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Design and Development of a Flexure-Based Dual-Stage Nanopositioning System With Minimum Interference Behavior Qingsong Xu, Member, IEEE

Abstract—Dual-servo systems (DSSs) are highly desirable in micro-/nanomanipulation when high positioning accuracy, long stroke motion, and high servo bandwidth are required simultaneously. This paper presents the design and development of a new flexure-based dual-stage nanopositioning system. A coarse voice coil motor (VCM) and a fine piezoelectric stack actuator (PSA) are adopted to provide long stroke and quick response, respectively. A new decoupling design is carried out to minimize the interference behavior between the coarse and fine stages by taking into account actuation schemes as well as guiding mechanism implementations. Both analytical results and finite-element model (FEM) results show that the system is capable of over 10 mm traveling, while possessing a compact structure. To verify the decoupling property, a single-input-single-output (SISO) control scheme is realized on a prototype to demonstrate the performance of the DSS without considering the interference behavior. Experimental results not only confirm the superiority of the dual-servo stage over the standalone coarse stage but reveal the effectiveness of the proposed idea of decoupling design. Note to Practitioners—In view of the requirements of both large workspace and rapid response for micro-/nanomanipuolation, a new dual-stage nanopositioning system is presented in this paper. It is composed of flexure-based compliant mechanisms and driven by coarse and fine actuators. The mechanism design has direct relation to automation of the nanopositioning system. Due to the interaction of the coarse and fine actuation, the implementation of SISO control scheme necessitates a proper structure design. This paper presents the design of a dual-stage to decouple the coarse and fine actuation in order to facilitate SISO control. The performed simulation and experimental studies validate the proposed design ideas. Thus, the automated dual-stage system can be controlled by any SISO controller. For illustration, popular PID control is adopted for both VCM and PSA stages. Experimental results demonstrate the merits of a dual-stage over the standalone coarse stage in terms of transient response speed as well as steady-state accuracy. More advanced SISO control strategies can be employed to realize the automation of the dual-stage nanopositioning system as well. Index Terms—Decoupling design, dual-servo system (DSS), flexure mechanisms, micro-/nanopositioning, motion control. Manuscript received October 19, 2011; revised February 13, 2012; accepted April 30, 2012. Date of publication May 30, 2012; date of current version June 28, 2012. This paper was recommended for publication by Associate Editor P. Lutz and Editor K. Bohringer upon evaluation of the reviewers’ comments. This work was supported in part by the Macao Science and Technology Development Fund under Grant 024/2011/A and in part by the Research Committee of the University of Macau under Grant SRG006-FST11-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/TASE.2012.2198918

I. INTRODUCTION DUAL-SERVO system (DSS) is highly desirable in the scenarios where the merits of high positioning accuracy, long stroke motion, and high servo bandwidth are simultaneously required. Usually, a coarse actuator and a fine actuator are employed together to endow a DSS with the aforementioned advantages. In such applications as scanning probe microscopy (SPM), a precise nanopositioning stage is used to implement an accurate and rapid scanning task to get surface profiles of the scanned specimen [1]–[3]. Nevertheless, only a small portion of the specimen can be put on the scanning table. For instance, an atomic force microscope (AFM) usually has a scanning range . In order to acquire surface inforless than mation of a large specimen (e.g., 20 mm 20 mm), a nanopositioning stage with both a large workspace and a high bandwidth is required to fully cover the whole specimen surface and to quickly acquire the surface profile on scanned areas. Thus, the DSS opens the way to overcome these issues. DSSs also have promising applications in biological micromanipulation [4] and microgripping [5]. Most of the existing DSSs are applied in hard disk drives [6]. Recently, DSSs have been extended to micro-/nanopositioning applications. For example, a dual-stage nanopositioning system is developed in [7], where a coarse permanent magnet stepper motor stage and a fine piezoelectric stack actuator stage are stacked together. In [8], a coarse-fine dual-stage system is reported by using a voice coil motor to drive a fine stage and a permanent magnet linear synchronous motor to drive a coarse stage. Additionally, the design of a linear dual-stage actuation system is presented in [9] by employing a voice coil motor and a piezoelectric stack actuator as coarse and fine drivers, respectively. In the above works, aerostatic bearings and maglev bearings are most adopted to guide the output motion of the stage. By contrast, flexure bearings are more preferred due to their merits of no backlash, no friction, vacuum compatibility, and easy manufacturing. Thus, flexures are employed in the recent development of nanopositioning systems [10]–[12]. A literature review of previous works reveals that it is challenging to develop a large-stroke dual-stage by using flexures only [13]–[15]. Although designing a general flexure stage with a large stroke (e.g., 10 mm) is possible intuitively, it is usually at the cost of a large physical dimension [16]. A compact design is necessary for the situations where the nanopositioning inside a limited space is required [17]. Although some new compact flexure stages with large stroke have been proposed in previous work [18] of the author, a dual-stage system is expected

