Patent Publication Number: US-10309428-B2

Title: Method for controlling gas-pressure-driven apparatus and gas-pressure-driven apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority based on Japanese Patent Application No. 2015-231395 filed on Nov. 27, 2015, and the entire contents of that application is incorporated by reference in this specification. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a gas-pressure-driven apparatus which moves a movable member in relation to a main body thereof in accordance with the pressure of a working chamber to which a working gas is supplied and from which the working gas is discharged. 
     2. Description of the Related Art 
     Conventionally, there has been known a method for calculating the moved position and movement amount of a piston (i.e., a movable member) in a hydraulic cylinder on the basis of the flow rate of pressurized fluid (see, e.g., Japanese Patent Gazette No. 5331986). Since the method disclosed in Japanese Patent Gazette No. 5331986 monitors the integrated flow rate of the pressurized fluid whose integration starts from a state in which the piston has stopped at its initial position, even when the piston stops at an intermediate position between the initial position and a displacement end position, the intermediate position to which the piston has moved can be detected. 
     However, the method disclosed in Japanese Patent Gazette No. 5331986 cannot determine the initial position of the piston in the case where the initial position of the piston is not one of the displacement end positions; i.e., opposite ends of the movement range of the piston. In such a case, the moved position of the piston (which correlates with the volume of the working chamber) cannot be calculated. 
     SUMMARY OF THE INVENTION 
     The present invention has been accomplished in view of the above-described problem, and its main object is to provide a method for controlling a gas-pressure-driven apparatus which can calculate the volume of a working chamber irrespective of the initial position of a movable member. 
     Aspects of the present invention for solving the above-described problem and their advantageous effects will now be described. 
     A first aspect of the present invention is a method for controlling a gas-pressure-driven apparatus comprising a main body having a working chamber to which a working gas is supplied and from which the working gas is discharged, a supply and discharge section for supplying the working gas to the working chamber and discharging the working gas from the working chamber, a movable member which moves relative to the main body in accordance with a pressure of the working chamber, a pressure sensor for detecting a pressure of a space including the working chamber, and a flow rate sensor for detecting a flow rate of the working gas flowing into and flowing out of the working chamber. 
     The present method comprises creating a state in which a volume of the working chamber cannot be changed and changing the pressure of the working chamber in this state by controlling the supply and discharge section; calculating a pressure change amount on the basis of the pressure detected by the pressure sensor and calculating an integrated flow rate on the basis of the flow rate detected by the flow rate sensor when the pressure of the working chamber is changed; calculating an initial volume of the working chamber on the basis of the pressure change amount and the integrated flow rate; and calculating a post-change volume of the working chamber after its volume has changed, on the basis of the initial volume and the integrated flow rate calculated from the flow rate detected by the flow rate sensor after creation of a state in which the volume of the working chamber can be changed from the initial volume. 
     In the above-described gas-pressure-driven apparatus, the working gas is supplied to and discharged from the working chamber by the supply and discharge section. The movable member is moved relative to the main body in accordance with the pressure of the working chamber. The pressure of the space including the working chamber is detected by the pressure sensor. The flow rate of the working gas flowing into and flowing out of the working chamber is detected by the flow rate sensor. 
     According the above-described method, a state in which the volume of the working chamber cannot be changed is created, and the pressure of the working chamber is changed by controlling the supply and discharge section. As a result, the working gas flows into the working chamber or flows out of the working chamber. At that time, the working gas flowing into the working chamber or flowing out of the working chamber contributes to change in the pressure of the working chamber in the state in which the volume of the working chamber cannot be changed. The amount of the change in the pressure of the working chamber caused by the working gas flowing into the working chamber or flowing out of the working chamber changes in accordance with the volume of the working chamber at the time when the volume of the working chamber is made unchangeable (i.e., the initial volume of the working chamber). Therefore, the relation between the pressure change amount of the working chamber and the integrated flow rate of the working gas (i.e., the amount of the working gas flowing into or flowing out of the working chamber) reflects the initial volume of the working chamber. Accordingly, the initial volume of the working chamber can be calculated from the pressure change amount of the working chamber and the integrated flow rate of the working gas flowing into the working chamber. 
     Further, after a state in which the volume of the working chamber can be changed from the initial volume has been created, the integrated flow rate is calculated from the flow rate of the working gas detected by the flow rate sensor. The integrated flow rate in the state in which the volume of the working chamber can be changed correlates with the volume change amount of the working chamber. Therefore, the post-change volume of the working chamber after its volume has changed can be calculated from the integrated flow rate and the initial volume. In addition, irrespective of the initial position of the movable member, the initial volume of the working chamber can be calculated, whereby the post-change volume of the working chamber can be calculated. 
     A second aspect of the present invention is a gas-pressure-driven apparatus. The gas-pressure-driven apparatus comprises a main body having a working chamber to which a working gas is supplied and from which the working gas is discharged; a supply and discharge section for supplying the working gas to the working chamber and discharging the working gas from the working chamber; a movable member which moves relative to the main body in accordance with a pressure of the working chamber; a pressure sensor for detecting a pressure of a space including the working chamber; a flow rate sensor for detecting a flow rate of the working gas flowing into and flowing out of the working chamber; and a control section. The control section creates a state in which a volume of the working chamber cannot be changed, changes the pressure of the working chamber in this state by controlling the supply and discharge section, and calculates a pressure change amount on the basis of the pressure detected by the pressure sensor and calculates an integrated flow rate on the basis of the flow rate detected by the flow rate sensor when the pressure of the working chamber is changed. The control section calculates an initial volume of the working chamber on the basis of the pressure change amount and the integrated flow rate, and calculates a post-change volume of the working chamber after its volume has changed, on the basis of the initial volume and the integrated flow rate calculated from the flow rate detected by the flow rate sensor after creation of a state in which the volume of the working chamber can be changed from the initial volume. 
