CN114270286B

CN114270286B - Stage position control device and stage position control method

Info

Publication number: CN114270286B
Application number: CN202080058134.2A
Authority: CN
Inventors: 境隼太
Original assignee: Panasonic Intellectual Property Management Co Ltd
Current assignee: Panasonic Intellectual Property Management Co Ltd
Priority date: 2019-09-02
Filing date: 2020-06-23
Publication date: 2024-03-26
Anticipated expiration: 2040-06-23
Also published as: JPWO2021044710A1; CN114270286A; KR20220054588A; JP7507355B2; WO2021044710A1

Abstract

Movement of the stage in the gantry mechanism in the yaw direction is suppressed. A stage position control device (1) for controlling the position of a stage in a rack mechanism (100) is provided with: a Y-axis thrust command output unit (30) that outputs a first Y-axis thrust command for indicating the thrust of the center of gravity of the Y1-axis drive system and the Y2-axis drive system; a Y-axis differential thrust command output unit (20) that outputs a first Y-axis differential thrust command for indicating a differential thrust between the Y1-axis drive system and the Y2-axis drive system; a feedforward section (11) that feedforward an X-axis position command (X) for indicating an X-axis position and a Y-axis center-of-gravity position command (Y1) for indicating a center-of-gravity position between a Y1-axis position and a Y2-axis position to a first Y-axis differential thrust command (F2) to output a second Y-axis differential thrust command (F2'); and a thrust conversion unit (50) that controls the position of the stage using the first Y-axis thrust command and the second Y-axis differential thrust command.

Description

Stage position control device and stage position control method

Technical Field

The present invention relates to a stage position control device and a stage position control method for controlling a position of a stage.

Background

Conventionally, a gantry mechanism is known which moves a stage in a plane defined by two axes orthogonal to each other.

For example, patent document 1 discloses a stage position control method for suppressing movement of a stage in a yaw direction in a rack mechanism.

The stage position control method disclosed in patent document 1 is a control method as follows: the position of the stage is detected, and information on the detected position of the stage is fed back to a command for moving the stage. Therefore, in this control method, the position of the stage can be controlled so that the movement of the stage in the yaw direction that occurs is suppressed. However, at a time point when the movement of the stage in the yaw direction does not occur, it is difficult to suppress the occurrence of the movement of the stage in the yaw direction itself.

Prior art literature

Patent literature

Patent document 1: japanese patent laid-open No. 2001-22448

Disclosure of Invention

Accordingly, an object of the present disclosure is to provide a stage position control device and a stage position control method that can suppress movement of a stage in a yaw direction in a rack mechanism as compared with the related art.

A stage position control device according to an aspect of the present disclosure is for controlling a position of a stage in a rack mechanism including: a Y1 axis and a Y2 axis which are parallel to each other; an X axis perpendicular to the Y1 axis and the Y2 axis; and a stage whose position is determined based on a Y1 axis position that is a driving position in a Y1 axis driving system on the Y1 axis, a Y2 axis position that is a driving position in a Y2 axis driving system on the Y2 axis, and an X axis position that is a driving position in an X axis driving system on the X axis, wherein the stage position control device includes: a Y-axis thrust command output unit that outputs a first Y-axis thrust command for indicating thrust of the center of gravity of the Y1-axis drive system and the Y2-axis drive system; a Y-axis differential thrust command output unit that outputs a first Y-axis differential thrust command for indicating a differential thrust between the Y1-axis drive system and the Y2-axis drive system; a feedforward section that feedforward an X-axis position command for indicating an X-axis position and a Y-axis center-of-gravity position command for indicating a center-of-gravity position of a Y1-axis position and a Y2-axis position to a first Y-axis differential thrust command to output a second Y-axis differential thrust command; and a thrust conversion unit that controls the position of the stage using the first Y-axis thrust command and the second Y-axis differential thrust command.

A stage position control method according to an embodiment of the present disclosure is for controlling a position of a stage in a rack mechanism having: a Y1 axis and a Y2 axis which are parallel to each other; an X axis perpendicular to the Y1 axis and the Y2 axis; and a stage whose position is determined based on a driving position in a Y1 axis driving system on a Y1 axis, that is, a Y1 axis position, a driving position in a Y2 axis driving system on a Y2 axis, that is, a Y2 axis position, and a driving position in an X axis driving system on an X axis, that is, an X axis position, in the stage position control method, a first Y axis thrust weight command for instructing a thrust of a center of gravity of the Y1 axis driving system and the Y2 axis driving system is calculated, a first Y axis thrust weight command for instructing a thrust of a difference of the Y1 axis driving system and the Y2 axis driving system is calculated, an X axis position command for instructing an X axis position and a Y axis thrust weight command for instructing a position of a center of gravity of the Y1 axis and the Y2 axis position are fed forward to the first Y axis thrust weight command, and a position of the stage is controlled using the first Y axis thrust weight command and the second Y axis thrust weight command.

According to the stage position control device and the stage position control method according to one embodiment of the present disclosure, the movement of the stage in the yaw direction in the rack mechanism can be suppressed as compared with the conventional one.

Drawings

Fig. 1 is a schematic diagram showing a configuration of a rack mechanism according to embodiment 1.

Fig. 2 is a block diagram showing a configuration of a stage position control device according to embodiment 1.

Fig. 3 is a schematic diagram showing an example of the inertia function calculated by the inertia function calculating unit according to embodiment 1.

Fig. 4 is a flowchart of inertia function calculation processing according to embodiment 1.

Fig. 5 is a flowchart of stage position control processing according to embodiment 1.

Fig. 6 is a block diagram showing a configuration of a stage position control device according to embodiment 2.

Detailed Description

(a pass by of one embodiment of the present disclosure)

As described above, in the stage position control method disclosed in patent document 1, it is difficult to suppress the occurrence of the movement of the stage in the yaw direction itself at a point in time when the movement of the stage in the yaw direction does not occur in the frame mechanism.

Accordingly, the inventors have conducted intensive studies and experiments to suppress the occurrence of the movement of the stage in the yaw direction at a time point when the movement of the stage in the yaw direction does not occur in the frame mechanism. The inventors have found the following insight: the position command for indicating the position of the stage is fed forward to the thrust command for moving the stage, and the component for causing the movement of the stage in the yaw direction is reduced from the thrust command in advance, so that the movement of the stage in the yaw direction itself can be suppressed at the time point when the movement of the stage in the yaw direction is not generated.

The inventors have further conducted intensive studies and experiments based on the findings, and have conceived a stage position detection device and a stage position detection method according to one embodiment of the present disclosure described below.

