RELATED APPLICATION

[0001] This application claims priority on U.S. Provisional Application Serial No. 62/344,262 filed on June 1 , 2016 and entitled "CONTROL SYSTEM FOR CONTROLLING A FLUID ACTUATOR". As far as permitted, the contents of U.S. Provisional Application Serial No. 62/344,262 is incorporated herein by reference.

BACKGROUND

[0002] Exposure apparatuses are commonly used to transfer images from a mask onto a workpiece such as an LCD flat panel display or a semiconductor wafer. A typical exposure apparatus includes an illumination source, a mask stage assembly that retains and precisely positions a mask, a lens assembly, a workpiece stage assembly that retains and precisely positions the workpiece, and a measurement system that monitors the position or movement of the mask and the workpiece. There is a never ending desire to reduce the cost of the actuators used to position the mask and/or the workpiece, while still accurately positioning these components.

SUMMARY

[0003] The present invention is directed to a stage assembly for positioning a workpiece along a movement axis. In one embodiment, the stage assembly includes a stage, a base, a fluid actuator assembly, and a control system. The stage is adapted to couple to and retain the workpiece. The fluid actuator assembly is coupled to and moves the stage along the movement axis relative to the base. The fluid actuator assembly can include a piston housing that defines a piston chamber, a piston that is positioned within and moves relative to the piston chamber along a piston axis, and a valve assembly that controls the flow of a piston fluid into the piston chamber. 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 utilizes an inverse of the first inlet valve characteristic to control the valve assembly.

[0004] In one embodiment, the piston fluid is a gas, and the present invention is described as a pneumatic control application. Alternatively, the piston fluid can be a liquid such as oil, and different equations can be utilized.

[0005] As provided herein, the control system precisely controls the fluid pressure on each side 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 embedded in the system. These nonlinearities include the valve characteristics of each valve. Non-exclusive examples of valve characteristics include (i) fluid pressure variations with chamber volumes, (ii) backlash and differential pressure dependency of proportional valves, and (iii) fluid flow nonlinearity associated with upstream and downstream pressure. The nonlinearities can be identified via testing, modeling, or simulation. Subsequently, the valve characteristics are inverted and used in a control loop of the control system to linearize the system and accurately control the fluid actuator assembly.

[0006] Thus, the problem of system nonlinearity of fluid cylinder pressure and valve dynamics associated with application of a fluid cylinder to stage trajectory motion has been solved by incorporating identified system dynamics models into the control design.

[0007] In certain embodiments, the piston separates the piston chamber into a first chamber and a second chamber that are on opposite sides of the piston. Further, the valve assembly controls the flow of the piston fluid into and out of the first chamber and the second chamber. [0008] In one embodiment, the valve assembly includes (i) the 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; and the second outlet valve has a second outlet valve characteristic. In this embodiment, the control system also utilizes an inverse of the first outlet valve characteristic, an inverse of the second inlet valve characteristic, and an inverse of the second outlet valve characteristic to control the valve assembly.

[0009] As one, non-exclusive example, the first inlet valve characteristic can be determined using experimental testing of the first inlet valve, the first outlet valve characteristic can be determined using experimental testing of the first outlet valve, the second inlet valve characteristic can be determined using experimental testing of the second inlet valve, and the second outlet valve characteristic can be determined using experimental testing of the second outlet valve.

[0010] As provided herein, for example, each valve characteristic can be (i) the relationship between current command and an effective orifice area for the valve; (ii) the relationship between current command and valve position for the valve; and/or (iii) the relationship between effective orifice area and valve position for the valve.

[0011] The present invention is also directed to an exposure apparatus, and a process for manufacturing a device that includes the steps of providing a substrate and forming an image to the substrate with the exposure apparatus.

[0012] The present invention is also directed to a method for positioning a workpiece along a movement axis. In one embodiment, the method includes (i) providing a base; (ii) coupling the workpiece to a stage; (iii) moving the stage along the movement axis with a fluid actuator assembly that includes a piston housing that defines a piston chamber, a piston that is positioned within and moves relative to the piston chamber along a piston axis, and a valve assembly that controls the flow of a piston fluid into the piston chamber; wherein the valve assembly includes a first inlet valve having a first inlet valve characteristic; 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 utilizes an inverse of the first inlet valve characteristic to control the valve assembly.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The novel features of this invention, as well as the invention itself, both as to its structure and its operation, will be best understood from the accompanying drawings, taken in conjunction with the accompanying description, in which similar reference characters refer to similar parts, and in which:

[0014] Figure 1 is a simplified side illustration of a stage assembly having features of the present invention;

[0015] Figure 2A is a control block diagram that illustrates a method for controlling a fluid actuator assembly;

[0016] Figure 2B is a control block diagram of a chamber controller;

[0017] Figure 3 is a simplified illustration of one of the piston chambers and one of the valve sub-assemblies having features of the present invention;

[0018] Figure 4 is a simplified illustration of a pipe that includes an orifice;

[0019] Figures 5A-5C are simplified cut-away views of one, non-exclusive example of a valve;

[0020] Figure 6A is a graph that illustrates a valve characteristic of the valve of Figures 5A-5C;

[0021] Figure 6B is a graph that illustrates an inverted valve characteristic of the valve of Figures 5A-5C;

[0022] Figures 7A-7D are simplified illustrations of another type of valve at various valve positions;

[0023] Figure 7E is a simplified illustration of an outlet and a valve body in a partly open position;

[0024] Figure 8A is a graph that illustrates a calculated, normalized effective orifice area versus normalized spool position for the valve illustrated in Figures 7A-7D;

[0025] Figure 8B is a graph that plots spool position versus normalized effective orifice area; [0026] Figure 9A is a graph that illustrates the test results of a spool valve;

[0027] Figure 9B is a graph that illustrates the simulated results of a spool valve;

[0028] Figure 10A illustrates the two valve characteristics of a spool valve;

[0029] Figure 10B illustrates two inverted valve characteristics;

[0030] Figure 1 1 is a schematic illustration of an exposure apparatus having features of the present invention; and

[0031] Figure 12 is a flow chart that outlines a process for manufacturing a device in accordance with the present invention.

DESCRIPTION

[0032] Embodiments of the present invention are described herein in the context of a stage assembly including a stage, and a control system that controls a fluid actuator assembly that moves the stage. Those of ordinary skill in the art will realize that the following detailed description of the present invention is illustrative only and is not intended to be in any way limiting. Other embodiments of the present invention will readily suggest themselves to such skilled persons having the benefit of this disclosure. Reference will now be made in detail to implementations of the present invention as illustrated in the accompanying drawings. The same or similar reference indicators will be used throughout the drawings and the following detailed description to refer to the same or like parts.

[0033] In the interest of clarity, not all of the routine features of the implementations described herein are shown and described. It will, of course, be appreciated that in the development of any such actual implementation, numerous implementation- specific decisions must be made in order to achieve the developer's specific goals, such as compliance with application-related and business-related constraints, and that these specific goals will vary from one implementation to another and from one developer to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking of engineering for those of ordinary skill in the art having the benefit of this disclosure. [0034] Figure 1 is a simplified illustration of a stage assembly 10 that includes a base 12, a stage 14, a stage mover assembly 16, a measurement system 18, and a control system 20 (illustrated as a box). 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 precisely positioning a workpiece 22 (also sometimes referred to as a device) during a manufacturing and/or an inspection process.

