Journal of System Design and Dynamics

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1 Electrostatic Suspension Using Variable Capacitors* Vol. 3, No. 4, 009 Takaaki KATO**, Shinya TSUKADA**, Yuji ISHINO***, Masaya TAKASAKI** and Takeshi MIZUNO** **Control Engineering Laboratory, Graduate School of Science and Engineering, Saitama University, Saitama, Japan *** Innovation research Organization, Saitama University, Saitama, Japan Abstract A new control system for electrostatic actuators was applied to electrostatic suspension. This control system was designed to use a variable capacitor connected with an electrostatic actuator in series. A high voltage was applied to this connection. The voltage applied to the actuator was controlled by varying the capacitance of the variable capacitor. An experimental apparatus was fabricated in order to study the controllability of electrostatic force using this control system. The experimental results show that electrostatic force can be controlled both statically and dynamically. Another experimental apparatus was fabricated for demonstrating the feasibility of electrostatic suspension. This apparatus was able to control the 3-DOF vertical motions of the suspended object. Non-contact suspension was achieved with the developed control system using variable capacitors. Key words: Electrostatic Actuator, Electrostatic Force, Electrostatic Suspension, Electrostatic Levitation, Variable Capacitor, Voice Coil Motor 1. Introduction *Received 8 Dec., 008 (No ) [DOI: /jsdd.3.617] In recent years, actuators that use electrostatic force have been actively investigated. These electrostatic actuators play a critical role in microelectromechanical systems (MEMS) because the static force per unit volume increases when the size of the object becomes small [1]. In addition, several studies on suspension and transportation using electrostatic actuators have been reported [1]-[5]. Transportation without contact is important for the next generation of industrial technology. Compared with magnetic suspension, electrostatic suspension is advantageous because it suspends various objects. It can also meet demands in many industrial fields such as semiconductor manufacturing. Electrostatic suspension systems for silicon wafers [1] and hard disk media [3] have been developed. Researchers have reported on the basic principles of electrostatic suspension, electrode design, and method of position control. Electrostatic suspension of glass plates has also been achieved [4], while other research has proven that a dielectric substance can be suspended by electrostatic force. Electrostatic force per unit area is, however, smaller than magnetic force, which means that high voltage must be applied to the electrodes in order to suspension. High voltage must be changed quickly in order to achieve stable non-contact suspension; consequently, high-speed and high-voltage amplifiers have been used in previous studies [1]-[3]. This causes an increase in cost, which is an obstacle that prevents industrialization. This paper proposes a new control system that uses variable capacitors as one method for avoiding the use of 617

2 Vol. 3, No. 4, 009 such amplifiers. This system can control electrostatic force without any high-voltage amplifiers. This paper is organized as follows. First, the principles of a new voltage control system that uses variable capacitors are described. Second, the basic experimental apparatuses that were fabricated to study the static and dynamic characteristics of the proposed control system are presented in detail. Third, the control system that was applied to a three-degree-of-freedom (3-DOF) electrostatic suspension system is discussed. Non-contact suspension was achieved successfully in this study.. Principle of control system.1 Voltage control system Figure 1 shows an equivalent circuitry for the proposed control system using a variable capacitor for electrostatic actuators [6]. The electrostatic actuator is treated as a capacitor C a. A variable capacitor C v is connected with the capacitor C a in series. A constant high voltage E is applied to this connection. The voltages across C a and C v are denoted by V a and V v, respectively. The voltage across the electrostatic actuator is given by V a Cv = E. (1) C + C v a Equation (1) shows that the voltage applied to the electrostatic actuator can be adjusted by changing the capacitance of the variable capacitor.. Variable capacitor There are various types of variable capacitors, which are classified according to the following parameters: the shape of the electrode, the motion of the movable electrode, the actuator used to move the electrode. Typical electrode shapes are circular and square; a comb-like structure is effective for obtaining large capacity. The motion of a movable electrode is classified as rotation or translation. Motors are used for rotation, while a linear motor and solid-element actuators such as piezoelectric elements are used for translation. In a parallel-plate capacitor, the capacitance is given by C = εs. () d Variable capacitor Electrostatic actuator V v V a C v C a E Fig. 1. Equivalent circuit of voltage control system. 618