     According to the above-described configuration, the working gas is supplied to and discharged from the working chamber by the supply and discharge section. The movable member is moved relative to the main body in accordance with the pressure of the working chamber. The pressure of the space including the working chamber is detected by the pressure sensor. The flow rate of the working gas flowing into and flowing out of the working chamber is detected by the flow rate sensor. 
     By the control section, a state in which the volume of the working chamber cannot be changed is created, and the pressure of the working chamber is changed by controlling the supply and discharge section. As a result, the working gas flows into the working chamber or flows out of the working chamber. At that time, the working gas flowing into the working chamber or flowing out of the working chamber contributes to change in the pressure of the working chamber in the state in which the volume of the working chamber cannot be changed. The amount of the change in the pressure of the working chamber caused by the working gas flowing into the working chamber or flowing out of the working chamber changes in accordance with the volume of the working chamber at the time when the volume of the working chamber is made unchangeable (i.e., the initial volume of the working chamber). Therefore, the relation between the pressure change amount of the working chamber and the integrated flow rate of the working gas (i.e., the amount of the working gas flowing into or flowing out of the working chamber) reflects the initial volume of the working chamber. Accordingly, the initial volume of the working chamber can be calculated from the pressure change amount of the working chamber and the integrated flow rate of the working gas flowing into the working chamber. 
     Further, after a state in which the volume of the working chamber can be changed from the initial volume has been created, the integrated flow rate is calculated from the flow rate of the working gas detected by the flow rate sensor. The integrated flow rate in the state in which the volume of the working chamber can be changed correlates with the volume change amount of the working chamber. Therefore, the post-change volume of the working chamber after its volume has changed can be calculated from the integrated flow rate and the initial volume. In addition, irrespective of the initial position of the movable member, the initial volume of the working chamber can be calculated, whereby the post-change volume of the working chamber can be calculated. 
     The above and other objects, features, and advantages of the present invention will be apparent from the following description when taken in conjunction with the accompanying drawings which illustrate preferred embodiments of the present invention by way of example. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a circuit diagram illustrating a chemical supply system; 
         FIG. 2  is a time chart showing the basic operation of the chemical supply system; 
         FIG. 3  is a flowchart showing a series of processes for calculating the post-change volume of a working chamber; 
         FIG. 4  is a set of formulas for calculating the working chamber volume of a pump from the pressure and flow rate of operation air; 
         FIG. 5  is a flowchart showing a series of processes for estimating suction-side hydraulic head pressure; 
         FIG. 6  is a flowchart showing a series of processes for moving the diaphragm of the pump to its neutral position; 
         FIG. 7  is a schematic diagram showing an air-operated valve; 
         FIG. 8  is a graph showing the relation between valve opening degree and Cv value. 
         FIG. 9  is a schematic diagram showing an air cylinder. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     First Embodiment 
     A first embodiment of the present invention which is embodied as a chemical supply system used in a semiconductor production line or the like will now be described with reference to the drawings. 
       FIG. 1  is a circuit diagram showing a chemical supply system  10  (i.e., a gas-pressure-driven apparatus). As shown in  FIG. 1 , the chemical supply system  10  supplies resist solution R, which is a chemical solution (liquid), from an end nozzle  47   n  to an area near the center of a semiconductor wafer W disposed on a rotating plate  48 . The resist solution R is spread from the area near the center of the semiconductor wafer W to the peripheral edge of the semiconductor wafer W by centrifugal force. 
     The chemical supply system  10  includes a diaphragm pump  13 , a pump drive section  59 , a chemical supply section  49 , a suction pipe  41 , a discharge pipe  47 , a discharge valve  46 , a flow rate sensor  71 , a pressure sensor  72 , a position sensor  73 , a controller  70 , etc. 
     The pump  13  includes a main body  14  having a pump chamber  25  and a working chamber  26  to which a pressurized operation air (i.e., a working gas) is supplied and from which the pressurized operation air is discharged; and a diaphragm  23  which separates the pump chamber  25  and the working chamber  26  from each other. The diaphragm  23  (i.e., a movable member) is displaced (i.e., moves) in relation to the main body  14  in accordance with the pressure of the working chamber  26 . The resist solution R is sucked into the pump chamber  25  through the suction pipe  41 , and then discharged from the pump chamber  25  to the discharge pipe  47 . 
     The pump drive section  59  (i.e., a supply and discharge section) includes a supply source  53  which supplies pressurized operation air (i.e., a working gas), a vacuum generation source  61  which generates a negative pressure, an electro-pneumatic regulator  51 , etc. 
     The operation air is supplied from the supply source  53  to the electro-pneumatic regulator  51  through a supply pipe  52 . The operation air is discharged from the electro-pneumatic regulator  51  through a discharge pipe  60  to the vacuum generation source  61 . The electro-pneumatic regulator  51  has a solenoid valve, etc. and switches a to-be-used source between the supply source  53  and the vacuum generation source  61 . The operation air is supplied to the working chamber  26  of the pump  13  from the electro-pneumatic regulator  51  through an air pipe  50  (i.e., a working gas passage). The operation air is discharged from the working chamber  26  of the pump  13  to the electro-pneumatic regulator  51  through the air pipe  50 . In response to a first instruction signal (for example, a target pressure) from the controller  70 , the electro-pneumatic regulator  51  controls the pressure of the operation air to a set pressure, which is the target pressure. The pump drive section  59  is not limited to that including the electro-pneumatic regulator  51 , and may be a circuit of any other type for controlling the pressure of the operation air. 
