JP4501115B2 - Positioning control method - Google Patents

Description

In the present invention, at least two X-axis motors with position sensors that are driven in the X-axis direction and at least two Y-axis motors with position sensors that are driven in the Y-axis direction are fixed to a slider that floats by air. The present invention relates to a positioning control method for positioning in a two-dimensional direction on a flat surface .

A positioning control device for constructing a planar servo motor system in the prior art is as shown in FIG. 4 (see, for example, Patent Document 1).
In FIG. 4, 11 is a slider, 12 is a grating platen, 13 is an X plane mirror, 14 is a Y plane mirror, 15 is a motor unit, 16 is a host controller, and 17 is an XY servo driver. , 18 is an X1 axis motor core, 19 is an X2 axis motor core, 20 is an X1 axis motor, 21 is an X2 axis motor, 22 is a Y1 axis motor core, 23 is a Y2 axis motor core, 24 is a Y1 axis motor, and 25 is a Y2 axis motor, 32 is a 3-axis laser interferometer, 55 is an X-axis position / speed control unit, 56 is a Y-axis position / speed control unit, 57 is an attitude control unit, 58 is an X1 current drive inverter, 59 is an X2 current drive inverter, and 60 is A Y1 current drive inverter, 61 is a Y2 current drive inverter, and 62 is a coordinate conversion unit. The slider 11 is levitated by air or the like with respect to a platen that is a fixed object, and is equipped with two motors, an X1-axis motor 20 and an X2-axis motor 21, in the X-axis direction, and a Y1-axis motor 22, Y2 in the Y-axis direction. A shaft motor 23 is mounted so that a two-dimensional plane can be driven. As for the control system, the slider position is measured by a three-dimensional laser interferometer, and the yaw angle is calculated by measuring two points in parallel with respect to the X coordinate and measuring the difference therebetween. As described above, the X coordinate position, the Y coordinate position, and the yawing coordinate θ angle are detected, the feedback control units 55, 56, and 63 are provided for each coordinate, the deviation from the target position is evaluated, and the thrust command is determined. In addition, the results of experimentally measuring the pitching angle and rolling angle are stored in the control system in advance as a table, and the current considering the pitching angle and rolling angle according to the detected X-axis coordinate, Y-coordinate, and θ-coordinate. The command is calculated by the attitude control unit 57, and a current amplitude command and a commutation angle command are output to each current drive inverter 58, 59, 60, 61.
As described above, the conventional positioning control device stabilizes the attitude of the floated slider and executes the positioning of the slider.
Japanese Patent Laying-Open No. 2004-38426 (page 12, FIG. 4)

The conventional positioning control apparatus calculates the mass center position of the slider and the rotation angle around the mass center only by the sum and difference of the coordinates between the two points measured in parallel by the X and Y coordinate laser interferometers. . Actually, since a load is mounted on the slider, the center point of mass does not exist at the mechanical center position of the slider. Therefore, if the position information regarding the center of mass is calculated only by the sum and difference of the position information, the accuracy is deteriorated. Therefore, it is necessary to perform calculations that take into account the center of mass position. However, it is very inefficient to manually determine the center of mass position under various load conditions, and the cable connected to the slider. There was a problem that it was difficult to measure accurately due to the influence of tension.
The present invention has been made in view of such problems, and even when some load is mounted on the slider and the center of mass passes, the center of mass coordinates are simply calculated, and the coordinate conversion accuracy thereby is improved. An object of the present invention is to provide a positioning control device and a positioning control method capable of obtaining good position control performance.

  In order to solve the above problem, the present invention is as follows.

