IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 2, FEBRUARY 2014

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Design and Development of a Compact Flexure-Based XY Precision Positioning System With Centimeter Range Qingsong Xu, Member, IEEE

Abstract—This paper presents the design and development of a novel flexure parallel-kinematics precision positioning stage with a centimeter range and compact dimension. The stage mechanism is devised using leaf flexures to achieve a decoupled and modular structure. Structural parameters are carefully designed to guarantee the range, stiffness, resonant frequency, and payload capabilities in consideration of manufacturing tolerance. The parametric design is verified by conducting finite-element analysis, which reveals a reachable motion range over 20 mm in each working axis. Moreover, a prototype XY stage is fabricated, which is actuated and sensed by two voice coil motors and laser displacement sensors, respectively. Experimental results demonstrate that the stage is capable of positioning with a workspace over 11 mm × 11 mm. It is more compact than existing works, which is reflected by a larger area ratio of workspace to planar dimension. Both static and dynamic tests exhibit a small crosstalk between the two axes, which indicates a well-decoupled motion property. The implemented feedback control enables a precision positioning with submicrometer resolution and accuracy. The control bandwidth and payload influences on stage performances are experimentally examined as well. Index Terms—Decoupling, flexure mechanisms, long stroke, micro-/nanopositioning, motion control, parallel mechanisms.

I. I NTRODUCTION

M

ICRO-/NANOPOSITIONING techniques play more and more crucial roles in precision engineering applications, such as microscopy [1], lithography [2], alignment [3], and biomedical science [4]. For example, in microinjection of zebra fish embryo, a precision positioning stage with a stroke longer than 10 mm is required to enable a reliable penetration and pulling-out operation [5], particularly in automated batch injection tasks. In addition, the application inside a limited space demands a precision positioning stage occupying a compact size [6], [7]. Furthermore, a compact physical size enables cost reduction in fabrication. Hence, this research is concentrated on the design and development of a compact precision positioning stage with centimeter range of planar motion. Manuscript received June 19, 2012; revised January 1, 2013; accepted March 16, 2013. Date of publication April 5, 2013; date of current version August 9, 2013. This work was supported in part by the Macao Science and Technology Development Fund under Grant 024/2011/A and Grant 070/2012/A3 and in part by the Research Committee of the University of Macau under Grant MYRG083(Y1-L2)-FST12-XQS. The author is with the Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Macao, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2013.2257139

As far as kinematic scheme is concerned, positioning stages which are capable of 2-D translations can be classified into two categories in terms of serial and parallel kinematics. Majority of commercial stages employ a serial-kinematics scheme. For example, some two-axis stages have been developed by stacking the second single-axis positioning stage on the top of the first one or nesting the second stage inside the first one [8]–[10]. By this way, the entire second stage is supported by the first one. Although a compact structure may be achieved using the serial kinematics [10], it is at the sacrifice of high inertia, low resonant frequency, and large cumulative errors. A further disadvantage is that the dynamic characteristics in the two axes are different for a serial-kinematics stage. On the contrary, a parallel-kinematics scheme [11], [12] overcomes the aforementioned disadvantages and allows the achievement of low inertia, high resonant frequency, no cumulative error, high load capacity, and identical dynamic features in the two working axes. In order to realize a precision positioning with ultrahigh accuracy, traditional mechanical joints are powerless, owing to the adverse effects of backlash and friction [13]. Alternatively, flexure-based compliant guiding mechanisms [14]– [16] have been widely employed due to the absence of the aforementioned disadvantages. The reason lies in that the flexure compliant mechanisms deliver motions by making use of elastic deformations of the material [17]. Consequently, they render attractive merits in terms of no backlash, no friction, vacuum compatibility, low cost, and repeatable motion [18]. Thus, parallel-kinematics flexure-based mechanisms pave a promising way to achieve ultrahigh precision positioning. In the literature, a large number of 2-D flexure-based parallel-kinematics positioning stages have been proposed by researchers. For instance, the designs of flexure parallel XY stages driven by piezoelectric stack actuators (PSAs) have been reported in [19]–[22], which produce motion ranges less than 150 μm. PSA typically delivers a short stroke up to 0.1% of its length [23], [24], i.e., a stroke of 1 mm requires the length of 1 m for a typical PSA. As a result, it is practically difficult to realize a translation over 10 mm, even though lever transmission mechanisms can be employed to amplify the output displacement [25]. In addition, piezoelectric actuators exhibit inherent hysteresis and drift nonlinearities, which complicates the achievement of precision positioning [26], [27]. Alternatively, electromagnetic actuators or voice coil motors (VCMs) have been applied in more recent development of flexure parallel XY stages. For instance, micropositioning stages with millimeter ranges were reported in [28]–[30], which were