[0035] As an overview, in certain embodiments, the stage mover assembly 16 includes a fluid actuator assembly 24 that is relatively inexpensive to manufacture. Further, 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 thereof, the stage assembly 10 is less expensive to manufacture and the workpiece 22 is still positioned with the desired level of accuracy.

[0036] The type of workpiece 22 positioned and moved by the stage assembly 10 can be varied. For example, the workpiece 22 can be an LCD flat panel display, a semiconductor wafer, or a mask, and the stage assembly 10 can be used as part of an exposure apparatus. Alternatively, for example, the stage assembly 10 can be used to move other types of devices during manufacturing and/or inspection, to move a device under an electron microscope (not shown), or to move a device during a precision measurement operation (not shown).

[0037] Some of the Figures provided herein include an orientation system that designates an X axis, a Y axis, and a Z axis. It should be understood that the orientation system is merely for reference and can be varied. For example, the X axis can be switched with the Y axis and/or the stage assembly 10 can be rotated. Moreover, these axes can alternatively be referred to as a first, second, or third axis.

[0038] The base 12 supports the stage 14. In the non-exclusive embodiment illustrated in Figure 1 , the base 12 is rigid and generally rectangular plate-shaped. Further, the base 12 can be fixedly secured to a base mount 26. Alternatively, the base 12 can be secured to another structure.

[0039] The stage 14 retains the workpiece 22. In one embodiment, the stage is precisely moved by the stage mover assembly 16 relative to the base 12 to precisely position the stage 14 and the workpiece 22. In Figure 1 , the stage 14 is generally rectangular-shaped and includes a device holder (not shown) for retaining the workpiece 22. The device holder can 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 retains the workpiece 22. Alternately, 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 can include a coarse stage (not shown) that is moved by the stage mover assembly 16, and a fine stage (not shown) that retains the workpiece 22 and that is moved relative to the coarse stage with a fine stage mover assembly (not shown).

[0040] Further, in Figure 1 , the stage 14 can be supported relative to the base 12 with a bearing assembly 28 that allows the movement of the stage 14 relative to the base 12. For example, the bearing assembly 28 can be a roller bearing, a fluid bearing, a linear bearing, or another type of bearing.

[0041] The measurement system 18 monitors the movement and/or the position of the stage 14 relative to a reference, such as an optical assembly (not shown in Figure 1 ) or the base 12, and provides measurement information to the control system 20. 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 according to the movement requirements of the stage 14. In one embodiment, the measurement system 18 can include a linear encoder that monitors movement of the stage 14 along the Y axis. Alternatively, the measurement system 18 can include an interferometer, or another type of movement or position sensor.

[0042] The stage mover assembly 16 is controlled by the control system 20 to move the stage 14 relative to the base 12. In Figure 1 , the stage mover assembly 16 includes the fluid actuator assembly 24 that moves the stage 14 along a single movement axis 30, e.g. the Y axis.

[0043] The design of the fluid actuator assembly 24 can be varied pursuant to the teachings provided herein. In one, non-exclusive embodiment, the fluid actuator assembly 24 includes (i) a piston assembly 31 that includes a piston housing 32 that defines a piston chamber 34, and a piston 36 that is positioned in the piston chamber 34; and (ii) a valve assembly 38 that controls the flow of a piston fluid 40 (illustrated 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 can be varied pursuant to the teaching provided herein.

[0044] In one embodiment, the piston housing 32 is rigid and defines a generally right, cylindrically-shaped piston chamber 34. In this embodiment, the piston housing 32 includes a tubular-shaped side wall 32A; a disk-shaped, first end wall 32B, and a disk-shaped, second end wall 32C that is spaced apart from the first end wall 32B. One or both end walls 32B, 32C can include a wall aperture 32D for receiving a portion of the piston 36.

[0045] The piston housing 32 can be fixedly secured to a piston mount 42. Alternatively, the piston housing 32 can be secured to another structure, such as the base 12. Still alternatively, because the piston housing 32 receives the reaction forces generated by the stage mover assembly 16, the piston housing 32 can be coupled to a reaction assembly that counteracts, reduces and minimizes the influence of the reaction forces from the stage mover assembly 16 on the position of other structures. For example, the piston housing 32 can be coupled to a large countermass (not shown) that is maintained above a countermass support (not shown) with a reaction bearing (not shown) that allows for motion of the piston housing 32 along the movement axis 30.

[0046] The piston 36 is positioned within and moves relative to the piston chamber 34 along a piston axis 36A. In certain embodiments, the piston axis 36A is coaxial with the movement axis 30. In the non-exclusive embodiment illustrated in Figure 1 , the piston 36 includes (i) a rigid, disk-shaped piston body 36B, (ii) a piston seal 36C that seals the area between the piston body 36B and the piston housing 32, (iii) a rigid, first beam 36D that is attached to and cantilevers away from the piston body 36B, and extends through the wall aperture 32D in the first end wall 32B, (iv) a rigid, second beam 36E that is attached to and cantilevers away from the piston body 36B, and extends through the wall aperture 32D in the second end wall 32C, (iv) a first beam seal (not shown) that seals the area between the first beam 36D and the first end wall 32B, and (v) a second beam seal (not shown) that seals the area between the second beam 36E and the second end wall 32C.

[0047] In this embodiment, the second beam 36E is also fixedly secured to the stage 14. Stated in another fashion, 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. Further, in this embodiment, the first beam 36D is included so that the effective area on each side of the piston body 36B is the same for ease of calculations. Alternatively, for example, the fluid actuator assembly 24 can be designed without the first beam 36D. In such alternative design, the effective area on the left side of the piston body 36B is greater than the effective area on the right side of the piston body 36B.

[0048] The piston body 36B separates the piston chamber 34 into a first chamber 34A (also referred to as "chamber 1 ") and a second chamber 34B (also referred to as "chamber 2") that are on opposite sides of the piston body 36B. In Figure 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. Further, the first chamber 34A has a chamber 1 effective piston area (Ai), and is filled with the piston fluid 40 that is at a first pressure (Pi), at a first temperature (Ti), and has a first volume (Vi). Similarly, the second chamber 34B has a chamber 2 effective piston area (A2), and is filled with the piston fluid 40 that is at a second pressure (P2), at a second temperature (T2), and has a second volume (V2). In this non-exclusive example illustrated in Figure 1 , the fluid actuator assembly 24 is designed so that the chamber 1 effective piston area (Ai) is approximately equal to the chamber 2 effective piston area (A2).

[0049] The first pressure (Pi) of the piston fluid 40 in the first chamber 34A generates a first force (Fi) on the piston body 36B, and the second pressure (P2) of the piston fluid 40 in the second chamber 34B generates a second force (F2) on the piston body 36B. A total force (F) 44 (illustrated by an arrow) generated by the fluid actuator assembly 24 is equal to the first force (Fi) minus the second force (F2) ((F =Fi - F ₂ ).