A stage position control device according to an embodiment of the present disclosure is for controlling a position of a stage in a rack mechanism having: a Y1 axis and a Y2 axis which are parallel to each other; an X axis perpendicular to the Y1 axis and the Y2 axis; and a stage whose position is determined based on a Y1 axis position that is a driving position in a Y1 axis driving system on the Y1 axis, a Y2 axis position that is a driving position in a Y2 axis driving system on the Y2 axis, and an X axis position that is a driving position in an X axis driving system on the X axis, wherein the stage position control device includes: a Y-axis thrust command output unit that outputs a first Y-axis thrust command for indicating thrust of the center of gravity of the Y1-axis drive system and the Y2-axis drive system; a Y-axis differential thrust command output unit that outputs a first Y-axis differential thrust command for indicating a differential thrust between the Y1-axis drive system and the Y2-axis drive system; a feedforward section that feedforward an X-axis position command for indicating an X-axis position and a Y-axis center-of-gravity position command for indicating a center-of-gravity position of a Y1-axis position and a Y2-axis position to a first Y-axis differential thrust command to output a second Y-axis differential thrust command; and a thrust conversion unit that controls the position of the stage using the first Y-axis thrust command and the second Y-axis differential thrust command.

According to the stage position control device having the above configuration, it is possible to feed forward the X-axis position command and the Y-axis center of gravity position command for indicating the position of the stage to the first Y-axis differential thrust command that may contain the component for causing the stage to move in the yaw direction, and generate the second Y-axis differential thrust command in which the component for causing the stage to move in the yaw direction is reduced. The generated second Y-axis differential thrust command is used to control the position of the stage. Therefore, according to the stage position control device having the above-described configuration, the movement of the stage in the yaw direction in the rack mechanism can be suppressed as compared with the conventional one.

The feedforward unit may store an inertia function indicating a relationship between an inertia difference, which is a difference between the inertia of the Y1 axis drive system and the inertia of the Y2 axis drive system, and the X axis position indicated by the X axis position command, calculate the inertia difference from the inertia function, and calculate a feedforward value that is feedforward to the first Y axis difference thrust command from the Y axis center of gravity position command and the calculated inertia difference.

The Y-axis thrust command output unit may output the first Y-axis thrust command based on the Y-axis thrust command.

In addition, the present invention may further include: a Y1 axis position detection unit that detects a Y1 axis position; and a Y2-axis position detection unit that detects a Y2-axis position, wherein the Y-axis gravity center thrust command output unit outputs a first Y-axis gravity center thrust command by receiving the Y-axis gravity center position as a feedback value, the Y-axis gravity center position indicating a center of gravity position of the Y1-axis position detected by the Y1-axis position detection unit and the Y2-axis position detected by the Y2-axis position detection unit, and the first Y-axis differential thrust command output unit outputs a first Y-axis differential thrust command by receiving the Y-axis differential position as a feedback value, the Y-axis differential position indicating a differential position between the Y1-axis position detected by the Y1-axis position detection unit and the Y2-axis position detected by the Y2-axis position detection unit.

The thrust conversion unit may calculate a Y1 axis drive system thrust command for indicating a thrust of the Y1 axis drive system and a Y2 axis drive system thrust command for indicating a thrust of the Y2 axis drive system based on the first Y axis gravity center thrust command and the second Y axis difference thrust command, and may drive the Y1 axis drive system using the Y1 axis drive system thrust command and the Y2 axis drive system using the Y2 axis drive system thrust command, thereby controlling the position of the stage.

In addition, the present invention may further include: an X-axis position detection unit that detects an X-axis position; and a feedback unit that feeds back the difference position and the X-axis position detected by the X-axis position detection unit to the first Y-axis thrust command to output a second Y-axis thrust command, and the thrust conversion unit controls the position of the stage by using the second Y-axis thrust command.

The feedback unit may store an inertia function, calculate an inertia difference from the inertia function and the X-axis position detected by the X-axis position detecting unit, and calculate a feedback value to be fed back to the first Y-axis thrust command from the difference position and the calculated inertia difference.

The thrust conversion unit may calculate a Y1 axis drive system thrust command for indicating a thrust of the Y1 axis drive system and a Y2 axis drive system thrust command for indicating a thrust of the Y2 axis drive system based on the second Y axis gravity center thrust command and the second Y axis difference thrust command, and may drive the Y1 axis drive system using the Y1 axis drive system thrust command and the Y2 axis drive system using the Y2 axis drive system thrust command, thereby controlling the position of the stage.

In addition, the present invention may further include: a Y1 axis position detection unit that detects a Y1 axis position; a Y2 axis position detection unit that detects a Y2 axis position; and an inertia function calculating section that outputs a Y1-axis drive system thrust instruction for instructing a thrust of the Y1-axis drive system and a Y2-axis drive system thrust instruction for instructing a thrust of the Y2-axis drive system, the inertia function being calculated based on (a) the Y1-axis drive system thrust instruction and the Y2-axis drive system thrust instruction that are output in a case where a position of the stage is determined according to the first X-axis position, (b) the Y1-axis position detected by the Y1-axis position detecting section and the Y2-axis position detected by the Y2-axis position detecting section in a case where the position of the stage is determined according to the first X-axis position, (c) the Y1-axis drive system thrust instruction and the Y2-axis drive system thrust instruction that are output in a case where the position of the stage is determined according to the second X-axis position, and (d) the Y1-axis position detected by the Y1-axis position detecting section and the Y2-axis position detected by the Y2-axis position detecting section in a case where the position of the stage is determined according to the second X-axis position.

According to the stage position control method of the above configuration, it is possible to feed forward the X-axis position command and the Y-axis center of gravity position command for indicating the position of the stage to the first Y-axis differential thrust command that may contain a component for causing the stage to move in the yaw direction, and generate the second Y-axis differential thrust command in which the component for causing the stage to move in the yaw direction is reduced. The generated second Y-axis differential thrust command is used to control the position of the stage. Therefore, according to the stage position control method of the above-described configuration, the movement of the stage in the yaw direction in the rack mechanism can be suppressed as compared with the conventional one.

A specific example of a stage position control device according to an embodiment of the present disclosure will be described below with reference to the drawings. Further, the embodiments described below each show a general or specific example. The numerical values, shapes, materials, components, arrangement positions of components, connection modes, and the like shown in the following embodiments are examples, and the gist thereof is not intended to limit the present disclosure. Among the constituent elements of the following embodiments, constituent elements not described in the independent claims showing the uppermost concepts are described as arbitrary constituent elements.

The drawings are schematic and are not necessarily strictly illustrated. In the drawings, substantially the same structures are denoted by the same reference numerals, and a repetitive description may be omitted or simplified.

In the drawings used in the following description of the embodiments, a coordinate system may be shown. The z-direction in the coordinate system is the direction perpendicular to the drawing sheet. The x-direction and the y-direction are mutually orthogonal directions in a plane perpendicular to the z-direction.