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 2, FEBRUARY 2014

driven by electromagnetic actuators. Several VCM-driven positioning stages with centimeter ranges were developed in [31] and [32]. As compared with PSA, VCM is capable of delivering a centimeter-level stroke along with a fine resolution [33], [34]. Although the centimeter stroke can be generated by selecting suitable actuators, it is challenging to devise a flexure parallel stage with a large range and a compact size simultaneously. The reason lies in that the two criteria are conflicting conditions indeed. To accomplish a large motion range, slender leaf flexures are usually employed [28], [29], [31], [32]. Intuitively, a longer stroke can be realized by using a narrower and longer leaf flexure. Nonetheless, the minimum width of the flexure is restricted by the practical tolerance of manufacturing, and the maximum length is constrained by the compactness requirement. In previous works, several designs have been proposed to tackle these issues. For instance, the compound parallelogram flexures (CPFs) were employed to design compliant XY stages with centimeter ranges [31], [35]. More recently, the new concept of multistage CPF (MCPF) was reported in [32] to achieve a larger pure translational motion. As compared with conventional CPF, it has been demonstrated that the motion range of an MCPF is enlarged by N times (N is the number of basic modules). Based on this state-of-the-art technique, a novel parallel flexure XY stage providing a centimeter motion range was developed [32], which achieves the most compact structure among the existing works in the literature. In that research, the compactness is quantified as the area ratio of the workspace to the minimum bounding rectangle around the planar dimension of the XY stage. The stage as reported in [32] was fabricated as a monolithic structure which is free of assembly. Nevertheless, the monolithic stage occupies a large planar space since the space has not been made full use of. The motivation of this research is to devise a more compact parallel flexure XY stage with a centimeter motion range. Specifically, the concept of stacked and modular structure is proposed to design a compact flexure stage along with parallel-kinematics properties. To facilitate control design for the positioning system, a stage with decoupled output motion is desirable. In addition, in order to isolate and protect the actuators, an input decoupling feature is preferable. Hence, the concept of total decoupling [20] is considered in the design procedure. Although the stack concept has been used to design a positioning stage in previous work [36], the stage only delivers a motion range up to 132 μm × 126 μm. Furthermore, it possesses an axial-symmetry structure and owns a large crosstalk up to 4.5% between the axes. In contrast, a new mirror-symmetric structure is proposed in the present research, and a smaller parasitic motion is produced. As a consequence, the single-input–single-output (SISO) control is easily implemented to achieve a precision positioning for the system. The major contribution of this paper lies in the design and development of a novel compact flexure-based precision positioning stage which owns integrated merits of centimeter range, parallel kinematics, modular structure, total decoupling, and submicrometer accuracy. The rest of this paper is organized as follows. The mechanism design procedure of the novel XY stage is presented in Section II. Then, the parametric design of the stage is outlined in Section III, which is carried out by

Fig. 1. (a) Ordinary CPF and (b) its deformation. (c) MCPF with N modules.

establishing analytical models for the quantification of motion range, stiffness, load capacity, and resonant frequency of the stage. These models are validated by conducting finite-element analysis (FEA). Afterward, a prototype stage is fabricated, and the static and dynamic performances are tested in Section IV, where the positioning resolution and accuracy are also characterized by realizing proportional–integral–derivative (PID) control, and an extensive discussion is provided. Section V concludes this paper. II. M ECHANISM D ESIGN In this section, the mechanism design of a compact precision positioning stage with parallel-kinematics, decoupled, and modular structure is presented. A. Design of a Long-Stroke Flexure XY Stage Regarding an ordinary CPF as shown in Fig. 1(a), when a force Fx is applied on the output stage, the deformed shape is illustrated in Fig. 1(b). Although various shapes of notch hinges can be used [37], the leaf flexures are employed to generate a large elastic deformation. Considering the boundary conditions of the deformation, the stiffness of the CPF is determined by K1 =

Fx Ebh3 = 3 x1 l

(1)

where l and h represent the length and width of the leaf flexure, respectively. In addition, b denotes the thickness of the plate material. Taking into account that the maximum translation is constrained by the maximum stress induced by the maximum force Fxmax , the maximum one-sided translation is calculated as xmax = 1

Fxmax σy l 2 = K1 3Eh

(2)

where σy is the yield stress and E is Young’s modulus of the material.

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Fig. 2. (a) Four-PP parallel mechanism with two P joints actuated. (b) Monolithic XY stage which is composed of MCPFs with N = 2.

The relationship (2) indicates that the maximum one-sided of a CPF is governed by the length l and translation xmax 1 width h of the leaf flexures for a given material. To obtain a , the flexures with larger length and smaller width larger xmax 1 are preferable. Practically, the physical parameter l is restricted by the compactness requirement of the device, and h is limited by the manufacturing tolerance as well as the restriction on minimum stiffness. Hence, the concept of MCPF was proposed [32] to achieve a large translation while keeping the values of l and h unchanged. An MCPF with N modules is depicted in Fig. 1(c). It is found that the output stage is connected to the base through N basic modules. The stiffness of the MCPF is determined by [32] KN =

Ebh3 . N l3

(3)

In addition, the maximum one-sided translation of the MCPF is governed by = xmax N

N σy l 2 . 3Eh

(4)