[0050] With the non-exclusive design illustrated in Figure 1 , when the first pressure (Pi) is greater than the second pressure (P2), the first force (Fi) is greater than the second force (F2), the total force (F) is positive and urges the piston body 36B and the stage 14 from left to right. In contrast, when the first pressure (Pi) is lesser than the second pressure (P2), the first force (Fi) is less than the second force (F2), the total force (F) is negative and urges the piston body 36B and the stage 14 from right to left.

[0051] 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. As one, non-exclusive embodiment, the valve assembly 38 includes (i) a first valve sub-assembly 38A that is controlled to control the flow of the piston fluid 40 into and out of the first chamber 34A, to accurately control the first pressure (Pi); and (ii) a second valve sub-assembly 38B that is controlled to control the flow of the piston fluid 40 into and out of the second chamber 34B, to accurately control the second pressure (P2). In this embodiment, the first valve sub-assembly 38A includes a first inlet valve 38C that is controlled to control the flow of the piston fluid 40 into the first chamber 34A, and a first outlet valve 38D that is controlled to control the flow of the piston fluid 40 out of the first chamber 34A. Similarly, the second valve sub-assembly 38B includes a second inlet valve 38E that is controlled to control the flow of the piston fluid 40 into the second chamber 34B, and a second outlet valve 38F that is controlled to control the flow of the piston fluid 40 out of the second chamber 34B.

[0052] In this embodiment, the fluid actuator assembly 24 can include one or more fluid pressure sources 46 (two are shown) that provide pressurized piston fluid 40 to the inlet valves 38C, 38E. Moreover, each of the fluid pressure sources 46 can include a fluid tank 46A, a compressor 46B that generates the pressurized piston fluid 40 in the tank 46A, and a pressure regulator 46C that controls the pressure of the piston fluid 40 delivered to the inlet valves 38C, 38E. Further, the outlet valves 38D, 38F can vent to the atmosphere or to a low pressure area, such as a vacuum chamber.

[0053] In certain embodiments, each of the valves 38C, 38D, 38E, 38F includes one or more valve characteristics that influence the control of these valves 38C, 38D, 38E, 38F. For example, (i) the 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 tested individually to determine the individual valve characteristics of the respective valve 38C, 38D, 38E, 38F. With this design, the individual valve characteristics of the respective 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 characteristics of that valve can be used to control all of the valves 38C, 38D, 38E, 38F.

[0054] The type of valve 38C, 38D, 38E, 38F utilized can be varied. As nonexclusive examples, each valve 38C, 38D, 38E, 38F can be a proportional valve such as a poppet ("mushroom") type valve or a spool-type valve.

[0055] The type of valve characteristics will vary according to the type of valve 38C, 38D, 38E, 38F utilized. A couple of non-exclusive types of valves 38C, 38D, 38E, 38F and non-exclusive examples of valve characteristics are described in detail below. It should be noted that the valves 38C, 38D, 38E, 38F can be different than the examples provided herein, and the valve characteristics can be different than the examples provided herein.

[0056] 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.

[0057] 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 can be controlled to generate the controllable force 44 ("F") on the piston body 36B that accurately moves the piston body 36B and the stage 14.

[0058] The control system 20 is electrically connected to, and controls the electrical current that is directed to the valve assembly 38 to precisely position the stage 14 and the workpiece 22. In one embodiment, the control system 20 uses the information from the measurement system 18 (i) to constantly determine the position ("x") of the stage 14; and (ii) to direct current to the valve assembly 38 to position the stage 14. The control system 20 can include one or more processors 20A and electronic data storage 20B. The control system 20 uses one or more algorithms to perform the steps provided herein.

[0059] In certain embodiments, the control system 20 individually controls each of the first valves 38C, 38D to control the first pressure (Pi) in the first chamber 34A to generate the desired first force (Fi). Similarly, the control system 20 individually controls each of the second valves 38E, 38F to control the second pressure (P2) in the second chamber 34B to generate the desired second force (F2). Thus, by controlling the valves 38C, 38D, 38E, 38F, the control system 20 can control the fluid actuator assembly 24 to generate the desired total force (F) 44 on the stage 14.

[0060] In certain embodiments, when the control system 20 determines the need to add piston fluid 40 to the first chamber 34A, the control system 20 controls the first outlet valve 38D to be closed, and the first inlet valve 38C to open the appropriate amount to add the piston fluid 40. Further, when the control system 20 determines the need to remove piston fluid 40 from the first chamber 34A, the control system 20 controls the first inlet valve 38C to be closed, and the first outlet valve 38C to open the appropriate amount to release the piston fluid 40. In this example, one of the first valves 38C, 38D is controlled to be closed at any given time. Alternatively, the control system 20 can control both first valves 38C, 38D to be open during adding and/or removing piston fluid 40 from the first chamber 34A.

[0061] Similarly, when the control system 20 determines the need to add piston fluid 40 to the second chamber 34B, the control system 20 controls the second outlet valve 38F to be closed, and the second inlet valve 38E to open the appropriate amount to add the piston fluid 40. Further, when the control system 20 determines the need to remove piston fluid 40 from the second chamber 34B, the control system 20 controls the second inlet valve 38E to be closed, and the second outlet valve 38F to open the appropriate amount to release the piston fluid 40. In this example, one of the second valves 38E, 38F is controlled to be closed at any given time. Alternatively, the control system 20 can control both second valves 38E, 38F to be open during adding and/or removing piston fluid 40 from the second chamber 34B.

[0062] 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, it is critical to determine the nonlinearities embedded in the system, such as (i) fluid pressure variations with chamber volumes, (ii) backlash and differential pressure dependency of proportional valves 38C, 38D, 38E, 38F, and (3) fluid flow nonlinearity associated with upstream and downstream pressure. Through experimental testing and/or modeling, these nonlinearities can be identified and compensated for by the control system 20.

[0063] For example, the control system 20 can utilize (i) an inverse of the first inlet valve characteristic to control the first inlet valve 38C; (ii) an inverse of the first outlet valve characteristic to control the first outlet valve 38D; (iii) an inverse of the second inlet valve characteristic to control the second inlet valve 38E; and (iv) an inverse of the second outlet valve characteristic to control the second outlet valve 38F. Because, the control system 20 utilizes an inverse of each valve characteristic, each valve 38C, 38D, 38E, 38F can be controlled with improved accuracy.

[0064] Figure 2A is a control block diagram 220 that illustrates one, non-exclusive example of the method for controlling the fluid actuator assembly 24 to accurately position the stage 14. More specifically, the control block diagram 220 illustrates one, non-exclusive method for directing 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 has a measured, momentary, stage position ("x") (e.g. along the measurement axis 30 (illustrated in Figure 1 )) as measured by the measurement system 18 (illustrated in Figure 1 ).