The invention described in claim 1 is levitated by air in which at least two X-axis motors with position sensors driven in the X-axis direction and at least two Y-axis motors with position sensors driven in the Y-axis direction are arranged. In the positioning control method of moving the slider in a two-dimensional direction on a fixed plane, the slider is driven at a constant acceleration a in the X-axis direction while performing coordinate conversion as the Y-axis mass center position lyg11 (Step 1). The rotational coordinate estimated disturbance dx11 around the mass center at the Y-axis mass center position lyg11 is calculated (Step 2), and the coordinate conversion is performed as the Y-axis mass center position lyg12, and the X-axis direction is driven at a constant acceleration a (Step 3). A rotation coordinate estimated disturbance dx12 around the mass center at the time of the Y-axis mass center position lyg12 is calculated (Step 4), (dx11-dx12), and The Y-axis mass center position lyg10 is calculated from (lyg11-lyg12) and the X1-axis motor thrust Fx11 and X2-axis motor thrust Fx21 at that time (Step 5), and the X-axis mass center position lxg11 is converted into the Y-axis direction. Is driven at a constant acceleration a (Step 6), a rotation center estimated disturbance dy11 around the center of mass at the X-axis mass center position lxg11 is calculated (Step 7), and the coordinate conversion is performed as the X-axis mass center position lxg12. Is driven at a constant acceleration a (Step 8), and the rotational coordinate estimated disturbance dy12 around the mass center at the X-axis mass center position lxg12 is calculated (Step9), (dy11-dy12) and (lxg11-lxg12) and Y1 at that time X-axis mass from shaft motor thrust Fy11 and Y2-axis motor thrust Fy21 Calculating a heart position lxg10 (Step10), in which took procedure of.

According to a second aspect of the present invention, there is provided air in which at least two X-axis motors with a position sensor driven in the X-axis direction and at least two Y-axis motors with a position sensor driven in the Y-axis direction are arranged. In a positioning control method for positioning a levitating slider by moving it in a two-dimensional direction on a fixed plane , a sinusoidal position command with a constant amplitude A in the X-axis direction while performing coordinate conversion as the Y-axis mass center position lyg21 (Step 101), a constant amplitude value dx21 of the rotational coordinate estimation disturbance around the mass center at the Y-axis mass center position lyg21 is calculated (Step 102), and the X-axis is obtained while performing the coordinate conversion as the Y-axis mass center position lyg22. Driven by a sinusoidal position command with a constant amplitude A in the direction (Step 103) and rotated around the center of mass at the Y-axis mass center position lyg22 A constant amplitude value dx22 of the target estimation disturbance is calculated (Step 104), from (dx21-dx22) and (lyg21-lyg22), and a constant amplitude value Fx12 of the X1-axis motor thrust at that time and a constant amplitude value Fx22 of the X2-axis motor thrust The Y-axis mass center position lyg20 is calculated (Step 105), and the X-axis mass center position lxg21 is driven by a sinusoidal position command with a constant amplitude A in the Y-axis direction while performing coordinate conversion (Step 106). The constant amplitude value dy21 of the rotational coordinate estimation disturbance around the center of mass at the position lxg21 is calculated (Step 107), and the coordinate conversion is performed as the X-axis mass center position lxg22, with a sinusoidal position command with a constant amplitude A in the Y-axis direction. Drive (Step 108) and rotate around the center of mass when the X-axis center of mass position is lxg22 A constant amplitude value dy22 of the estimated target disturbance is calculated (Step 109), (dy21-dy22) and (lxg21-lxg22), and a constant amplitude value Fy21 of the Y1-axis motor thrust at that time and a constant amplitude value Fy22 of the Y2-axis motor thrust The X-axis mass center position lxg20 is calculated (Step 110).

According to the first or second aspect of the invention, the center of mass position can be automatically obtained using the estimated disturbance of the disturbance observer unit, and the result of driving twice by changing the center of mass coordinates By removing the constant disturbance due to the tension of the cable connected to the slider, the mass center position can be obtained with high accuracy, and the coordinate conversion unit is configured using the mass center position. Control performance can be obtained.

  Hereinafter, specific examples of the method of the present invention will be described with reference to the drawings.

  FIG. 1 is a schematic configuration diagram of an example of a positioning control device of the present invention. Here, two motors for each axis are mounted on the X-axis and two on the Y-axis, and four position sensors are mounted on the X-axis and two on the Y-axis. In the figure, 101 is an upper position command device, 102 is a positioning control unit, 103 is a gate signal for voltage generation to each electric force conversion unit, 104 is a disturbance observer unit, 105 is a mass center position estimation unit, and 106 is a coordinate conversion unit. 107 is an X1 axis electric force converter, 108 is an X2 axis electric force converter, 109 is a Y1 axis electric force converter, 110 is a Y2 axis electric force converter, 111 is an X1 axis motor, 112 is an X2 axis motor, 113 Is a Y1 axis motor, 114 is a Y2 axis motor, 115 is an X1 axis position sensor, 116 is an X2 axis position sensor, 117 is a Y1 axis position sensor, 118 is a Y2 axis position sensor, 119 is a slider, and 120 is a positioning control device. . The present invention is different from Patent Document 1 in that a disturbance observer unit and a mass center position estimation unit are provided. As a result, even if the slider load fluctuates and the mass center position changes, by calculating the mass center position using the estimated disturbance estimated by the disturbance observer unit, each position information of the coordinate conversion unit is calculated. Since the accuracy is maintained, good control performance can be maintained.

