KR102214590B1 - Control system for controlling fluid actuators - Google Patents

Abstract

The stage assembly 10 for positioning the workpiece 22 comprises a stage 14, a base 12, a fluid actuator assembly 24, and a control system 20. The fluid actuator assembly 24 moves the stage 14 along the movement axis 30 relative to the base 12. The fluid actuator assembly 24 comprises a piston housing 32 defining a piston chamber 34, a piston 36 positioned within the piston chamber 34 and moving relative to the piston chamber 34 along the piston axis 36A. , And a valve assembly 38 that controls the flow of the piston fluid into the piston chamber 34. The valve assembly 38 includes an inlet valve 38C having inlet valve characteristics. The control system 20 controls the valve assembly 38 to control the flow of the piston fluid into the piston chamber 34. The control system 20 can use the reverse of the inlet valve characteristics to control the valve assembly 38.

Description

Control system for controlling fluid actuators

Related application

This application claims priority to US Provisional Application No. 62/344,262, filed on June 1, 2016 and entitled "CONTROL SYSTEM FOR CONTROLLING A FLUID ACTUATOR". To the extent permitted, the contents of US Provisional Application No. 62/344,262 are incorporated herein by reference.

Exposure apparatus is typically used to transfer images from a mask onto a workpiece such as an LCD flat panel display or semiconductor wafer. Typical exposure devices include an illumination source, a mask stage assembly that holds and accurately positions the mask, a lens assembly, a workpiece stage assembly that holds and accurately positions the workpiece, and monitors the position and movement of the mask and workpiece. It includes a measuring system. There is a constant desire to reduce the cost of actuators used to position these components while accurately positioning the mask and/or workpiece.

The present invention relates to a stage assembly for positioning a workpiece along an axis of movement. In one embodiment, the stage assembly includes a stage, a base, a fluid actuator assembly, and a control system. The stage is coupled to and configured to hold the workpiece. The fluid actuator assembly is coupled to the stage and moves the stage along an axis of movement relative to the base. The fluid actuator assembly comprises a piston housing defining a piston chamber, a piston positioned within the piston chamber and moving relative to the piston chamber along the piston axis, and a valve that controls the flow of piston fluid into the piston chamber. May contain assembly. The valve assembly includes a first inlet valve having a first inlet valve characteristic. The control system controls the valve assembly to control the flow of the piston fluid into the piston chamber. In certain embodiments, the control system uses an inverse of the first inlet valve characteristic to control the valve assembly.

In one embodiment, the piston fluid is a gas, and the invention is described as a pneumatic control application. Alternatively, the piston fluid may be a liquid such as oil, and other formulations may be used.

As provided herein, the control system accurately controls the fluid pressure on each piece of the piston to generate the desired force to accurately drive and position the stage. In certain embodiments, the valve assembly is evaluated to identify nonlinearities inherent in the system. These nonlinearities include the valve characteristics of each valve. Non-exclusive examples of valve properties include (i) chamber volumes and fluid pressure changes, (ii) backlash and differential pressure dependence of proportional valves, and (iii) upstream and It includes fluid flow nonlinearity associated with downstream pressure. Nonlinearities can be identified by testing, modeling, or simulation. As a result, the valve characteristics are inverted and used in the control loop of the control system to linearize the system and accurately control the fluid actuator assembly.

Thus, the problem of system nonlinearity of valve dynamics associated with the application of fluid cylinders to fluid cylinder pressure and stage trajectory motion was solved by incorporating the identified system dynamics models into the control design.

In certain embodiments, the piston separates the piston chamber into a first chamber and a second chamber on opposite sides of the piston. The valve assembly also controls the flow of the piston fluid into and out of the first and second chambers.

In one embodiment, the valve assembly comprises: (i) a first inlet valve that controls the flow of the piston fluid into the first chamber; (ii) a first outlet valve that controls the flow of the piston fluid out of the first chamber; (iii) a second inlet valve that controls the flow of the piston fluid into the second chamber; And (iv) a second outlet valve that controls the flow of the piston fluid out of the second chamber. Further, the first outlet valve has a first outlet valve characteristic; The second inlet valve has a second inlet valve characteristic; The second outlet valve has a second outlet valve characteristic. In this embodiment, the control system also uses the reverse of the first outlet valve feature, the reverse of the second inlet valve feature, and the reverse of the second outlet valve feature to control the valve assembly.

As one non-exclusive example, the first inlet valve characteristic can be determined using experimental testing of the first inlet valve, and the first outlet valve characteristic can be determined using experimental testing of the first outlet valve. In addition, the second inlet valve characteristics may be determined using experimental testing of the second inlet valve, and the second outlet valve characteristics may be determined using experimental testing of the second outlet valve.

As provided herein, each valve characteristic includes (i) a relationship between the current command and the effective orifice area for the valve; (ii) the relationship between the current command for the valve and the valve position; And/or (iii) the relationship between the effective orifice area for the valve and the valve position.

The present invention also relates to an exposure apparatus, and a process for manufacturing a device comprising providing a substrate and forming an image on the substrate with the exposure apparatus.

The invention also relates to a method for positioning a workpiece along an axis of movement. In one embodiment, the method comprises the steps of: (i) providing a base; (ii) coupling the work piece to the stage; (iii) a piston housing defining a piston chamber, a piston positioned within the piston chamber and moving relative to the piston chamber along the piston axis, and a valve assembly that controls the flow of the piston fluid into the piston chamber, the valve assembly comprising: a first A fluid actuator assembly comprising the valve assembly, comprising a first inlet valve having inlet valve characteristics, moving the stage along an axis of movement; And, (iv) controlling the valve assembly with a control system to control the flow of the piston fluid into the piston chamber, wherein the control system uses an inverse of the first inlet valve characteristic to control the valve assembly. It includes controlling.

The novel features of this invention, and the invention itself, will be best understood from the accompanying drawings, taken in conjunction with the accompanying description, where like reference numerals indicate like parts, both in terms of its structure and its operation. will be.
1 is a simplified side view of a stage assembly having features of the present invention.
2A is a control block diagram illustrating a method for controlling a fluid actuator assembly.
2B is a control block diagram of the chamber controller.
3 is a simplified illustration of one of the piston chambers and one of the valve sub-assemblies with features of the present invention.
4 is a simplified illustration of a pipe including an orifice.
5A-5C are simplified cutaway views of one non-exclusive example of a valve.
6A is a graph showing valve characteristics of the valves of FIGS. 5A to 5C.
6B is a graph showing inverted valve characteristics of the valves of FIGS. 5A to 5C.
7A-7D are simplified illustrations of different types of valves at various valve positions.
7E is a simplified illustration of the valve body and outlet in a partially open position.
8A is a graph showing the calculated, normalized effective orifice area versus normalized spool position for the valve shown in FIGS. 7A-7D.
8B is a graph plotting spool position versus normalized effective orifice area.
9A is a graph showing test results of a spool valve.
9B is a graph showing simulated results of a spool valve.
10A shows two valve characteristics of a spool valve.
10B shows two inverted valve characteristics.
11 is a schematic illustration of an exposure apparatus having features of the present invention.
12 is a flow chart outlining a process for manufacturing a device according to the present invention.

Embodiments of the present invention are described herein in the context of a stage assembly comprising a stage, and a control system that controls a fluid actuator assembly that moves the stage. Those of ordinary skill in the art (hereinafter referred to as'common technician') will recognize that the following detailed description of the present invention is illustrative only and is not intended to be limiting in any way. . Other embodiments of the present invention will readily suggest themselves to those skilled in the art who have the benefit of this disclosure. Reference will now be made in detail to implementations of the invention as illustrated in the accompanying drawings. The same or similar reference indicators will be used throughout the drawings and in the detailed description below to indicate the same or similar parts.

For the sake of clarity, not all of the general features of implementations described herein are shown and described. Of course, in the deployment of these actual implementations, numerous implementation-specific decisions must be made to achieve the specific goals of the developer, such as compliance with application-related and business-related constraints, and these specific goals will vary from implementation to implementation and from developer to developer. You will understand Moreover, while this development effort may be complex and time consuming, it will be understood that it will nevertheless be a routine practice of engineering for those skilled in the art having the benefit of this disclosure.

1 shows a stage assembly 10 comprising a base 12, a stage 14, a stage mover assembly 16, a measurement system 18, and a control system 20 (shown as a box). It is a simplified city. The design of each of these components can be varied to suit the design requirements of the stage assembly 10. The stage assembly 10 is particularly useful for accurately positioning the workpiece 22 (also sometimes referred to as a device) during the manufacturing and/or inspection process.

As an overview, in certain embodiments, the stage mover assembly 16 includes a fluid actuator assembly 24 that is relatively inexpensive to manufacture. Also, after the unique calibration and identification process provided herein, the control system 20 can control the fluid actuator assembly 24 to accurately position the workpiece 22. As a result, the stage assembly 10 is less expensive to manufacture, and the workpiece 22 is still positioned to the desired level of accuracy.