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XU: DESIGN AND DEVELOPMENT OF A FLEXURE-BASED DUAL-STAGE NANOPOSITIONING SYSTEM WITH MINIMUM INTERFERENCE BEHAVIOR

to achieve much quicker response. One objective of the current research is to design and develop a new monolithic flexure dual-servo stage with a stroke greater than 10 mm along with a compact dimension for nanopositioning applications. To the knowledge of the author, there exists no such flexure nanopositioning stage in the open literature. In consideration of the long stroke and high accuracy requirements, a voice coil motor (VCM) and a piezoelectric stack actuator (PSA) are employed for the coarse and fine drives of the DSS, respectively. However, a DSS exhibits the interference behavior which means the interaction between the coarse and fine actuators/stages. Based on the sensory information available for the output position, a DSS can be modeled as a dual-input-single-output (DISO) or a dual-input-dual-output (DIDO) system, which is a special case of multiple-input-multiple-output (MIMO) system. Thus, it is natural to design a DSS controller by employing MIMO techniques [19]. Although MIMO control strategy is capable of handling the interference behavior explicitly, it usually produces a controller of very high order, which blocks its practical implementation in real-time control [6]. Therefore, some approaches have been proposed to deal with the DISO or DIDO plant by using SISO control schemes such as master–slave architecture [20], PQ method [21], and sensitivity decoupling approach [22]. The aforementioned SISO techniques have been applied based on the assumption that the interference behavior in the DSS is neglected. However, such an assumption does not always hold in practice. For instance, it has been shown in [8] that the interference behavior of a DSS is so severe that the open-loop system of the fine stage is unstable. In addition, an impact force controller is employed in [23] to control the fine stage so as to overcome the interference behavior. However, this control strategy requires excessive hardware since two fine actuators are used to realize both forward and backward actuation. Thus, it is desirable to properly design a DSS by minimizing the interference behavior so that the SISO control technique applies. Some general guidelines have been presented to design a DSS in the literature. For example, by analyzing the dynamic equation of the DSS, it has been suggested that the weight of the fine stage and stiffness of coarse stage should be minimized to reduce the interference behavior [13]. Also, a large stiffness of the fine stage has been reported in [24], [25] to neglect the coupling effect in a DSS. Nevertheless, the suggestions available are inadequate to design a specific DSS with minimized interference. In the current research, the design of actuation scheme as well as guiding mechanism of fine actuator is proposed to minimize the interference effect. A new single-axis DSS with minimal interference is developed as an illustration. The presented design guidelines are verified by employing finite element model (FEM) simulations. Moreover, a SISO control scheme is realized in experimental studies to demonstrate the performance of the DSS without considering the interference behavior, which achieves a positioning resolution of 500 nm within the motion stroke over 10 mm along with a quick transient response than the standalone coarse stage. In the rest of this paper, the mechanism design processes of the dual-servo stage are outlined in Section II. A prototype dual-stage nanopositioning stage is then developed in Section III, where the plant performances are

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Fig. 1. Schematic diagrams of (a) dual-actuation and (b)–(c) dual-stage nanopositioning systems.