Inspecting (4) with (2), it can be deduced that, using the flexures with the same physical parameters (l and h) and material, the maximum stroke of the MCPF is enlarged by N times as compared with that of the ordinary CPF. It is noticed that N = 1 represents the special case of traditional CPF. Without loss of generality, N = 2 is selected to construct an MCPF, which is then adopted to create a monolithic parallelkinematics XY stage as shown in Fig. 2(b). To achieve a decoupled motion, the stage is designed as a four-PP (P stands for prismatic joint) parallel mechanism as depicted in Fig. 2(a). This stage has been developed in the previous work [32], which achieves an area ratio of 0.2407% between the workspace size and planar dimension. To further improve the area ratio, a basic module structure as shown in Fig. 3(a) is proposed in this paper. Once driven by a linear actuator (e.g., VCM), the input motion of the module is transferred as the pure translation of center output platform along the x-axis direction. The output motion is guided by four MCPFs located at the corners of the module. By mounting the second module on the top of the first module, a modular XY stage is devised as depicted in Fig. 3(b), where the two identical

Fig. 3. (a) Basic module, whose four mounting holes construct a square with the edge length of w. (b) Stacked parallel-kinematics XY stage with two basic modules. (c) Enhanced basic module. (d) Stacked parallel-kinematics XY stage with two enhanced basic modules.

stages are arranged in an orthogonal way to construct a four-PP architecture. The XY stage features a parallel-kinematics and stacked structure. The modular design allows the cost reduction in terms of manufacturing and maintenance. If the XY stage is driven by VCM #1, a pure translation of the center output stage in the x-axis is produced and guided by the four corner MCPFs of the first module as well as the two other MCPFs of the second module. Similarly, once driven by VCM #2, a pure translation of the stage along the y-axis direction is generated. Hence, a decoupled 2-D translation is achieved by the XY stage benefiting from the four-PP parallel mechanism. Moreover, due to large transverse stiffness of the MCPFs located at the corners [see Fig. 3(a)], they can tolerate a large transverse load applied in the direction orthogonal to the working axis in the xy plane. As a result, VCM #1 does not suffer from transverse displacement if the stage is driven by VCM #2. Similarly, VCM #2 does not move in transverse direction once the stage is actuated by VCM #1. Therefore, an input decoupling is accomplished by the XY stage. It follows that the proposed XY stage owns an attractive totally decoupling property. As a result, the stage [see Fig. 3(b)] possesses a much compact size, which indicates a larger area ratio than the previous one as shown in Fig. 2(b). B. Structure Improvement for the XY Stage Once the XY stage is driven by a linear actuator, e.g., VCM #1, the leaf flexures in the two centered MCPFs (denoted by dashed ellipses) in Fig. 3(a) suffer from bending deformations. The undesirable bended flexures cause reduced translational displacement of the stage output platform.

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TABLE I M AIN S TRUCTURAL PARAMETERS OF THE XY S TAGE

In order to overcome this shortcoming, two connecting rods are used to join the secondary stages of each basic module together, as depicted in Fig. 3(c), which is called an enhanced basic module. The secondary stages can be joined together because they undergo identical displacements. As a result, an improved structure of the XY stage is generated as shown in Fig. 3(d). Since the bending deformations of the concerned flexures are eliminated, the improved design is capable of delivering much larger output displacement than the original one, as shown in Fig. 3(b). III. PARAMETRIC D ESIGN To develop an XY stage with desired characteristics in terms of motion range, stiffness, load capability, and resonant frequency, the key structural parameters (l, h, and b) are carefully designed, as shown in Table I. In addition, for the sake of easy assembly, the four mounting holes of the basic module are designed as a square with the edge length of w, as described in Fig. 3(a). Taking into account that the XY stage owns a welldecoupled structure, its main performance can be derived by examining the translation along a single working axis. In the parametric design carried out hereinafter, it is assumed that the axial deformations of the flexures are neglected, and only the bending deformations are considered.

Fig. 4. Contour plot of the static FEA result of deformation induced by an input displacement of 5 mm.

20 mm × 20 mm. Moreover, with an assigned Dmax = 5 mm, the deformation generated by static structural analysis is shown in Fig. 4. It is found that the maximum stress of 226.9 MPa is caused, which indicates a high safety factor of 2.2 (= 503 MPa/226.9 MPa) for the material. B. Stiffness and Actuation Force By inserting N = 2 into (3), the stiffness of the MCPF in its working axis is determined as K2 =

Ebh3 . 2l3

Once driven by a linear actuator, e.g., VCM #1, the deformation of the XY stage is undergone by six MCPFs which connect the stage output platform to the fixed base in parallel. Hence, the stage stiffness in each working direction is derived as

A. Motion Range The maximum one-sided translation of the XY stage in each axis can be determined by substituting N = 2 into (4) 2

dmax =

2σy l . 3Eh

(5)

It follows that the motion range in each working axis is ±dmax , which produces a reachable workspace of 2dmax × 2dmax with boundaries defined by the yield stress. In view of the material parameters (E = 71.7 GPa, σy = 503 MPa, Poisson s ratio = 0.33, and density = 2810 kg/m3 ), dmax = 5.85 mm is calculated. To guarantee the safety of the material, the actual workspace should locate inside the reachable workspace, as calculated earlier. That is, for an assigned maximum one-sided translation Dmax = 5 mm of the stage, the parameters should be designed to meet the condition 2σy l2 ≥ Dmax . 3Eh