The type of workpiece 22 positioned and moved by the stage assembly 10 can be varied. For example, the workpiece 22 may be an LCD flat panel display, a semiconductor wafer, or a mask, and the stage assembly 10 may be used as part of an exposure apparatus. Alternatively, for example, the stage assembly 10 may be used to move other types of devices during manufacturing and/or inspection, to move the device under an electron microscope (not shown), or to perform a precision measurement operation (not shown). It can be used to move the device while.

Some of the drawings provided herein include a directional system designating the X, Y, and Z axes. It should be understood that the orientation system is for reference only and can be varied. The X axis can be switched to the Y axis and/or the stage assembly 10 can be rotated. Also, these axes may alternatively be referred to as a first, second, or third axis.

The base 12 supports the stage 14. In the non-exclusive embodiment illustrated in FIG. 1, the base 12 is rigid and generally rectangular plate-shaped. Also, the base 12 can be firmly fixed to the base mount 26. Alternatively, the base 12 can be fixed to another structure.

The stage 14 holds the workpiece 22. In one embodiment, the stage is precisely moved by the stage mover assembly 16 relative to the base 12 in order to precisely position the stage 14 and the workpiece 22. In FIG. 1, the stage 14 is generally rectangular in shape and includes a device holder (not shown) for holding the workpiece 22. The device holder may be a vacuum chuck, an electrostatic chuck, or some other type of clamp that directly couples the workpiece 22 to the stage 14. In the embodiments illustrated herein, the stage assembly 10 includes a single stage 14 that holds the workpiece 22. Alternatively, for example, the stage assembly 10 can be designed to include multiple stages that are independently moved and positioned. As an example, the stage assembly 10 holds a coarse stage (not shown), which is moved by the stage mover assembly 16, and the workpiece 22, and coarse with a precision stage mover assembly (not shown). It may include a fine stage (not shown) that is moved relative to the stage.

Additionally, in FIG. 1, stage 14 can be supported against base 12 with a bearing assembly 28 that allows movement of stage 14 relative to base 12. For example, the bearing assembly 28 may be a roller bearing, a fluid bearing, a linear bearing, or other type of bearing.

The measurement system 18 monitors the movement and/or position of the stage 14 relative to a reference such as an optical assembly (not shown in FIG. 1) or a base 12, and transmits measurement information to the control system 20. To provide. With this information, the stage mover assembly 16 can be controlled with the control system 20 to precisely position the stage 14. The design of the measurement system 18 can be varied depending on the movement requirements of the stage 14. In one embodiment, the measurement system 18 may comprise a linear encoder that monitors the movement of the stage 14 along the Y axis. Alternatively, the measurement system 18 may include an interferometer, or other type of motion or position sensor.

The stage mover assembly 16 is controlled by the control system 20 to move the stage 14 relative to the base 12. In FIG. 1, the stage mover assembly 16 includes a fluid actuator assembly 24 that moves the stage 14 along a single axis of movement 30, eg, the Y axis.

The design of the fluid actuator assembly 24 can be varied according to the teachings provided herein. In one, non-exclusive embodiment, the fluid actuator assembly 24 comprises (i) a piston housing 32 defining a piston chamber 34, and a piston 36 positioned in the piston chamber 34. Piston assembly 31; And (ii) a valve assembly 38 that controls the flow of the piston fluid 40 (shown as small circles) into and out of the piston chamber 34. For example, the piston fluid 40 can be air or another type of fluid. The design of these components may vary in accordance with the teachings provided herein.

In one embodiment, the piston housing 32 defines a rigid, generally straight, cylindrical piston chamber 34. In this embodiment, the piston housing 32 comprises a tube-shaped side wall 32A; A disk-shaped first end wall 32B, and a disk-shaped second end wall 32C spaced apart from the first end wall 32B. One or both end walls 32B, 32C may comprise a wall opening 32D for receiving a portion of the piston 36.

The piston housing 32 can be firmly fixed to the piston mount 42. Alternatively, the piston housing 32 can be fixed to another structure such as the base 12. Also alternatively, since the piston housing 32 receives the reaction forces generated by the stage mover assembly 16, the piston housing 32 is affected by the reaction forces from the stage mover assembly 16 on the position of other structures. Can be coupled to a reaction assembly that offsets, reduces and minimizes For example, the piston housing 32 is a large counter held on a countermass support (not shown) with a reaction bearing (not shown) that allows movement of the piston housing 32 along the moving axis 30. It can be coupled to a mass (not shown).

The piston 36 is positioned within the piston chamber 34 and moves relative to the piston chamber 34 along the piston axis 36A. In certain embodiments, the piston shaft 36A is coaxial with the moving shaft 30. In the non-exclusive embodiment shown in FIG. 1, the piston 36 defines (i) a rigid, disk-shaped piston body 36B, (ii) the area between the piston body 36B and the piston housing 32. Sealing piston seal (36C), (iii) attached to the piston body (36B) and cantilevered away from the piston body (36B) and extends through the wall opening (32D) at the first end wall (32B) And (iv) a first beam of rigidity (36D) attached to the piston body (36B) and cantilever supported away from the piston body (36B) and extending through the wall opening (32D) in the second end wall (32C). A rigid second beam 36E, (iv) a first beam seal (not shown) sealing the area between the first beam 36D and the first end wall 32B, and (v) a second beam ( 36E) and a second beam seal (not shown) sealing the area between the second end wall 32C.

In this embodiment, the second beam 36E is also firmly fixed to the stage 14. Stated another way, the second beam 36E extends between the piston body 36B and the stage 14 so that movement of the piston body 36B results in movement of the stage 14. Additionally, in this embodiment, the first beam 36D is included so that the effective area of each piece of the piston body 36B is the same for ease of calculation. Alternatively, for example, the fluid actuator assembly 24 can be designed without the first beam 36D. In this alternative design, the effective area on the left side of the piston body 36B is larger than the effective area on the right side of the piston body 36B.

The piston body 36B connects the piston chamber 34 to a first chamber 34A (also referred to as “chamber 1”) and a second chamber 34B (also referred to as “chamber 2” on opposite sides of the piston body 36B). (Referred to as "). In Fig. 1, the first chamber 34A is on the left side of the piston body 36B, and the second chamber 34B is on the right side of the piston body 36B. Additionally, the first chamber 34A has a chamber 1 effective piston area A ₁ and is filled with a piston fluid 40 at a first pressure P ₁ at a first temperature T ₁ , Has a first volume (V ₁ ). Similarly, the second chamber 34B has a chamber 2 effective piston area A ₂ , is filled with a piston fluid 40 at a second pressure P ₂ at a second temperature T ₂ , and a second It has a volume (V ₂ ). In the non-exclusive example illustrated in FIG. 1, the fluid actuator assembly 24 is designed such that the chamber 1 effective piston area A ₁ is approximately equal to the chamber 2 effective piston area A ₂ .

The first pressure P ₁ of the piston fluid 40 in the first chamber 34A generates a first force F ₁ against the piston body 36B, and the piston fluid 40 in the second chamber 34B A second pressure P _{2 of} ) generates a second force F ₂ against the piston body 36B. The total force (F) 44 (shown by the arrows) generated by the fluid actuator assembly 24 is equal to the first force (F ₁ ) minus the second force (F ₂ ) (F = Fi-F ₂ ).

In the non-exclusive design illustrated in FIG. 1, when the first pressure (P ₁ ) is greater than the second pressure (P ₂ ), the first force (F ₁ ) is greater than the second force (F ₂ ) , The total force F is a positive value, pushing the piston body 36B and the stage 14 from left to right. On the other hand, when the first pressure (P ₁ ) is less than the second pressure (P ₂ ), the first force (F ₁ ) is smaller than the second force (F ₂ ), and the total force (F) is negative Value, and pushes the piston body 36B and stage 14 from right to left.

In one embodiment, the valve assembly 38 is controlled by the control system 20 to accurately and individually control the pressure in each chamber 34A, 34B. In one non-exclusive embodiment, the valve assembly 38 (i) controls the flow of the piston fluid 40 into and out of the first chamber 34A to accurately control the first pressure P ₁ . A first valve sub-assembly 38A that is controlled to operate; And (ii) a second valve sub-assembly 38B controlled to control the flow of the piston fluid 40 into and out of the second chamber 34B to accurately control the second pressure P ₂ . Include. In this embodiment, the first valve sub-assembly 38A is a first inlet valve 38C controlled to control the flow of the piston fluid 40 into the first chamber 34A, and the first chamber 34A. ) And a first outlet valve 38D that is controlled to control the flow of the piston fluid 40 out. Similarly, the second valve sub-assembly 38B has a second inlet valve 38E controlled to control the flow of the piston fluid 40 into the second chamber 34B, and out of the second chamber 34B. It comprises a second outlet valve (38F) that is controlled to control the flow of the piston fluid (40).