[0065] In this embodiment, the control block diagram 220 includes (i) a stage reference block 260 that provides a stage, desired reference position or trajectory ("Xd") (e.g. along the movement axis 30 (illustrated in Figure 1 )) of the stage 14, a desired velocity (" x _d "), a desired acceleration (" x _d "), and a stage jerk reference (" x _d "); (ii) a stage feedback ("FB") controller 262; (iii) a stage feedforward ("FF") controller 264; (iv) a feedback converter 266 that converts a feedback force command to a feedback pressure command; (v) a feedforward converter 268 that converts a feedforward force command to a feedforward pressure command; (vi) a first chamber controller 270; (vii) a second chamber controller 272; and (vii) a chamber volume estimator 278 that estimates the current first chamber volume ("Vi") and the rate of first volume change (" ¼ ") of the first chamber based on the measured position ("x") of the stage 14, and estimates the current second chamber volume ("V2") and the rate of second volume change (" V ₂ ") of the second chamber based on the measured position of the stage 14.

[0066] It should be noted that some of the blocks of the control block diagram 220 of Figure 2A are optional and/or the control block diagram 220 can include additional control blocks. For example, the control block diagram 220 can be designed without the stage feedforward controller 264 loop. Additionally, or alternatively, the control block diagram 220 can be designed to include an iterative learning loop (not shown).

[0067] In the control block diagram 220, moving left to right, the stage desired reference 260 position or trajectory fx ) is compared to the stage measured position fx") to generate a stage following error ("e") which represents the error between the desired position and the measured position of the stage 14. Next, the stage following error ("e") is fed to the stage feedback controller 262 which generates a stage, feedback force command ("F¾") which represents the force command necessary to move the stage 14 from the measured position to the reference position. Concurrently, the desired reference position ("xd"), the stage velocity reference (" ·½ "), the stage acceleration reference (" ¾ "), and the stage jerk reference (" ¾ ") are fed to the stage feedforward controller 264 which generates a stage, feedforward force command ("Fff") which represents the force command necessary to compensate for such things as system time delay, and the trajectory.

[0068] Next, in this embodiment, the stage, feedback force command ("Fft>") and the feedforward force command ("Fff") are combined to generate the combined force command ("F _C md") that is fed to the feedback converter 266 which converts the combined force command to a first feedback pressure command ("P1 ft>" or "Pi, _C md") for the first chamber, and a second feedback pressure command ("P2ft>" or "P2,cmd") for the second chamber. Similarly, the stage, feedforward force command ("Fff") is fed to the feedforward converter 268 which converts the feedforward force command to a first feedforward rate of change pressure command (" ") for the first chamber, and a second feedforward rate of change pressure command (" ") for the second chamber.

[0069] Subsequently, the first chamber controller 270 uses the fir feedback pressure command ("Pi , _C md") , the first feedforward pressure command the first measured pressure ("P i"), the first chamber volume ("V/'), and the rate of first volume change (" ¼ ") to determine a first valve subassembly current command ("u ') that is directed to the first valve subassembly. Similarly, the second chamber controller 272 uses the second feedback pressure command ("P2,cmd"), the second feedforward pressure command (" "), the second measured pressure ("P ), the second chamber volume ("V2"), and the rate of second volume change (" V ₂ ") to determine a second valve subassembly current command ("112") that is directed to the second valve subassembly. The current to the valve assembly 38 controls the piston fluid to the piston assembly 31 and generates the force ("F") on the stage 14.

[0070] As provided herein, the chamber controllers 270, 272 utilize the inverse of the valve characteristics to accurately determine the respective current commands necessary to accurately control the pressure in the two chambers. This process is described in more detail below in reference to Figure 2B.

[0071] It should be noted in the embodiments where one of the valves of each valve subassembly is closed at any given time, a single current command is all that is needed for each valve subassembly. Alternatively, if both of the valves of each valve subassembly can be open at any given time, then the chamber controllers 270, 272 will need to be designed to provide separate current commands to each valve.

[0072] A number of equations are useful for understanding 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 that is generated by the stage mover assembly 16 is provided as follows:

F = F _l - F ₂ . Equation 1 As provided above, F s the total force; F ₁ is the force generated by the first chamber; and F ₂ is the force generated by the second chamber.

[0073] Equation 1 can be rewritten as follows:

F = P _l A _l - P ₂ A ₂ . Equation 2

As provided above, P[ 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 the effective piston area for the second chamber 34B.

[0074] Further, the force on the stage can be expressed as follows:

F = Mx + Cx . Equation 3

In Equation 3 and elsewhere, M is mass of the stage (including the workpiece), C is damping coefficient, X is the acceleration of the mass of the stage, and x is velocity of stage.

[0075] The gas equation can be expressed as follows:

P _j V _j = mflT _j . Equation 4

In Equation 4 and elsewhere, i is the respective chamber (either the first chamber (Ί ") or the second chamber ("2")); P _t is the pressure in the respective chamber; V _i is the volume in the respective chamber; R is the gas constant; f _t - j _s the gas mass in the respective chamber; and T _i is the temperature in the respective chamber,

[0076] Equation 4 can be rewritten as follows:

P _i V _i + P . = . Equation 5

In Equation 5 and elsewhere, _t is a rate of pressure change in the respective chamber; V _{ is a rate of volume change in the respective chamber and ^m i is the mass flow rate in the respective chamber.

[0077] Equation 5 can be rewritten as chamber pressure modeling as follows: • _ - py _r +

ri _v Equation 6

i

[0078] Further, Equation 5 can be rewritten as a chamber mass flow rate control as follows: m —

Equation 7

RT

[0079] The first volume V ₁ of the first chamber 34A can be written as a function of stage position as follows:

Equation 8

Similarly, the second volume V ₂ of the second chamber 34B can be written as a function of stage position as follows: Equation 9

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 current position of the stage; ^x ₀ is dead length of the first chamber; and -¾, ₀ is dead length of the second chamber.

[0080] Equation 8 can be rewritten as follows:

V _l = Α _λ Χ . Equation 10

Similarly, Equation 9 can be rewritten as follows:

^2 ⁼ ~^2 ^X . Equation 1 1

In these equations and elsewhere, V _l is a rate of volume change in the first chamber; and V ₂ is a rate of volume change in the second chamber.

[0081] The chamber pressure control of each chamber 34A, 34B can be expressed as follows: Mx + Equation s

F _cm d ⁼ Equation 13

7 f

In Equations 12 and 13, and elsewhere, _cm d is the force command; feedforwad is the feedforward force command; F feedback is the feedback force command; ¾ is the stage acceleration reference; ¾ is stage velocity reference; X<j is stage jerk reference, ¾ is the reference position; C is damping ratio of the stage and actuator system; C _fb (s) is stage feedback control filter; ^x is the current measured position of the stage; Pi, _C md is the pressure command to the first chamber; and ^cmd is the pressure command to the second chamber.