(6)

The FEA simulation conducted with ANSYS predicts that dFEA max = 11.08 mm, which reveals a usable workspace of

(7)

K = 6K2 =

3Ebh3 . l3

(8)

In order to generate a desired motion range by using VCMs, the stage should be sufficiently compliant so that the elastic deformation energy can be overcome by the driving force of VCMs. Given the required motion range of ±Dmax , the desired maximum driving force can be obtained as Fmax = KDmax =

3Ebh3 Dmax . l3

(9)

To ensure that the stage is compliant enough, the parameters should be designed to satisfy the condition 3Ebh3 dmax ≤ FVCM . l3

(10)

By selecting the VCM with the maximum output force of 194.6 N, the designed structural parameters (see Table I) result in the relationship 86.0 N ≤ FVCM . Hence, the stiffness requirement is met by the parametric design. FEA = 102.7 N < In addition, the FEA result indicates that Fmax FVCM , which also confirms the suitability of the designed parameters.

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TABLE II F IRST-S IX R ESONANT F REQUENCIES OF THE XY S TAGE ( IN H ERTZ )

C. Critical Load of Buckling It is observed that the leaf flexures associated with the MCPFs, which are connected to the output platform of the XY stage, suffer from axial load during the operation. Due to a slender architecture, they are prone to elastic buckling under compressive loads. Buckling causes instability of the structure and leads to the decrease of motion range of the stage. Hence, the maximum force Fmax producing the desired motion range should not excite buckling deformation of the leaf flexures. The critical load is derived as follows. The critical compressive load which induces elastic buckling of the leaf flexure can be calculated by P =

π 2 EI 2 lcr

(11)

where I = bh3 /12 is the area moment of inertia of the cross section. In addition, the critical length lcr is determined by lcr = kl

(12)

where the coefficient k takes the value from 0.5 to 2, depending on the boundary conditions. Since the two secondary ends of each MCPF are joined by a connecting rod, as shown in Fig. 3(c), the concerned flexures can be considered as fixed–fixed columns. For a beam with fixed–fixed boundary condition, the coefficient is taken as k = 0.5 [38]. Hence, the critical load can be computed as Fcr = 2P =

8π 2 EI . l2

(13)

In order not to excite elastic buckling deformation during the movement of the stage within the motion range, the following condition should be met: FVCM ≤ Fcr

(14)

i.e., FVCM

2π 2 Ebh3 ≤ . 3l2

(15)

The relationship can be calculated as FVCM ≤ 943.5 N. Obviously, the maximum actuation force of 194.6 N will not induce any elastic buckling deformation of the flexures. D. Resonant Frequency For the generation of a high bandwidth of the servo system, a high resonant frequency of the stage is desired. Based on Lagrange’s equation, the free motion of the XY stage can be described by the dynamic equation M¨ q + Kq = 0

(16)

where M = diag{M, M } and K = diag{K, K} are the matrices of equivalent mass M and stiffness K, respectively. In addition, q = [x y]T denotes a vector of the generalized coordinates x and y, i.e., the displacements in the two working axes. Based on the theory of vibrations, the mode equation can be derived as (K − ωi2 M)Φi = 0

(17)

Fig. 5. First-six resonant mode shapes of the XY stage.

where the eigenvector Φi (for i = 1 and 2) represents a mode shape and eigenvalue ωi2 describes the corresponding natural cyclic frequency, which can be obtained by solving the characteristic equation |K − ωi2 M| = 0.

(18)

Then, the resonant frequency is computed as fi = (1/2π)ωi (hertz). Specifically, f1 = f2 = 54.6 Hz is calculated for the XY stage. In addition, the first-six resonant frequencies as predicted by the modal analysis with ANSYS are shown in Table II, and the corresponding mode shapes are illustrated in Fig. 5. The FEA results reveal that the first-two mode shapes are contributed by the translations along the two working axes, respectively. The third mode is an in-plane rotation with a resonant frequency of 128.5 Hz, which is more than twice the first-two frequencies. This indicates a robust translational motion along the working directions. E. Out-of-Plane Payload Capability The out-of-plane payload that can be supported by the output platform of the XY stage is assessed by carrying out FEA simulations. With a load of 20 kg applied on the output platform, the induced out-of-plane displacement is only 0.4 mm. At the same time, the maximum stress experienced by the material arrives at 82.7 MPa, which is far less than the yield stress (503 MPa). Hence, the XY stage exhibits a good out-of-plane payload capability.