In this embodiment, the fluid actuator assembly 24 can include one or more fluid pressure sources 46 (two shown) that provide pressurized piston fluid 40 to the inlet valves 38C, 38E. have. In addition, each of the fluid pressure sources 46 is delivered to the fluid tank 46A, the compressor 46B generating the pressurized piston fluid 40 in the tank 46A, and the inlet valves 38C, 38E. It may comprise a pressure regulator (46C) to control the pressure of the piston fluid (40). Additionally, the outlet valves 38D, 38F can be discharged to the atmosphere or to a low pressure region such as a vacuum chamber.

In certain embodiments, each of the valves 38C, 38D, 38E, 38F includes one or more valve characteristics that affect the control of these valves 38C, 38D, 38E, 38F. For example, (i) first inlet valve 38C has one or more first inlet valve characteristics; (ii) the first outlet valve 38D has one or more first outlet valve characteristics; (iii) the second inlet valve 38E has one or more second inlet valve characteristics; And/or (iv) the second outlet valve 38F has one or more second outlet valve characteristics. In one embodiment, each valve 38C, 38D, 38E, 38F is individually tested to determine individual valve characteristics of each valve 38C, 38D, 38E, 38F. With this design, the individual valve characteristics of each valve 38C, 38D, 38E, 38F are used to control each valve 38C, 38D, 38E, 38F. Alternatively, if each valve 38C, 38D, 38E, 38F is similar and has similar valve characteristics, one of the valves 38C, 38D, 38E, 38F can be tested and the valve of that valve Properties can be used to control all of the valves 38C, 38D, 38E, 38F.

The types of valves 38C, 38D, 38E, 38F can be varied. As non-exclusive examples, each valve 38C, 38D, 38E, 38F can be a proportional control valve such as a poppet ("mushroom") type valve or a spool-type valve.

The type of valve characteristics will vary depending on the type of valve 38C, 38D, 38E, 38F used. Non-exclusive types of valves 38C, 38D, 38E, 38F and a couple of non-exclusive examples of valve characteristics are described in detail below. It should be noted that the valves 38C, 38D, 38E, 38F may be different from the examples provided herein, and valve characteristics may be different from the examples provided herein.

As provided herein, for each valve 38C, 38D, 38E, 38F, its corresponding valve characteristic(s) can be determined through experimental testing, through simulation, or a combination of both.

The control system 20 controls the valve assembly 38 to control the flow of the piston fluid 40 into and out of each chamber 34A, 34B. By selectively controlling the flow of the piston fluid 40 into and out of each chamber 34A, 34B, the valve assembly 38 allows the piston body 36B to accurately move the piston body 36B and stage 14. It can be controlled to generate a controllable force 44 ("F") for.

The control system 20 is electrically connected to the valve assembly 38 and controls the current to the valve assembly 38 to precisely position the stage 14 and the workpiece 22. In one embodiment, the control system 20 is configured to: (i) constantly determine the position of the stage ("x"); And (ii) use the information from the measurement system 18 to send a current to the valve assembly 38 to position the stage 14. The control system 20 may include one or more processors 20A and electronic data storage 20B. Control system 20 uses one or more algorithms to perform the steps provided herein.

In certain embodiments, the control system 20 includes the first valves 38C, for controlling the first pressure P ₁ in the first chamber 34A to generate the desired first force F ₁ . Each of 38D) is controlled individually. Similarly, the control system 20 is to control the second pressure (P ₂ ) in the second chamber (34B) to generate the desired second force (F ₂ ) of the second valves (38E, 38F). Each is controlled individually. Thus, by controlling the valves 38C, 38D, 38E, 38F, the control system 20 controls the fluid actuator assembly 24 to generate the desired total force (F) 44 against the stage 14. can do.

In certain embodiments, in the event that the control system 20 determines that it is necessary to add the piston fluid 40 to the first chamber 34A, the control system 20 is configured to add the piston fluid 40. Control is made so that the first inlet valve 38C is opened and the first outlet valve 38D is closed in an appropriate amount. In addition, in the event that the control system 20 determines that it is necessary to remove the piston fluid 40 from the first chamber 34A, the control system 20 is in an appropriate amount to discharge the piston fluid 40. Control is made so that the first outlet valve 38D is opened and the first inlet valve 38C is closed. In this example, one of the first valves 38C, 38D is controlled to close at any given time. Alternatively, the control system 20 can control both first valves 38C, 38D to open while adding and/or removing the piston fluid 40 from the first chamber 34A.

Similarly, if the control system 20 determines that it is necessary to add the piston fluid 40 to the second chamber 34B, the control system 20 will do so in an appropriate amount to add the piston fluid 40. Control is made so that the second inlet valve 38E is opened and the second outlet valve 38F is closed. In addition, in the event that the control system 20 determines that it is necessary to remove the piston fluid 40 from the second chamber 34B, the control system 20 is in an appropriate amount to discharge the piston fluid 40. Control is made so that the second outlet valve 38F is opened and the second inlet valve 38E is closed. In this example, one of the second valves 38E, 38F is controlled to close at any given time. Alternatively, the control system 20 can control the opening of both second valves 38E, 38F while adding and/or removing the piston fluid 40 from the second chamber 34B.

It takes precise fluid pressure control of the two chambers 34A, 34B to generate the desired force 44 to drive the stage 14. In order to accurately control the fluid actuator assembly 24, (i) chamber volumes and fluid pressure changes, (ii) backlash and differential pressure dependence of proportional control valves 38C, 38D, 38E, 38F, and (iii) ) It is important to determine the nonlinearities inherent in the system, such as fluid flow nonlinearities associated with upstream and downstream pressures. Through experimental testing and/or modeling, these nonlinearities can be identified and corrected by the control system 20.

For example, the control system 20 may (i) reverse the first inlet valve characteristic to control the first inlet valve 38C; (ii) reverse the first outlet valve characteristic to control the first outlet valve 38D; (iii) reverse the second inlet valve characteristic to control the second inlet valve 38E; And (iv) the reverse of the second outlet valve characteristic can be used to control the second outlet valve 38F. The control system 20 uses the inverse of each valve characteristic, and each valve 38C, 38D, 38E, 38F can be controlled with improved accuracy.

2A is a control block diagram 220 illustrating one non-exclusive example of a method for controlling the fluid actuator assembly 24 to accurately position the stage 14. More specifically, the control block diagram 220 shows one non-exclusive way to direct current to the valve assembly 38 to control the piston assembly 31 to precisely position the stage 14. In the control block diagram 220, the stage 14 measures (e.g., along the measurement axis 30 (shown in FIG. 1)) as measured by the measurement system 18 (shown in FIG. 1). Has an instantaneous stage position ("x").

") , 요망되는 가속도 ("

"), 및 스테이지 저크 (jerk) 레퍼런스 ("

") 를 제공하는 스테이지 레퍼런스 블록 (260); (ii) 스테이지 피드백 ("FB") 제어기 (262); (iii) 스테이지 피드포워드 ("FF") 제어기 (264); (iv) 피드백 포스 커맨드 (force command) 를 피드백 압력 커맨드로 변환하는 피드백 컨버터 (converter) (266); (v) 피드포워드 포스 커맨드를 피드포워드 압력 커맨드로 변환하는 피드포워드 컨버터 (268); (vi) 제 1 챔버 제어기 (270); (vii) 제 2 챔버 제어기 (272); 및 (viii) 스테이지 (14) 의 측정된 포지션 ("x") 에 기초하여 제 1 챔버의 현재의 제 1 챔버 체적 ("V₁") 및 제 1 체적 변화율 ("

") 을 추정하고, 스테이지 (14) 의 측정된 포지션에 기초하여 제 2 챔버의 현재의 제 2 챔버 체적 ("V₂") 및 제 2 체적 변화율 ("

") 을 추정하는 챔버 체적 추정기 (278) 를 포함한다.In this embodiment, the control block diagram 220 shows (i) a stage of stage 14 (eg, along the measurement axis 30 (shown in FIG. 1)), a desired reference position or trajectory (“x _d "), desired speed ("

"), desired acceleration ("

"), and stage jerk reference ("

A stage reference block 260 providing "); (ii) a stage feedback ("FB") controller 262; (iii) a stage feedforward ("FF") controller 264; (iv) a feedback force command ( a feedback converter 266 for converting the force command to a feedback pressure command; (v) a feedforward converter 268 for converting a feedforward force command to a feedforward pressure command; (vi) a first chamber controller 270 ); (vii) the second chamber controller 272; and (viii) the current first chamber volume (“V ₁ ”) of the first chamber based on the measured position (“x”) of the stage 14 and First volumetric rate of change ("

") and based on the measured position of the stage 14, the current second chamber volume ("V ₂ ") and the second volume change rate ("

And a chamber volume estimator 278 that estimates ").

It should be noted that some of the blocks of control block diagram 220 of FIG. 2A are optional and/or control block diagram 220 may include additional control blocks. For example, the control block diagram 220 can be designed without a stage feedforward controller 264 loop. Additionally, or alternatively, the control block diagram 220 can be designed to include an iterative learning loop (not shown).