[0082] Equations 12 and 13 can be rewritten as follows:

^P \,cmd ^A \ = ^F o + ^{r ' F} , and Equation 14

^P 2,cmd ^A 2 = F ₀ - (l- r) - F . Equation 15

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

[0083] Equations 14 and 15 can be rewritten as follows: p — _ F£ + r - F

i,cmrf ^ and Equation 16

_ F _o -{\- r) - F

2,cmd ^~ _& . Equation 17

^A 2 [0084] The chamber pressure control can be expressed as follows:

Pi,cmd ⁼ ^i, feedforward + ^i, feedback (^) ^' ^i,cmd ^~ )■ Equation 18

Further, Equation 18 can be expressed as follows:

A ^ feedforward ^^ ^' d

1, feedforward - _Λ - _Λ , and Equation 19

^ feedforward ^^^d ^" ^' ^d

I eedforward 2A _' Equation 20

[0085] Similar to Equation 7, the chamber mass flow control can be expressed as follows: Equation 21

YYl

In Equation 21 , and elsewhere, i,cmd is the mass flow rate command for one of the first chamber and the second chamber.

[0086] Figure 2B is a control block diagram that illustrates how one of the chamber controllers 270, 272 (illustrated in Figure 2A) can be configured. In this embodiment, the chamber controller includes (i) a pressure feedback controller 290; (ii) a pressure to mass flow converter 292; (iii) an inlet mass flow to orifice area converter 294; (iv) an outlet mass flow to orifice area converter 296; (v) an inlet orifice area to current converter 297; and (vi) an outlet orifice area to current converter 298. In this embodiment, the pressure feedback controller 290 receives the pressure error P _{t ^err} for the respective chamber, and generates a rate of pressure change feedback

(" Pi _, fl ")■ The pressure to mass flow converter 292 receives a rate of pressure change command (" ^ _,cm '), the chamber pressure {" P "), the current chamber volume ("V,") and the rate of volume change (" ¼ ") and generates the mass flow rate command (" ^rn i,cmd+ ") for the inlet valve, and the mass flow rate command (" i,cmd- ") for the outlet valve. The pressure to mass flow converter 292 can use Equations 21 and 22 provided herein.

[0087] The inlet mass flow to orifice area converter 294 receives the mass flow rate command (" ^i,cmd+ ") and the chamber pressure (" P _t ") and generates an inlet orifice area command {" ty,cmd + ") for the inlet valve. The inlet mass flow to orifice area converter 294 can use Equation 24 provided herein. Somewhat similarly, the outlet mass flow to orifice area converter 296 receives the mass flow rate command

{" ^i,cmd - ") and the chamber pressure {" i ") and generates an outlet orifice area command (" ^i,cmd - ") for the outlet valve. The outlet mass flow to orifice area converter 296 can use Equation 25 provided herein.

[0088] Next, the inlet orifice area to current converter 297 uses the inlet orifice area command (" ty,cmd + ") to generate the inlet current command (" ^i,cmd + ") for the inlet valve. The inlet orifice area to current converter 297 can use Equation 27 provided herein. Similarly, the outlet orifice area to current converter 298 uses the outlet orifice area command (" i,cmd - ") to generate the outlet current command (" ^i,cmd - ") for the outlet valve. The outlet orifice area to current converter 298 can use Equation 28 provided herein.

[0089] Figure 3 is a simplified illustration of one of the piston chambers 334i and one of the valve sub-assemblies 338i. As illustrated in Figure 3, in this embodiment, the chamber mass flow rate command into and out of the chamber 334i is controlled by an inlet valve 338N and an outlet valve 338io. In this embodiment, the pressure source 346 provides pressurized piston fluid 340 at a pressure referred to as P _SOU rce to the inlet of the inlet valve 338N. Further, the outlet of the outlet valve 338io is at a pressure of Pdmm■ The chamber mass flow control of Equation 21 can be rewritten as follows: mi,cmd ^{= m} i,cmd+ ~~ ^m i,cmd- . Equation 22

In Equation 22, and elsewhere, ^i,cmd+ is the mass flow rate command for the inlet valve 338M for the selected chamber 334i; and ^m i,cmd- is the mass flow rate command for the outlet valve 338io for the selected chamber 334i. As provided herein, in certain embodiments, if it is desired to increase the mass flow rate into the chamber

334i ( ) and the mass flow rate command is set to be equal to the mass flow rate command of the inlet valve 338M is set to the mass flow rate command ( ^i,cmd+ ~ ^cmd ). Similarly, in certain embodiments, if it is desired to increase the mass flow rate out of the chamber

334i { li,cmd ^< 0 ) _t hen the inlet valve 338N is closed (™i,cmd+ ~ ^ ) and the mass flow rate command is set to be equal to the mass flow rate command of the outlet valve 338io is set to the mass flow rate command ( ^i,cmd- ~ ^cmd ).

[0090] The valve flow equation can be written as follows: m— a ^■ f (P _upsream , P downstream ) . Equation 23

In Equation 23, and elsewhere, CI is the area of the valve orifice that is open; is a mathematical function; ^upstr am ί s the pressure upstream of the valve orifice; and

^downstream s the pressure downstream of the valve orifice. Thus, the mass flow rate is equal to the area of valve orifice that is open multiplied by and a function of the pressure upstream and the pressure downstream.

[0091] Figure 4 is a simplified illustration of a pipe 400 that includes an orifice 402 that is analogous to a valve orifice of a valve when it is open. In this example, the pressure upstream and pressure downstream are labeled, and the orifice 402 has an orifice area. With reference to Figures 3 and 4, Equation 23 can be rewritten as the following valve orifice area commands:

ΐΐΐ i,cmd+

a i,cmd+ p and Equation 24

J ^ source ' i '

i,cmd

a i,cmd- r p p Equation 25

J ^r i -> ^Γ drain )

In these Equations, and elsewhere, &i,cmd+ is the valve orifice command for the inlet valve 338M of the selected chamber 334i; and ^a i ,cmd- is the mass flow rate command for the outlet valve 338io for the selected chamber 334i.

[0092] The valve area equation can be written as follows:

a = A u) . Equation 26

In Equation 26, # is the valve orifice area; is a valve area equation; and is the valve current. The valve area equation is described in more detail below.

[0093] Equation 26 can be rewritten as valve current commands as follows: ui,cmd+ ⁼ Equation 27 ui,cmd- ⁼ ^i,- ( ^a i,cmd- ^ . Equation 28

In Equations 27 and 28, and elsewhere, ^U i,cmd+ is the valve current command to the inlet valve; A,+ is the inverse of the valve area equation for the inlet valve; ^a i,cmd+ is valve orifice area of the inlet valve; ^U i,cmd- is the valve current command to the outlet valve; ^i - is the inverse of the valve area equation for the outlet valve; and i,cmd- is valve orifice area of the outlet valve. [0094] E uations 24 and 25 can be written more generically as follows:

Equation 29

For subsonic flow, the pressure upstream divided by the pressure downstream is less p

than or equal to theta ("Θ") (—≤ Θ) then

Equation 30

personic flow, when the pressure upstream divided by the pressure downstream is greater than theta ("Θ") (- - > Θ) then

d

f(P _u ,P _d ) = /3P _u . Equation 31

In these equations, =

with c being a discharge coefficient; M _m is the gas molecular mass; Z is the gas compressibility factor; k is the specific heat ratio; R is the universal gas law constant; and T is temperature.