(embodiment 1)

Next, a stage position control device according to embodiment 1 will be described with reference to the drawings. The stage position control device is a device for controlling the position of the stage of the rack mechanism.

Fig. 1 is a schematic diagram showing a configuration of a rack mechanism 100 according to embodiment 1. The gantry mechanism 100 has a stage to which the stage position control device is a target of position control.

As shown in fig. 1, the gantry mechanism 100 includes a Y1 axis 110, a Y2 axis 120, an X axis 130, a stage 140, a first X axis support 135, a second X axis support 136, a Y1 axis drive system 111, a Y2 axis drive system 121, and an X axis drive system 131.

The Y1 axis 110 and the Y2 axis 120 are axes extending in the Y direction shown in fig. 1, respectively. That is, the Y1 axis 110 and the Y2 axis 120 are axes parallel to each other. The Y1 axis 110 and the Y2 axis 120 are realized by, for example, a metal quadrangular prism extending in the Y direction shown in fig. 1.

The X-axis 130 is an axis extending in the X-direction shown in fig. 1. That is, the X axis 130 is an axis perpendicular to the Y1 axis 110 and the Y2 axis 120. The X-axis 130 is implemented by, for example, a metal quadrangular prism extending in the X-direction shown in fig. 1.

The first X-axis support section 135 is a support member that supports the X-axis 130 at one end of the X-axis 130. The first X-axis bearing 135 is implemented, for example, by metal.

The second X-axis supporting portion 136 is a supporting member that supports the X-axis 130 at the other end of the X-axis 130. The second X-axis bearing 136 is made of metal, for example.

The Y1 axis drive system 111 is disposed on the Y1 axis 110, and drives the first X axis support section 135 so as to be capable of moving in the Y direction shown in fig. 1. The Y1 axis drive system 111 is implemented by, for example, a linear motor capable of moving in the Y direction shown in fig. 1. Alternatively, the Y1 axis drive system 111 is implemented by, for example, a rotary motor and a ball screw extending in the Y direction shown in fig. 1.

The Y2 axis drive system 121 is disposed on the Y2 axis 120, and drives the second X axis support 136 to be capable of moving in the Y direction shown in fig. 1. The Y2 axis drive system 121 is implemented, for example, by a linear motor capable of moving in the Y direction shown in fig. 1. Alternatively, the Y2 axis drive system 121 is implemented by, for example, a rotary motor and a ball screw extending in the Y direction shown in fig. 1.

Stage 140 is a flat plate. The stage 140 is implemented by a metal plate, for example.

The X-axis drive system 131 is disposed on the X-axis 130, and is a drive system for driving the stage 140 to move straight in the X-direction shown in fig. 1. The X drive system 131 is realized, for example, by a linear motor capable of moving in the X direction shown in fig. 1. Alternatively, the X-axis driving system 131 is implemented by, for example, a rotary motor and a ball screw extending in the X-direction shown in fig. 1.

The Y1-axis drive system 111 and the Y2-axis drive system 121 drive the first X-axis bearing 135 and the second X-axis bearing 136 in translation, thereby driving the X-axis 130 to be slidable in the Y direction shown in fig. 1. In addition, as described above, the X-axis drive system 131 drives the stage so that it can be advanced straight in the X-direction shown in fig. 1. Thus, the gantry mechanism 100 can move the stage 140 in a plane defined by the X-direction and the Y-direction shown in fig. 1 toward a position determined from the driving position in the Y1-axis driving system 111, that is, the Y1-axis position, the driving position in the Y2-axis driving system 121, that is, the Y2-axis position, and the driving position in the X-axis driving system 131, that is, the X-axis position.

In the gantry mechanism 100, the inertia of the Y1 axis drive system 111 and the inertia of the Y2 axis drive system 121 vary according to the position of the stage 140 on the X axis 130. Therefore, when the position of the stage 140 on the X axis 130 is the first X axis position and when the position of the stage 140 on the X axis 130 is the second X axis position, the driving speeds of the first X axis support 135 driven by the Y1 axis driving system 111 are different from each other even if the same thrust is applied to the Y1 axis driving system 111. Similarly, in the case where the position of the stage 140 on the X axis 130 is the first X axis position and in the case where the position of the stage 140 on the X axis 130 is the second X axis position, even if the same thrust is applied to the Y2 axis drive system 121, the drive speeds of the second X axis support 136 driven by the Y2 axis drive system 121 are different from each other.

In the gantry mechanism 100, when the driving speed of the first X-axis support 135 driven by the Y1-axis driving system 111 and the driving speed of the second X-axis support 136 driven by the Y2-axis driving system 121 are different from each other, the stage 140 moves in the yaw direction, which is the rotational direction around the z direction shown in fig. 1. In order to suppress this movement in the yaw direction, it is necessary to suppress the difference between the driving speed of the first X-axis bearing 135 driven by the Y1-axis driving system 111 and the driving speed of the second X-axis bearing 136 driven by the Y2-axis driving system 121.

Fig. 2 is a block diagram showing the structure of stage position control device 1 according to embodiment 1. However, fig. 2 does not show all the components of the stage position control device 1. Fig. 2 illustrates components of the stage position control device 1 for outputting a Y1-axis drive system thrust command for instructing to drive the thrust of the Y1-axis drive system 111 and components of the Y2-axis drive system thrust command for instructing to drive the thrust of the Y2-axis drive system 121. On the other hand, the components of the stage position control device 1 for outputting an X-axis drive system thrust command for instructing the driving of the X-axis drive system 131 are not shown in fig. 2. However, the stage position control device 1 is configured to include components, not shown in fig. 2, for outputting an X-axis drive system thrust command for instructing to drive the X-axis drive system 131.

As shown in fig. 2, the stage position control device 1 includes a feedforward section 10, a Y-axis differential thrust command output section 20, a Y-axis gravity center thrust command output section 30, a Y1-axis position detection section 41, a Y2-axis position detection section 42, an X-axis position detection section 43, a thrust conversion section 50, an inertia function calculation section 60, a position conversion section 70, an X-axis position command acquisition section 81, a Y-axis gravity center position command acquisition section 82, and a phase delay compensation section 83.

The Y1 axis position detection unit 41 detects a Y1 axis position which is a driving position in the Y1 axis driving system 111. The Y1 axis position detecting section 41 is implemented by an encoder provided in a linear motor or a rotary motor of the Y1 axis driving system 111, for example. Hereinafter, the Y1 axis position is referred to as Y1. The first derivative of the time of the Y1 axis position is referred to as

[ number 1]

The second order differential in time of the Y1 axis position is referred to as

[ number 2]

The Y2 axis position detection unit 42 detects a Y2 axis position which is a driving position in the Y2 axis driving system 121. The Y2 axis position detecting section 42 is implemented by an encoder provided in a linear motor or a rotary motor of the Y2 axis drive system 121, for example. Hereinafter, the Y2 axis position is referred to as Y2. The first derivative of the time of the Y2 axis position is referred to as

[ number 3]

The second order differential in time of the Y2 axis position is referred to as

[ number 4]

The X-axis position detection unit 43 detects an X-axis position which is a driving position in the X-axis driving system 131. The X-axis position detecting section 43 is implemented by an encoder provided in a linear motor or a rotary motor of the X-axis driving system 131, for example. Hereinafter, the X-axis position is referred to as X.