") , 스테이지 가속도 레퍼런스 ("

"), 및 스테이지 저크 레퍼런스 ("

") 는 시스템 시간 지연, 및 궤적과 같은 것들에 대해 보정하기 위해 필요한 포스 커맨드를 나타내는 스테이지, 피드포워드 포스 커맨드 ("F_ff") 를 생성하는 스테이지 피드포워드 제어기 (264) 에 공급된다.In the control block diagram 220, moving from left to right, the stage desired reference 260 to generate a stage following error ("e") indicating an error between the desired position of stage 14 and the measured position. ) The position or trajectory ("x _d ") is compared against the stage measured position ("x"). Next, the stage following error ("e") is a stage representing the force command required to move the stage 14 from the measured position to the reference position, a stage feedback controller that generates a feedback force command ("F _fb ") 262. At the same time, the desired reference position ("x _d "), the stage speed reference ("

"), stage acceleration reference ("

"), and stage jerk reference ("

") is supplied to the stage feedforward controller 264 which generates a feedforward force command ("F _ff "), a stage representing the force command required to correct for things like system time delay, and trajectory.

"), 및 제 2 챔버에 대한 제 2 피드포워드 압력 변화율 커맨드 ("

") 로 변환한다.Next, in this embodiment, the stage, the feedback force command ("F _fb ") and the feedforward force command ("F _ff ") are combined so that the combined force command supplied to the feedback converter 266 ("F _cmd "), and this feedback converter 266 sends the combined force command to a first feedback pressure command for the first chamber ("P1 _fb " or "P _1,cmd "), and a second for the second chamber. It converts to a feedback pressure command ("P2 _fb " or "P _2,cmd "). Similarly, a stage, a feedforward force command ("F _ff ") is supplied to a feedforward converter 268, which feeds a feedforward force command to the first feedforward pressure change rate for the first chamber. Command ("

"), and the second feedforward pressure rate of change command for the second chamber ("

Convert to ").

"), 제 1 측정된 압력 ("P₁"), 제 1 챔버 체적 ("V₁"), 및 제 1 체적 변화율 ("

") 을 이용한다. 유사하게, 제 2 챔버 제어기 (272) 는 제 2 밸브 서브어셈블리에 보내지는 제 2 밸브 서브어셈블리 전류 커맨드 ("u₂") 를 결정하기 위해 제 2 피드백 압력 커맨드 ("P_2,cmd"), 제 2 피드포워드 압력 커맨드 ("

"), 제 2 측정된 압력 ("P₂"), 제 2 챔버 체적 ("V₂"), 및 제 2 체적 변화율 ("

") 을 이용한다. 밸브 어셈블리 (38) 에 대한 전류는 피스톤 어셈블리 (31) 에 대한 피스톤 유체를 제어하고 스테이지 (14) 에 대한 포스 ("F") 를 발생시킨다.Subsequently, the first chamber controller 270 performs a first feedback pressure command ("P _1,cmd ") to determine the first valve subassembly current command ("u ₁ ") sent to the first valve subassembly. First feedforward pressure command ("

"), the first measured pressure ("P ₁ "), the first chamber volume ("V ₁ "), and the first volume rate of change ("

Similarly, the second chamber controller 272 uses a second feedback pressure command ("P ₂ ") to determine the second valve subassembly current command ("u ₂ ") sent to the second valve subassembly. _,cmd "), second feedforward pressure command ("

"), the second measured pressure ("P ₂ "), the second chamber volume ("V ₂ "), and the second volume change rate ("

The current to the valve assembly 38 controls the piston fluid to the piston assembly 31 and generates a force ("F") against the stage 14.

As provided herein, chamber controllers 270, 272 use the inverse of valve characteristics to accurately determine the respective current commands required to accurately control the pressure in the two chambers. This process is described in more detail below with reference to FIG. 2B.

It should be noted that, in embodiments, one of the valves of each valve subassembly closes at any given time, and all that is required for each valve subassembly is a single current command. Alternatively, if both of the valves of each valve subassembly can be opened at any given time, the chamber controllers 270, 272 will need to be designed to provide separate current commands for each valve. .

A number of equations are useful to understand the forces generated by the stage mover assembly 16 and to understand the control of the stage mover assembly 16 by the control system 20. As provided above, the total force generated by the stage mover assembly 16 is provided as follows:

식 1

Equation 1

As provided above, F is the total force; F ₁ is the force generated by the first chamber; F ₂ is the force generated by the second chamber.

Equation 1 can be rewritten as:

식 2

Equation 2

As provided above, P ₁ is the first chamber pressure in the first chamber; A ₁ is the effective piston area for the first chamber; P ₂ is the second chamber pressure in the second chamber 34B; And, A ₂ is an effective piston area for the second chamber 34B.

Also, the force on the stage can be expressed as:

식 3

Equation 3

는 스테이지의 질량의 가속도이고,

는 스테이지의 속도이다. In Equation 3 and elsewhere, M is the mass of the stage (including the workpiece), C is the damping factor,

Is the acceleration of the mass of the stage,

Is the speed of the stage.

The gas equation can be expressed as:

식 4

Equation 4

In equation 4 and elsewhere, i is each chamber (either the first chamber (“1”) or the second chamber (“2”)); P _i is the pressure in each chamber; V _i is the volume in each chamber; R is a gas constant; m _i is the gas mass in each chamber; And, T _i is the temperature in each chamber.

Equation 4 can be rewritten as:

식 5

Equation 5

는 각 챔버에서의 압력 변화율이고;

는 각 챔버에서의 체적 변화율이며,

는 각 챔버에서의 질량 유량 (mass flow rate) 이다.Equation 5 and elsewhere,

Is the rate of pressure change in each chamber;

Is the rate of volume change in each chamber,

Is the mass flow rate in each chamber.

Equation 5 can be rewritten as the chamber pressure modeling as follows:

식 6

Equation 6

Also, Equation 5 can be rewritten as the chamber mass flow control as follows:

식 7

Equation 7

The first volume V ₁ of the first chamber 34A can be written as a function of the stage position as follows:

식 8

Equation 8

Similarly, the second volume V ₂ of the second chamber 34B can be written as a function of the stage position as follows:

식 9

Equation 9

는 제 1 챔버의 데드 렝스 (dead length) 이고;

는 제 2 챔버의 데드 렝스이다.In equations 8 and 9, and elsewhere, A ₁ is the effective piston area of the first chamber; A ₂ is the effective piston area of the second chamber; x is the current position of the stage;

Is the dead length of the first chamber;

Is the dead length of the second chamber.

Equation 8 can be rewritten as:

식 10

Equation 10

Similarly, Equation 9 can be rewritten as:

식 11

Equation 11

은 제 1 챔버에서의 체적 변화율이고,

는 제 2 챔버에서의 체적 변화율이다.In these equations and elsewhere,

Is the rate of volume change in the first chamber,

Is the rate of volume change in the second chamber.

The chamber pressure control of each chamber 34A, 34B can be expressed as follows:

식 12

Equation 12

식 13

Equation 13

는 스테이지 가속도 레퍼런스이고;

는 스테이지 속도 레퍼런스이며;

는 스테이지 저크 레퍼런스이고, x_d 는 레퍼런스 포지션이고; C 는 스테이지 및 액추에이터 시스템의 댐핑 비율이고; C_fb(s) 는 스테이지 피드백 제어 필터이고; x 는 스테이지의 현재 측정된 포지션이고; P_1,cmd 는 제 1 챔버에 대한 압력 커맨드이고; 그리고, P_2,cmd 는 제 2 챔버에 대한 압력 커맨드이다.In Equations 12 and 13, and elsewhere, F _cmd is a force command; F _feedforward is a feedforward force command; F _feedback is a feedback force command;

Is the stage acceleration reference;

Is the stage speed reference;

Is the stage jerk reference, x _d is the reference position; C is the damping ratio of the stage and actuator system; C _fb (s) is a stage feedback control filter; x is the current measured position of the stage; P _1,cmd is the pressure command for the first chamber; And, P _2,cmd is a pressure command for the second chamber.

Equations 12 and 13 can be rewritten as:

및 식 14

And Equation 14

식 15

Equation 15

In Equations 14 and 15, and elsewhere, F _O is an offset force command; r is the distribution ratio between the first chamber and the second chamber. In certain embodiments, r has a value greater than 0 but less than 1 (0<r<1) and nominal r = 0.5.

Equations 14 and 15 can be written as:

및 식 16

And Equation 16

식 17

Equation 17

Chamber pressure control can be expressed as:

식 18

Equation 18

Also, Equation 18 can be expressed as:

및 식 19

And Equation 19

식 20

Equation 20

Similar to Equation 7, the chamber mass flow control can be expressed as:

식 21

Equation 21

는 제 1 챔버 및 제 2 챔버 중 하나에 대한 질량 유량 커맨드이다.Equation 21, and elsewhere,

Is the mass flow command for one of the first chamber and the second chamber.