tested by open-loop experiments. Section IV reports the design procedure of a closed-loop control scheme and experimental results. Finally, Section V concludes this paper. II. MECHANISM DESIGN AND ANALYSIS In this section, some mechanism design considerations are proposed to minimize the interference behavior as well as to achieve a large stroke for the DSS. A. Mechanism Design to Minimize Interference Behavior The interference behavior of a DSS means the interaction between the coarse and fine actuators or the coarse and fine stages. In order to facilitate the control system (e.g., SISO) design, it is desirable to minimize the interference behavior. 1) Design of Actuation Scheme: According to actuation schemes, DSSs can be classified into two categories in terms of dual-actuation and dual-stage types. The former [23], [26] implies that a single common stage is driven by a coarse and a fine actuators, where the two actuators are connected in series. The latter [7], [9] indicates that two stages are driven by a coarse and a fine actuators, respectively, and these two stages are then connected in series, i.e., in a stacked or nested manner. For illustration, a dual-actuation nanopositioning stage is depicted in Fig. 1(a). The single stage is driven by the coarse VCM and fine PSA which are connected in series. A dual-stage nanopositioning stage is shown in Fig. 1(b), where the PSAdriven fine stage is nested inside the VCM-driven coarse stage and the fine stage consists of two parallelogram flexures. The output displacement of PSA is guided by a flexure mechanism which is composed of eight right-circular hinges. For a dual-ac(including the moving coil of VCM, tuation DSS, the mass one half of PSA, and one half of PSA guiding mechanism) is is the mass of the remaining part depicted in Fig. 1(a) and (i.e., one half of PSA, one half of PSA guiding mechanism, and (including one coarse stage). For a dual-stage DSS, the mass half of PSA, one half of PSA guiding mechanism, and fine stage) is denoted in Fig. 1(b) and the mass of the remaining part (i.e., one half of PSA, one half of PSA guiding mechanism, coarse

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Fig. 2. Mechanical model of a DSS.

stage, and moving coil of VCM) is represented by . It is oband hold for served that the conditions of a dual-actuation and dual-stage DSSs, respectively. In order to design a suitable actuation scheme, the dynamic model of a DSS is established by referring to a two-mass meand repchanical model, as shown in Fig. 2. Parameters resent the stiffness of the coarse and fine stages, respectively. In addition, and denote the damping coefficients of the coarse and fine stages, respectively. For the VCM, only the damping coefficient is considered due to the nature of back electromotive force [23]. By applying Newton’s second law, the dynamic equations can be derived (1) (2) and are the displacements of the coarse and fine where and denotes the actuation forces created by stages, and VCM and PSA actuators/stages, respectively. By taking the Laplace transform of the dynamic equations, it can be deduced that (3) (4) and ( and 2) represent the Laplace transwhere forms of displacement and force signals, respectively. Moreover, the four coefficients take on the forms (5) (6) where (7) Generally, to minimize the interference behavior, the values and should be minimized. In view of the of coefficients and and large numerators, it can be deduced that small are desirable. For both actuation schemes of the DSS, the PSA and high stiffness . has a small damping coefficient However, in the case of dual-actuation DSS, the relationship of holds, i.e., there always exists interference effect. is designed for the Therefore, a dual-stage scheme DSS in the current research in order to minimize the interference behavior. 2) Guiding Mechanism Design of Fine Actuator: It is known that PSA cannot bear large transverse loads due to the risk of

Fig. 3. (a)–(b) Parameters of the guiding mechanism and (c)–(d) amplification principle and parameters of the displacement amplifier.

damage. Thus, a suitable guiding mechanism is required for the PSA actuation. Fig. 1(a) and (b) present a motion guiding mechanism with a PSA embedded. The guiding mechanism is directly driven by the nested PSA. By referring to the one-quarter mechanism, as shown in Fig. 3(b), the input and output displacements and , respectively. In addition, asare assumed to be sume that the compliances of the right-circular hinges mainly and rotational motion come from the translational and denote the translational and of the hinges, and let rotational stiffness of one hinge, respectively. Then, it can be deduced from the virtual work principle (8) is the actuation force of PSA and represents the where external force applied at the output end of the amplifier. In view , it can be derived that of (9) It is observed from (3) that, in order to further reduce the interaction of fine stage on the coarse stage for a dual-stage DSS, the force acting on the coarse stage should be alleviated. For such purpose, a bridge-type displacement amplifier is adopted as a guiding mechanism [see Fig. 1(c)] due to its compactness property. A close-up view of the amplifier is shown in Fig. 3(c). The employed displacement amplifier acts as a displacement guiding and amplification device as well as an interaction-force reducer. Once driven by an input displacement, the device produces an amplified vertical output displacement along the backward direction. By referring to the one-quarter amplifier as shown in Fig. 3(d), it can be deduced from the virtual work principle that (10)