     The chemical supply section  49  includes a resist bottle  42  which stores the resist solution R, a suction valve  40 , a supply source  44  which supplies the pressurized operation air, a pressure-adjusting valve  45 , a switching valve  43 , etc. 
     The resist bottle  42  (i.e., a liquid container) is connected by the suction pipe  41  (i.e., an inflow passage) to the suction valve  40  with a filter  41   a  disposed in the suction pipe  41 . The resist bottle  42  may be located at a position higher or lower than the pump chamber  25 . The filter  41   a  removes impurities such as minute particles contained in the resist solution R. The suction valve  40  opens and closes the suction pipe  41 . The operation air is supplied from the supply source  44  to the suction valve  40  through the pressure-adjusting valve  45  and the switching valve  43 . The pressure-adjusting valve  45  adjusts the pressure of the operation air supplied from the supply source  44  to a pressure for operating the suction valve  40 . The switching valve  43  is a solenoid valve for switching the connection state of the flow passage by an electromagnetic switching section  43   a  having an electromagnetic solenoid. In response to a second instruction signal (for example, ON instruction or OFF instruction) from the controller  70 , the switching valve  43  switches the connection state of the flow passage alternatingly between a state in which the operation air is supplied to the suction valve  40  and a state in which the suction valve  40  communicates with the atmosphere. The resist solution R flows into the pump chamber  25  of the pump  13  through the suction pipe  41  when the suction valve  40  is opened. 
     The pump chamber  25  of the pump  13  is connected by the discharge pipe  47  (i.e., an outflow passage) to the end nozzle  47   n  through the discharge valve  46 . The discharge valve  46  has the same structure as the suction valve  40  described above. In response to a third instruction signal (for example, ON instruction or OFF instruction) from the controller  70 , the discharge valve  46  is switched alternatingly between an open state and a closed state. The resist solution R flows out of the pump chamber  25  of the pump  13  through the discharge pipe  47  when the discharge valve  46  is opened. Thus, the resist solution R is supplied to the end nozzle  47   n  through the discharge pipe  47 . 
     The flow rate sensor  71  detects the flow rate of the operation air which flows through the air pipe  50 ; namely, the flow rate of the operation air which flows into or flows out of the working chamber  26  of the pump  13 . 
     The pressure sensor  72  detects the pressure of the operation air inside the air pipe  50 ; namely, the pressure of the space including the working chamber  26  and the air pipe  50 . Specifically, the pressure sensor  72  detects the pressure at a pressure detection point  72   p  provided in the air pipe  50  between the pump  13  and the flow rate sensor  71 . 
     The position sensor  73  detects the position of the diaphragm  23 . Specifically, the position sensor  73  enters an off state when the diaphragm  23  is located on the pump chamber  25  side (i.e., on the discharge side) with respect to the neutral position. The position sensor  73  enters an on state when the diaphragm  23  is located at the neutral position or on the working chamber  26  side (i.e., on the suction side) with respect to the neutral position. The neutral position is a position where the tension generated in the diaphragm  23  due to movement of the diaphragm  23  becomes smaller than a predetermined value (for example, the tension becomes zero); namely, a position where the tension generated in the diaphragm can be ignored. 
     The controller  70  (i.e., a control section) is an electronic control apparatus mainly composed of a microcomputer which includes a CPU, and various kinds of memories, etc. The controller  70  controls the states of supply and discharge of the resist solution R by the pump  13 . The controller  70  receives an input signal (for example, a suction instruction signal or a discharge instruction signal) from an unillustrated administration computer which administers the entirety of the present system. The controller  70  receives a flow rate detection signal from the flow rate sensor  71 , a pressure detection signal from the pressure sensor  72 , and a position detection signal from the position sensor  73 . On the basis of these input signals, the controller  70  controls the open/closed states of the suction valve  40  and the discharge valve  46  and the state of the electro-pneumatic regulator  51  (i.e., the pump drive section  59 ). In the present embodiment, the controller  70  estimates the volume of the working chamber  26  and the suction-side hydraulic head pressure (i.e., fluid pressure) of the resist solution R. At that time, in the chemical supply system  10 , the temperatures of the operation air and the resist solution R are constant or can be considered to be constant. 
       FIG. 2  is a time chart showing the basic operation of the chemical supply system  10 . The chemical supply system  10  operates by repeating a cycle including discharge of the resist solution R from the pump  13  and suction of the resist solution R into the pump  13 . The operation of the chemical supply system  10  is controlled by the controller  70  described above. 
     As shown in  FIG. 2 , the suction valve  40  is opened and the discharge valve  46  is closed before time t 1 . The pressure of the working chamber  26  is a negative pressure which is the set pressure. In this state, the pump chamber  25  has expanded to have the maximum volume, and the working chamber  26  has contracted to have the minimum volume. 
     At time t 1 , while the discharge valve  46  remains in the closed state, the suction valve  40  is closed. After the suction valve  40  is closed, the set pressure of the electro-pneumatic regulator  51  is changed to a positive pressure. Consequently, the pressure of the working chamber  26  is quickly controlled to the set positive pressure by the electro-pneumatic regulator  51 . In this state, since both the suction valve  40  and the discharge valve  46  are in the closed state, the pump chamber  25  is in a state (specifically, a standstill state) in which a positive pressure (set pressure) is applied from the working chamber  26  side to the pump chamber  25  via the diaphragm  23 . 