") 을 생성한다. 압력 대 질량 유동 컨버터 (292) 는 압력 변화율 커맨드 ("

"), 챔버 압력 ("P_i"), 현재 챔버 체적 ("V_i") 및 체적 변화율 ("

") 을 수신하고, 유입 밸브에 대한 질량 유량 커맨드 ("

") 및 유출 밸브에 대한 질량 유량 커맨드 ("

") 를 생성한다. 압력 대 질량 유동 컨버터 (292) 는 본원에서 제공된 식 21 및 식 22 를 이용할 수 있다.2B is a control block diagram illustrating how one of the chamber controllers 270, 272 (shown in FIG. 2A) may be configured. In this embodiment, the chamber controller includes (i) a pressure feedback controller 290; (ii) pressure to mass flow converter 292; (iii) inlet mass flow to orifice area converter 294; (iv) effluent mass flow to orifice area converter 296; (v) inlet orifice area to current converter 297; And (vi) an outflow orifice area to current converter 298. In this embodiment, the pressure feedback controller 290 receives the pressure error (P _i,err ) for each chamber, and the ratio of pressure change feedback ("

The pressure to mass flow converter 292 generates a pressure rate of change command ("

"), chamber pressure ("P _i "), current chamber volume ("V _i ") and volume change rate ("

") and the mass flow command for the inlet valve ("

") and mass flow command for the outlet valve ("

"). The pressure to mass flow converter 292 can use Equations 21 and 22 provided herein.

") 및 챔버 압력 ("P_i") 을 수신하고, 유입 밸브에 대한 유입 오리피스 면적 커맨드 ("

") 를 생성한다. 유입 질량 유동 대 오리피스 면적 컨버터 (294) 는 본원에서 제공된 식 24 를 이용할 수 있다. 다소 유사하게, 유출 질량 유동 대 오리피스 면적 컨버터 (296) 는 질량 유량 커맨드 ("

") 및 챔버 압력 ("P_i") 을 수신하고, 유출 밸브에 대한 유출 오리피스 면적 커맨드 ("

") 를 생성한다. 유출 질량 유동 대 오리피스 면적 컨버터 (296) 는 본원에서 제공된 식 25 를 이용할 수 있다.Inlet mass flow to orifice area converter 294 is the mass flow command ("

") and chamber pressure ("P _i "), and the inlet orifice area command for the inlet valve ("

The inlet mass flow to orifice area converter 294 can use Equation 24 provided herein. Somewhat similarly, the outflow mass flow to orifice area converter 296 can use the mass flow command ("

") and chamber pressure ("P _i "), and the outlet orifice area command ("

The output mass flow to orifice area converter 296 can use Equation 25 provided herein.

") 를 생성하기 위해 유입 오리피스 면적 커맨드 ("

") 를 이용한다. 유입 오리피스 면적 대 전류 컨버터 (297) 는 본원에서 제공된 식 27 을 이용할 수 있다. 유사하게, 유출 오리피스 면적 대 전류 컨버터 (298) 는 유출 밸브에 대한 유출 전류 커맨드 ("

") 를 생성하기 위해 유출 오리피스 면적 커맨드 ("

") 를 이용한다. 유출 오리피스 면적 대 전류 컨버터 (298) 는 본원에서 제공된 식 28 을 이용할 수 있다.Next, the inlet orifice area to current converter 297 determines the inrush current command for the inlet valve ("

") to generate the inlet orifice area command ("

The inlet orifice area to current converter 297 can use Equation 27 provided herein. Similarly, the outlet orifice area to current converter 298 is the outlet current command for the outlet valve ("

") to generate the outflow orifice area command ("

The outflow orifice area to current converter 298 can use Equation 28 provided herein.

3 is a simplified illustration of one of the piston chambers 334i and one of the valve sub-assemblies 338i. As illustrated in FIG. 3, in this embodiment, the chamber mass flow command into and out of chamber 334i is controlled by inlet valve 338ii and outlet valve 338io. In this embodiment, pressure source 346 provides a pressurized piston fluid 340 at a pressure referred to as P _{source at} the inlet of inlet valve 338ii. Also, the outlet of the outlet valve 338io is at the pressure of P _drain . The chamber mass flow control in Equation 21 can be rewritten as:

식 22

Equation 22

는 선택된 챔버 (334i) 에 대한 유입 밸브 (338ii) 에 대한 질량 유량 커맨드이고;

는 선택된 챔버 (334i) 에 대한 유출 밸브 (338io) 에 대한 질량 유량 커맨드이다. 본원에서 제공된 바와 같이, 특정 실시형태들에서, 챔버 (334i) 내로의 질량 유량을 증가 (

) 시키는 것이 요망되는 경우에는, 유출 밸브 (338io) 는 닫히고 (

) 질량 유량 커맨드는 유입 밸브 (338ii) 의 질량 유량 커맨드와 동일하도록 설정되고, 질량 유량 커맨드 (

) 로 설정된다. 유사하게, 특정 실시형태들에서, 챔버 (334i) 밖으로의 질량 유량을 증가 (

) 시키는 것이 요망되는 경우에는, 유입 밸브 (338ii) 는 닫히고 (

) 질량 유량 커맨드는 유출 밸브 (338io) 의 질량 유량 커맨드와 동일하도록 설정되고, 질량 유량 커맨드 (

) 로 설정된다.Equation 22, and elsewhere,

Is the mass flow command for the inlet valve 338ii for the selected chamber 334i;

Is the mass flow command for the outlet valve 338io for the selected chamber 334i. As provided herein, in certain embodiments, increasing the mass flow rate into chamber 334i (

), the outlet valve 338io is closed (

) The mass flow command is set to be the same as the mass flow command of the inlet valve 338ii, and the mass flow command (

) Is set. Similarly, in certain embodiments, increasing the mass flow rate out of the chamber 334i (

), the inlet valve 338ii is closed (

) The mass flow command is set to be the same as the mass flow command of the outlet valve 338io, and the mass flow command (

) Is set.

The valve flow equation can be written as:

식 23

Equation 23

Equation 23, and elsewhere, a is the area of the valve orifice that opens; f is a mathematical function; P _upstream is the upstream pressure of the valve orifice; And, P _downstream is the pressure _downstream of the valve orifice. Thus, the mass flow rate is equal to a function of the area of the valve orifice that opens times the upstream and downstream pressures.

4 is a simplified illustration of a pipe 400 including an orifice 402 similar to the valve orifice of a valve when opened. In this example, the upstream pressure and the downstream pressure are labeled, and the orifice 402 has an orifice area. 3 and 4, equation 23 can be rewritten as the following valve orifice area commands:

및 식 24

And equation 24

식 25

Equation 25

는 선택된 챔버 (334i) 의 유입 밸브 (338ii) 에 대한 밸브 오리피스 커맨드이고;

는 선택된 챔버 (334i) 의 유출 밸브 (338io) 에 대한 질량 유량 커맨드이다.In these equations, and elsewhere,

Is the valve orifice command for the inlet valve 338ii of the selected chamber 334i;

Is the mass flow command for the outlet valve 338io of the selected chamber 334i.

The valve area equation can be written as:

식 26

Equation 26

In equation 26, a is the valve orifice area; A is the valve area formula; And, u is the valve current. The valve area equation is described in more detail below.

Equation 26 can be rewritten as valve current commands as follows:

및 식 27

And equation 27

식 28

Equation 28

는 유입 밸브에 대한 밸브 전류 커맨드이고;

는 유입 밸브에 대한 밸브 면적 식의 역이며;

는 유입 밸브의 밸브 오리피스 면적이고;

는 유출 밸브에 대한 밸브 전류 커맨드이고;

는 유출 밸브에 대한 밸브 면적 식의 역이고; 그리고,

는 유출 밸브의 밸브 오리피스 면적이다.Equations 27 and 28, and elsewhere,

Is the valve current command for the inlet valve;

Is the inverse of the valve area equation for the inlet valve;

Is the valve orifice area of the inlet valve;

Is the valve current command for the outlet valve;

Is the inverse of the valve area equation for the outlet valve; And,

Is the valve orifice area of the outlet valve.

Equations 24 and 25 can be written more generally as follows:

식 29

Equation 29

), 그러면,For subsonic flow, the upstream pressure divided by the downstream pressure is less than or equal to theta ("θ") (

), then,

식 30

Equation 30

) 일 때, 그러면,For supersonic flow, the upstream pressure divided by the downstream pressure is equal to or greater than theta ("θ") (

), then,

식 31

Equation 31

;

; 및

이고, c 는 방출 계수이고; M_m 은 가스 분자 질량이며; Z 는 가스 압축성 인자이고; k 는 비열비이며; R 은 일반 기체 법칙 상수이고; T 는 온도이다.In these equations,

;

; And

And c is the emission coefficient; M _m is the gas molecular mass; Z is the gas compressibility factor; k is the specific heat ratio; R is a general gas law constant; T is the temperature.

5A is a simplified cutaway view of one non-exclusive example of a valve 538 that may be used as one of the valves 38C, 38D, 38E, 38F from FIG. 1. In this embodiment, the valve 538 is resilient pushing the valve body 539B against the valve housing 539A, the movable valve body 539B, the inlet conduit 539C, the outlet conduit 539D, and the inlet conduit 539C. It is a poppet type valve comprising a member 539E (eg, a spring), and a solenoid 539F.