XU: DESIGN AND DEVELOPMENT OF A FLEXURE-BASED DUAL-STAGE NANOPOSITIONING SYSTEM WITH MINIMUM INTERFERENCE BEHAVIOR

Fig. 4. Deformation and parameters of a leaf-spring flexure.

In view of the amplification ratio of the amplifier, it . Thus, (10) can be rewritten as is derived that

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1) Displacement and Stiffness Analysis: The dimensions of these leaf springs need to be well designed to ensure a large output motion without the material fatigue. Referring to Fig. 1(b), each flexure in the four folded leaf springs suffers from the identical deformation. The deformed shape of one flexure hinge is shown in Fig. 4. It is seen that each flexure and moment . In view of the bears a combined force boundary conditions in terms of rotational angle and translational displacement, it can be deduced that (16)

(11) which indicates that the force exerted on the output end of the times the former result (9). amplifier is reduced to about It follows that the interaction force between the fine and coarse times using the bridge-type stages has been reduced by about displacement amplifier. 3) Amplification Ratio and Input Stiffness Calculation: applied by the Without considering the external force parallelogram fine stage, the amplification ratio and actuation stiffness of the amplifier can be calculated as [27]

denotes the transverse displacement of one flexure, where is the area moment of inertia of the cross secand tion with respect to the neutral axis. Then, the stiffness of one leaf flexure seen at the output end can be derived as (17) If the maximum moment is exerted by the flexures, the maximum stress occurs at the outermost edge of the cross section, which can be calculated by

(12) (13) where the amplifier parameters and are shown in Fig. 3(d). and , the equations with the best Concerning the stiffness accuracy as suggested in [28] are adopted in the current research. Generally, the bridge-type amplifier owns a large lateral stiffness. In practice, the output end of the amplifier is connected to the output platform for drives. The high lateral stiffness of the amplifier is useful to tolerate the external load even if a large lateral load [see Fig. 3(c)] is exerted on the amplifier. More details about the amplifier can be found in [27]. In addition, the stiffness of the parallelogram fine stage can be derived with reference to Fig. 4 (14) and are where is the Young’s modulus of the material, the width and length of one leaf flexure, respectively. To guarantee a proper operation of the amplification device, the selected PSA should be powerful enough to drive the amplifier which is connected to the fine stage, i.e., the stiffness of PSA should satisfy (15)

(18) which gives the moment value (19) Considering that and taking into account (16), (19), and (22), allows the calculation of the maximum translation of one leaf flexure (20) which indicates that the maximum one-sided translation of the leaf flexure is governed by the length and thickness of the leaf flexures for a given material. Thus, to obtain a larger , longer and thinner flexures are desirable. flexures conSince each folded leaf spring consists of nected in series, the maximum translation of the coarse stage can be derived as (21) By comparing (20) with (21), the effect of the folded springs is evident, i.e., they are used to increase the translation by times as compared with a single leaf flexure. is exerted on the stage Assume that an external force of the stage output platform, which induces a displacement in axis direction, the stage stiffness seen at the output end can be derived as

B. Mechanism Design to Achieve Large Stroke In order to achieve a large motion range, folded leaf springs flexures are used. In this research, which are composed of is adopted to illustrate the concept design, although more or fewer flexures may also be employed for the design.