The X-axis position instruction acquisition unit 81 acquires an X-axis position instruction for instructing an X-axis position. The X-axis position command may be a function indicating a relationship between the indicated X-axis position and time, or may be a correspondence table that associates the indicated X-axis position with time.

The Y-axis center-of-gravity position instruction acquisition unit 82 acquires a Y-axis center-of-gravity position instruction for instructing the center-of-gravity positions of the Y1-axis position and the Y2-axis position. In this specification, the sum of the Y1 axis position and the Y2 axis position is referred to as a Y axis center of gravity position. Hereinafter, the Y-axis center of gravity position is referred to as Y1. The relationship between Y1 and Y2 is expressed by the formula y1=y1+y2. The Y-axis centroid position command may be a function indicating a relationship between the indicated Y-axis centroid position and time, or may be a correspondence table in which the indicated Y-axis centroid position and time are associated with each other.

The position conversion unit 70 calculates a Y-axis center of gravity position indicating the sum of the Y1-axis position and the Y2-axis position and a Y-axis difference position indicating the difference between the Y1-axis position and the Y2-axis position from the Y1-axis position detected by the Y1-axis position detection unit 41 and the Y2-axis position detected by the Y2-axis position detection unit 42. In this specification, the difference between the Y1 axis position and the Y2 axis position is referred to as a Y axis difference position. Hereinafter, the Y-axis difference position is referred to as Y2. The relationship between Y2 and Y1 and Y2 is represented by the formula y2=y1-Y2.

The phase delay compensation unit 83 compensates for a phase difference between the Y-axis center of gravity position indicated by the Y-axis center of gravity position instruction acquisition unit 82 and the Y-axis center of gravity position calculated by the position conversion unit 70 when the Y-axis center of gravity position calculated by the position conversion unit 70 is fed back to the Y-axis center of gravity thrust instruction output unit 30 described later.

The Y-axis thrust command output section 30 calculates and outputs a first Y-axis thrust command F1 for indicating the thrust of the center of gravity of the Y1-axis drive system 111 and the Y2-axis drive system 121. In this specification, the sum of the Y1-axis drive system thrust and the Y2-axis drive system thrust is referred to as the Y-axis thrust. Hereinafter, the Y-axis thrust command is referred to as F1. The Y1-axis drive system thrust command for indicating the thrust of the Y1-axis drive system 111 is referred to as f1. The Y2-axis drive system thrust command for indicating the thrust of the Y2-axis drive system 121 is referred to as f2.

The Y-axis thrust command output unit 30 receives the Y-axis thrust command, the phase difference of which has been compensated by the phase delay compensation unit 83, and performs feedback processing on the Y-axis thrust command, the Y-axis thrust command being calculated by the position conversion unit 70, as a feedback value, to output a first Y-axis thrust command F1.

Next, the output of the first Y-axis thrust command F1 by the Y-axis thrust command output unit 30 will be described in more detail.

As shown in fig. 2, the Y-axis thrust command output unit 30 includes a position feedback unit 31 and a speed feedback unit 32.

The position feedback unit 31 feeds back the Y-axis centroid position calculated by the position conversion unit with respect to the Y-axis centroid position command after the phase difference compensation unit 83, and performs PID (Proportional Integral Differential: proportional-integral-derivative) processing to output a Y-axis centroid speed command for instructing the barycenter speeds of the Y1-axis drive system 111 and the Y2-axis drive system 121. In this specification, the sum of the Y1 axis drive system speed and the Y2 axis drive system speed is referred to as the Y axis center of gravity speed. Hereinafter, the Y-axis gravity center speed command is referred to as V1.

The velocity feedback unit 32 feeds back the first-order differential of the time of the Y-axis centroid position calculated by the position conversion unit with respect to the Y-axis centroid velocity command V1 outputted by the position feedback unit 31

[ number 5]

PID processing is performed to output a first Y-axis thrust command F1.

The Y-axis differential thrust command output unit 20 calculates and outputs a first Y-axis differential thrust command for instructing the differential thrust between the Y1-axis drive system 111 and the Y2-axis drive system 121. In the present specification, the difference between the Y1-axis drive system thrust f1 and the Y2-axis drive system thrust f2 is referred to as a Y-axis differential thrust. Hereinafter, the first Y-axis differential thrust command is referred to as F2.

As described above, in the gantry mechanism 100, the Y1-axis drive system 111 and the Y2-axis drive system 121 drive the X-axis 130 to be slidable in the Y direction shown in fig. 1 by translational driving of the first X-axis support 135 and the second X-axis support 136. Thus, the Y-axis difference position command for indicating the difference position of the Y1-axis position and the Y2-axis position is 0 at any time. Thus, the Y-axis differential thrust command output section 20 performs feedback processing for the Y-axis differential position command that is 0 at any time by receiving the Y-axis differential position calculated by the position conversion section 70 as a feedback value to output a second Y-axis differential thrust command F2.

Next, the output of the second Y-axis differential thrust command F2 by the Y-axis differential thrust command output unit 20 will be described in more detail.

As shown in fig. 2, the Y-axis differential thrust command output unit 20 includes a position feedback unit 21 and a speed feedback unit 22.

The position feedback unit 21 performs PID processing for the Y-axis difference position calculated by the position conversion unit in response to the Y-axis difference position command of 0 at any time, and outputs a Y-axis differential speed command for instructing the differential speed of the Y1-axis drive system 111 and the Y2-axis drive system 121. In this specification, the difference between the Y1-axis drive system speed and the Y2-axis drive system speed is referred to as a Y-axis differential speed. Hereinafter, the Y-axis differential command is referred to as V2.

The speed feedback unit 22 feeds back the first-order differential of the time of the Y-axis difference position calculated by the position conversion unit, with respect to the Y-axis differential command V2 output by the position feedback unit 21

[ number 6]

PID processing is performed to output a first Y-axis differential thrust command F2.

The inertia function calculating unit 60 calculates an inertia function indicating a relationship between an inertia difference between the inertia of the Y1 axis drive system 111 and the inertia of the Y2 axis drive system 121 and the X axis position. Hereinafter, the inertia of the Y1 axis drive system 111 is referred to as m1. The inertia of the Y2 axis drive system 121 is referred to as m2.

Fig. 3 is a schematic diagram showing an example of the inertia function calculated by the inertia function calculating unit 60 according to embodiment 1.