[0095] Figure 5A is a simplified cut-away view of one, non-exclusive example of a valve 538 that can be used as one of the valves 38C, 38D, 38E, 38F from Figure 1 . In this embodiment, the valve 538 is a poppet type valve that includes a valve housing 539A, a movable valve body 539B, an inlet conduit 539C, an outlet conduit 539D, a resilient member 539E (e.g. a spring) that urges the valve body 539B against the inlet conduit 539C, and a solenoid 539F.

[0096] In this simplified example, the valve housing 538A is somewhat cylindrical- shaped, the valve body 539B is disk-shaped, and the conduits 539C, 539D are tubular- shaped. Further, in Figure 5A, the valve 538 is illustrated in the closed position when the control system (not shown in Figure 5A) is not directing current to the solenoid 539F. As a result thereof, the resilient member 539E urges the valve body 539B against the top of the inlet conduit 539C to close the valve 538.

[0097] It should be noted that when no current is directed to the solenoid 539F, the valve remains closed as long as the spring preload force is greater than the force generated by the pressure difference between the pressure upstream and the pressure downstream.

[0098] Figure 5B is a simplified cut-away view the valve 538 of Figure 5A with the valve 538 is an open position. At this time, the control system (not shown in Figure 5B) is directing current to the solenoid 539F. When current is directed to the solenoid, this generates a solenoid force F _solenoid that urges (attracts) the valve body 539B upward away from the top of the inlet conduit 539C. Typically, the magnitude of solenoid force is proportional to the current. When sufficient current is directed to the solenoid 539F, the spring preload force of the resilient member 539F is overcome, the valve body 539B is moved away from the top of the inlet conduit 539C, and the valve 538 is opened. Further, the amount of current will determine how far the valve 538 is opened. Generally, the size of the valve opening increases as current increases.

[0099] As illustrated in Figure 5B, the amount in which the valve body 539B has moved from the closed position to the open position is referred to as "y".

[00100] Figure 5C is a simplified cut-away view the valve 538 of Figure 5A with the inlet conduit removed 539C, the solenoid 539F is not activated, and there is no pressure in the conduits 539C, 539D. At this time the resilient member 539E urges the valve body 539B downward a preload distance y _o . The valve body 539B is illustrated in the closed position in phantom for reference. When the inlet conduit 539D is in place (as illustrated in Figure 5A), the resilient member 539E applies a spring preload force that is equal to the spring constant k _s of the resilient member 539E multiplied by the preload distance y _o .

[00101] The control of the valve 538 can be expressed as follows: M _v y + C _v y + k _s y + k ^ = k _f u + πΤΑΡ

spring s^odd air pressure force ^■ Equation 32 preload f _orce

force p so ,lenoid

In Equation 32 and elsewhere, M _v is the mass of the valve body 539B; y is the acceleration of the valve body 539B; C _v is damping caused by spring friction; y is the velocity of the valve body 539B; k _s is the spring constant of the resilient member 539E; y _o is the preload distance; k _f is the solenoid force constant; u is the current command directed to the solenoid; r is the radius at the top of the inlet conduit 539C; and delta pressure is the difference between the pressure upstream and the pressure downstream ( = P _u — P _d

[00102] The effective orifice area "a" of the valve 538 illustrated in Figures 5A-5C can be expressed as follows:

3 = A{y) ~ 2M ^■ y and Equation 33 y = A (a) ~ - Equation 34

In Equations 33 and 34, and elsewhere, is the valve area equation; and ^ is the inverse of the valve area equation.

[00103] The dead-zone current u _o necessary to overcome the spring preload force can be expressed as follows:

k y -πτ ² ΑΡ

u _o ( P) - . Equation 35

k _f

[00104] With the valve 538 illustrated in Figures 5A-5C, the maximum allowed pressure difference P _max without leakage can be expressed as follows: ■ Equation 36 [00105] With the valve 538 illustrated in Figures 5A-5C, the static control current can be expressed as follows: on 37

effective orifice area

[00106] As provided above, in order to accurately control the fluid actuator assembly 24, it is critical to determine the nonlinearities embedded 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 ).

[00107] Figure 6A is a graph that illustrates the valve effective orifice area versus current command for the various delta pressures {"AP "). This graph was generated by experimentally testing a poppet valve at various delta pressures. For example, while maintaining a delta pressure of 350kPa, the flow rate was measured at a plurality of different current commands to the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted in Figure 6A as a small box. Subsequently, line 600A was generated by curve fitting these data points. Line 600A represents the relationship between valve area orifice versus current command for a delta pressure of 350kPa.

[00108] Next, while maintaining a delta pressure of 300kPa, the flow rate was measured at a plurality different current commands to the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted in Figure 6A as a small circle. Subsequently, line 602A was generated by curve fitting these data points. Line 602A represents the relationship between valve area orifice versus current command for a delta pressure of 300kPa. [00109] Similarly, while maintaining a delta pressure of 250kPa, the flow rate was measured at a plurality different current commands to the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted in Figure 6A as a small "x". Subsequently, line 604A was generated by curve fitting these data points. Line 604A represents the relationship between valve area orifice versus current command for a delta pressure of 250kPa.

[00110] Further, while maintaining a delta pressure of 200kPa, the flow rate was measured at a plurality different current commands to the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted in Figure 6A as a small "z". Subsequently, line 606A was generated by curve fitting these data points. Line 606A represents the relationship between valve area orifice versus current command for a delta pressure of 200kPa.

[00111] Moreover, while maintaining a delta pressure of 150kPa, the flow rate was measured at a plurality different current commands to the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted in Figure 6A as a small triangle. Subsequently, line 608A was generated by curve fitting these data points. Line 608A represents the relationship between valve area orifice versus current command for a delta pressure of 150kPa.

[00112] Additionally, while maintaining a delta pressure of 10OkPa, the flow rate was measured at a plurality different current commands to the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted in Figure 6A as a small "+". Subsequently, line 61 OA was generated by curve fitting these data points. Line 61 OA represents the relationship between valve area orifice versus current command for a delta pressure of 10OkPa.

[00113] Finally, while maintaining a delta pressure of 50kPa, the flow rate was measured at a plurality different current commands to the solenoid. Subsequently, the effective orifice area was calculated for each measured flow rate and plotted in Figure 6A as a "D". Subsequently, line 612 was generated by curve fitting these data points. Line 612 represents the relationship between valve area orifice versus current command for a delta pressure of 50kPa. [00114] In this example, the valve characteristic 614 of this valve represents the relationship of effective valve orifice area versus current command for a number of different delta pressures. Alternatively, for example, the valve characteristic 614 can be (i) the relationship between effective valve orifice area versus voltage for a number of different delta pressures; (ii) the relationship between flow rate versus current command for a number of different delta pressures; and/or (iii) the relationship between flow rate versus voltage for a number of different delta pressures.