(22) Since the PSA is nested inside the amplifier and the stiffness of the amplifier seen at the output end is assumed to be infinite,

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TABLE I MAIN PARAMETERS OF A NANOPOSITIONING STAGE

the stiffness of the dual-actuation stage in as

axis can be derived

(23) 2) Actuation Issues Consideration: As far as the coarse actuation is concerned, VCM is selected to drive the positioning stage to generate a centimeter-level motion range. In comparison with other types of actuators based on smart materials such as PSA, VCM possesses a larger stroke. However, VCM has a low blocking force compared to PSA. To facilitate the VCM actuation, the stage should be designed with low-enough stiffness seen at the actuator. Given the required maximum one-sided displacement of the stage in output ( axis) direction, the maximum force needed for the motor can be expressed by (24) In the selection of motors, the VCM should be chosen such satisfying that the maximum actuation force

Fig. 5. FEM results of the initial design with (a) VCM and (b) PSA driven, respectively. Only the four mounting holes are fixed, and the coarse stage is left free in (b).

(25) The above condition guarantees that the selected motor is powerful enough to drive the coarse positioning stage. C. FEM Simulation and Design Improvement In the simulation study, the alloy material of Al 7075 is adopted for the stage. Without loss of generality, the material and main kinematic parameters of a dual-stage nanopositioning stage are shown in Table I, where the subscripts 1 and 2 indicate the parameters for the coarse and fine stages, respectively. Both static and dynamic performances of the stage are verified by using FEM simulation. The analytical models reveal that the maximum allowable . one-sided displacement of the stage is Thus, the motion range in working axis is . By assigning the motion range as , the . maximum force needed to drive the stage is In addition, the amplification ratio and actuation stiffness of the and , amplifier are calculated as respectively. 1) Static Performance Test: In order to access the static performance of the stage, FEM simulation is carried out by ap-

plying an input displacement at the input end. With a 5-mm PSA displacement input, VCM displacement input and 14.5the FEM results are illustrated in Fig. 5(a) and (b), respectively. Note that the coarse stage is left free when the fine stage is actuated, as shown in Fig. 5(b). Due to a well decoupling property, the coarse stage remains almost stationary. Thus, no cross-coupled motion is observed for the coarse stage in Fig. 5(b). It is found that the required VCM actuation force is 113.36 N, and the maximum stress arrives at 405.14 MPa. By adopting the yield strength as the maximum allowable stress of the material, a . safety factor can be calculated as 503 MPa/405.14 Besides, the PSA actuation with the maximum input displacement reveals a safety factor of 6.86. Considering the FEM result as the benchmark, it is seen that the analytical model overestimates the force requirement and maximum allowable displacement by 1.9% and 4.2%, respectively. In addition, the FEM reveals that the amplification ratio of . the amplifier is 5.60 along with an input stiffness of 8.74 Thus, in comparison with FEM results, the analytical model overestimates the amplification ratio by 36.6% and underestimates the input stiffness by 8.5%, respectively. The relatively large discrepancy mainly comes from the assumptions em-

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TABLE II FIRST SIX MODE FREQUENCIES OF THE INITIAL AND IMPROVED STAGES

Fig. 6. The first two mode shapes of (a) initial design and (b) improved design. The first and second modes are associated with the major motion direction and transverse motion direction, respectively.

ployed in the analytical models, where only the compliances of flexure hinges are considered. The modeling accuracy can be improved by considering the compliances of other components between the hinges as well. 2) Interference Test Results: In order to verify the interference between the coarse and fine stages for the two dual-stage designs, as shown in Fig. 1(b) and (c), an identical actuation force is applied on the input end of the two fine stages. Note that only the four mounting holes (see, Fig. 1) are fixed, and the coarse stage is left free during the simulation. To characterize the interference behavior, the axis displacement of the input end of coarse stage is defined as the interference motion caused by the fine stage. By applying an input force of 10 N, interference motions of are obtained for the two designs [see 0.5160 and 0.0648 Fig. 1(b) and (c)], respectively. Thus, the interference motion of the improved design [see, Fig. 1(c)] has been reduced to 1/7.96 times the former design in Fig. 1(b). According to Hooke’s law, it follows that the interference force has been reduced to 1/7.96 times the former design as well. In addition, the simulation result agrees well with the analytical result which is predicted by (11). Moreover, FEM shows that the interference motion of the 1% coarse stage accounts for only of the motion of the fine stage, which demonstrates a negligible interference behavior in the improved design. 3) Modal Analysis and Structure Design Improvement: The modal analysis is conducted for the dual-stage design, as depicted in Fig. 1(c). The first six mode frequencies are tabulated in Table II, and the first two mode shapes are shown in Fig. 6(a). It is found that the first mode is associated with the major motion, i.e., the translation along the working direction ( axis), and the second one is the translation in the transverse direction ( axis). Moreover, the first two mode frequencies are very close to each other, which indicates that the stage is prone to transverse motion under external forces due to a low transverse stiffness. Since the transverse motion is passive and cannot be controlled by the actuators, it poses an obstacle to the control system design. Thus, in order to improve the robustness of the stage

