ultrahigh resolution at a level of 0.1 nanometers in linear motion; a micro rotating mechanism was designed according to the composite motion principle of the flexible hinge, which could transform the linear motion of piezoelectric ceramics into rotating motion accurately. Second, the drive performance was analyzed based on the drive performance experiment. Third, kinematics, simulation, and experiments were carried out to analyze the transformation performance of the system. Finally, the positioning performance equation of the system was established based on the two performance equations, and the maximum rotary displacements and positioning error of the system were calculated. The study results showed that the system can provide precision motion at the sub-arc-second and good linearity of motion. This study has a certain reference value in ultra-precision positioning and micromachining for research on rotary motion systems at the sub-arc-second level.

Grating-based 2D displacement measurement with quadruple optical subdivision of a single incident beam.

We propose a new symmetrical heterodyne grating displacement measurement method, based on 2D grating and single diffraction quadruple subdivision method. Using a dual-frequency laser with a wavelength of 632.8 nm, output power of 2.2 mW, and a 1200 l/mm 2D grating, eight diffracted light beams interfere in pairs in the X and Y directions through a turning element. The detection system's measurement accuracy was assessed experimentally. The system measurement resolution in the X and Y directions is better than 3 nm; the grating displacement measurement errors within a 10 mm range are better than ±30 nm and ±40 nm, and the repeatability error is better than ±25 nm. The method is not only applicable to nanoscale 2D displacement measurement technology but also can be used for ultra-precision positioning and ultra-precision processing, with the potential for picometer-level improvement.

Two-Photon Direct Laser Writing Beyond the Diffraction Limit Using the Nanopositioning and Nanomeasuring Machine

Since the first realization of two-photon direct laser writing (DLW) in Maruo et al. (Opt Lett 22:132–134, 1997), the manufacturing using direct laser writing techniques spread out in many laboratories all over the world. Photosensitive materials with different material properties open a new field for micro- and nanofabrication. The achievable structuring resolution using this technique is reported to be sub-100 nm (Paz et al. in J. Laser Appl. 24:042004, 2012), while a smallest linewidth of 25 nm could be shown in Tan et al. (Appl Phys Lett 90:071106, 2007). In our approach, the combination of DLW with the nanopositioning and nanomeasuring machine NMM-1 offers an improvement of the technique from the engineering side regarding the ultra-precise positioning (Weidenfeller et al. in Adv Fabr Technol Micro/Nano Opt Photon XI 10544:105440E, 2018). One big benefit besides the high positioning resolution of 0.1 nm is offered by the positioning range of 25,hbox {mm} times 25,hbox {mm} times 5,hbox {mm} (Jäger et al. in Technisches Messen 67:319–323, 2000; Manske et al. in Meas Sci Technol 18:520–527, 2007). Thus, a trans-scale fabrication without any stitching or combination of different positioning systems is necessary. The immense synergy between the highly precise positioning and the DLW is demonstrated by the realization of resist lines and trenches whose center-to-center distance undergoes the modified diffraction limit for two-photon processes. The precise positioning accuracy enables a defined distance between illuminated lines. Hence, with a comparable huge width of the trenches of 1.655,upmu hbox {m} due to a low effective numerical aperture of 0.16, a resist line of 30 nm between two written trenches could be achieved. Although the interrelationships for achieving such narrow trenches have not yet been clarified, much smaller resist lines and trench widths are possible with this approach in the near future.

Learning Piezoelectric Actuator Dynamics Using a Hybrid Model Based on Maxwell-Slip and Gaussian Processes

Piezoelectric actuators (PEAs) are increasingly applied to the field of ultraprecision positioning; however, unwanted nonlinearities, such as hysteresis, degrade their performance. This article integrates a Gaussian process (GP) with a Maxwell-slip (MS) model to capture nonlinearities in PEAs. The GP predicts the output of a PEA or the error of the MS model by using the current and historical applied input voltages, as well as the measured historical output displacements, as input. The measured output is replaced by the output of the MS model in the case that a displacement sensor is unavailable. The experimental results show that by properly selecting system order, the proposed approach achieves a precise result and provides the boundary of the prediction error in terms of variance. If the output displacement is available and the GP predicts the output of a PEA directly, the normalized root-mean-square error (NRMSE) is as low as 0.29%. The NRMSE is reduced further to 0.14% if the dataset used for prediction is updated online.