3 Vol. 3, No. 4, 009 Equation () indicates that the capacitance can be varied using the following three physical quantities: (a) gap, d, (b) area, S, (c) permittivity, ε. Figure shows examples of variable gap and area. In Example (a), the capacitor composed of two rectangular electrodes. One electrode is fixed, and the other is movable in translation. A linear motor is used for changing the gap between the electrodes. In Example (b), the electrodes are semicircular. A rotary motor is used to change the area that is overlapped. In this work, a former-type variable capacitor will be adopted because of the simplicity of its structure..3 Electrostatic suspension Figure 3 shows a basic model of a conventional electrostatic suspension. The electrodes are electrified by applying a voltage across the electrodes. The electrostatic force F between the electrodes is approximately given by εs Va F =, (3) 8 d Motor Linear motor (a) Variable gap. (b) Variable area. Fig.. Examples of variable capacitors. High-speed amplifier Electrode Floator Gap sensor Controller Fig. 3. Basic model of conventional electrostatic suspension. V a S d F Fig. 4. Attractive force. 619

4 Vol. 3, No. 4, 009 where ε : permittivity, S : area of electrode, d : gap between the floator and the electrodes (see Fig. 4). Equation (3) indicates that the force can be changed by voltage V a. In this work, the control method using variable capacitors was applied to control the voltage V a. The electrodes and the object to be suspended (commonly called the floator) comprise a capacitor, which is treated as C a in Fig.1. Substituting Eq. (1) into Eq. (3) gives S Cv F = ε E 8d Cv C. (4) + a Equation (4) indicates that the electrostatic force can be controlled by the variable capacitor. 3. Experiments on basic characteristics 3.1 Experimental apparatus An experimental apparatus was fabricated for measuring electrostatic force. Figure 5 shows the fabricated apparatus. The electrodes of the force measurement apparatus were circular disks made of aluminum; the area of disks was 6600 mm. An insulating tape with a thickness of 85 µm was pasted on the surface of the electrodes. The relative permittivity of this tape was approximately 3. This apparatus had three load cells for detecting the electrostatic attractive force. A voltage control system had a variable capacitor. Figure 6 shows a fabricated variable capacitor. The electrodes had the same shape as the electrodes used in the force measurement apparatus. An insulating tape was pasted on the surface of the electrode fixed on the stator. A voice coil motor (VCM) was used as an actuator for changing the gap between the electrodes. The gap was detected by an eddy-current-type gap sensor mounted on the top. Fig. 5. Photo of the experimental apparatus. Fig. 6. Photo of the variable capacitor. 60

5 Vol. 3, No. 4, Characteristic of the variable capacitor The controllability of the voltage control system is highly dependent on the response of the variable capacitor. High-voltage must be changed quickly in order to achieve stable electrostatic suspension. The transfer function of the variable capacitor is given by T () s = m s 1 K i + cs + k s, (5) where m 1 : equivalent mass of moving part of VCM (0.3 kg), k s : stiffness factor (41 kn/m), K i : current-force factor (16.9 N/A). The input signal and output signals are the current of coil and the displacement of the moving part, respectively. Figure 7 shows a frequency response of the variable capacitor in the open loop. It has a peak at 60 Hz. The other two variable capacitors have similar characteristics. Because no time delay is expected between the variable capacitors and the control voltage, the variable capacitors have a sufficient response speed for achieving electrostatic suspension. 3.3 Control of electrostatic force Figure 8 shows a conceptual diagram of the experimental apparatus that was used to study the controllability of electrostatic force by the proposed method. The variable capacitor, the fabricated apparatus for detecting attractive force, and a DC power supply were connected in series. Three load cells were used for the measurement of attractive force. The applied voltage was 1 kv. The gap between the plate electrodes d a was 0.3 mm. The attractive force was measured as the gap of variable capacitor d v was changed. The input signal to VCM was a triangular wave of very low frequency such that the detected Gain [db (m/a)] Gain [m/a db] Phase [deg] Phase [deg] Frequency [Hz] Fig. 7. Frequency response of the variable capacitor. Force measurement apparatus Load cell d a Load cells F a DC power supply Topofviewof Variable capacitor d v VCM Fig. 8. Conceptual diagram of experimental apparatus. 61