Fig. 7. (a) Schematic diagram and (b) CAD model of the improved design of dual-stage nanopositioning system.

motion along the major motion direction, an improved structure design is necessary to enhance the transverse stiffness. An insight into the deformations in Fig. 5(a) indicates that the two passive moving stages located at each outer side of the stage translate the identical value of displacement. Thus, they can be connected together with connecting bars while without influencing the motion property of the stage. A schematic view and CAD model of the improved design are shown in Fig. 7. Concerning the improved design, the FEM results of the first six mode frequencies are also shown in Table II, and the first two mode shapes are depicted in Fig. 6(b). It is observed that the first and second modes are also associated with the major motion direction ( axis) and transverse motion direction ( axis), respectively. Although the first mode frequency is slightly reduced by 3.0% (due to an addition of the connecting bars’ mass), the second one is significantly increased by 105.9% as compared to the original design. As a result, the second mode frequency is more than twice higher than the first one, which reveals a robust motion along the major direction. Thus, from the control point of view, the improved design is more preferable than the original design. It is noticeable that the amplification ratio and input stiffness of the fine stage are not changed since only the design of the coarse stage is improved. III. PROTOTYPE DEVELOPMENT AND OPEN-LOOP TEST Using the architecture parameters, as shown in Table I, a stage prototype is fabricated from Al 7075 alloy by wire electrical discharge machining (EDM) process, which produces a compact dimension of 142 mm 82 mm. To achieve a motion range of

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Fig. 8. Experimental setup of a dual-stage nanopositioning system. Fig. 9. Open-loop output–input relations with (a) VCM and (b) PSA driven, respectively.

, FEM results suggest that the VCM actuation force and PSA stiffness should be chosen as (26)

A. Experimental Setup In view of the force capability and motion range requirements, the VCM (model: NCC05-18-060-2X, from H2W Techniques, Inc.) is selected. Driven by a current amplifier, it provides a large enough output force of and a stroke of 12.7 mm. According to the stiffness requirement, a PSA (model: TS18-H5-202, from Piezo Systems, Inc.) and a stroke is chosen. It offers a large stiffness of 230 . Additionally, a high-voltage amplifier (model: of 14.5 EPA-104 from Piezo Systems, Inc.) is used to amplify the to for the drives of PSA. The input voltage of fabricated prototype is graphically shown in Fig. 8. The stage output motion in the working axis is detected by a non-contact laser displacement sensor (model: LK-H055, from Keyence Corporation) with a resolution of 25 nm over a measuring range of 20 mm. The digital output of the laser sensor is acquired by a computer through a USB or RS-232 interface, which provides the maximum sampling rate of 392 kHz. The controller is implemented with a NI USB-6259 board (from National Instruments Corporation) with 16-bit D/A and A/D channels. Control algorithms are developed with LabVIEW software. B. Static Performance Tests First, static open-loop performance tests are conducted to examine the stroke of the system. With 1-Hz quasi-static sinusoidal voltage signals applied to VCM and PSA, the sensor readings are plotted in Fig. 9(a) and (b), respectively. It is observed from Fig. 9 that the VCM coarse actuator produces a motion stroke of 10.25 mm and the PSA fine actuator delivers an output . Thus, the dual-stage has an overall stroke of about of 94.92 10.3 mm. The hysteresis effects mainly come from the adopted actuators, which can be suppressed by employing suitable control strategies [12], [29]. The aforementioned motion range of the fine stage is obtained by leaving the VCM moving during the actuation of the PSA. On the other hand, when the moving coil of the VCM is fixed at the base, the motion range of the PSA-driven fine stage is generated . It is slightly larger than the aforementioned value as 95.56 (94.92 ) which is obtained under the interaction of coarse