A Novel Flexure Piezomotor With Minimized Backward and Nonlinear Motion Effect

Continuous, smooth, and highly linear displacement output with centimeter-scale stroke and nanometer-scale resolution is greatly attractive for an ultraprecision positioning system. On the foundation of piezoelectric actuation and compliant mechanism, a novel linear piezomotor with minimized backward and nonlinear motion property is designed. Specifically, a driving unit capable of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$xy$</tex-math></inline-formula> -direction decoupling displacement output is proposed to make the generated motion linear, and a flexure mechanism is introduced into the contact part to make the motion output continuous and nonbackward. Combined with double driving units and the flexure contact mechanism, a motion generation strategy is presented. For performing the motion generation strategy well, the kinematics model of the piezomotor is established. Then, the dimension parameters are optimized. After theoretical derivations, the piezomotor is analyzed and evaluated by finite-element analysis simulation. Finally, a proper control waveform is designed, and the motion generation performance tests are successfully carried out. The results uniformly confirm that the proposed piezomotor can output ultraprecision motion with 8-nm resolution and 10-mm stroke in a continuous and smooth manner, and the backward and nonlinear effects are successfully minimized within 100 Hz.

Theoretical analysis and experimental investigation on a linear ultrasonic motor with a compact slider.

A compact slider for linear ultrasonic motors (LUMs) to improve the ability of LUMs for precision positioning is proposed in this article. The compact slider can avoid the effect of variable stiffness of the traditional slider on ultra-precision positioning, which consists of two pieces of ceramic with little lubricating oil on the sliding interface. Based on contact theory and lubrication theory, the contact mechanism and the lubricating state between the slider and the support plate are analyzed. Subsequently, a dynamic model for LUMs considering the lubricating state and the ultrasonic vibration condition is obtained. Furthermore, the output speed and output force of the motor are analyzed under the influence of film lubrication. Moreover, some experiments are designed to test the feasibility and effectiveness of the compact slider for precision positioning. The results indicate that the compact slider is more effective in inhibiting the fluctuation of the output speed compared to the traditional slider, and it can improve the displacement resolution of LUMs up to 7 nm.

Modeling and analysis for the position and posture errors of laser focal spot in large-scale fabrication via two photon polymerization

The position and posture errors of laser focal spot significantly affect the fabrication quality and functionality of microstructures in two photon polymerization, especially over a large area. These errors can be greatly reduced by using ultra-precision positioning device, such as piezoelectric stage and scanning galvanometer. However, the position and posture errors cannot be neglected in large-scale fabrication using large stroke linear stages which are necessary tools in most instances. In the present work, the relationship between the geometric errors of large stroke positioning platform and the position and posture of laser focal spot were revealed and modeled by homogeneous transformation matrix. Key errors affecting on the position and posture of focal spot were found out by sensitivity analysis and compensated during the construction of machine tool. Proof-of-concept experiments were performed in a millimeter-level (1 mm × 1 mm) fabrication of microfluidic whose surface was measured by an optical profiler. The measuring results showed that arithmetical mean height (Sa) and root mean square height (Sq) of the measured surface were less than 100 nm and maximum height (Sz) of the measured surface was less than 500 nm. The compensated machine tool demonstrated a high precise performance within a large continuous area. This work was expected to provide references for the rational layout of optical components in optical system or error compensation in laser process equipment over a large area.