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The static FEA simulation reveals that the stiffness of the XY stage in each working direction is 2.05 × 104 N/m in the absence of out-of-plane load. With an out-of-plane load of 20 kg applied on the output platform, the stiffness is assessed as 2.34 × 104 N/m in the working axes. Hence, as compared with the free-of-load stiffness, a 20-kg load causes an increase of 14% in the actuation stiffness. In order to produce a motion range of 10 mm under such an external load, a maximum actuation force of 117.2 N is required, which is still less than the driving force (194.6 N) of VCMs. Therefore, an out-of-plane load of 20 kg can be easily sustained without influencing the achievement of centimeter range for the XY stage. F. Influences of Manufacturing Tolerance The preceding parametric design leads to an XY stage with desired characteristics. However, the actual values of the parameters are determined by the manufacturing tolerance. Hence, it is important to ensure that the nominal parameters with the uncertainty of tolerances also produce desired characteristics for the XY stage. As compared with FEA simulations, the established analytical models are computationally more effective. However, there are certain discrepancies between the analytical results and FEA outputs. The discrepancies are mainly induced by the assumption adopted in the modeling procedure, which only considers the bending deformations of flexures. In contrast, more accurate results are produced by FEA simulation since all possible (including bending and axial) deformations are taken into account. Even so, the analytical models can be corrected by multiplying specific compensation factors. Hence, the derived models are employed to discover the influences of manufacturing tolerance on the stage performances. For a given plate material, its thickness b is a fixed value (10 mm). Hence, no tolerance is assigned to parameter b. The tolerances of both wire-electrical discharge machining (WEDM) and drilling machining are ±10 μm. Considering other errors caused in assembly process, the tolerance is conservatively assigned as ±Δ = ±30 μm for the structural parameters l and h. 1) Motion Range: Considering a discrepancy of −47.2% between the analytical prediction and FEA result, a compensation factor of ηd = 1/(1 − 47.20%) = 1.89 is employed to correct the analytical model (5). In view of the motion range dmax as given in (5), it is deduced that the lower value is produced if the actual parameters l and h take the lower and upper deviations, respectively. On the contrary, the upper value is achieved if l and h are machined with the upper and lower deviations, respectively. That is 2σy (l − Δ)2 ηd 2σy (l + Δ)2 ηd ≤ dcmax ≤ 3E(h + Δ) 3E(h − Δ)

(19)

where dcmax = ηd dmax denotes the analytical result corrected by the compensation factor ηd . The boundary values are calculated as 10.40 mm ≤

dcmax

≤ 11.78 mm

(20)

which means that the lower value of motion range still satisfies the design requirement of dmax > Dmax = 5 mm.

Fig. 6. Exploded view of CAD model for the XY precision positioning stage.

2) Actuation Force: Concerning the model of maximum driving force Fmax as given in (9), it is compensated by a factor of ηF = 1/(1 − 16.26%) = 1.19 to produce the result as accurate as the FEA simulation. In consideration of (9), the range of the maximum actuation force value can be derived as 3Eb(h−Δ)3 Dmax ηF 3Eb(h+Δ)3 Dmax ηF c ≤ Fmax ≤ (21) 3 (l+Δ) (l−Δ)3 i.e., c 84.7 N ≤ Fmax ≤ 122.4 N

(22)

c where Fmax = ηF Fmax represents the compensated analytical result. It is found that the upper value of the maximum actuation force still meets the requirement of Fmax < FVCM = 194.6 N. The aforementioned analysis reveals that, under the influences of manufacturing tolerance, the large motion range is still well guaranteed and the stage can be sufficiently driven by the given VCMs. Therefore, the parametric design satisfies the requirement in the present research. A computer-aided design (CAD) model of the developed XY stage is illustrated in Fig. 6. The stage is driven by two VCMs, and the output position is measured by two laser displacement sensors.

IV. E XPERIMENTAL I NVESTIGATIONS In this section, the designed XY precision positioning stage is developed, and its performances are tested by carrying out a series of experimental studies. A. Prototype Development The experimental setup of the developed precision positioning system is shown in Fig. 7. Because the two basic modules are designed with identical parameters, they are fabricated of the material of Al-7075 alloy by the approach of WEDM at one time. This leads to a reduction of manufacturing cost, which

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Fig. 8. Motion range test results with 0.2-Hz sinusoidal signal input. (a) and (b) Results obtained with VCM #1 driven. (c) and (d) Results obtained with VCM #2 driven.

Fig. 7.

Experimental setup of the XY precision positioning system.

is the advantage of modular design. The XY stage possesses dimensions of 120 mm × 120 mm × 25 mm. The stage is driven by two VCMs, which deliver a stroke of 12.7 mm with a maximum driving force of 194.6 N. The position output is measured by two laser displacement sensors (model: LK-H055, from Keyence Corporation), which provide a resolution of 25 nm within a measurement range of 20 mm. In order to eliminate Abbe errors, the sensors are mounted in such a manner that the two measuring directions are coincident with the two working axes of the stage, respectively. In addition, a National Instruments (NI) cRIO-9075 real-time controller equipped with NI-9263 analog output module and NI-9870 RS232 serial interface module is adopted to produce excitation signals and acquire sensor readings, respectively. The NI cRIO-9075 combines a real-time processor and a reconfigurable field-programmable gate array within the same chassis, which is connected to a computer via the Ethernet port for communication. Moreover, LabVIEW software is employed to implement a real-time control of the positioning system. B. Static Performance Test By applying a 0.2-Hz quasi-static sinusoidal voltage signal to each VCM, the stage displacements in the two working axes are measured using the two laser sensors. By driving VCM #1 with a conservative voltage amplitude of ±6-V magnitude, a motion range of 11.75 mm is achieved for the x-axis positioning, as shown in Fig. 8(a), which is larger than the desired value of 2Dmax = 10 mm. In addition, the induced parasitic motion in the y-axis is depicted in Fig. 8(b). It exhibits that the parasitic motion range (146.14 μm) is about 1.24% of the primary x-axis motion range. Similarly, by applying the same input signal to