and fine stages. Thus, the interference motion of the coarse stage , which induced by the fine stage can be calculated as 0.64 is less than 0.7% of the fine stage’s motion. It is observed that the experimental result is consistent with the FEM simulation result (1%). In addition, the experimental result indicates an amplification ratio of 6.59 for the displacement amplifier, which is 17.7% higher than the simulation result. The discrepancy mainly stems from the preloading effect of mounting the PSA [12]. C. Dynamic Performance Tests Second, dynamic performance of the dual-stage system is tested by the frequency response method. The frequency responses of the stage are shown in Fig. 10(a) and (b), which are obtained with standalone VCM and PSA driven, respectively. With the two types of actuation, the resonant frequencies of 35 and 495 Hz are identified. The low resonant frequency of VCM actuation mainly comes from the mass of moving coil of the motor, which is not considered in FEM simulation (70 Hz). Additionally, the PSA actuation produces a much higher resonant frequency, which enables a quicker response than the VCM actuation. The aforementioned frequency response of the fine stage is obtained by leaving the VCM moving during the actuation of the PSA. When the moving coil of VCM is fixed, the generated frequency response is also shown in Fig. 10(b), which indicates the first resonant frequency of 417 Hz. It is seen that the interference behavior increases the first resonant frequency by 18.7% as compared to the result with VCM fixed. Within the frequency range of 0 to 300 Hz, the deviations of the magnitude and phase of the frequency responses are within 2.2 dB and 19.3 degree, respectively. Thus, the interference behavior between the fine and coarse stages is negligible up to 300 Hz. Due to the lack of accurate physical parameters of the actuators, the frequency responses are used to estimate the plant models of the system. As shown in Fig. 10, a fourth-order model and a 14th-order model are identified for the coarse and fine stages, respectively. The estimated models are used for controller design in Section IV. IV. CONTROLLER DESIGN AND EXPERIMENTAL STUDIES The dual-servo control has been investigated extensively [6]. In order to verify the presented design ideas of the dual-stage

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Fig. 11. Global control scheme for the dual-stage nanopositioning system. The observer is employed to provide the position output of the VCM coarse stage.

with the positioning error , where and represent the desired and actual system output at the th time step, and , , and denote the proportional, integral, and derivative gains, respectively. The key issue in PID design lies in the controller parameters tuning. In this research, the Ziegler-Nichols (Z-N) method is adopted due to its popularity. It is noticeable that the position error of the coarse stage is used as the reference input to the fine stage. Initially, this error may be very large relative to the motion range of PSA stage. Moreover, the PSA is very quick as compared with the VCM. Consequently, there may be an over-demand for the PSA during a long duration until the position error of coarse stage is kept ) of PSA stage. To avoid poswithin the motion range (94 sible destruction of the actuators, saturation functions are used in both VCM and PSA control loops to limit the control action and , respectively. within Fig. 10. Open-loop frequency responses with (a) VCM and (b) PSA driven, respectively.

nanopositioning system and to achieve a precise positioning, a global control scheme [9] is realized and tested by a series of experimental studies in this section. A. Controller Design In the current research, a control scheme is implemented on the nanopositioning system by taking the error of the coarse stage as the reference input to the fine stage (see Fig. 11). Since only one absolute position sensor for the fine stage is available, the relative position between the two stages is generated by employing an estimation technique. Different from the existing control scheme where an extra relative displacement sensor is of the coarse stage is yielded used [9], the position output by an observer, as shown in Fig. 11. The role of the observer is to produce the position information of the coarse stage by passing through the identified model of the the input voltage of the coarse stage. Afterwards, the relative displacement fine stage is generated by subtracting the coarse stage output . from the sensor reading, i.e., The popular PID control is employed for both coarse and fine stages. As is known that, PID is a model-free controller which solves the control command by making use of the control error only. A digital PID scheme can be expressed as follows: (27)