As shown in fig. 3, the inertia function is a function representing the relationship between the inertia differences m1-m2 and the X-axis position X. Here, as shown in fig. 3, the inertia function is a function in which the inertia difference m1 to m2 is expressed by a linear expression of the X-axis position X. However, the inertia function may be a function representing the relationship between the inertia differences m1 to m2 and the X-axis position X, and is not necessarily limited to a function representing the inertia differences m1 to m2 by a linear expression of the X-axis position X. For example, the inertia difference m1 to m2 may be expressed by a function other than the first order expression of the X-axis position X.

The inertia function calculating unit 60 outputs a Y1-axis drive system thrust command f1 for indicating the thrust of the Y1-axis drive system 111, a Y2-axis drive system thrust command f2 for indicating the thrust of the Y2-axis drive system 121, and an X-axis thrust command fx for indicating the thrust of the X-axis drive system 131. The inertia function calculating unit 60 acquires the Y1 axis position Y1 detected by the Y1 axis position detecting unit 41, the Y2 axis position Y2 detected by the Y2 axis position detecting unit 42, and the X axis position X detected by the X axis position detecting unit 43. The inertia function calculating unit 60 calculates an inertia function based on the output Y1-axis drive system thrust command f1, the output Y2-axis drive system thrust command f2, the acquired Y1-axis position Y1, the acquired Y2-axis position Y2, and the acquired X-axis position X.

Next, the calculation of the inertia function by the inertia function calculation unit 60 will be described in more detail.

Fig. 4 is a flowchart of inertia function calculation processing according to embodiment 1. The inertia function calculation process is an example of the process performed by the inertia function calculation unit 60 to calculate the inertia function.

When the inertia function calculation process starts, the inertia function calculation unit 60 outputs the X-axis thrust command fx to the gantry mechanism 100, and moves the stage 140 to the first X-axis position (step S100). At this time, the inertia function calculating unit 60 obtains the X-axis position X from the X-axis position detecting unit 43 to confirm the X-axis position of the stage 140, and moves the stage 140 to the first X-axis position.

When the stage 140 is moved to the first X-axis position, the inertia function calculating unit 60 outputs the Y1-axis drive system thrust command f1 and the Y2-axis drive system thrust command f2, which are synchronized with each other, to the gantry mechanism 100, and excites the Y1-axis drive system 111 and the Y2-axis drive system 121 (step S110).

When the Y1-axis drive system 111 and the Y2-axis drive system 121 are excited, the inertia function calculating unit 60 acquires the Y-axis position Y1 and the Y-axis position Y2 from the Y1-axis position detecting unit 41 and the Y2-axis position detecting unit 42, respectively (step S120).

When the Y1 axis position Y1 and the Y2 axis position Y2 are acquired, the inertia function calculating section 60 calculates the inertia m1 of the Y1 axis drive system 111 and the inertia m2 of the Y2 axis drive system 121 based on the output Y1 axis drive system thrust command f1 and Y2 axis drive system thrust command f2 and the acquired Y1 axis position Y1 and Y2 axis position Y2. That is, the inertia function calculating unit 60 calculates the inertia m1 of the Y1 axis driving system 111 and the inertia m2 of the Y2 axis driving system 121 when the stage 140 is positioned at the first X axis position (step S130).

Next, the inertia function calculating unit 60 outputs the X-axis thrust command fx to the gantry mechanism 100, and moves the stage 140 to the second X-axis position (step S140). At this time, the inertia function calculating unit 60 obtains the X-axis position X from the X-axis position detecting unit 43 to confirm the X-axis position of the stage 140, and moves the stage 140 to the second X-axis position.

When the stage 140 is moved to the second X-axis position, the inertia function calculating unit 60 outputs the Y1-axis drive system thrust command f1 and the Y2-axis drive system thrust command f2, which are synchronized with each other, to the gantry mechanism 100, and excites the Y1-axis drive system 111 and the Y2-axis drive system 121 (step S150).

When the Y1-axis drive system 111 and the Y2-axis drive system 121 are excited, the inertia function calculating unit 60 acquires the Y-axis position Y1 and the Y-axis position Y2 from the Y1-axis position detecting unit 41 and the Y2-axis position detecting unit 42, respectively (step S160).

When the Y1 axis position Y1 and the Y2 axis position Y2 are acquired, the inertia function calculating section 60 calculates the inertia m1 of the Y1 axis drive system 111 and the inertia m2 of the Y2 axis drive system 121 based on the output Y1 axis drive system thrust command f1 and Y2 axis drive system thrust command f2 and the acquired Y1 axis position Y1 and Y2 axis position Y2. That is, the inertia function calculating unit 60 calculates the inertia m1 of the Y1 axis driving system 111 and the inertia m2 of the Y2 axis driving system 121 when the stage 140 is positioned at the second X axis position (step S170).

Next, the inertia function calculating unit 60 calculates an inertia function 180 based on the inertia m1 of the Y1 axis drive system 111 and the inertia m2 of the Y2 axis drive system 121 when the stage 140 is located at the first X axis position calculated in the process of step S130, and the inertia m1 of the Y1 axis drive system 111 and the inertia m2 of the Y2 axis drive system 121 when the stage 140 is located at the second X axis position calculated in the process of step S170 (step S180).

When the process of step S180 ends, the inertia function calculating unit 60 ends the inertia function calculating process.

As described above, the inertia function calculating unit 60 outputs the Y1-axis drive system thrust command for instructing the thrust of the Y1-axis drive system 111 and the Y2-axis drive system thrust command for instructing the thrust of the Y2-axis drive system 121, and calculates the inertia function based on the following (a) to (d). (a) A Y1 axis drive system thrust command and a Y2 axis drive system thrust command are output with the position of stage 140 determined from the first X axis position. (b) The Y1 axis position detected by the Y1 axis position detecting section 41 and the Y2 axis position detected by the Y2 axis position detecting section 42 in the case where the position of the stage 140 is determined based on the first X axis position. (c) A Y1 axis drive system thrust command and a Y2 axis drive system thrust command are output with the position of stage 140 determined from the second X axis position. (d) The Y1 axis position detected by the Y1 axis position detecting section 41 and the Y2 axis position detected by the Y2 axis position detecting section 42 in the case where the position of the stage 140 is determined based on the second X axis position.

The feedforward section 10 feedforward the X-axis position command acquired by the X-axis position command acquisition section 81 and the Y-axis center of gravity position command acquired by the Y-axis center of gravity position command acquisition section 82 to the first Y-axis differential thrust command F2 output from the Y-axis differential thrust command output section 20, and outputs a second Y-axis differential thrust command. Hereinafter, the second Y-axis differential thrust command is referred to as F2'.