[00115] As provided above, in certain embodiments, the valve characteristic 614 is inverted to create an inverted valve characteristic 616 that is subsequently used in the control of that valve. For example, the data in Figure 6A can be inverted (switch the X and Y axes of the graph) to create the inverted valve characteristic 616 illustrated in Figure 6B.

[00116] More specifically, Figure 6B is a graph that illustrates valve current command versus the effective orifice area which is an inversion of the graph in Figure 6A. In this example, the data from Figure 6A is inverted to create the data in Figure 6B. Subsequently, curve fitting is used to generate the curves in Figure 6B.

[00117] For example, at a delta pressure of 350kPa, the data is represented as small boxes. Subsequently, line 600B was generated by curve fitting these data points. Line 600B represents the relationship between valve current command and valve area orifice for a delta pressure of 350kPa.

[00118] Next, at a delta pressure of 300kPa, the data is represented as small circles. Subsequently, line 602B was generated by curve fitting these data points. Line 602B represents the relationship between valve current command and valve area orifice for a delta pressure of 300kPa.

[00119] Similarly, at a delta pressure of 250kPa, the data is represented as small "x's". Subsequently, line 604B was generated by curve fitting these data points. Line 604B represents the relationship between valve current command and valve area orifice for a delta pressure of 250kPa.

[00120] Further, at a delta pressure of 200kPa, the data is represented as small "z's". Subsequently, line 606B was generated by curve fitting these data points. Line 606B represents the relationship between valve current command and valve area orifice for a delta pressure of 200kPa.

[00121] Moreover, at a delta pressure of 150kPa, the data is represented as small triangles. Subsequently, line 608B was generated by curve fitting these data points. Line 608B represents the relationship between valve current command and valve area orifice for a delta pressure of 150kPa.

[00122] Additionally, at a delta pressure of 10OkPa, the data is represented as small "+'s". Subsequently, line 610B was generated by curve fitting these data points. Line 610B represents the relationship between valve current command and valve area orifice for a delta pressure of 100kPa.

[00123] Finally, at a delta pressure of 50kPa, the data is represented as small "D's". Subsequently, line 612B was generated by curve fitting these data points. Line 612B represents the relationship between valve current command and valve area orifice for a delta pressure of 50kPa.

[00124] It should be noted that the inverted valve characteristic 616 data from the Figure 6B graph can be used by the control system to accurately control the valve. It should also be noted that the control system can utilize interpolation to generate data for other delta pressures to accurately control the valve at other delta pressures.

[00125] Figures 7A-7D are simplified cut-away illustrations of another type of valve 738 at various valve positions that can be used as one of the valves 38C, 38D, 38E, 38F from Figure 1 . More specifically, Figure 7A is a simplified side illustration of a spool type valve 738 at a fully closed position; Figure 7B is a simplified side illustration of the spool type valve 738 at a closed, baseline (ready to open) position; Figure 7C is a simplified side illustration of the spool type valve 738 at a partly open position; and Figure 7D is a simplified side illustration of the spool type valve 738 at a fully open position.

[00126] In this embodiment, the valve 738 is a spool type valve that includes a valve housing 739A, a movable valve body 739B (sometimes referred to as a "spool"), an inlet opening (not shown), an outlet opening 739D, a resilient member 739E (e.g. a spring) that urges the valve body 739B from right to left, and a solenoid 739F that moves the valve body 739B from the left to the right. [00127] In this simplified example, the valve housing 738A is somewhat hollow cylindrical-shaped, the valve body 739B is disk-shaped, and the openings 739D are circular-shaped and are positioned on opposite sides of the valve housing 738A with the valve body 739B positioned therebetween.

[00128] It should be noted that because the pressure upstream and the pressure downstream are orthogonal to the valve body 739B, the delta pressure will not influence the opening or closing of the valve 738.

[00129] Further, in Figure 7A, the valve 738 is illustrated in the fully closed position when the control system (not shown in Figure 7A) is not directing current to the solenoid 739F. At this time, the valve body 739B covers both the inlet and the outlet 739D to close the valve 738.

[00130] Figure 7B is a simplified cut-away view the valve 738 of Figure 7A with the valve 738 in a baseline position, right before it is open. At this time, the control system (not shown in Figure 7B) is directing current to the solenoid 739F. When current is directed to the solenoid, this generates a solenoid force F _solenoid that urges the valve body 739B to a baseline position y _b in which the valve 738 is ready to open.

[00131] Figure 7C is a simplified cut-away view the valve 738 of Figure 7A with the valve 738 in a partly open position. At this time, the control system (not shown in Figure 7C) is directing current to the solenoid 739F. When current is directed to the solenoid, this generates a solenoid force F _solenoid that urges the valve body 739B to a position y in which the valve 738 is partly open.

[00132] Typically, the magnitude of solenoid force is proportional to the current. When sufficient current is directed to the solenoid 739F, the spring preload force of the resilient member 739F is overcome, and the valve body 739B is moved. Further, the amount of current will determine how far the valve 738 is opened. Generally, the size of the valve opening increases as current increases.

[00133] Figure 7D is a simplified cut-away view the valve 738 of Figure 7A with the valve 738 in a fully open position. [00134] In this embodiment, the valve mechanical dynamics for the valve 738 illustrated in Figures 7A-7D can be expressed as follows:

M + ^C + Z + f preload = ^k f ^U

— v— ' ^t ~ ^—l _J . Equation 38

spring solenoid

pre-load force

force ^solenoid

In Equation 38 and elsewhere, M _v is the mass of the valve body 739B; X is the acceleration of the valve body 739B; c _v is damping caused by spring friction; X is the velocity of the valve body 739B; k _s is the spring constant of the resilient member 739E; y _o is the preload distance; k _f is the solenoid force constant; u is the current command directed to the solenoid; and f _pre ioad is pre-load force of the resilient member 739E.

[00135] Figure 7E is a simplified illustration of the outlet 739D and the valve body 739B in the partly open position which helps in the explanation of the effective orifice area. In this example, X— Y ₀ + Y . Further, effective orifice area A _eff of this type of valve 738 can be calculated as follows:

A _eff (y) = 0 - r ² - (r - y)^r ² - (r - y) , and Equation 39

Θ - acos . Equation 40

r

[00136] Figure 8A is a graph that illustrates normalized effective orifice area versus normalized spool position that was calculated using the above formulas for the valve illustrated in Figures 7A-7D. In this example, the valve characteristic 814 of this valve represents the relationship of normalized effective orifice area versus normalized spool position.

[00137] As provided above, in certain embodiments, the valve characteristic 814 is inverted to create an inverted valve characteristic 816 illustrated in Figure 8B that is subsequently used in the control of that valve. For example, the data in Figure 8A can be inverted (switch the X and Y axes of the graph) to create the inverted valve characteristic 816 illustrated in Figure 8B that plots spool position versus normalized effective orifice area.

[00138] Certain valves (e.g. 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.