     The pressure at the pressure detection point  72   p  (i.e., the pressure of the working chamber  26 ) is detected by the pressure sensor  72  in real time. The flow rate of the operation air that flows into or out of the working chamber  26  is detected by the flow rate sensor  71  in real time. The above-described state is maintained until time t 2  at which the flow rate detected by the flow rate sensor  71  becomes smaller than a predetermined value (for example, the flow rate becomes zero). Time t 2  may be the time at which fluctuation of the pressure detected by the pressure sensor  72  becomes smaller than a predetermined value (for example, the fluctuation of the pressure becomes zero). 
     At time t 2 , the discharge valve  46  is opened. This allows discharge of the resist solution R from the pump chamber  25  through the discharge valve  46 . Therefore, as a result of pressing of the diaphragm  23  by the operation air in the direction from the working chamber  26  to the pump chamber  25 , the discharge of the resist solution R from the pump chamber  25  is started. This state is maintained during a period during which the working chamber  26  can be expanded to the maximum volume and the pump chamber  25  can be contracted to the minimum volume; namely, a period from time t 2  to time t 3 . Thus, the discharge of the resist solution R from the pump  13  ends. 
     At time t 3 , the discharge valve  46  is closed. At time t 4  after elapse of a predefined time after t 3 , the suction valve  40  is opened. 
     From time t 4  to t 5 , the set pressure of the operation air is not changed rapidly. Rather, it is gradually changed from a positive pressure to a negative pressure at a predetermined rate. This restrains occurrence of a bubble generation phenomenon which occurs when the pressure of the pump chamber  25  decreases rapidly. As the set pressure of the operation air decreases (for example, to a negative pressure), the diaphragm  23  is sucked from the pump chamber  25  side toward the working chamber  26  side. This state is maintained during a period during which the pump chamber  25  can be expanded to the maximum volume and the working chamber  26  can be contracted to the minimum volume; namely, a period from time t 5  to time t 6 . Thus, the suction of the resist solution R into the pump  13  ends. Then, at time t 6 , the control same as that at time t 1  is executed. 
     Calculation of Post-Change Volume: 
       FIG. 3  is a flowchart showing a series of processes for calculating the post-change volume of the working chamber  26 . This series of processes is executed by the controller  70 . 
     First, the controller  70  closes the discharge valve  46  and the suction valve  40  (S 11 , S 12 ). Namely, the controller  70  temporarily closes the two valves  46  and  40  to thereby create a state in which the volume of the working chamber  26  cannot be changed. 
     Subsequently, the controller  70  changes the set pressure of the working chamber  26  (S 13 ). Specifically, the the controller  70  changes the set pressure to a pressure at which a change in the flow rate of the operation air with a change in the pressure of the working chamber  26  can be detected accurately in a state in which the discharge valve  46  and the suction valve  40  are closed; i.e., in a state in which the diaphragm  23  does not move. For example, the controller  70  raises the set pressure from the atmospheric pressure to a predetermined pressure. 
     Subsequently, the controller  70  outputs the set pressure changed in S 13  to the electro-pneumatic regulator  51  (S 14 ). As a result, the electro-pneumatic regulator  51  starts an operation of controlling the pressure of the working chamber  26  to the set pressure. 
     Subsequently, the controller  70  reads the pressure of the working chamber  26  detected by the pressure sensor  72  (S 15 ) and reads the flow rate of the operation air flowing into and out of the working chamber  26  detected by the flow rate sensor  71  (S 16 ). 
     Subsequently, the controller  70  calculates the volume of the operation chamber (S 17 ). Specifically, the controller  70  calculates an operation chamber volume V which is the total of the volume V(n) of the working chamber  26  at that time and the volume of the air pipe  50  by using Formula F 5  of  FIG. 4 . Since the diaphragm  23  does not move, detected flow rate QA(n+1) which is the flow rate of the operation air detected by the flow rate sensor  71  at that time can be considered to be equal to pressure change corresponding flow rate QP(n+1). The pressure change corresponding flow rate QP(n+1) is a flow rate which contributes to change in the pressure of the working chamber  26  but does not contribute to change in the volume thereof. QA(n+1) represents the flow rate detected this time; P 0  represents a reference pressure; ΔP(n+1) represents a pressure change (the pressure P(n+1) detected this time—the pressure P(n) detected last time); and Δt represent a predetermined sampling interval. Notably, the product of the detected flow rate QA(n+1) and the time Δt corresponds to the integrated flow rate. 
     Subsequently, the controller  70  calculates an initial volume V( 0 ) of the working chamber  26  by subtracting the volume of the air pipe  50  from the operation chamber volume V (S 18 ). Notably, the volume of the air pipe  50  is known. 
     Subsequently, the controller  70  opens the suction valve  40  (S 19 ). Namely, the controller  70  creates a state in which the volume of the working chamber  26  can be changed from the initial volume V( 0 ). 