Next, the output of the second Y-axis differential thrust command F2' by the feedforward section 10 will be described in more detail.

As shown in fig. 2, the feedforward section 10 includes an inertia function storage section 11 and a calculation section 12.

The inertia function storage unit 11 stores the inertia function calculated by the inertia function calculation unit 60.

The calculating section 12 calculates an inertia difference from the X-axis position indicated by the X-axis position command acquired by the X-axis position command acquiring section 81 and the inertia function stored in the inertia function storage section 11. The calculating unit 12 calculates a feedforward value of feedforward to the first Y-axis difference thrust command output by the Y-axis difference thrust command output unit 20 based on the calculated inertial difference and the Y-axis center of gravity position command acquired by the Y-axis center of gravity position command acquiring unit 82. More specifically, the calculating unit 12 calculates the inertia difference m1-m2 by substituting the X-axis position X indicated by the X-axis position command into the inertia function. The calculating unit 12 multiplies the calculated inertial difference m1-m2 by the second order derivative of the time of the Y-axis gravity center position command

[ number 7]

To calculate the feedforward value

[ number 8]

The feedforward section 10 subtracts the calculated feedforward value from the first Y-axis difference thrust command F2 output from the Y-axis difference thrust command output section 20

[ number 9]

To calculate a second Y-axis differential thrust command F2', and to output the second Y-axis differential thrust command F2'.

The thrust conversion unit 50 uses the first Y-axis thrust command F1 and the second Y-axis differential thrust command F2' to control the position of the stage 140. More specifically, the thrust conversion section 50 calculates a Y1-axis drive system thrust command F1 for indicating the thrust of the Y1-axis drive system 111 and a Y2-axis drive system thrust command F2 for indicating the thrust of the Y2-axis drive system 121 based on the second Y-axis difference thrust command F2' output by the feedforward section 10 and the first Y-axis gravity thrust command F1 output by the Y-axis gravity thrust command output section. The thrust conversion unit 50 outputs the calculated Y1-axis drive system thrust command f1 and Y2-axis drive system thrust command f2 to the frame mechanism 100. The thrust conversion unit 50 drives the Y1 axis drive system 111 using the Y1 axis drive system thrust command f1, and drives the Y2 axis drive system 121 using the Y2 axis drive system thrust command f2, thereby controlling the position of the stage 140.

The stage position control device 1 configured as described above controls the position of the stage 140 in the rack mechanism 100.

Next, control of the position of the stage 140 by the stage position control device 1 will be described with reference to the drawings.

Fig. 5 is a flowchart of stage position control processing according to embodiment 1. The stage position control process is an example of the process performed by the stage position control device 1 to control the position of the stage 140.

When the stage position control process starts, the Y1 axis position detecting unit 41 detects the Y1 axis position which is the driving position in the Y1 axis driving system 111, and the Y2 axis position detecting unit 42 detects the Y2 axis position which is the driving position in the Y2 axis driving system 121 (step S200).

When the Y1 axis position and the Y2 axis position are detected, the position conversion section 70 calculates a Y axis center of gravity position and a Y axis difference position from the Y1 axis position and the Y2 axis position (step S210).

When the Y-axis center of gravity position and the Y-axis difference position are calculated, the Y-axis center of gravity thrust command output unit 30 feeds back the Y-axis center of gravity position to output a first Y-axis center of gravity thrust command (step S220). The Y-axis difference thrust command output unit 20 feeds back the Y-axis difference position to output a first Y-axis difference thrust command (step S230).

When the first Y-axis differential thrust command is output, the feedforward section 10 feedforward the X-axis position command acquired by the X-axis position command acquisition section 81 and the Y-axis center of gravity position command acquired by the Y-axis center of gravity position command acquisition section 82 to the first Y-axis differential thrust command to output a second Y-axis differential thrust command (step S240).

When the second Y-axis differential thrust command is output, the thrust conversion section 50 calculates a Y1-axis drive system thrust command for indicating the thrust of the Y1-axis drive system 111 and a Y2-axis drive system thrust command for indicating the thrust of the Y2-axis drive system 121 based on the second Y-axis differential thrust command and the first Y-axis thrust command (step S250). The calculated Y1-axis drive system thrust command and Y2-axis drive system thrust command are output to the gantry mechanism 100 (step S260) to control the position of the stage 140.

When the process of step S260 ends, the stage position control device 1 again proceeds to the process of step S200. In this way, the loop processing including the processing from step S200 to step S260 is repeated.

Next, the stage 140 position control by the stage position control device 1 will be examined.

If the transformation matrix J is set to

[ number 10]

The transformation of the first differential of the time of the Y-axis center of gravity position Y1, i.e., the first differential of the time of the Y-axis center of gravity speed and the Y-axis difference position Y2, i.e., the first differential of the time of the Y-axis difference speed and the Y1-axis position Y1, i.e., the first differential of the time of the Y1-axis speed and the Y2-axis position Y2, i.e., the Y2-axis speed, is represented by the following (formula 1).

[ number 11]

The first Y-axis thrust command F1 and the first Y-axis differential thrust command F2 are expressed by the following expression (2), and the conversion of the Y1-axis drive system thrust commands F1 and Y2-axis drive system thrust commands F2 is expressed by the following expression (2).

[ number 12]

The equations of motion of the Y1 axis drive system 111 and the Y2 axis drive system 121 are expressed by the following (expression 3).

[ number 13]

When the motion equation is subjected to coordinate transformation using the transformation matrix J, the motion equation after coordinate transformation is expressed by the following (expression 4).

[ number 14]

The expansion 1 and expansion 2 of the transformed equation of motion are expressed by the following (equations 5) and (equation 6), respectively.

[ number 15]

In the case where m1 and m2 in the expansion 1, the expansion 2 are different from each other, the interference term 1

[ number 16]

Interference term 2

[ number 17]

Is not removed but remains.

In the case where the disturbance term 1 is not removed from the expansion 1 and in the case where the disturbance term 2 is not removed from the expansion 2, the difference between the driving speed of the first X-axis bearing portion 135 driven by the Y1-axis driving system 111 and the driving speed of the second X-axis bearing portion 136 driven by the Y2-axis driving system 121 cannot be suppressed. That is, the stage 140 moves in the yaw direction.

Further, if the interference term 2 is removed from the expansion 2, the interference term 1 naturally converges to 0. Therefore, by removing the disturbance term 2 from the expansion 2, the movement of the stage 140 in the yaw direction can be suppressed.

In the stage position control device 1, the feedforward section 10 calculates the disturbance term 2 based on the X-axis position command acquired by the X-axis position command acquisition section 81 and the Y-axis center of gravity position command acquired by the Y-axis center of gravity position command acquisition section 82

[ number 18]

The interference term 2 is taken as a feedforward value. The feedforward section 10 calculates a second Y-axis differential thrust command F2 'by subtracting the disturbance term 2, which is the calculated feedforward value, from the first Y-axis differential thrust command F2 output from the Y-axis differential thrust command output section 20, and outputs the second Y-axis differential thrust command F2'. Thus, the component of the disturbance term 2 is removed from the second Y-axis differential thrust command F2'.