VCM #2, the test result of motion range in the y-axis is shown in Fig. 8(d). It is found that the y-axis range is 11.66 mm, which is also greater than the desired value (10 mm). Moreover, the caused parasitic motion in the x-axis, as shown in Fig. 8(c), reveal that the maximum crosstalk is 72.17 μm, i.e., 0.62% of the primary y-axis motion. The area ratio of workspace to planar dimension is calculated as 0.9514%, which is almost four times higher than the best one of 0.2407% achieved in the existing literature [32]. That is, the developed XY stage is about four times as compact as the existing one. Evidently, the design objective of decoupled and centimeter range of motion is well achieved. In addition, it is found that the open-loop position–voltage relations of the primary motion are nonlinear, as shown in Fig. 8(a) and (d), and certain nonlinear hysteretic effects exist in the parasitic motion, as exhibited in Fig. 8(b) and (c). The presence of nonlinearities necessitates the implementation of control techniques in order to achieve a precision positioning. C. Dynamic Performance Test Next, the open-loop dynamic performance of the XY positioning system is tested by the swept-sine approach. Specifically, sine waves with an amplitude of 0.1 V and a frequency range of 1–200 Hz are produced by the digital-to-analog converter channels of the NI-9263 module to drive the VCMs. Spectral analysis is then conducted to obtain the frequency responses of the stage in the two working axes. By applying the swept-sine signal to VCM #1, the magnitudes of frequency responses associated with the x- and y-axis motion are illustrated in Fig. 9(a) and (c) (solid lines), respectively. It is observed that the most significant coupling of the two axes occurs around the resonant frequency. At lower frequencies below the resonant frequency, the coupling effect becomes weaker, and it can be characterized by the static crosstalk. Hence, in this research, the dynamic crosstalk is defined as the difference between the magnitudes of frequency

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Fig. 9. Magnitudes of frequency responses of the XY precision positioning system. (a) Gx1 , (b) Gy1 , (c) Gx2 , and (d) Gy2 . Gni means the response in the n-axis excited by the ith motor.

Fig. 10. Phases of frequency responses of the XY precision positioning system. (a) Gx1 , (b) Gy1 , (c) Gx2 , and (d) Gy2 . Gni means the response in the n-axis excited by the ith motor.

responses at the resonant frequency for the parasitic and dominant motion. It is found that the response in the y-axis is about −33 dB lower than that in the primary x-axis at the resonant frequency. Similarly, with VCM #2 driven alone, the magnitudes of frequency responses in the two working axes are plotted in Fig. 9(c) and (d), respectively. It is seen that the x-axis response is −37 dB lower than the primary y-axis response at the resonant frequency. Hence, a small magnitude of dynamic crosstalk in both working axes of the XY stage is demonstrated. It is noticeable that, in the aforementioned openloop tests, when VCM #1 (or #2) is driven, the other VCM is free and no feedback control is applied. In addition, the phase plots of frequency responses are given in Fig. 10. From the results as shown in Fig. 9(a) and (d), the resonant frequencies of 29.3 and 29.6 Hz can be identified for the x- and y-axes, respectively. It is found that the frequencies obtained by experiments are lower than the simulation results,

Fig. 11. load.

(a) Resonant frequency and (b) dynamic crosstalk versus out-of-plane

as described in Table II. The discrepancy mainly comes from the mass of moving coils of the VCMs, which is not considered in FEA simulations. Moreover, the similar resonant frequency of the x- and y-axes indicates almost identical dynamic properties in the two working directions. Moreover, to discover the influence of load effect on the stage performance, the frequency responses of the XY stage are experimentally tested under different out-of-plane loads. The magnitude and phase responses for three load cases (0, 0.6, and 1.0 kg) are illustrated in Figs. 9 and 10, respectively. It is observed from Fig. 9(a) and (d) that, under different loads, the magnitude responses in the x- and y-axes at lower frequencies (e.g., 1 Hz) are not changed. This indicates that the quasi-static motion ranges along the two working axes at low frequencies (less than 1 Hz) are not affected by the loads. As the varying of the load (0, 0.25, 0.6, 0.8, and 1.0 kg), the resonant frequencies and dynamic crosstalk of the two axes are shown in Fig. 11(a) and (b), respectively. It is observed that, as the external load increases, the resonant frequency is reduced gradually and the dynamic coupling between the two axes tends to get worse at the resonant frequencies. In order to alleviate the dynamic coupling effect, a suitable controller is required to mitigate the interference between the working axes. D. Positioning Performance Test Owing to the decoupled open-loop static and dynamic responses of the XY stage, as verified before, the positioning system can be controlled by resorting to SISO control schemes. Specifically, the PID control is adopted to achieve a precision positioning due to its popularity. Two PID controllers are implemented for the two working axes, respectively. The control gains are tuned to produce no overshoot by resorting to the Ziegler–Nichols method through experimental studies. With the designed controllers, the experimental results of simultaneous set-point positioning of the two axes are generated as shown in Fig. 12. It is observed that the 5% settling times for the x- and y-axes are 0.18 and 0.14 s, respectively, which