     Subsequently, the controller  70  changes the set pressure of the working chamber  26  (S 20 ), outputs the set pressure changed in S 20  to the electro-pneumatic regulator  51  (S 21 ), reads the pressure of the working chamber  26  detected by the pressure sensor  72  (S 22 ), and reads the flow rate of the operation air flowing into and out of the working chamber  26  detected by the flow rate sensor  71  (S 23 ). The processes of the S 20  to S 23  are the same as those of S 13  to S 16 . However, in S 20 , the controller  70  changes the set pressure in accordance with the driven state of the pump  13 ; specifically, the state in which the pump  13  is driven for suction. Notably, S 19  may be replaced with a step of opening the discharge valve  46 , and S 20  may be replaced with a step of changing the set pressure in accordance with the driven state of the pump  13 ; specifically, the state in which the pump  13  is driven for discharge. 
     Subsequently, the controller  70  calculates the post-change volume V(n+1) of the working chamber  26  (S 24 ). This calculation will be described in detail with reference to  FIG. 4 . 
     Subsequently, the controller  70  calculates a displacement amount of the diaphragm  23  on the basis of the volume change amount ΔV(n+1) of the working chamber  26  (S 25 ). Specifically, the controller  70  calculates a displacement amount of the diaphragm  23  on the basis of a preset relation between the volume change amount ΔV(n+1) of the working chamber  26  and the displacement amount of the diaphragm  23  and the volume change amount ΔV(n+1) from the initial volume V( 0 ) of the working chamber  26  to the post-change volume V(n+1). The relation between the volume change amount ΔV(n+1) of the working chamber  26  and the displacement amount of the diaphragm  23  is previously determined. Therefore, the relation between the volume change amount ΔV(n+1) of the working chamber  26  and the displacement amount of the diaphragm  23  is set in advance on the basis of the results of an experiment or design values. 
     After that, the controller  70  ends of this series of processes (END). Notably, this series of processes corresponds to the method for controlling a gas-pressure-driven apparatus. 
     Calculation of Post-Change Volume of Working Chamber: 
       FIG. 4  is a set of formulas for calculating the post-change volume of the working chamber  26  of the pump  13  on the basis of the pressure and flow rate of the operation air. Formulas F 1  to F 4  in  FIG. 4  are calculation formulas for calculating the post-change volume of the working chamber  26  from the pressure and flow rate of the operation air supplied to the working chamber  26 , in consideration of the compressibility of the operation air, in a state in which both the pressure and volume of the working chamber  26  change. 
     Formula F 1  is used for calculating the post-change volume of the working chamber  26  at the present moment (n+1). Specifically, formula F 1  is used for calculating the post-change volume V(n+1) of the working chamber  26  at the present moment (n+1) by adding, to the volume V(n) of the working chamber  26  at the previous moment (n), a change in the volume of the working chamber  26  during the predetermined sampling interval of Δt, which change is represented by Qv(n+1)·Δt. Namely, the post-change volume V(n+1) is calculated by adding, to the initial volume V( 0 ) of the working chamber  26 , a change in the volume of the working chamber  26  during each sampling interval of Δt, which change is represented by Qv(k)·Δt. 
     Formula F 2  is used for calculating the unit-time volume change Qv(n+1) of the working chamber  26  at the present detected pressure P(n+1) (the pressure of the working chamber  26  detected at the present moment (n+1)) from the flow rate QM(n+1) at a reference pressure P 0 . The detected pressure P(n+1) is the pressure of the working chamber  26  detected by the pressure sensor  72 . The unit-time volume change means the flow rate, and the integrated volume change means the integrated flow rate. Thus, the flow rate at the assumed reference pressure P 0  can be converted to the flow rate at the pressure P(n+1) and used. The volume change Qv(n+1) calculated from Formula F 2  is substituted in Formula F 1 . 
     Formula F 3  is used for calculating the flow rate QM(n+1) at the reference pressure P 0  through use of the detected flow rate QA(n+1). The detected flow rate QA(n+1) is the flow rate of the operation air detected by the flow rate sensor  71 . The flow rate QM(n+1) at the reference pressure P 0  is calculated by subtracting a pressure change corresponding flow rate QP(n+1) from the detected flow rate QA(n+1). The pressure change corresponding flow rate QP(n+1) is a flow rate which contributes to change in the pressure of the working chamber  26  and does not contribute to change in the volume of the working chamber  26 . In other words, the flow rate QM(n+1) is a flow rate which contributes to change in the volume of the working chamber  26 ; i.e., a volume change corresponding flow rate. The flow rate QM(n+1) at the reference pressure P 0  calculated by Formula F 3  is substituted in Formula F 2 . 
     Formula F 4  is used for calculating the pressure change corresponding flow rate QP(n+1). The pressure change corresponding flow rate QP(n+1) is a portion of the flow rate of the operation air which contributes only to change in the pressure of the working chamber  26 . The pressure change corresponding flow rate QP(n+1) assumes a positive value when the pressure of the working chamber  26  is increasing and assumes a negative value when the pressure of the working chamber  26  is decreasing. The pressure change (P(n+1)−P(n)) is the change in the pressure detected by the pressure sensor  72  during the sampling interval Δt. The actually measured value of the pressure change (P(n+1)−P(n)) may be used as is. Alternatively, the average of the measured values of the pressure change (P(n+1)−P(n)) within a predetermined time period may be used. The calculated value of the pressure change corresponding flow rate QP(n+1) depends on the operation chamber volume V which is the sum of the volume V(n) of the working chamber  26  at that time and the volume of the air pipe  50 . The pressure change corresponding flow rate QP(n+1) calculated by Formula F 4  is substituted in Formula F 3 . As described above, the post-change volume of the working chamber  26  can be calculated through use of Formula F 1 . 
     Estimation of Suction-Side Hydraulic Head Pressure 
       FIG. 5  is a flowchart showing a series of processes for estimating the hydraulic head pressure on the suction-side. The series of processes is executed by the controller  70 . 