The thrust conversion section 50 calculates a Y1-axis drive system thrust command F1 for indicating the thrust of the Y1-axis drive system 111 and a Y2-axis drive system thrust command F2 for indicating the thrust of the Y2-axis drive system 121 based on the first Y-axis gravity thrust command F1 and the second Y-axis difference thrust command F2' from which the component of the disturbance term 2 is removed, and outputs the Y1-axis drive system thrust command F1 and the Y2-axis drive system thrust command F2 to the frame mechanism 100.

Thus, the stage position control device 1 can suppress the occurrence of the movement of the stage 140 in the yaw direction itself at the time point when the movement of the stage 140 in the yaw direction does not occur.

(embodiment 2).

Next, a stage position control device according to embodiment 2, which is configured by changing a part of the stage position control device 1 according to embodiment 1, will be described.

The stage position control device actively removes the component of the disturbance term 1 from the first Y-axis thrust command F1 in addition to the component of the disturbance term 2 from the first Y-axis differential thrust command F2.

Fig. 6 is a block diagram showing the structure of stage position control device 1a according to embodiment 2. However, in fig. 6, as in the case of fig. 1, not all the components of the stage position control device 1a are illustrated. Hereinafter, the same components of the stage position control device 1a as those of the stage position control device 1 according to embodiment 1 are denoted by the same reference numerals, and detailed description thereof will be omitted, focusing on differences from the stage position control device 1.

As shown in fig. 6, the stage position control device 1a is configured by adding a feedback unit 90 to the stage position control device 1 according to embodiment 1 and changing the thrust conversion unit 50 to the thrust conversion unit 50 a.

The feedback unit 90 feeds back the X-axis position detected by the X-axis position detection unit 43 and the Y-axis difference position calculated by the position conversion unit 70 to the first Y-axis thrust command output from the Y-axis thrust command output unit 30, and outputs a second Y-axis thrust command. Hereinafter, the second Y-axis thrust command is referred to as F1'.

Next, the output of the second Y-axis thrust command F1' by the feedback unit 90 will be described in more detail.

As shown in fig. 6, the feedback unit 90 includes an inertia function storage unit 11 and a calculation unit 92.

The calculating section 92 calculates an inertia difference from the X-axis position detected by the X-axis position detecting section 43 and the inertia function stored in the inertia function storing section 11. The calculating unit 92 calculates a feedback value to be fed back to the first Y-axis thrust command output by the Y-axis thrust command output unit 30, based on the calculated inertial difference and the Y-axis difference position calculated by the position converting unit 70. More specifically, the calculating unit 92 calculates the inertia difference m1-m2 by substituting the X-axis position X detected by the X-axis position detecting unit into the inertia function, and multiplies the calculated inertia difference m1-m2 by the second order differential of the time of the Y-axis difference position

[ number 19]

To calculate the feedback value

[ number 20]

The feedback unit 90 subtracts the calculated feedback value from the first Y-axis thrust command F1 output from the Y-axis thrust command output unit 30

[ number 21]

To calculate a second Y-axis thrust command F1 'and output the second Y-axis thrust command F1'.

The thrust conversion section 50a calculates a Y1-axis drive system thrust command F1 for indicating the thrust of the Y1-axis drive system 111 and a Y2-axis drive system thrust command F2 for indicating the thrust of the Y2-axis drive system 121 based on the second Y-axis difference thrust command F2 'output by the feedforward section 10 and the second Y-axis gravity center thrust command F1' output by the feedback section 90. The thrust conversion section 50a outputs the calculated Y1-axis drive system thrust command f1 and Y2-axis drive system thrust command f2 to the frame mechanism 100, and drives the Y1-axis drive system 111 using the Y1-axis drive system thrust command f1 and drives the Y2-axis drive system 121 using the Y2-axis drive system thrust command f2, thereby controlling the position of the stage 140.

Next, the stage 140 position control by the stage position control device 1a having the above-described configuration will be examined.

In the stage position control device 1a, the feedback unit 90 calculates the disturbance term 1 based on the X-axis position detected by the X-axis position detecting unit 43 and the Y-axis difference position calculated by the position converting unit 70

[ number 22]

The interference term 1 is taken as a feedback value. The feedback unit 90 calculates a second Y-axis thrust command F1 'by subtracting the interference term 1, which is the calculated feedback value, from the first Y-axis thrust command F1 output from the Y-axis thrust command output unit 30, and outputs the second Y-axis thrust command F1'. Thus, the component of the disturbance term 2 is removed from the second Y-axis thrust command F1'.

The thrust conversion section 50a calculates a Y1-axis drive system thrust command F1 for indicating the thrust of the Y1-axis drive system 111 and a Y2-axis drive system thrust command F2 for indicating the thrust of the Y2-axis drive system 121 based on the second Y-axis difference thrust command F2 'from which the component of the disturbance term 2 is removed and the second Y-axis center of gravity thrust command F1' from which the component of the disturbance term 1 is removed, and outputs the Y1-axis drive system thrust commands F1 and Y2-axis drive system thrust commands F2 to the frame mechanism 100.

Thus, the stage position control device 1a can suppress the occurrence of the movement of the stage 140 in the yaw direction itself at the time point when the movement of the stage 140 in the yaw direction does not occur.

(supplement)

As described above, as an example of the technology of the present disclosure, embodiments 1 and 2 are described. However, the technology of the present disclosure is not limited to the embodiments, and may be applied to embodiments and modified examples in which modification, substitution, addition, omission, and the like are appropriately performed without departing from the spirit of the present disclosure.

For example, in embodiment 1, the stage position control device 1 is described as follows: the stage position control device 1 includes an inertia function calculation unit 60 that calculates an inertia function, and the inertia function storage unit 11 stores the inertia function calculated by the inertia function calculation unit. However, the stage position control device 1 may use an inertia function, and does not necessarily need to calculate the inertia function. The stage position control device 1 may have the following structure: the inertial function calculation unit 60 is not provided, and the inertial function storage unit 11 acquires and stores the inertial function calculated by the external device from the external device.

Industrial applicability

The photodetector according to the present disclosure can be widely used for a device or the like for controlling the position of a stage.