In this simplified example, the valve housing 539A is somewhat cylindrical, the valve body 539B is disk-shaped, and the conduits 539C and 539D are tubular. Also, in FIG. 5A, valve 538 is shown in a closed position when the control system (not shown in FIG. 5A) is not sending current to solenoid 539F. As a result, the elastic member 539E closes the valve 538 by pushing the valve body 539B against the top of the inlet conduit 539C.

It should be noted that when no current is sent to the solenoid 539F, the valve remains closed as long as the spring preload force is greater than the force created by the pressure difference between the upstream and downstream pressures.

5B is a simplified cutaway view of the valve 538 of FIG. 5A when the valve 538 is in an open position. At this time, the control system (not shown in Fig. 5B) is sending a current to the solenoid 539F. When current is sent to the solenoid, this creates a solenoid force F _solenoid that pushes (pulls) the valve body 539B away from the top of the inlet conduit 539C. Typically, the magnitude of the solenoid force is proportional to the current. When sufficient current is sent to the solenoid 539F, the spring preload force of the elastic member 539E is overcome, the valve body 539B is moved away from the top of the inlet conduit 539C, and the valve 538 is opened. . Also, the amount of current will determine how far the valve 538 opens. In general, the size of the valve opening increases as the current increases.

As illustrated in FIG. 5B, the amount by which the valve body 539B has moved from the closed position to the open position is referred to as “y”.

5C is a simplified cutaway view of the valve 538 of FIG. 5A with the inlet conduit 539C removed, the solenoid 539F not activated, and the presence of pressure in the conduits 539C, 539D. . At this time, the elastic member 539E pushes the valve body 539B down by the preload distance y ₀ . The valve body 539B is shown in the closed position in the dashed line with respect to the reference. When the inlet conduit 539D is in place (as shown in Fig. 5A), the elastic member 539E calculates the spring preload force equal to the spring constant K _s of the elastic member 539E times the preload distance y ₀ . Approved.

The control of valve 538 can be expressed as follows:

식 32

Equation 32

는 밸브 보디 (539B) 의 가속도이며; C_v 는 스프링 마찰에 의해 야기되는 감쇠이고;

는 밸브 보디 (539B) 의 속도이고; K_s 는 탄성 부재 (539E) 의 스프링 상수이고; y₀ 는 프리로드 거리이며; k_f 는 솔레노이드 포스 상수이고; u 는 솔레노이드에 보내지는 전류 커맨드이고; r 은 유입 도관 (539C) 의 상부에서의 반경이고; 델타 압력은 업스트림 압력과 다운스트림 압력 사이의 차이 (

) 이다.In equation 32 and elsewhere, M _v is the mass of the valve body 539B;

Is the acceleration of the valve body 539B; C _v is the damping caused by spring friction;

Is the speed of the valve body 539B; K _s is the spring constant of the elastic member 539E; y ₀ is the preload distance; k _f is the solenoid force constant; u is the current command sent to the solenoid; r is the radius at the top of the inlet conduit 539C; Delta pressure is the difference between upstream and downstream pressure (

) to be.

The effective orifice area “a” of the valve 538 illustrated in FIGS. 5A-5C can be expressed as follows:

및 식 33

And Equation 33

식 34

Equation 34

은 밸브 면적 식의 역이다.Equations 33 and 34, and elsewhere, A is the valve area equation; And

Is the inverse of the valve area equation.

The dead-zone current u ₀ required to overcome the spring preload force can be expressed as:

식 35

Equation 35

For the valve 538 illustrated in FIGS. 5A-5C, the maximum allowable pressure difference ΔP _max without leakage can be expressed as follows:

식 36

Equation 36

For the valve 538 illustrated in FIGS. 5A-5C, the static control current can be expressed as follows:

식 37

Equation 37

As provided above, in order to accurately control the fluid actuator assembly 24, it is important to determine the nonlinearities inherent in each of the valves 38C, 38D, 38E, 38F. In certain embodiments, each valve 38C, 38D, 38E, 38F is not disassembled to identify the valve characteristics of each valve 38C, 38D, 38E, 38F. Instead, each physical valve 38C, 38D, 38E, 38F of the valve assembly 24 is tested to determine its respective valve characteristic(s). For example, for each valve 38C, 38D, 38E, 38F, the flow rate is measured with various valve current commands with various inlet/outlet pressure differences. Subsequently, for each valve 38C, 38D, 38E, 38F, the effective orifice area can be calculated from the flow rate information using the flow equation (see equations 24-31).

6A is a graph showing valve effective orifice area versus current command for various delta pressures (“ΔP”). This graph was created by experimentally testing the poppet valve at various delta pressures. For example, while maintaining a delta pressure of 350 kPa, the flow rate was measured at a plurality of different current commands for the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted in FIG. 6A as a small box. Subsequently, line 600A was created by curve fitting these data points. Line 600A represents the relationship between valve orifice area versus current command for a delta pressure of 350 kPa.

Next, while maintaining a delta pressure of 300 kPa, the flow rate was measured at a plurality of different current commands for the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted in FIG. 6A as a small circle. Subsequently, line 602A was created by curve fitting these data points. Line 602A shows the relationship between valve orifice area versus current command for a delta pressure of 300 kPa.

Similarly, while maintaining a delta pressure of 250 kPa, flow rates were measured at multiple different current commands for the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted in FIG. 6A as a small “x”. Subsequently, line 604A was created by curve fitting these data points. Line 604A shows the relationship between valve orifice area versus current command for a delta pressure of 250 kPa.

Additionally, while maintaining a delta pressure of 200 kPa, the flow rate was measured at a plurality of different current commands for the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted in FIG. 6A as a small “z”. Subsequently, line 606A was created by curve fitting these data points. Line 606A shows the relationship between valve orifice area versus current command for a delta pressure of 200 kPa.

In addition, while maintaining a delta pressure of 150 kPa, the flow rate was measured at a plurality of different current commands for the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted in FIG. 6A as a small triangle. Subsequently, line 608A was created by curve fitting these data points. Line 608A shows the relationship between valve orifice area versus current command for a delta pressure of 150 kPa.

Additionally, while maintaining a delta pressure of 100 kPa, flow rates were measured at multiple different current commands for the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted in FIG. 6A as a small “+”. Subsequently, line 610A was created by curve fitting these data points. Line 610A shows the relationship between valve orifice area versus current command for a delta pressure of 100 kPa.

Finally, while maintaining a delta pressure of 50 kPa, the flow rate was measured at multiple different current commands to the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted as D in FIG. 6A. Subsequently, line 612 was created by curve fitting these data points. Line 612 shows the relationship between valve orifice area versus current command for a delta pressure of 50 kPa.

In this example, the valve characteristic 614 of this valve represents the relationship between the effective valve orifice area versus the current command for a number of different delta pressures. Alternatively, for example, the valve characteristic 614 may include (i) the relationship between effective valve orifice area versus voltage for a number of different delta pressures; (ii) the relationship between the flow versus current command for a number of different delta pressures; And/or (iii) a relationship between flow rate versus voltage for a number of different delta pressures.

As provided above, in certain embodiments, the valve characteristic 614 is inverted to create an inverted valve characteristic 616 that is used subsequent to control of the valve. For example, the data in FIG. 6A can be inverted (the X and Y axes of the graph are switched) to produce the inverted valve characteristic 616 shown in FIG. 6B.

More specifically, FIG. 6B is a graph showing the effective orifice area versus valve current command, which is the inversion of the graph in FIG. 6A. In this example, the data from Fig. 6A is inverted to produce the graph in Fig. 6B. Subsequently, curve fitting is used to generate the curves in FIG. 6B.

For example, at a delta pressure of 350 kPa, the data are presented as small boxes. Subsequently, line 600B was created by curve fitting these data points. Line 600B represents the relationship between the valve orifice area and the valve current command for a delta pressure of 350 kPa.

Next, at a delta pressure of 300 kPa, the data are represented as small circles. Subsequently, line 602B was created by curve fitting these data points. Line 602B represents the relationship between the valve orifice area and the valve current command for a delta pressure of 300 kPa.

Similarly, at a delta pressure of 250 kPa, the data are expressed as small "x"s. Subsequently, line 604B was created by curve fitting these data points. Line 604B represents the relationship between the valve orifice area and the valve current command for a delta pressure of 250 kPa.

Additionally, at a delta pressure of 200 kPa, the data are expressed as small "z"s. Subsequently, line 606B was created by curve fitting these data points. Line 606B represents the relationship between the valve orifice area and the valve current command for a delta pressure of 200 kPa.

Also, at a delta pressure of 150 kPa, the data are represented as small triangles. Subsequently, line 608B was created by curve fitting these data points. Line 608B represents the relationship between the valve orifice area and the valve current command for a delta pressure of 150 kPa.

Additionally, at a delta pressure of 100 kPa, the data are expressed as small "+"s. Subsequently, line 610B was created by curve fitting these data points. Line 610B represents the relationship between the valve orifice area and the valve current command for a delta pressure of 100 kPa.