[00139] Figure 9A is a graph that illustrates the test results of a spool valve. In Figure 9A, the graph illustrates spool positon versus voltage. Further, Figure 9B is a graph that illustrates the simulated results of a spool valve. In Figure 9B, the graph illustrates spool positon versus current. These Figures illustrate that for the same current command (or voltage command), the spool position can be different, depending on the previous command history. For example, with reference to Figure 9A, for the same command, (e.g. 5 volts), the spool position will different depending on the previous command. Similarly, with reference to Figure 9B, for the same command, (e.g. 0.5 amperes), the spool position will different depending on the previous command.

[00140] As provided herein, with reference to Figure 9A, another valve characteristic 914 of this valve is represented by the relationship of spool positon versus voltage. Yet another valve characteristic 915 of this valve, with reference to Figure 9B, is represented by the relationship of spool positon versus current. Thus, as provided herein, the spool valve nonlinearities (backlash and effective orifice geometry) can be calibrated and modeled. Subsequently, their inverse can be applied to the control software to linearize the spool valve.

[00141] The method utilized to calculate backlash of the valve can be varied. In one embodiment, calibration can be performed by gradually increasing the current (or voltage) command from zero to maximum and then gradually reduce 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.

[00142] In certain embodiments, the baseline position y _o of the valve can be determined while calibrating backlash. The baseline position can be determined by slightly increasing the current command, while checking the outlet flow of the valve to determine when the orifice starts to open. [00143] Figure 10A illustrates the two valve characteristics of the spool valve. More specifically, Figure 10A includes (i) a first valve characteristic 1014, e.g. a graph that illustrates normalized effective orifice area versus normalized spool position; and (ii) a second valve characteristic 1015, e.g. a graph that illustrates spool position versus current. The data for the graphs 1014, 1015 can be acquired experimentally, or calculated.

[00144] As provided above, in certain embodiments, the valve characteristics 1014,

1015 are inverted to create inverted valve characteristics 1016, 1017 illustrated in Figure 10B that are subsequently used in the control of that valve. For example, the data from graph 1014 is inverted (switch the X and Y axes of the graph) to create graph

1016 which plots normalized spool position versus normalized effective orifice area. Further, the data from graph 1015 is inverted (switch the X and Y axes of the graph) to create graph 1017 which plots current versus spool position. As provided herein, the inverted valve characteristics 1016, 1017 help to accurately control the effective orifice area of the valve despite the nonlinearities of the valve.

[00145] It should be noted that the inverted valve characteristics 1016, 1017 can be in the form of a look-up table, map, graphs, charts, or an analytical or fitted model.

[00146] Figure 1 1 is a schematic view illustrating an exposure apparatus 1 170 useful with the present invention. The exposure apparatus 1 170 includes an apparatus frame 1 172, an illumination system 1 182 (irradiation apparatus), a mask stage assembly 1 184, an optical assembly 1 186 (lens assembly), a plate stage assembly 1 1 10, and a control system 1 120 that controls the mask stage assembly 1 184 and the plate stage assembly 1 1 10.

[00147] The exposure apparatus 1 170 is particularly useful as a lithographic device that transfers a pattern (not shown) of liquid crystal display device from the mask 1 188 onto the workpiece 1 122.

[00148] The apparatus frame 1 172 is rigid and supports the components of the exposure apparatus 1 170. The design of the apparatus frame 1 172 can be varied to suit the design requirements for the rest of the exposure apparatus 1 170.

[00149] The illumination system 1 182 includes an illumination source 1 192 and an illumination optical assembly 1 194. The illumination source 1 192 emits a beam (irradiation) of light energy. The illumination optical assembly 1 194 guides the beam of light energy from the illumination source 1 192 to the mask 1 188. The beam selectively illuminates different portions of the mask 1 188 and exposes the workpiece 1 122.

[00150] The optical assembly 1 186 projects and/or focuses the light passing through the mask 1 188 to the workpiece 1 122. Depending upon the design of the exposure apparatus 1 170, the optical assembly 1 186 can magnify or reduce the image illuminated on the mask 1 188.

[00151] The mask stage assembly 1 184 holds and positions the mask 1 188 relative to the optical assembly 1 186 and the workpiece 1 122. Similarly, the plate stage assembly 1 1 10 holds and positions the workpiece 1 122 with respect to the projected image of the illuminated portions of the mask 1 188.

[00152] There are a number of different types of lithographic devices. For example, the exposure apparatus 1 170 can be used as scanning type photolithography system that exposes the pattern from the mask 1 188 onto the glass workpiece 1 122 with the mask 1 188 and the workpiece 1 122 moving synchronously. Alternatively, the exposure apparatus 1 170 can be a step-and-repeat type photolithography system that exposes the mask 1 188 while the mask 1 188 and the workpiece 1 122 are stationary.

[00153] However, the use of the exposure apparatus 1 170 and the stage assemblies provided herein are not limited to a photolithography system for liquid crystal display device manufacturing. The exposure apparatus 1 170, for example, can be used as a semiconductor photolithography system that exposes an integrated circuit pattern onto a wafer or a photolithography system for manufacturing a thin film magnetic head. Further, the present invention can also be applied to a proximity photolithography system that exposes a mask pattern by closely locating a mask and a substrate without the use of a lens assembly. Additionally, the present 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.

[00154] A photolithography system according to the above described embodiments can be built by assembling various subsystems, including each element listed in the appended claims, in such a manner that prescribed mechanical accuracy, electrical accuracy, and optical accuracy are maintained. In order to maintain the various accuracies, prior to and following assembly, every optical system is adjusted to achieve its optical accuracy. Similarly, every mechanical system and every electrical system are adjusted to achieve their respective mechanical and electrical accuracies. The process of assembling each subsystem into a photolithography system includes mechanical interfaces, electrical circuit wiring connections and air pressure plumbing connections between each subsystem. Needless to say, there is also a process where each subsystem is assembled prior to assembling a photolithography system from the various subsystems. Once a photolithography system is assembled using the various subsystems, a total adjustment is performed to make sure that accuracy is maintained in the complete photolithography system. Additionally, it is desirable to manufacture an exposure system in a clean room where the temperature and cleanliness are controlled.

[00155] Further, a device can be fabricated using the above described systems, by the process shown generally in Figure 12. In step 1201 , the device's function and performance characteristics are designed. Next, in step 1202, a mask (reticle) having a pattern is designed according to the previous designing step, and in a 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 a photolithography system described hereinabove in accordance with the present invention. In step 1205 the flat panel display device is assembled (including the dicing process, bonding process and packaging process), finally, the device is then inspected in step 1206.

[00156] It is understood that although a number of different embodiments of the stage assembly 10 have been illustrated and described herein, one or more features of any one embodiment can be combined with one or more features of one or more of the other embodiments, provided that such combination satisfies the intent of the present invention.

[00157] While a number of exemplary aspects and embodiments of the stage assembly 10 have been shown and disclosed herein above, those of skill in the art will recognize certain modifications, permutations, additions and sub-combinations thereof. It is therefore intended that the following appended claims and claims hereafter introduced are interpreted to include all such modifications, permutations, additions and sub-combinations as are within their true spirit and scope, and no limitations are intended to the details of construction or design herein shown.