6 Vol. 3, No. 4, 009 attractive force F a was considered to be static. Figure 9 shows the experimental results. Electrostatic force F a is the total of the output of the three load cells. Capacitance C v is calculated from d v. It can be confirmed that the capacitance C v and as a result, the electrostatic force increased as the gap decreased. The measured force agreed with the theoretical force. Figure 10 shows dynamic responses of electrostatic force. The gap d v was changed sinusoidally at (a) Hz and (b) 0 Hz. It has previously been demonstrated that the electrostatic force can be controlled by changing the gap without phase delay. These results show that electrostatic force can be controlled both statically and dynamically by the proposed control system. Fig. 9. Static characteristic of electrostatic force and capacitance of variable capacitor. Gap d v [mm] d v F a Time [0.s/div] (a). Hz Electrostatic force F a [mn] Gap d v [mm] F a d v Time [0.0s/div] (b). 0 Hz. Fig.10. Dynamic characteristic of electrostatic force. Electrostatic force F a [mn] 6

7 4. Electrostatic suspension Vol. 3, No. 4, Experimental apparatus Figure 11 shows a developed experimental system that achieved non-contact suspension. This system can be divided into a suspension system and a voltage control system. The suspension system was mainly composed of electrodes, a floator, three positioners for setting an initial position for the floator and sensors as shown in Fig. 1. Electrodes were divided into six parts as shown in Fig. 13(a). The area of each part was same. Each pair of electrodes (E1, E) (E3, E4) and (E5, E6) operated as an electrostatic actuator, denoted by Act1, Act, and Act3. To prevent short-circuits when the floator came into contact with the actuator, an insulating tape was pasted on the surface of the actuator. The thickness of this tape was 85 µm. This apparatus was able to control the three degrees of freedom of motion of the floator using these three actuators. The vertical displacements of the floator were detected by three optical sensors that were mounted on the top. There were three holes for the beams of the optical sensors to pass through the electrodes. Figure 13(b). shows a disk-like floator made of aluminum; the mass of the floator was 18 g. The external diameter was 95 mm, the internal diameter was 5 mm, the area was 6600 mm, and the thickness was 0.8 mm. Variable capacitors Controller Gap sensor Floator Electrodes Fig. 11. Schematic view of an experimental apparatus. Gap sensor Electrodes Positioner Floator Fig. 1. Photo of the suspension system. E 1 E E 6 E 5 E 4 E 3 (a). Electrodes. Fig. 13. Electrostatic actuator (b). Floator. 63

8 Vol. 3, No. 4, Experimental results First, one of three actuators was controlled by the proposed control system. The other two actuators were driven by high-voltage amplifiers (Trek, MODEL609D-6). The voltage DSP Variable capacitor Electrostatic actuator e i K i1 K 1 x 1 ms 1 + cs+ k s 1 ms -k 1 P +sp d1 v1 D 1 Fig. 14. Block diagram of electrostatic suspension using a variable capacitor. Displacement [mm] Time [s] (a). Floator s displacement. 1.4 Gap [mm] Time [s] (b). A gap of electrodes of variable capacitor. Fig. 15. Step response of the floator and variable capacitor. DSP Variable capacitor Electrostatic actuator K i 1 K 1 ms+ k ms k s1 x 1 P+sP d v D 1 e i K i 1 K ms+ k ms -k s x P+sP d v D K i 1 K 3 ms+ k ms -k 3 3 s3 x 3 P+sP d v D 3 Fig. 16. Block diagram of 3-DOF electrostatic suspension. 64