FIG. 2 is a flowchart showing a positioning control method according to the second embodiment of the present invention. In the figure, 201 is the coordinate conversion as the Y-axis mass center position lyg11 and is driven at a constant acceleration a in the X-axis direction (Step 1), 202 is the rotational coordinate estimation disturbance dx11 around the mass center at the Y-axis mass center position lyg11. Step of calculating (Step 2), 203 is coordinate conversion as Y-axis mass center position lyg12, step of driving at constant acceleration a in the X-axis direction (Step 3), 204 is rotation coordinates around mass center at Y-axis mass center position lxg12 Step (Step 4) for calculating the estimated disturbance dx12, 205 is a step for calculating the Y-axis mass center position lyg10 from (dx11-dx12) and (lyg11-lyg12) and the X1-axis motor thrust Fx11 and X2-axis motor thrust Fx21 at that time (Step 5), 206 is the X-axis mass center position l. Step of converting the coordinates as g11 and driving at a constant acceleration a in the Y-axis direction (Step 6), 207 calculating a rotational coordinate estimated disturbance dy11 around the center of mass at the X-axis mass center position lxg11 (Step 7), 208 is X A step of converting the coordinates as the axial mass center position lxg12 and driving at a constant acceleration a in the Y-axis direction (Step 8), and a step 209 calculating a rotational coordinate estimation disturbance dy12 around the mass center at the X-axis mass center position lxg12 (Step 9). , 210 is a step of calculating the X-axis mass center position lxg10 from (dy11-dy12) and (lxg11-lxg12) and the Y1-axis motor thrust Fy11 and Y2-axis motor thrust Fy21 at that time (Step 10). Hereinafter, the flow of processing will be described with reference to FIG.
First, signals from the X1, X2, Y1, and Y2 axis sensors are input to the coordinate conversion unit 106, and from these signals, the slider mass center X coordinate position X, the slider mass center Y coordinate position Y, and the slider mass center around The angle θ is derived. For example, if the X coordinate in the position sensor X1 is X1, the X coordinate in the position sensor X2 is X2, the Y coordinate in the position sensor Y1 is Y1, and the Y coordinate in the position sensor Y2 is Y2, the following equation is used to calculate the slider mass center X coordinate: X, slider mass center Y coordinate position Y, and slider mass center angle θ are obtained.

X = (1 / L) {(L-Ly) .X1 + Ly.X2} (1)
Y = (1 / L) {(L−Lx) · Y1 + Lx · Y2} (2)
θ = (1 / 2L) {(X2-X1) + (Y1-Y2)} (3)

    Here, L is the length of one side of the slider, Ly is the length to the center of mass of the slider in the Y-axis direction, and Lx is the length to the center of mass of the slider in the X-axis direction. Thus, in order to calculate the information regarding each mass center position, the length information to the mass center is required, and the accuracy greatly affects the control performance. Thereafter, the slider mass center X coordinate position X, the slider mass center Y coordinate position Y, and the slider mass center angle θ are sent to the position / velocity control unit of each coordinate, and are relative to the target position output from the upper position command device. Control is applied. The control here may be so-called PID control or advanced control represented by H∞ control. Further, a thrust or torque command is output from each position speed controller. That is, a thrust command Fx is output from the X position speed control unit, a thrust command Fy is output from the Y position speed control unit, and a torque command τ is output from the θ position speed control unit.

  Here, the slider mass center X coordinate position X, the slider mass center Y coordinate position Y calculated by the coordinate converter, the slider mass center angle θ, the thrust command Fx from the X position speed controller, and the Y position speed controller The thrust command Fy and the torque command τ from the position / speed control unit are input to the disturbance observer unit. The disturbance observer here may be configured as a rigid system for each axis, and the configuration may be a so-called minimum-dimensional observer type or an all-dimensional observer (same-dimensional observer). These may be published in, for example, the document “Introduction to System Control Theory” (Koji Kogo and Tsutomu Mita, Jikkyo Publishing Co., Ltd. (1979)).