Structure optimization of connection frames based on frequency sensitivity in macro-micro motion platforms

High-performance connection frames are of great significance for ultra-high acceleration and ultra-precision positioning in macro-micro motion platforms. This paper first takes the connection frame as a research object, builds a finite element model (FEM) of the natural frequency of the frame, and then verifies the correctness of this model. The frequency sensitivity method is then used to perturb the structural parameters of the FEM of the connection frame, and the sensitivities of the first-order natural frequency and mass of the corresponding structural parameters are obtained by calculation and analysis. The design variables are also determined. The natural frequency is used as the optimization objective, and the design parameters and mass of the connection frame are constrained. The structural parameters of the connecting frame are obtained through optimization, and the model is built and verified by experiments. The results show that the first-order natural frequency of the connecting frame is effectively improved by the frequency sensitivity method, avoids resonance between the connecting frame and the voice coil motor, and realizes the lightweight design of the connection frame. This research provides a reliable basis for the stable operation and ultra-precision positioning of ultra-high acceleration macro-motion platforms.

Feed-forward pressure control of balancing cylinder for hybrid electric-pneumatic ultra-precision vertical positioning device

One of the positioning methods in vertical direction of machine tools, a hybrid electric-pneumatic ultra-precision vertical positioning device has been developed and utilized. In this method, because the weight of the stage is supported by the pneumatic pressure of the balancing cylinder, the linear motor can drive the stage motion without so much affected by the weight of the stage. Therefore, lower electric energy consumption, less heat generation, higher power and speed, can be expected with the linear motor. However, hybrid electric-pneumatic ultra-precision vertical positioning device has a drawback. When the tool change occurs, the total weight of the stage changes. Then the pressure in the balancing cylinder should be adjusted accordingly. But the pressure adjustment takes a bit of time with the conventional method that uses a diaphragm type pressure regulator. In this paper, in order to enhance the performance of the hybrid electric-pneumatic ultra-precision vertical positioning device, a new pressure adjustment method in the balancing cylinder when the tool change occurred is proposed. The proposed method utilizes a feed-forward control and a high precision quick response pneumatic regulator (HPQR) that was developed in our previous research. By the experimental results using a hybrid electric-pneumatic ultra-precision vertical positioning device, the validity of the proposed control method is evaluated and its superiority is indicated.

Semi-active joint for ultra-precision positioning using sliding/rolling bearings

A novel semi-active joint for connecting mechanical (i.e., sliding/rolling) bearings or guideways to an ultra-precision motion stage is presented. The semi-active joint enables the benefits of bearing/guideway friction on in-position stability while avoiding its adverse effects on rapid ultra-precision positioning. The joint is equipped with solenoids that switch its stiffness from low, during settling, to high once the stage gets into position. A two-step scheme is implemented to mitigate adverse effects of switching on positioning performance. Experiments demonstrate up to 81% and 60% improvements in settling time and in-position stability, respectively, compared to cases with solely low- or high-stiffness joints.

Development of precision blank carriage for manufacturing large gratings and echelles

A long-travel positioning device, which combines a ball-screw-driven coarse stage with a fine one, driven by piezoelectric translator, to achieve the long-distance traveling, up to 500 mm, as well as high-precision positioning, is crucial in the field of diffraction grating fabrication at nanometer scale. In this article, we present the design of the fine-feed drive stage with resolution as high as 20 nm and propose a single neuron-based proportional–integral–derivative controller to realize ultra-precision positioning. A high-performance piezoelectric translator is used to drive the mechanism, and the parallel leaf springs are used to guide the moving platform with preload force. A dynamic model of the precision positioning mechanism has been established by considering the Hertzian contact. In addition, the static and dynamic properties are investigated with the laser interferometry tracking methodology. The experimental results indicate that the positioning accuracy of less than 10 nm is obtained with the single neuron-based proportional–integral–derivative controller and also demonstrate the excellent performance of the proposed mechanism and control strategy.

Dynamic surface control of bellows-driven ultra-precision positioning system based on nonlinear extended state observer

Dynamic surface control of bellows-driven ultra-precision positioning system based on nonlinear extended state observer