Finally, at a delta pressure of 50 kPa, the data are expressed as small "Ds". Subsequently, line 612B was created by curve fitting these data points. Line 612B represents the relationship between the valve orifice area and the valve current command for a delta pressure of 50 kPa.

It should be noted that the inverted valve characteristic 616 data from the FIG. 6B graph can be used by the control system to accurately control the valve. It should also be noted that the control system can use interpolation to generate data for different delta pressures to accurately control the valve at different delta pressures.

7A-7D are simplified cutaway views of another type of valve 738 at various valve positions that may be used as one of the valves 38C, 38D, 38E, 38F from FIG. 1. More specifically, FIG. 7A is a simplified side view of the spool type valve 738 in a fully closed position; 7B is a simplified side view of the spool type valve 738 in a closed, baseline (ready to open) position; 7C is a simplified side view of the spool type valve 738 in a partially open position; And, Fig. 7D is a simplified side view of the spool type valve 738 in the fully open position.

In this embodiment, the valve 738 is a valve housing 739A, a movable valve body 739B (sometimes referred to as a “spool”), an inlet opening (not shown), an outlet opening 739D, and a valve body. It is a spool type valve including an elastic member 739E (e.g., a spring) that pushes 739B from right to left, and a solenoid 739F that moves the valve body 739B from left to right.

In this simplified example, the valve housing 739A is in the shape of a slightly hollow cylinder, the valve body 739B is in the shape of a disk, the openings 739D are in a circular shape and are located on opposite sides of the valve housing 738A. A valve body 739B is positioned between them.

It should be noted that since the upstream and downstream pressures are orthogonal to the valve body 739B, the delta pressure will not affect the opening or closing of the valve 738.

Additionally, in Fig. 7A, the valve 738 is shown in a fully closed position when the control system (not shown in Fig. 7A) is not sending current to the solenoid 739F. At this time, the valve body 739B covers both the inlet port and the outlet port 739D to close the valve 738.

7B is a simplified cutaway view of the valve 738 of FIG. 7A with the valve 738 in the baseline position just before it opens. At this time, the control system (not shown in Fig. 7B) is sending a current to the solenoid 739F. When current is sent to the solenoid, this creates a solenoid force F _solenoid that pushes the valve body 739B to the baseline position (y _b ) where the valve 738 is ready to open.

7C is a simplified cutaway view of the valve 738 of FIG. 7A with the valve 738 in a partially open position. At this time, the control system (not shown in Fig. 7C) is sending a current to the solenoid 739F. When current is sent to the solenoid, this creates a solenoid force F _solenoid that pushes valve body 739B into position y where valve 738 is partially open.

Typically, the magnitude of the solenoid force is proportional to the current. When sufficient current is sent to the solenoid 739F, the spring preload force of the elastic member 739F is overcome, and the valve body 739B is moved. Also, the amount of current will determine how far the valve 738 opens. In general, the size of the valve opening increases as the current increases.

7D is a simplified cutaway view of the valve 738 of FIG. 7A with the valve 738 in the fully open position.

In this embodiment, the valve mechanical dynamics for the valve 738 shown in FIGS. 7A-7D can be expressed as follows:

식 38

Equation 38

는 밸브 보디 (739B) 의 가속도이며; C_v 는 스프링 마찰에 의해 야기되는 감쇠이고;

는 밸브 보디 (739B) 의 속도이고; K_s 는 탄성 부재 (739E) 의 스프링 상수이고; y₀ 는 프리로드 거리이며; k_f 는 솔레노이드 포스 상수이고; u 는 솔레노이드에 보내지는 전류 커맨드이고; f_preload 는 탄성 부재 (739E) 의 프리-로드 포스이다.In equation 38 and elsewhere, M _v is the mass of the valve body 739B;

Is the acceleration of the valve body 739B; C _v is the damping caused by spring friction;

Is the speed of the valve body 739B; K _s is the spring constant of the elastic member 739E; y ₀ is the preload distance; k _f is the solenoid force constant; u is the current command sent to the solenoid; f _preload is the pre-load force of the elastic member 739E.

이다. 추가로, 이 타입의 밸브 (738) 의 유효 오리피스 면적 (A_eff) 은 다음과 같이 계산될 수 있다:7E is a simplified illustration of the valve body 739B and outlet 739D in the partially open position, which aids in the explanation of the effective orifice area. In this example,

to be. Additionally, the effective orifice area A _eff of this type of valve 738 can be calculated as follows:

및 식 39

And equation 39

식 40

Equation 40

8A is a graph showing normalized effective orifice area versus normalized spool position calculated using the above formulas for the valve shown in FIGS. 7A-7D. In this example, the valve characteristic 814 of this valve represents the relationship of normalized effective orifice area versus normalized spool position.

As provided above, in certain embodiments, the valve characteristic 814 is inverted to create the inverted valve characteristic 816 shown in FIG. 8B that is used subsequent to the control of that valve. For example, the data in FIG. 8A can be inverted (the X and Y axes of the graph are switched) to produce the inverted valve characteristic 816 shown in FIG. 8B plotting the spool position versus the normalized effective orifice area. have.

Certain valves (eg, spool valves) have backlash-like hysteresis. In these valves, for the same current command, the spool position can be different depending on the previous command history.

9A is a graph showing test results of a spool valve. In Fig. 9A, the graph shows the spool position versus voltage. Also, FIG. 9B is a graph showing the simulated results of the spool valve. In Figure 9B, the graph shows the spool position versus current. These figures show that for the same current command (or voltage command), the spool position may be different depending on the previous command history. For example, referring to FIG. 9A, for the same command (eg, 5 volts), the spool position will be different depending on the previous command. Similarly, referring to FIG. 9B, for the same command (eg, 0.5 amps), the spool position will be different depending on the previous command.

As provided herein, referring to FIG. 9A, another valve characteristic 914 of this valve is represented by the relationship of spool position versus voltage. Referring to Fig. 9B, another valve characteristic 915 of this valve is represented by the relationship of spool position versus current. Thus, as provided herein, spool valve nonlinearities (backlash and effective orifice geometry) can be corrected and modeled. Subsequently, their inverse can be applied to the control software to linearize the spool valve.

The method used to calculate the backlash of the valve can be varied. In one embodiment, calibration may be performed by gradually increasing the current (or voltage) command from zero to maximum and then gradually decreasing it to zero while monitoring the position of the valve body. The current (or voltage) command versus spool position data is subsequently used as a compensation map.

In certain embodiments, the valve's baseline position (y ₀ ) can be determined during backlash correction. The baseline position can be determined by slightly increasing the current command while checking the outflow flow of the valve to determine when the orifice begins to open.

10A shows two valve characteristics of a spool valve. More specifically, FIG. 10A is a graph showing (i) a first valve characteristic 1014, eg, normalized effective orifice area versus normalized spool position; And (ii) a graph showing the second valve characteristic 1015, eg, spool position versus current. Data for graphs 1014 and 1015 can be obtained or calculated experimentally.

As provided above, in certain embodiments, the valve characteristics 1014, 1015 are subsequently reversed to create the inverted valve characteristics 1016, 1017 shown in FIG. 10B used for control of that valve. do. For example, data from graph 1014 is inverted (the X and Y axes of the graph are switched) to create a graph 1016 that plots the normalized spool position versus the normalized effective orifice area. In addition, the data from graph 1015 is inverted (the X and Y axes of the graph are switched) to create a graph 1017 that plots current versus spool position. As provided herein, inverted valve characteristics 1016, 1017 help to accurately control the effective orifice area of the valve despite the nonlinearities of the valve.

Inverted valve characteristics 1016 and 1017 may be in the form of a look-up table, map, graphs, charts, or analytic or fitted model.

11 is a schematic diagram showing an exposure apparatus 1170 useful in the present invention. The exposure apparatus 1170 includes an apparatus frame 1172, an illumination system 1182 (irradiation apparatus), a mask stage assembly 1184, an optical assembly 1186 (lens assembly), a plate stage assembly 1110, and a mask stage assembly. 1184 and a control system 1120 that controls the plate stage assembly 1110.

The exposure apparatus 1170 is particularly useful as a lithographic device for transferring a pattern (not shown) of a liquid crystal display device from a mask 1188 to a workpiece 1122.

The apparatus frame 1172 is rigid and supports the components of the exposure apparatus 1170. The design of the apparatus frame 1172 can be varied to suit the design requirements for the rest of the exposure apparatus 1170.

The illumination system 1182 includes an illumination source 1192 and an illumination optical assembly 1194. The illumination source 1192 emits a beam of light energy (rays). The illumination optical assembly 1194 guides a beam of light energy from the illumination source 1192 to the mask 1188. The beam selectively illuminates different portions of the mask 1188 and exposes the workpiece 1122.

The optical assembly 1188 projects and/or focuses the light passing through the mask 1188 onto the workpiece 1122. Depending on the design of the exposure apparatus 1170, the optical assembly 1188 can enlarge or reduce the image illuminated on the mask 1188.

The mask stage assembly 1184 holds and positions the mask 1188 with respect to the optical assembly 1188 and the work piece 1122. Similarly, the plate stage assembly 1110 holds and positions the workpiece 1122 against the projected image of the illuminated portions of the mask 1188.