  Here, attention is focused on the coordinate system around the center of mass. First, coordinate conversion is performed with the Y-axis mass center position as Ly = lyg11, and driving is performed at a constant acceleration a in the X-axis direction (Step 1). The driving time and driving distance at this time may be appropriately determined according to mechanical and specification restrictions at that time. During this constant acceleration, an estimated disturbance around the center of mass estimated by the disturbance observer unit is set to dx11 (Step 2). At this time, the relationship between the thrust Fx111 generated by the X1-axis motor, the thrust Fx211 generated by the X2-axis motor, and the torque τ111 around the center of mass is shown below.

τ111 = {Fx211 (L-lyg11) −Fx111 · lyg11} + d (4)

  Here, d is a constant disturbance such as cable tension. At this time, if the coordinates of the true Y-axis mass center position are set as Ly = lyg10 and lyg11 = lyg10 + Δy1, the equation (4) is transformed as follows.

τ111
= {Fx211 · (L-lyg10−Δy1) −Fx111 · (lyg10
+ Δy1)} + d
= {Fx211 · (L-lyg10) −Fx111 · lyg10}
-Δy1 · (Fx111 + Fx211) + d
= Τ101 + dx11 (5)
(∵τ101 = Fx211 (L-lyg10) −Fx111 · lyg10,
dx11 = −Δy1 · (Fx111 + Fx211) + d)

  Similarly, driving is performed at a constant acceleration as lyg12 = lyg10 + Δy2 = lyg10 + Δy1 + Δ in Step 3, and an estimated disturbance at that time is obtained (Step 4). At that time, assuming that the thrust Fx112 generated by the X1-axis motor and the thrust Fx212 generated by the X2-axis motor, the torque τ112 around the center of mass is obtained as follows.

τ112 = {Fx212 · (L-lyg10−Δy2)
−Fx112 · (lyg10 + Δy2)} + d
= {Fx212 · (L-lyg10) −Fx112 · lyg10}
-Δy2 · (Fx112 + Fx212) + d
= {Fx212 · (L-lyg10) −Fx112 · lyg10}
−Δy1 · (Fx112 + Fx212) −Δ · (Fx112 + Fx212) + d
= Τ102 + dx12 (6)
(∵τ102 = Fx212 (L-lyg10) −Fx112 · lyg10,
dx12 = −Δy1 · (Fx112 + Fx212)
−Δ · (Fx112 + Fx212) + d)

Since the disturbance observer section estimates dx11 in the equation (5) and dx12 in the equation (6), a certain disturbance such as cable tension can be subtracted by dx11-dx12. Get the following formula.
dx11-dx12
= −Δy1 · (Fx111 + Fx211) + Δy1 · (Fx112 + Fx212) + Δ · (Fx112 + Fx212)
= Δy1 (Fx112 + Fx212−Fx111−Fx211)
+ Δ · (Fx112 + Fx212) (7)

Since Δ, Fx111, Fx211, Fx112, and Fx212 in the equation (7) are already known, the deviation Δy1 from the Y-axis mass center position can be finally obtained from the equation (7). Therefore, the mass center Y-axis coordinate lyg10 can be obtained (Step 5).

  As for the X-axis direction mass center position, the X-axis direction mass center position lxg10 can be obtained by driving at a constant acceleration in the Y-axis direction in the same manner as in Steps 1 to 5 (Steps 6 to 10).

  As described above, since the procedure for obtaining the estimated mass center position by obtaining the estimated disturbance for the two types of set mass center positions in the X-axis direction and the Y-axis direction, the true mass center position is obtained. Since the center of mass position can be obtained with high accuracy, the coordinate calculation accuracy in the coordinate conversion unit can be increased and good control performance can be obtained.