B. Experimental Studies With the designed global control scheme, experimental studies are conducted to verify the performance of the nanopositioning system. A sampling time of 5 ms is employed to implement the real-time controller. By experiments, the PID control parameters are tuned with the Z-N approach to eliminate the overshoot. Concerning the coarse stage, the PID controller , , and parameters are tuned as: . For the fine stage, , , are obtained. and set-point positioning is carried out. For illustration, a 200The experimental results of coarse actuation and dual actuation are compared in Fig. 12(a), and the histograms of steady-state errors are shown in Fig. 12(b). With VCM actuation alone, a 5% settling time of 0.495 s and a steady-state root-mean-square is produced. By using the VCM and error (RMSE) of 0.306 PSA dual actuation, the settling time is reduced to 0.357 s and . As compared with the the RMSE is suppressed to 0.257 standalone coarse stage, the dual-stage scheme has substantially improved the transient response speed by 28% and reduced the steady-state error by 16%, which results in a significant increase of the bandwidth along with a positioning resolution of 500 nm. It is noticeable that the Z-N method does not produce optimal parameters for the PID controller. The steady-state error can be further reduced by optimally tuning the PID controllers and employing displacement sensors with higher resolution. In addition, for the dual-stage nanopositioning system, the components of coarse and fine control actions are shown in Fig. 13. It is observed that the PSA-driven fine stage takes effect

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of coarse stage system. Considering that the plant model is used as an observer to obtain the coarse stage output in the control scheme, the results also indicate the accuracy of the identified plant model. It is noticeable that the hysteretic nonlinearity of PSA is not treated explicitly since the hysteresis effect over a small portion of stroke is not significant and hence adequately suppressed by the feedback control. However, it seems that the fast response of PSA is not fully utilized by the PID control. In the future, more effective control scheme (e.g., the time-optimal control [30]) will be employed to further improve the performance of the dual-stage nanopositioning system. V. CONCLUSION

m

Fig. 12. (a) 200- set-point positioning results. (b) Histograms of steadystate errors of the coarse stage and dual-stage systems.

A dual-stage nanopositioning stage driven by a voice coil motor and a piezoelectric stack actuator is developed in this research. The major contribution lies in the proposal of new ideas of structure design to minimize the interaction between the two stages. The decoupling design is verified by both finite-element model simulations and experimental studies. A global control scheme is employed to realize a precise positioning. It is shown that the proposed decoupling design allows the employment of a simple control scheme since SISO control is applicable to both coarse and fine stages. Experimental results reveal that the dual-actuation scheme is superior to the standalone coarse-actuation one in terms of transient response as well as steady-state response. A quick positioning with a 500-nm resolution and over 10-mm stroke has been achieved by the coarse-fine cooperative system, which reveals the potential of the proposed dual-actuation system in the field of nanopositioning. In the future, more sophisticated control strategies will be exploited to further improve the positioning performance of the system. REFERENCES

Fig. 13. Control action components of the dual-stage system.

mainly at the initial states. Then, its control action decays gradually to a constant value as the time elapses. As a result of the fine actuation, the transient response speed is improved and the positioning error is suppressed toward zero gradually. The experimental results demonstrate the effectiveness of the control scheme for the dual-stage servo system. Since the control scheme is implemented without considering the interaction behavior between the coarse and fine stages, the experimental results indirectly reveal the effectiveness of the proposed ideas for the decoupling design of the dual-stage

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Qingsong Xu (M’09) received the B.S. degree (Hons.) in mechatronics engineering from the 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 at the Swiss Federal Institute of Technology (ETH), Zurich, Switzerland. He is currently an Assistant Professor of Electromechanical Engineering with the University of Macau. His current research interests include parallel manipulators, MEMS devices, micro-/nanorobotics, micro-/nanomanipulation, smart materials and structures, and computational intelligence. Dr. Xu is a member of the American Society of Mechanical Engineers (ASME).