There are many different types of lithographic devices. For example, the exposure apparatus 1170 is a scanning type photolithography system in which a pattern from the mask 1188 is exposed on a glass workpiece 1122 while the mask 1188 and the workpiece 1122 move synchronously. Can be used as Alternatively, the exposure apparatus 1170 may be a step-and-repeat type of photolithography system that exposes the mask 1188 while the mask 1188 and workpiece 1122 are stationary.

However, the use of the exposure apparatus 1170 and stage assemblies provided herein is not limited to a photolithography system for manufacturing a liquid crystal display device. The exposure apparatus 1170 can be used, for example, as a semiconductor photolithography system for exposing an integrated circuit pattern on a wafer or a photolithography system for manufacturing a thin film magnetic head. Additionally, the present invention can also be applied to a close-up photolithography system that exposes a mask pattern by placing the mask and substrate close together without the use of a lens assembly. Additionally, the invention provided herein can be used in other devices including other flat panel display processing equipment, elevators, machine tools, metal cutting machines, inspection machines and disk drives.

A photolithographic system according to the above-described embodiments can be built by assembling various systems including each element recited in the appended claims in such a way that the specified mechanical, electrical, and optical accuracy are maintained. I can. In order to maintain various accuracies, prior to assembly and following assembly, all optical systems are adjusted to achieve their optical accuracy. Similarly, all mechanical systems and all electrical systems are tuned to achieve their respective mechanical and electrical accuracy. The process of assembling each subsystem into a photolithographic system includes mechanical interfaces, electrical circuit wiring connections, and air pressure piping connections between each subsystem. Of course, there is also a process in which each subsystem is assembled prior to assembling the photolithographic system from the various subsystems. Once the photolithography system has been assembled using the various subsystems, a total adjustment is made to ensure that accuracy is maintained in the finished photolithography system. Additionally, it is desirable to manufacture an exposure system in a clean room in which temperature and cleanliness are controlled.

Further, the device can be manufactured using the systems described above by the process generally shown in FIG. 12. In step 1201, the functional and performance characteristics of the device are designed. Next, in step 1202, a mask (reticle) with a pattern is designed according to the previous design step, and in parallel step 1203, a glass plate is made. The mask pattern designed in step 1202 is exposed onto the glass plate from step 1203 in step 1204 by the photolithography system described herein above according to the present invention. In step 1205, the flat panel display device is assembled (including the dicing process, bonding process and packaging process), and finally, the device is then inspected in step 1206.

While a number of different embodiments of stage assembly 10 have been illustrated and described herein, one or more features of any one embodiment may be implemented in one or more of the other embodiments, provided the combination satisfies the intent of the present invention. It is to be understood that one or more features of the forms may be combined.

While a number of exemplary aspects and embodiments of stage assembly 10 have been shown and disclosed herein above, one of ordinary skill in the art will recognize certain variations, substitutions, additions and sub-combinations thereof. Accordingly, the following appended claims and the claims introduced hereinafter are intended to be construed as including all such modifications, substitutions, additions and sub-combinations as within their true spirit and scope, and this specification No limitations are intended to the configuration or designs shown in.

Claims (20)

A stage assembly for positioning a workpiece along an axis of movement,
The stage assembly,
A stage configured to couple to the workpiece;
Base;
A fluid actuator assembly coupled to the stage and moving the stage with respect to the base along the axis of movement, the fluid actuator assembly being positioned within the piston housing defining a piston chamber, and positioned in the piston chamber along the piston axis. A piston moving relative to the piston, and a valve assembly for controlling a flow of the piston fluid into the piston chamber, the valve assembly comprising a first inlet valve having a first inlet valve characteristic; And
A control system for controlling the valve assembly to control the flow of the piston fluid into the piston chamber, the control system defined as a relationship of at least two variables to the first inlet valve to control the valve assembly. The control system using an inverse of the first inlet valve characteristic to be,
The first inlet valve characteristic is determined by experimental testing of the first inlet valve. The method of claim 1,
The piston separates the piston chamber into a first chamber and a second chamber on opposite sides of the piston; Wherein the valve assembly controls the flow of the piston fluid into the first chamber and the second chamber. The method of claim 2,
The valve assembly controls the flow of the piston fluid out of the first chamber and the second chamber. The method of claim 3,
The valve assembly comprises: (i) the first inlet valve for controlling the flow of the piston fluid into the first chamber; (ii) a first outlet valve that controls the flow of the piston fluid out of the first chamber; (iii) a second inlet valve for controlling the flow of the piston fluid into the second chamber; And (iv) a second outlet valve that controls the flow of the piston fluid out of the second chamber. The method of claim 4,
The first outlet valve has a first outlet valve characteristic, the second inlet valve has a second inlet valve characteristic, and the second outlet valve has a second outlet valve characteristic; The control system is also further configured to control the valve assembly with an inverse of the first outlet valve characteristic, defined as a relationship of at least two variables for the first outlet valve, with a relationship of at least two variables for the second inlet valve A stage assembly using an inverse of the second inlet valve characteristic defined, and an inverse of the second outlet valve characteristic defined by a relationship of at least two variables to the second outlet valve. The method of claim 4,
The first outlet valve characteristic is determined using experimental testing of the first outlet valve, the second inlet valve characteristic is determined using experimental testing of the second inlet valve, and the second outlet valve characteristic is the Stage assembly as determined using experimental testing of the second outlet valve. delete The method of claim 1,
Wherein the first inlet valve characteristic is a relationship between an effective orifice area and a current command for the first inlet valve. The method of claim 1,
Wherein the first inlet valve characteristic is a relationship between a current command for the first inlet valve and a valve position. The method of claim 1,
Wherein the first inlet valve characteristic is a relationship between a valve position and an effective orifice area for the first inlet valve. An exposure apparatus comprising an illumination source and the stage assembly according to claim 1 for moving the stage with respect to an illumination system. As a process for manufacturing a device,
A process for manufacturing a device comprising providing a substrate and forming an image on the substrate with the exposure apparatus according to claim 11. A method for positioning a workpiece along an axis of movement, comprising:
The above method,
Providing a base;
Coupling the workpiece to the stage;
A piston housing defining a piston chamber, a piston positioned within the piston chamber and moving relative to the piston chamber along a piston axis, and a valve assembly for controlling the flow of a piston fluid into the piston chamber, the valve assembly comprising a first inlet valve A fluid actuator assembly comprising the valve assembly comprising a first inlet valve having a characteristic, moving the stage with respect to the base along the moving axis; And
Controlling the valve assembly with a control system to control the flow of the piston fluid into the piston chamber, the control system comprising a relationship of at least two variables to the first inlet valve to control the valve assembly Controlling the valve assembly using an inverse of the first inlet valve characteristic defined as,
And determining the first inlet valve characteristic using experimental testing of the first inlet valve. 2. A method for positioning a workpiece along an axis of movement. The method of claim 13,
The step of moving the stage comprises the piston separating the piston chamber into a first chamber and a second chamber on opposite sides of the piston, and the valve assembly into the first chamber and into the second chamber. A method for positioning a workpiece along an axis of movement comprising controlling the flow of the piston fluid of. The method of claim 14,
Wherein the step of moving the stage includes the valve assembly controlling the flow of the piston fluid out of the first chamber and out of the second chamber. The method of claim 15,
The step of moving the stage comprises: (i) the first inlet valve for controlling the flow of the piston fluid into the first chamber; (ii) a first outlet valve that controls the flow of the piston fluid out of the first chamber; (iii) a second inlet valve for controlling the flow of the piston fluid into the second chamber; And (iv) a second outlet valve that controls the flow of the piston fluid out of the second chamber. 2. A method for positioning a workpiece along an axis of movement. The method of claim 16,
The step of moving the stage includes the first outlet valve having a first outlet valve characteristic, the second inlet valve having a second inlet valve characteristic, and the second outlet valve having a second outlet valve characteristic Further comprising having; The step of controlling the valve assembly, wherein the control system is an inverse of the first outlet valve characteristic defined by the relationship of at least two variables with respect to the first outlet valve, with a relationship between the at least two variables with respect to the second inlet valve Controlling the valve assembly by also using an inverse of the second inlet valve characteristic defined, and an inverse of the second outlet valve characteristic defined as a relationship of at least two variables for the second outlet valve. Method for positioning the workpiece along an axis. The method of claim 16,
Determining the first outlet valve characteristics using experimental testing of the first outlet valve; Determining the characteristics of the second inlet valve using experimental testing of the second inlet valve; And determining the second outlet valve characteristics using experimental testing of the second outlet valve. 2. A method for positioning a workpiece along an axis of movement. delete The method of claim 13,
The step of moving the stage may include: (i) a relationship between a current command for the first inlet valve and an effective orifice area, and (ii) a current command for the first inlet valve and a valve position. A relationship between, and (iii) a relationship between the valve position and the effective orifice area for the first inlet valve. 2. A method for positioning a workpiece along an axis of movement.

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