  FIG. 3 is a flowchart showing a positioning control method according to Embodiment 3 of the present invention. In the figure, 301 is a step in which coordinates are converted as a Y-axis mass center position lyg21 and driven by a sinusoidal position command with a constant amplitude A in the X-axis direction (Step 101), 302 is a mass center around the Y-axis mass center position lyg21 A step of calculating a constant amplitude value dx21 of the rotational coordinate estimation disturbance (Step 102), 303 a coordinate conversion as the Y-axis mass center position lyg22, and a step of driving with a sinusoidal position command with a constant amplitude A in the X-axis direction (Step 103) , 304 is a step of calculating a constant amplitude dx22 of the rotational coordinate estimation disturbance around the mass center at the Y-axis mass center position lyg22 (Step 104), 305 is (dx21-dx22) and (lyg21-lyg22) and the X1 axis at that time Constant amplitude Fx12 of motor thrust and constant X2 axis motor thrust A step of calculating the Y-axis mass center position lyg20 from the width value Fx22 (Step 105), 306 is a coordinate conversion as the X-axis mass center position lxg21, and a step of driving by a sinusoidal position command with a constant amplitude A in the Y-axis direction (Step 106) ) 307 is a step of calculating a constant amplitude value dy21 of the rotational coordinate estimation disturbance around the mass center at the X-axis mass center position lxg21 (Step 107), and 308 is coordinate-transformed as the X-axis mass center position lxg22 and is constant in the Y-axis direction. A step of driving with a sinusoidal position command with an amplitude A (Step 108), 309 is a step of calculating a constant amplitude value dy22 of a rotational coordinate estimation disturbance around the center of mass at the X-axis mass center position lxg22 (Step 109), and 310 is (dy21) -Dy22) and (lxg21-lxg22) and its A step (STEP110) to calculate the X-axis centroid position lxg20 than a predetermined amplitude value Fy22 constant amplitude Fy12 and Y2-axis motor thrust Kino Y1-axis motor thrust.

  In the third embodiment, the calculation formula for obtaining the center of mass and the concept thereof are the same as those in the second embodiment. However, in the second embodiment, the driving pattern is driven in one direction of the X axis or the Y axis at a constant acceleration. The third embodiment is characterized in that a constant amplitude sinusoidal position command is given and obtained by using each estimated amplitude value of the estimated disturbance and thrust command at that time. Specifically, the coordinate transformation is performed with the Y-axis mass center position as Ly = lyg21, and the maximum amplitude value of the estimated disturbance in the rotational coordinates around the mass center when driven by a constant amplitude sinusoidal position command in the X-axis direction at that time is dx21. The maximum amplitude value of the X1-axis motor thrust command is Fx121, the maximum amplitude value of the X2-axis motor thrust command is FX221, and the Y-axis mass center position is Ly = lyg22. The coordinates are converted, and a constant amplitude sine wave in the X-axis direction at that time When the maximum amplitude value of the estimated disturbance in the rotational coordinates around the center of mass when driven by the position command is dx22, the maximum amplitude value of the X1-axis motor thrust command is Fx122, and the maximum amplitude value of the X2-axis motor thrust command is FX222, dx21 And dx22 are expressed as follows.

dx21-dx22
= −Δy1 · (Fx121 + Fx221)
+ Δy1 · (Fx122 + Fx222) + Δ · (Fx122 + Fx222)
= Δy1 (Fx122 + Fx222− Fx121−Fx221)
+ Δ · (Fx122 + Fx222) (7)
(∵Δy1: Deviation of mass center position set value from mass center position lyg20 in the Y-axis direction,
Δ = lyg22−lyg21)

  From the above, since dx21, dx22, Fx121, Fx221, Fx122, Fx222, and Δ are known, Δy1 that is a deviation between the set value and the true mass center position can be obtained. As a result, the true mass center position lyg20 Can be requested. However, at this time, it is necessary to adjust the algorithm of each axis control law of the positioning control unit so that dx21, Fx121, Fx221 and dx22, Fx122, Fx222 have the same phase state quantity. Specifically, for example, the same phase can be realized by using so-called position proportional velocity proportional feedback compensation.

  As for the X-axis direction mass center position, the X-axis direction mass center position lxg20 can be obtained by driving with a constant amplitude sinusoidal position command in the Y-axis direction in the same manner as in Step 301 to Step 305 (Steps 306 to 310).

  In this way, the procedure for obtaining the true mass center position by obtaining the estimated disturbance for the two types of set mass center positions in each of the X-axis direction and the Y-axis direction is taken. Thus, the true mass center can be obtained by subtracting the influence of the above, and the mass center position coordinate is obtained with high accuracy. As a result, the coordinate calculation accuracy in the coordinate conversion unit is increased, and good control performance can be obtained. Also, by driving with a constant amplitude sinusoidal position command, unlike the case of the second embodiment, a minute amplitude is set even for a specification with a severe mechanical drive range restriction. It becomes possible to obtain the effect.

  Since the control for stabilizing the posture is performed by measuring the position of each driving motor of a fixed plane, for example, a planar motor system, the present invention can be applied to the positioning application of the planar motor system.