9 Vol. 3, No. 4, 009 of the DC power supply was kv. The simplified block diagram of this electrostatic suspension system is shown by Fig. 14, where m: equivalent mass of the floator, k 1 : force-displacement factor, K 1 : capacitance-force factor, D k : sensor gain (k = 1,,3), P d : proportional feedback gain, P v : differential feedback gain, e i : command signal, x k : displacement of the floator (k = 1,,3). After subtle adjustments, electrostatic suspension was achieved. Figure 15(a) shows the step response of the floator when a command signal changed from 0.17 mm to 0.15 mm. Figure 15(b) shows the gap between variable capacitor s electrodes. The displacement of the floator can be changed by varying the gap of the variable capacitor. Next, all three actuators were controlled by the proposed method. The voltage applied to each actuator was varied by using the variable capacitor. A simplified block diagram is shown in Fig. 16. The parameters are same as in Fig. 14. Each of the three actuators was independently controlled by feeding back the output of the collocated gap sensor. Figure 17 Displacement [mm] x1 x x3 Gain [db (m/a)] Time [s] Fig. 17. Displacement of the floator Phase [deg] Frequency [Hz] -360 Fig. 18. Frequency response of the variable capacitor when local feedback was added to the controller Displacement [mm] Floator Capacitor Time [s] Fig. 19. Displacement of the floator and a gap between the variable capacitor s electrodes when local feedback was added to the controller. Gap [mm] 65

10 Vol. 3, No. 4, 009 shows the displacements of the floator. At start, the floator was on the positioners, and the target position was set to 0.15 mm from the surface of the insulating tape. The applied DC voltage was approximately kv, and the voltage was applied at t = 0. The displacements of the floator changed from 0.5 mm to 0.15 mm. This study confirmed that the floator can follow the command signal and that the transient response is well damped. These results demonstrate the realization of electrostatic suspension using variable capacitors. Next, the controllability was improved by feeding back the gap between electrodes of the variable capacitor (local feedback). Figure 18 shows a frequency response of the variable capacitor with this loop. A comparison of Fig. 18 and Fig. 7 shows that the response of the variable capacitor improved. Figure 19 shows the displacement of the floator and the gap of the variable capacitor. It demonstrates that the position of the floator can be adjusted more quickly. 7. Conclusions This paper described the principles of a new voltage control system that uses variable capacitors. The basic experimental apparatuses were fabricated for studying the static and dynamic characteristics of the proposed control system. The results showed that the variable capacitors had sufficient response speed for achieving electrostatic suspension. A 3-DOF electrostatic suspension system was fabricated to demonstrate the applicability of the control system to electronic suspension. Non-contact suspension was achieved successfully. Moreover, the controllability was improved by introducing local feedback into the variable capacitor. Acknowledgement This work is financially supported in part by Japan Science and Technology Agency. References 1. Jin, J. Higuchi, T. Kanemoto, M., Electrostatic Silicon Wafer Suspension, Proc. 4th International Symposium on Magnetic Bearings, ETH Zürich, pp , F. M. Moesner, T. Higuchi, "Devices for Particle Handling by an AC Electric Field", Proc. IEEE Micro Electro Mechanical Systems,pp.66-71, Jin, J. Higuchi, T. Kanemoto, M., Electrostatic Levitator for Hard Disk Media, IEEE Trans. Industrial Electronics, Vol.4, No.5, pp , Jeon, U.J. and Higuchi, T., Electrostatic Suspension of Dielectrics, IEEE Transactions on Industrial Electronics, Vol.45, No.6, pp , Yamashita, N., Yamamoto, A., Higuchi, T. and Yasui, H., Noncontact Electrostatic Levitation of 400mm Silicon Wafer, Journal of the Japan Society of Precision Engineering, Vol.71, No.3, pp , Tsukada, S., Ishino, Y., Takasaki, M., and Mizuno, T., Proposal of an Electrostatic Actuator Control System Using a Variable Capacitor Mechanism, Proc. 8th International Conference on Motion and Vibration Control, TE3-,