     First, the controller  70  closes the discharge valve  46  and the suction valve  40  (S 31  and S 32 ). Namely, both the valves  46  and  40  are closed temporarily. 
     Subsequently, the controller  70  moves the diaphragm  23  to the neutral position described above (S 33 ). The neutral position is a position where the tension generated in the diaphragm  23  due to movement of the diaphragm  23  becomes smaller than a predetermined value (for example, the tension becomes zero). The details of this process will be described later. 
     Subsequently, the controller  70  reads the set pressure which was used in the series of processes performed last time (S 34 ). Specifically, the controller  70  reads the set pressure which was output to the electro-pneumatic regulator  51  when the series of processes for estimating the suction-side hydraulic head pressure was performed last time. 
     Subsequently, the controller  70  outputs the set pressure read in S 34  to the electro-pneumatic regulator  51  (S 35 ). As a result, the electro-pneumatic regulator  51  starts an operation of controlling the pressure of the working chamber  26  to the set pressure. The controller  70  then opens the suction valve  40  (S 16 ). Namely, the controller  70  starts the process for estimating the hydraulic head pressure from the state in which the pressure of the working chamber  26  has been controlled to the set pressure in the series of processes performed last time. In the case where the controller  70  cannot acquire the set pressure which was used in the series of processes performed last time, the controller  70  starts the process for estimating the hydraulic head pressure while using a predetermined initial set pressure. 
     Subsequently, the controller  70  reads the pressure of the working chamber  26  detected by the pressure sensor  72  (S 37 ), and reads the flow rate of the working air flowing into and out of the working chamber  26  detected by the flow rate sensor  71  (S 38 ). 
     Subsequently, the controller  70  closes the suction valve  40  (S 39 ). The controller  70  then calculates the change in the volume of the working chamber  26  on the basis of the detected pressure and flow rate (S 40 ). The volume change ΔV of the working chamber  26  can be calculated on the basis of the formulas of  FIG. 4  as in the case of the post-change volume V(n+1) of the working chamber  26 . 
     Subsequently, the controller  70  determines whether or not the calculated volume change is zero (S 41 ). Specifically, the controller  70  determines whether or not the calculated volume change is smaller than a determination value. The determination value is determined such that when the calculated volume change is smaller than the determination value, the controller  70  can determine that the change in the volume of the working chamber  26  is substantially zero or approximately zero. For example, the determination value is set to a value slightly greater than zero. 
     In the case where the controller  70  determines in S 41  that the calculated volume change is not zero (S 41 : NO), the controller  70  moves the diaphragm  23  to the neutral position described above (S 42 ). In the case where the diaphragm  23  is located at the above-mentioned neutral position, the diaphragm  23  receives only the pressure of the operation air within the working chamber  26  and the pressure of the resist solution R in contact with the surface of the diaphragm  23  opposite the working chamber  26 . 
     The controller  70  then changes the set pressure (S 43 ). Specifically, the controller  70  changes the set pressure in accordance with the calculated volume change such that the volume change can quickly become close to zero. For example, in the case where the volume of the working chamber  26  has decreased, the controller  70  raises the set pressure, and in the case where the volume of the working chamber  26  has increased, the controller  70  lowers the set pressure. Further, the controller  70  changes the set pressure such that the greater the rate at which the volume of the working chamber  26  decreases, the greater the degree to which the set pressure is raised and such that the greater the rate at which the volume of the working chamber  26  increases, the greater the degree to which the set pressure is lowered. Subsequently, the controller  70  again executes the series of processes from the process of S 35 . 
     Meanwhile, in the case where the controller  70  determines in S 41  that the calculated volume change is zero (S 41 : YES), the controller  70  estimates the suction-side hydraulic head pressure (namely, the pressure of the fluid) (S 44 ). Specifically, the controller  70  uses, as an estimated suction-side hydraulic head pressure, the set pressure for the working chamber  26  in a state in which the change in the volume of the working chamber  26  has become zero; namely, the pressure detected by the pressure sensor  72  in the state in which the change in the volume of the working chamber  26  has become zero. After that, the controller  70  ends the series of processes (END). 
     Movement of Diaphragm to Neutral Position: 
       FIG. 6  is a flowchart showing the series of processes for moving the diaphragm  23  to the neutral position (S 33  in  FIG. 5 ). The series of processes is executed by the controller  70 . 
     First, the controller  70  changes the set pressure for the working chamber  26  (S 50 ). Specifically, the controller  70  changes the set pressure to a predetermined pressure at which the diaphragm  23  can be quickly moved toward the pump chamber  25  side with respect to the neutral position. The controller  70  then outputs the changed set pressure to the electro-pneumatic regulator  51  (S 51 ). Thus, the electro-pneumatic regulator  51  controls the pressure of the working chamber  26  to the set pressure. 
     Subsequently, the controller  70  opens the discharge valve  46  (S 52 ). Notably, the suction valve  40  has already been closed in the process of S 32  in  FIG. 5 . 
     Subsequently, the controller  70  determines whether or not the position sensor  73  has entered the off state (S 53 ). Specifically, the controller  70  determines whether or not the diaphragm  23  has moved to the pump chamber  25  side with respect to the neutral position. In the case where the controller  70  determines that the position sensor  73  has not yet entered the off state (S 53 : NO), the controller  70  waits by repeatedly executing the determination in S 53 . 
