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Fig. 4. Cross-sectional side view of the novel two-axis actuator. 3.2. Actuator units for the Y-stage — Figure 4 Cross-sectional side view of the novel two-axis actuator. 3.2. Actuator units for the Y-stage

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Comparison with other technologies Table |

Fig. 2. Photograph of the Y-stage. Fig. 2 shows a photograph of the Y-maglev stage. “Y” refers to the shape of the levitated single-moving platen. The Y-stage possesses several competitive advantages over the A-stage in terms of travel range, payload capacity, simplicity in mechanical design, and power consumption:

V: vertical actuator, H: horizontal actuator. Properties of actuators [27] Table 2

Fig. 3. Schematics of (a) the horizontal-actuator unit and (b) the vertical-actuato unit.

Fig. 5. Exploded views of (a) the vertical-coil and (b) the horizontal-coil assem- blies. the magnet becomes the following quintuple integration.

Fig. 6. Fixture to pot the vertical coil to its coil holder.

Fig. 7. Fixture to pot the horizontal coil within its coil holder. The horizontal coils needed to be placed at the same horizon- tal level as that of the platen. An inverted-T-shaped coil holder was designed and fabricated that could hold the horizontal coil from inside and support it from the bottom. An exploded view of the assembly is shown in Fig. 5(b). A fixture similar to the

Fig. 8. Exploded views of (a) the A-stage and (b) the Y-stage. Effective packaging is important for any assembly. Thus, we designed all parts and their assemblies in SolidWorks® in such a way that (1) the platens must be close enough to all coils for sufficient force generation, (2) the bottom surfaces of the platens must be in the sensing range of all capacitance probes, and (3) the HeNe laser beams from the interferometers should not be blocked.

Fig. 9. Tooling used to fix the plane mirrors to the A-platen core. ihe horizontal and vertical actuator assembues were described in the previous section. There are three pairs of arms protruded on the sides of the platen to hold the magnet assem- blies for horizontal actuation. Each arm has a hole with its diameter 10 p.m larger than that of the cylindrical magnet. The three setscrews on the outer, top and bottom surfaces of the arm were tightened to hold the magnet. Since the magnetization directions of the magnets are parallel to the sides of the triangular platen, these units generate horizontal force parallel to the sides of the platen. Each of the three vertical actuator assemblies con- sists of a cylindrical magnet and a cylindrical aluminum mount with three holes potted together. Each assembly is mounted on the platen using three screws.

The assembly process of the platen is shown in Fig. 10. The three cuboid-shaped (25.4 mm x 25.4mm x 12.7 mm) perma- nent magnets were attached around the platen core, and then

Fig. 11. Fixing process of the magnet with the Y-platen core.

Fig. 12. Photograph of the bottom view of the base plate with nine M3 holes to mount the three capacitance probes. Three additional 10-32 brass screws were inserted to fasten the vertical coils.

Fig. 13. Tooling for mounting vertical coils to the base plate.

Fig. 14. Tooling to fix the horizontal coil to its coil holder.

Fig. 15. The base plate for the Y-stage showing the locations of various holes to fix the stationary parts.

The design of three SISO controllers for vertical motion control was performed similarly. A continuous-time lead-lag controller was designed to control the vertical motions that has phase margin of 70.1° at crossover frequency of 65 Hz. The compensator is given as Fig. 16. Block diagram for stochastic transfer function identification.

All the designed controllers were converted to discrete-time difference equations using the zero-order-hold (ZOH) equiva- lence method with a 5 kHz sampling rate. The control laws were implemented in C on a digital signal processor with the user interface running on VME PC for the real-time control of the positioners.

Fig. 17. Closed-loop frequency responses of the analytical model (dashed line) and the plant TFs from the FFTs of the input-output signals (solid line).

Fig. 19. (a) A 10 nm step response of the A-stage and (b) 50 nm step response of the Y-stage. Since we have full control over the excitation signal, it is desired to use the signals that persistently excite the plant. Thus, the model validation was performed with a zero-mean, white- Gaussian noise (WGN) as the reference input signal. A detailed treatment of stochastic modeling is covered in classical texts such as [29]. Fig. 16 shows the block diagram to obtain the plant TE. The random disturbance is generated in the software with

Fig. 20. (a) A 15 nm and (b) 15 xm consecutive steps generated by the Y-stage with command-tracking errors.

Fig. 21. (a) A 50 nm-radius circle traversed by the A-stage, (b) 50 nm-radius circle traversed by the Y-stage, and (c) 2.5 mm-radius circle traversed by the Y-stage The characteristics and performance specifications of the two maglev stages are summarized in Tables 1 and 3. Sev- The experimental results on the position noise for horizontal motion of the A-stage is shown in Fig. 18(a). The position reg- ulation is around 2 nm rms. Fig. 18(b) shows a position noise profile for horizontal motion of the Y-stage, which is better than 3nmrms. The position noise for the vertical motion is higher due to sensor noise, analog-to-digital conversion (ADC) noise, and ADC quantization. Despite the noise in the vertical axes the hor-

Figure 4 – uploaded by Shobhit Verma

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