XU: DESIGN AND DEVELOPMENT OF COMPACT XY PRECISION POSITIONING SYSTEM WITH CENTIMETER RANGE

Fig. 12. Set-point positioning results in the two axes, which indicate a rapid response without overshoot. In addition, the positioning in one axis has small influence on the other axis.

901

Fig. 14. Histograms of set-point positioning errors in (a) x- and (b) y-axes.

Fig. 15. Frequency responses of the control system for the (left) x- and (right) y-axes. The 30◦ -lag bandwidth is denoted.

Fig. 13. Resolution test results of (a) x- and (b) y-axes, which reveal a positioning resolution of 200 nm in each axis.

are obtained without overshoot effect. In addition, it is found that the amount of maximum response in the perpendicular axis accounts for 0.9% of the response in the dominant axis. Hence, the positioning in one working axis poses a small influence on the other axis, which reveals a robust closed-loop positioning in the two working axes. Next, the 200-nm consecutive step positioning results for each axis are illustrated in Fig. 13. The fact that the step size can be clearly identified reveals that the positioning resolution is better than 200 nm for each working axis. Moreover, the histograms of the positioning errors in the two axes are plotted in Fig. 14. By calculating the standard deviation (σ) of the errors in both axes, the 3σ confidence intervals corresponding to the confidence levels of 99.7% are also depicted in Fig. 14. It

means that it can be 99.7% confident that the positioning error will fall within the range between −3σ and 3σ. Experimental results show that the 3σ positioning accuracy values are 0.338 and 0.328 μm for the x- and y-axes, respectively. Moreover, the control bandwidth of the XY stage is tested by applying a sinusoidal signal with an amplitude of 10 μm along with varying frequency (0.1–30 Hz). The closed-loop frequency responses in the x- and y-axes are shown in Fig. 15(a) and (b), respectively. It is found that there are large phase lags (over 90◦ ) within the ordinary −3-dB bandwidth, which lead to large tracking errors. Hence, in this research, the closedloop control bandwidth is defined as the frequency at which the phase lag arrives at 30◦ . With the PID control, 30◦ -lag bandwidths of 5.9 and 5.1 Hz are achieved for the x- and y-axes, which are equivalent to 20% and 17% of the resonant frequencies, respectively. These cutoff frequencies correspond to small errors of 0.03 and 0.56 dB for the magnitude responses in the x- and y-axes, respectively.

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 2, FEBRUARY 2014

TABLE III M AIN P ERFORMANCES OF THE XY P RECISION P OSITIONING S YSTEM W ITHOUT L OAD

sensors. In the future, displacement sensors with higher resolution and lower noise will be adopted to further improve the positioning performance for the XY precision positioning system. Moreover, advanced control techniques [39], [40] will be implemented to realize better accuracy and higher bandwidth for the precision positioning system. V. C ONCLUSION

E. Discussion and Future Work The main performances of the XY positioning system are summarized in Table III. It is noticeable that, although the actual area ratio is 0.9514% due to the limited strokes of the employed VCMs, an area ratio of 2.7778% is achievable by considering a reachable workspace of 20 mm × 20 mm. In addition, the stage architectural parameters are not optimized. In the future, a more compact stage will be produced by resorting to an optimum parametric design. It is noticed that the area ratio is calculated without considering the size of actuators. Generally, VCM provides a larger stroke than PSA at the cost of larger physical size. However, to achieve the same long stroke (e.g., 10 mm), the length of PSA (typically, 10 m) is much bigger than VCM (fully retracted length of 58 mm in this research). From this point of view, VCM is more suitable for long-range positioning applications. It is noticeable that, although a two-layered structure is employed in the XY stage, both layers are fixed at the base through the four mounting holes [see Fig. 3], i.e., both layers support the identical mass of moving components. Hence, the stage belongs to a parallel-kinematics architecture, which results in similar frequencies in the two working axes. The resonant frequency of about 30 Hz is relatively low for highspeed positioning applications. Thus, the large motion ranges are achieved at the cost of low resonant frequency. The resonant frequency can be improved by conducting an optimum parametric design of the stage and employing VCMs with smaller mass of the moving coils. During the control of the positioning stage, it is important to prevent the occurrence of plastic deformation to ensure the safety of the material. The FEA, as performed in Section III-A, reveals that a motion range of 10 mm along each axis is achieved with a high safety factor of 2.2. Correspondingly, the motion range that is produced by the employed VCMs leads to a safety factor of about 1.9 for each working axis. When the output platform translates within the workspace of the stage, the safety of material is guaranteed by the safety factor greater than one. Otherwise, mechanical stoppers may be employed to restrict the motion range in each direction to prevent the plastic deformation of the flexures. In addition, the positioning results (see Figs. 12 and 13) of the conducted experiments are obtained by employing low-pass filters with a cutoff frequency of 30 Hz to reduce the noise of laser sensors. The positioning resolution and accuracy are dependent on the performance of the employed displacement