     Meanwhile, in the case where the controller  70  determines in S 53  that the position sensor  73  has entered the off state (S 53 : YES), the controller  70  closes the discharge valve  46  (S 54 ), and changes the set pressure for the working chamber  26  (S 55 ). Specifically, the controller  70  changes the set pressure to a predetermined pressure at which the diaphragm  23  can be moved to the neutral position at a proper speed. The predetermined pressure is set to a pressure at which the diaphragm  23  can be moved to the neutral position without fail and the diaphragm  23  does not move greatly toward the working chamber  26  side with respect to the neutral position. The controller  70  then outputs the changed set pressure to the electro-pneumatic regulator  51  (S 56 ). Thus, the electro-pneumatic regulator  51  controls the pressure of the working chamber  26  to the set pressure. 
     Subsequently, the controller  70  opens the suction valve  40  (S 57 ). 
     Subsequently, the controller  70  determines whether or not the position sensor  73  has entered the on state (S 58 ). Specifically, the controller  70  determines whether or not the diaphragm  23  has moved to the neutral position. In the case where the controller  70  determines that the position sensor  73  has not yet entered the on state (S 58 : NO), the controller  70  waits by repeatedly executing the determination in S 58 . 
     Meanwhile, in the case where the controller  70  determines in S 58  that the position sensor  73  has entered the on state (S 58 : YES), the controller  70  closes the suction valve  40  (S 59 ). Thus, the diaphragm  23  stops at the neutral position. The controller  70  then returns to the process of S 33  and subsequent processes in  FIG. 5  (RET). 
     The present embodiment having been described in detail has the following advantages.
         By the controller  70 , a state in which the volume of the working chamber  26  cannot be changed is created, and the pressure of the working chamber  26  is changed by controlling the pump drive section  59 . As a result, the operation air flows into or flows out of the working chamber  26 . In a state in which the volume of the working chamber  26  cannot be changed, the operation air flowing into or flowing out of the working chamber  26  contributes to change in the pressure of the working chamber  26 . The amount of change in the pressure of the working chamber  26  caused by the operation air flowing into or flowing out of the working chamber  26  changes with the volume of the working chamber  26  at the time of creation of a state in which the volume of the working chamber  26  cannot be changed (namely, changes with the initial volume V( 0 ) of the working chamber  26 ). Therefore, the relation between the pressure change amount of the working chamber  26  and the integrated flow rate of the operation air (i.e., the amount of the operation air flowing into or flowing out of the working chamber  26 ) reflects the initial volume V( 0 ) of the working chamber  26 . Accordingly, the initial volume V( 0 ) of the working chamber  26  can be calculated from the pressure change amount of the working chamber  26  and the integrated flow rate of the operation air flowing into the working chamber  26 .   After a state in which the volume of the working chamber  26  can be changed from the initial volume V( 0 ) has been created, the integrated flow rate is calculated from the flow rate of the operation air detected by the flow rate sensor  71 . The integrated flow rate in the state in which the volume of the working chamber  26  can be changed correlates with the volume change amount ΔV(n+1) of the working chamber  26 . Therefore, the post-change volume V(n+1) of the working chamber  26  after its volume has changed can be calculated from the integrated flow rate and the initial volume V( 0 ). In addition, irrespective of the initial position of the diaphragm  23 , the initial volume V( 0 ) of the working chamber  26  can be calculated, whereby the post-change volume V(n+1) of the working chamber  26  can be calculated.   The pressure change corresponding flow rate QP(n+1) which is an operation air flow rate contributing to change in the pressure of the working chamber  26  is calculated by the controller  70  on the basis of the post-change volume V(n+1) and the pressure detected by the pressure sensor. Therefore, the pressure change corresponding flow rate QP(n+1) can be calculated accurately from the post-change volume V(n+1) of the working chamber  26  at that time. The integrated flow rate is then calculated from the flow rate QM(n+1) which corresponds to change in the volume of the working chamber  26  and is calculated by subtracting the pressure change corresponding flow rate QP(n+1) from the flow rate detected by the flow rate sensor  71 . Therefore, the post-change volume V(n+1) of the working chamber  26  can be calculated accurately from the integrated flow rate contributing to change in the volume of the working chamber  26 .   The displacement amount of the diaphragm  23  is calculated by the controller  70  on the basis of the preset relation between the volume change amount ΔV(n+1) of the working chamber  26  and the displacement amount of the diaphragm  23  and the volume change amount ΔV(n+1); i.e., the amount of change in volume from the initial volume V( 0 ) to the post-change volume V(n+1). Therefore, the displacement amount of the diaphragm  23  can be calculated from the post-change volume V(n+1) of the working chamber  26 .   By the controller  70 , a state in which the volume of the working chamber  26  can be changed is created, and the pump drive section  59  is controlled such that the diaphragm  23  stops moving. In the case where the diaphragm  23  stops moving in the state in which the volume of the working chamber  26  can be changed, the force acting on the diaphragm  23  from the working chamber  26  side balances with the force acting on the diaphragm  23  from the side opposite the working chamber  26 . In this state, the diaphragm  23  receives only the pressure of the operation air within the working chamber  26  and the pressure of the resist solution R in contact with the surface of the diaphragm  23  opposite the working chamber  26 . Therefore, the pressure of the operation air and the pressure of the resist solution R balance with each other. Accordingly, the pressure detected by the pressure sensor in the state in which the diaphragm  23  stands still can be used as the pressure of the resist solution R.       

     The first embodiment may be modified as follows.