Description of the reference numerals

1. 1a: stage position control means; 10: a feed-forward section; 11: an inertia function storage unit; 12. 92: a calculation unit; 20: a Y-axis differential thrust command output unit; 21. 31: a position feedback unit; 22. 32: a speed feedback unit; 30: a Y-axis gravity center thrust command output unit; 41: a Y1 axis position detecting section; 42: a Y2 axis position detecting section; 43: an X-axis position detecting section; 50. 50a: a thrust conversion unit; 60: an inertia function calculation unit; 70: a position conversion unit; 81: an X-axis position instruction acquisition unit; 82: a Y-axis gravity center position instruction acquisition unit; 83: a phase delay compensation unit; 90: a feedback section; 100: a frame mechanism; 110: a Y1 axis; 111: a Y1 axis drive system; 120: a Y2 axis; 121: a Y2 axis drive system; 130: an X axis; 131: an X-axis driving system; 135: a first X-axis supporting part; 136: a second X-axis supporting part; 140: and a stage.

Claims

1. An object stage position control device for controlling the position of an object stage in a rack mechanism, the rack mechanism having:

the stage having a position determined based on a Y1 axis position which is a driving position in a Y1 axis driving system on a Y1 axis, a Y2 axis position which is a driving position in a Y2 axis driving system on a Y2 axis parallel to the Y1 axis, and an X axis position which is a driving position in an X axis driving system on an X axis perpendicular to the Y1 axis and the Y2 axis,

The stage position control device is provided with:

a Y-axis thrust command output unit that outputs a first Y-axis thrust command for indicating a thrust of a center of gravity that is a sum of a thrust of the Y1-axis drive system and a thrust of the Y2-axis drive system;

a Y-axis differential thrust command output unit that outputs a first Y-axis differential thrust command for instructing a differential thrust that is a difference between a thrust of the Y1-axis drive system and a thrust of the Y2-axis drive system;

a feedforward section that feedforward the first Y-axis differential thrust command with an X-axis position command for indicating the X-axis position and a Y-axis gravity center position command showing a relationship with a Y-axis gravity center position that is a sum of the Y1-axis position and the Y2-axis position, to output a second Y-axis differential thrust command; and

a thrust conversion unit for controlling the position of the stage by using the first Y-axis thrust command and the second Y-axis differential thrust command,

wherein the Y-axis thrust command output section outputs the first Y-axis thrust command by receiving, as a feedback value, a Y-axis thrust command representing a position of a center of gravity of the Y1-axis position and the Y2-axis position,

the Y-axis differential thrust command output section outputs the first Y-axis differential thrust command by receiving, as a feedback value, a Y-axis differential position indicating a differential position between the Y1-axis position and the Y2-axis position,

The inertial difference is the difference between the inertia of the Y1 axis drive system and the inertia of the Y2 axis drive system, the inertial function represents the relationship between the difference in inertia and the X axis position,

the feedforward section calculates an inertia difference from an inertia function and an X-axis position indicated by the X-axis position instruction,

the feedforward section calculates a feedforward value that is feedforward to the first Y-axis differential thrust command based on the Y-axis gravity center position command and the calculated inertial difference.

2. The stage position control device according to claim 1, wherein,

the feedforward section stores the inertial difference and the inertial function.

3. The stage position control device according to claim 1, further comprising:

a Y1 axis position detection unit that detects the Y1 axis position; and

and a Y2 axis position detection unit that detects the Y2 axis position.

4. The stage position control device according to any one of claims 1 to 3, wherein,

the thrust conversion section calculates a Y1-axis drive system thrust instruction for indicating a thrust of the Y1-axis drive system and a Y2-axis drive system thrust instruction for indicating a thrust of the Y2-axis drive system based on the first Y-axis gravity center thrust instruction and the second Y-axis difference thrust instruction, and drives the Y1-axis drive system using the Y1-axis drive system thrust instruction and drives the Y2-axis drive system using the Y2-axis drive system thrust instruction, thereby controlling a position of the stage.

5. The stage position control device according to claim 4, further comprising:

a feedback unit that calculates a feedback value to be fed back to the first Y-axis thrust command based on the Y-axis difference position and the inertia difference calculated based on the inertia function and the X-axis position detected by the X-axis position detecting unit for detecting the X-axis position, and feeds back the feedback value to the first Y-axis thrust command to output a second Y-axis thrust command,

the thrust conversion unit controls the position of the stage by using the second Y-axis thrust command.

6. The stage position control device according to claim 5, wherein,

the X-axis position detecting unit is further provided.

7. The stage position control device according to claim 5, wherein,

the thrust conversion section calculates a Y1-axis drive system thrust instruction for indicating a thrust of the Y1-axis drive system and a Y2-axis drive system thrust instruction for indicating a thrust of the Y2-axis drive system based on the second Y-axis gravity center thrust instruction and the second Y-axis difference thrust instruction, and drives the Y1-axis drive system using the Y1-axis drive system thrust instruction and drives the Y2-axis drive system using the Y2-axis drive system thrust instruction, thereby controlling a position of the stage.

8. The stage position control device according to claim 1, further comprising:

an inertia function calculating section that outputs a Y1-axis drive system thrust instruction for instructing a thrust of the Y1-axis drive system and a Y2-axis drive system thrust instruction for instructing a thrust of the Y2-axis drive system, and calculates an inertia function based on (a) the Y1-axis drive system thrust instruction and the Y2-axis drive system thrust instruction that are output when a position of the stage is determined according to a first X-axis position, (b) the Y1-axis position and the Y2-axis position when the position of the stage is determined according to the first X-axis position, (c) the Y1-axis drive system thrust instruction and the Y2-axis drive system thrust instruction that are output when the position of the stage is determined according to a second X-axis position, and (d) the Y1-axis position and the Y2-axis position when the position of the stage is determined according to the second X-axis position.

9. A stage position control method for controlling a position of a stage in a rack mechanism, the rack mechanism having:

In the stage position control method described above,

calculating a first Y-axis center-of-gravity thrust instruction for instructing a center-of-gravity thrust which is a sum of a thrust of the Y1-axis drive system and a thrust of the Y2-axis drive system, using a Y-axis center-of-gravity position representing a center-of-gravity position of the Y1-axis position and the Y2-axis position as a feedback value,

calculating a first Y-axis differential thrust command indicating a differential thrust between a thrust of the Y1-axis drive system and a thrust of the Y2-axis drive system using a Y-axis differential position indicating a differential position between the Y1-axis position and the Y2-axis position as a feedback value,

the inertial difference is calculated from the inertial function and the X-axis position indicated by the X-axis position command,

feeding forward the calculated inertial difference and a Y-axis centroid position command showing a relationship with a Y-axis centroid position that is a sum of the Y1-axis position and the Y2-axis position to the first Y-axis difference thrust command to calculate a second Y-axis difference thrust command,

using the first Y-axis thrust command and the second Y-axis differential thrust command to control the position of the stage,

the inertial difference is the difference between the inertia of the Y1 axis drive system and the inertia of the Y2 axis drive system,

An inertia function represents a relationship between the difference in inertia and the X-axis position.