The block diagram which shows the structure of the positioning control apparatus of Example 1 of this invention. The flowchart which shows the process sequence of the method of Example 2 of this invention. The flowchart which shows the process sequence of the method of Example 3 of this invention. Block diagram showing the configuration of a conventional positioning control device

Explanation of symbols

11, 119 Slider 12 Grating platen 13 X plane mirror 14 Y plane mirror 15 Motor unit 16 Host controller 17 XY servo driver unit 18 X1 axis motor core 19 X2 axis motor core 20, 111 X1 axis motor 21, 112 X2 axis motor 22 Y1 axis motor core 23 Y2-axis motor core 24, 113 Y1-axis motor 25, 114 Y2-axis motor 32 3-axis laser interferometer 55 X-axis position / speed control unit 56 Y-axis position / speed control unit 57 Attitude control unit 58 X1 current drive inverter 59 X2 current Drive inverter 60 Y1 current drive inverter 61 Y2 current drive inverter 62, 106 Coordinate conversion unit 101 Upper position command device 102 Positioning control unit 103 Voltage generation gate signal 104 to each electric force conversion unit Disturbance observer unit 105 Mass center position estimation unit 107 X Axis electric force converter 108 X2 axis electric force converter 109 Y1 axis electric force converter 110 Y2 axis electric force converter 115 X1 axis position sensor 116 X2 axis position sensor 117 Y1 axis position sensor 118 Y2 axis position sensor 120 Positioning control device 201 A step of converting the coordinates as the Y-axis mass center position lyg1 and driving in the X-axis direction at a constant acceleration a (Step 1)
202 Step of calculating a rotation coordinate estimated disturbance dx1 around the center of mass at the Y-axis center of mass position lyg1 (Step 2)
203 A step of converting the coordinates as the Y-axis mass center position lyg2 and driving at a constant acceleration a in the X-axis direction (Step 3)
204 Step of calculating rotation coordinate estimated disturbance dx2 around the mass center at the Y-axis mass center position lyg2 (Step 4)
205 (dx1-dx2) and (lyg1-lyg2) and a step of calculating the Y-axis mass center position lyg from the X1-axis motor thrust Fx1 and the X2-axis motor thrust Fx2 at that time (Step 5)
206 Step of converting the coordinates as the X-axis mass center position lxg1 and driving in the Y-axis direction at a constant acceleration a (Step 6)
207 Step of calculating a rotation coordinate estimated disturbance dy1 around the mass center at the X-axis mass center position lxg1 (Step 7)
208 Step of transforming the coordinates as the X-axis mass center position lxg2 and driving at a constant acceleration a in the Y-axis direction (Step 8)
209 Step of calculating a rotational coordinate estimated disturbance dy2 around the center of mass at the X-axis center of mass position lxg2 (Step 9)
210 A step of calculating the Y-axis mass center position lxg from (dy1-dy2) and (lxg1-lxg2) and the Y1-axis motor thrust Fy1 and Y2-axis motor thrust Fy2 at that time (Step 5)
301 A step of converting coordinates as the Y-axis mass center position lyg21 and driving with a sinusoidal position command with a constant amplitude A in the X-axis direction (Step 101)
302 Step of calculating a constant amplitude value dx21 of the rotational coordinate estimation disturbance around the mass center at the Y-axis mass center position lyg21 (Step 102)
303 A step of converting the coordinates as the Y-axis mass center position lyg22 and driving with a sinusoidal position command with a constant amplitude A in the X-axis direction (Step 103)
304 Step of calculating a constant amplitude value dx22 of the rotational coordinate estimated disturbance around the mass center at the Y-axis mass center position lyg22 (Step 104)
305 (dx21-dx22) and (lyg21-lyg22) and a step of calculating the Y-axis mass center position lyg20 from the constant amplitude value Fx12 of the X1-axis motor thrust at that time and the constant amplitude value Fx22 of the X2-axis motor thrust (Step 105)
306 Step of converting the coordinates as the X-axis mass center position lxg21 and driving with a sinusoidal position command with a constant amplitude A in the Y-axis direction (Step 106)
307 Step of calculating a constant amplitude value dy21 of the rotational coordinate estimated disturbance around the mass center at the X-axis mass center position lxg21 (Step 107)
308 Step of converting the coordinates as the X-axis mass center position lxg22 and driving with a sinusoidal position command with a constant amplitude A in the Y-axis direction (Step 108)
309 Step of calculating a constant amplitude value dy22 of the estimated rotational coordinate around the mass center at the X-axis mass center position lxg22 (Step 109)
310 (dy21-dy22) and (lxg21-lxg22) and a constant amplitude value Fy12 of the Y1-axis motor thrust at that time and a constant amplitude value Fy22 of the Y2-axis motor thrust to calculate the X-axis mass center position lxg20 (Step 110)