The design, fabrication, and testing of a novel large-range XY precision positioning system have been presented in this paper. FEA simulation results show that a reachable workspace of 20 mm × 20 mm is obtained, which indicates an area ratio (workspace size to planar dimension of the stage) of 2.7778%. Due to the hardware constraint, a workspace range of 11.75 mm × 11.66 mm is generated. It corresponds to an area ratio of 0.9514%, which is almost fourfold more compact than the best one in existing literature. In addition, the buckling effect is eliminated, and the stage has an out-of-plane payload capability over 20 kg. Experimental studies on the prototype system reveal a static crosstalk less than 1.3% and a dynamic coupling lower than −33 dB, which indicates a decoupled motion between the two working axes. The dynamic characteristics in both axes are almost identical, as revealed by similar resonant frequencies of 30 Hz. By realizing PID SISO control, a resolution of 200 nm and a positioning accuracy better than 340 nm are accomplished. The experimental results confirm the effectiveness of the developed micropositioning system as well as its promising application in planar precision positioning with centimeter range and submicrometer accuracy. R EFERENCES [1] N. Bonnail, D. Tonneau, F. Jandard, G.-A. Capolino, and H. Dallaporta, “Variable structure control of a piezoelectric actuator for a scanning tunneling microscope,” IEEE Trans. Ind. Electron., vol. 51, no. 2, pp. 354– 363, Apr. 2004. [2] L. Zhang and J. Dong, “High-rate tunable ultrasonic force regulated nanomachining lithography with an atomic force microscope,” Nanotechnology, vol. 23, no. 8, p. 085303, Mar. 2012. [3] J. Zhao, H. Wang, R. Gao, P. Hu, and Y. Yang, “A novel alignment mechanism employing orthogonal connected multi-layered flexible hinges for both leveling and centering,” Rev. Sci. Instrum., vol. 83, no. 6, pp. 065102-1–065102-7, Jun. 2012. [4] Y. Zhang, K. Tan, and S. Huang, “Vision-servo system for automated cell injection,” IEEE Trans. Ind. Electron., vol. 56, no. 1, pp. 231–238, Jan. 2009. [5] H. B. Huang, D. Sun, J. K. Mills, and S. H. Cheng, “Robotic cell injection system with position and force control: Toward automatic batch biomanipulation,” IEEE Trans. Robot., vol. 25, no. 3, pp. 727–737, Jun. 2009. [6] C. Dubois, P. E. Bisson, A. A. Manuel, Ø. Fischer, and S. Reymond, “Compact design of a low temperature XY stage scanning tunneling microscope,” Rev. Sci. Instrum., vol. 77, no. 4, pp. 043712-1–043712-5, Apr. 2006. [7] Q. Xu, “Design and development of a flexure-based dual-stage nanopositioning system with minimum interference behavior,” IEEE Trans. Autom. Sci. Eng., vol. 9, no. 3, pp. 554–563, Jul. 2012. [8] R.-F. Fung, Y.-L. Hsu, and M.-S. Huang, “System identification of a dualstage XY precision positioning table,” Precis. Eng., vol. 33, no. 1, pp. 71– 80, Jan. 2009. [9] B. J. Kenton and K. K. Leang, “Design and control of a three-axis serialkinematic high-bandwidth nanopositioner,” IEEE/ASME Trans. Mechatronics, vol. 17, no. 2, pp. 356–369, Apr. 2012. [10] S. Wadikhaye, Y. K. Yong, and S. O. R. Moheimani, “Design of a compact serial-kinematic scanner for high-speed atomic force microscopy: An analytical approach,” IET Micro Nano Lett., vol. 7, no. 4, pp. 309–313, Apr. 2012.

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Qingsong Xu (M’09) received the B.S. degree in mechatronics engineering (with honors) from Beijing Institute of Technology, Beijing, China, in 2002 and the M.S. and Ph.D. degrees in electromechanical engineering from the University of Macau, Macao, China, in 2004 and 2008, respectively. He was a Visiting Scholar with the Swiss Federal Institute of Technology (ETH), Zurich, Switzerland, and the National University of Singapore, Singapore. He is currently an Assistant Professor of electromechanical engineering with the University of Macau. His current research interests include micro-/nanosystems, microelectromechanical devices, micro-/nanoassembly, smart materials and structures, and computational intelligence. Dr. Xu is a member of the American Society of Mechanical Engineers. He currently serves on the Editorial Boards or is a Guest Editor of six international journals.