Claims (2)

At least two X-axis motors with a position sensor driven in the X-axis direction and at least two Y-axis motors with a position sensor driven in the Y-axis direction are placed on a fixed plane with a slider that floats by air. In a positioning control method for positioning in a two-dimensional direction,
While performing coordinate conversion as the Y-axis mass center position lyg11, it is driven at a constant acceleration a in the X-axis direction (Step 1),
A rotation coordinate estimated disturbance dx11 around the mass center at the time of the Y-axis mass center position lyg11 is calculated (Step 2),
While performing coordinate conversion as the Y-axis mass center position lyg12, it is driven at a constant acceleration a in the X-axis direction (Step 3),
The rotation coordinate estimated disturbance dx12 around the mass center at the time of the Y-axis mass center position lyg12 is calculated (Step 4),
The Y-axis mass center position lyg10 is calculated from (dx11-dx12) and (lyg11-lyg12) and the X1-axis motor thrust Fx11 and X2-axis motor thrust Fx21 at that time (Step 5),
While performing coordinate conversion as the X-axis mass center position lxg11, drive at a constant acceleration a in the Y-axis direction (Step 6),
Calculate a rotational coordinate estimated disturbance dy11 around the mass center at the X-axis mass center position lxg11 (Step 7),
While performing coordinate conversion as the X-axis mass center position lxg12, drive at a constant acceleration a in the Y-axis direction (Step 8),
Calculate a rotational coordinate estimated disturbance dy12 around the mass center at the X-axis mass center position lxg12 (Step 9),
The X-axis mass center position lxg10 is calculated from (dy11-dy12) and (lxg11-lxg12) and the Y1-axis motor thrust Fy11 and Y2-axis motor thrust Fy21 at that time (Step 10).
A positioning control method characterized in that processing is performed according to the following procedure. At least two X-axis motors with a position sensor driven in the X-axis direction and at least two Y-axis motors with a position sensor driven in the Y-axis direction are placed on a fixed plane with a slider that floats by air. In a positioning control method for positioning in a two-dimensional direction,
While performing coordinate conversion as the Y-axis mass center position lyg21, it is driven by a sinusoidal position command with a constant amplitude A in the X-axis direction (Step 101).
A constant amplitude value dx21 of the rotational coordinate estimation disturbance around the mass center at the Y-axis mass center position lyg21 is calculated (Step 102),
While performing coordinate conversion as the Y-axis mass center position lyg22, it is driven by a sinusoidal position command with a constant amplitude A in the X-axis direction (Step 103),
A constant amplitude value dx22 of the rotational coordinate estimated disturbance around the mass center at the time of the Y-axis mass center position lyg22 is calculated (Step 104),
The Y-axis mass center position lyg20 is calculated from (dx21-dx22) and (lyg21-lyg22) and the constant amplitude value Fx12 of the X1-axis motor thrust at that time and the constant amplitude value Fx22 of the X2-axis motor thrust (Step 105),
While performing coordinate conversion as the X-axis mass center position lxg21, it is driven by a sinusoidal position command with a constant amplitude A in the Y-axis direction (Step 106).
A constant amplitude value dy21 of the rotational coordinate estimation disturbance around the mass center at the X-axis mass center position lxg21 is calculated (Step 107),
While performing coordinate conversion as the X-axis mass center position lxg22, it is driven by a sinusoidal position command with a constant amplitude A in the Y-axis direction (Step 108),
A constant amplitude value dy22 of the rotational coordinate estimation disturbance around the mass center at the X-axis mass center position lxg22 is calculated (Step 109),
The X-axis mass center position lxg20 is calculated from (dy21-dy22) and (lxg21-lxg22) and the constant amplitude value Fy21 of the Y1-axis motor thrust at that time and the constant amplitude value Fy22 of the Y2-axis motor thrust (Step 110).
A positioning control method characterized in that processing is performed according to the following procedure.

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