         The relation between the volume of the working chamber  26  and the position of the diaphragm  23  is predetermined. Therefore, the relation between the volume of the working chamber  26  and the position of the diaphragm  23  can be set in advance on the basis of the results of an experiment or design values. In such a case, the controller  70  may be configured to calculate the position of the diaphragm  23  on the basis of the post-change volume V(n+1) and the preset relation between the volume of the working chamber  26  and the position of the diaphragm  23 .   The fluid in contact with the diaphragm  23  (i.e., movable member) is not limited to liquid such as the resist solution R, and may be gas.   The pump  13  may be used as an apparatus for measuring the static pressure of the fluid. Specifically, by a procedure similar to the flowchart of  FIG. 5 , the static pressure of the fluid in a state in which the suction valve  40  is opened and the discharge valve  46  is closed can be measured. Also, by modifying the procedure to close the suction valve  40  instead of opening it and open the discharge valve  46  instead of closing it, the static pressure of the fluid in a state in which the suction valve  40  is closed and the discharge valve  46  is opened can be measured. Also, the static pressure of the fluid in a state in which both the suction valve  40  and the discharge valve  46  are opened can be measured. Notably, a static pressure measurement apparatus which operates in the same principle may be provided separately from the pump  13 .       

     Second Embodiment 
     A second embodiment which is embodied as a gas-pressure-driven apparatus including a single-acting-type air-operated valve  113  instead of the pump  13  of  FIG. 1  will now be described with reference to the drawings. The difference from the first embodiment will be mainly described. Members identical with those of the first embodiment are denoted by the same symbols and their description will be omitted. 
     As shown in  FIG. 7 , the valve  113  includes a main body  114 , a piston  123 , a spring  116  (i.e., an urging member), etc. The main body  114  has a working chamber  126  into which pressurized operation air is supplied through the air pipe  50  and from which the pressurized operation air is discharged. A piston  123  (i.e., a movable member) separates the working chamber  126  from a spring chamber  127 . The spring  116  urges the piston  123  from the spring chamber  127  side toward the working chamber  126  side. A valve seat  143  is provided between an inflow passage  141  and an outflow passage  147 . A valve body  124  is connected to the piston  123 . The valve body  124  comes into contact with and moves away from the valve seat  143 . The piston  123  moves (displaces) relative to the main body  114  in accordance with the pressure of the working chamber  126 . As a result, the area of a flow passage from the inflow passage  141  to the outflow passage  147  is adjusted by the valve body  124  of the valve  113 . In the present embodiment, the pressurized fluid is supplied to the inflow passage  141 , and the flow rate of the fluid is adjusted by the valve  113 . 
     In a state in which the set pressure of the working chamber  126  is set to a pressure at which the valve body  124  is located at the fully closed position (a pressure lower than the lowest operation pressure of the piston  123 ), the initial volume V( 0 ) of the working chamber  126  is calculated by the processing of S 11  to S 18  of  FIG. 3 . After that, in a state in which the set pressure of the working chamber  126  is set to a predetermined pressure equal to or higher than the lowest operation pressure of the piston  123 , the post-change volume V(n+1) of the working chamber  126  is calculated by the processing of S 19  to S 24  of  FIG. 3 . The volume change amount ΔV(n+1) is calculated by subtracting the initial volume V( 0 ) from the post-change volume V(n+1). Then, the volume change amount ΔV(n+1) is divided by the cross-sectional area of the working chamber  126  so as to obtain the displacement amount of the piston  123 ; i.e., the degree of opening of the valve  113 . 
     The degree of opening of the valve  113  correlates with a flow rate coefficient Cv. Therefore, the flow rate coefficient Cv is calculated on the basis of the degree of opening of the valve  113 ; specifically, is calculated on the basis of the relation of  FIG. 8 . 
     The present embodiment having been described in detail has the following advantages. Notably, here, only the advantages different from those of the first embodiment will be described.
         The displacement amount of the piston  123  can be calculated by dividing the volume change amount ΔV(n+1) by the cross-sectional area of the working chamber  126 . Therefore, the displacement amount of the piston  123  can be calculated simply.       

     Notably, the second embodiment may be modified as follows.
         The initial volume V( 0 ) may be calculated in a state in which the pressure of the working chamber  126  is equal to or higher than the lowest operation pressure of the piston  123 , if the piston  123  does not move due to the pressure of the operation air.   The present invention can be embodied as a gas-pressure-driven apparatus including a double-acting-type air-operated valve which does not have the spring  116  and is configured such that the operation air is supplied to and discharged from two working chambers separated by the piston  123 . In this case, in a state in which the valve body  124  has been moved to the fully closed position by supplying the operation air to the working chamber  127 , the initial volume V( 0 ) of the working chamber  126  is calculated by the processing of S 11  to S 18  of  FIG. 3 . After that, by a procedure similar to that of the second embodiment, the displacement amount of the piston  123  (the degree of opening of the valve  113 ) and the flow rate coefficient Cv can be calculated. Also, the initial volume V( 0 ) of the working chamber  126  can be calculated by the processing of S 11  to S 18  of  FIG. 3  in a state in which the valve body  124  has been moved to the fully opened position by supplying the operation air to the working chamber  126 . After that, the piston  123  is moved by supplying the operation air to the working chamber  127 , and the displacement amount of the piston  123  from the fully opened position can be calculated by a procedure similar to that of the second embodiment. Notably, in a state in which the piston  123  does not move due to the pressure of the operation air, the initial volume V( 0 ) can be calculated irrespective of the pressures within the working chambers  26  and  27 .   The present invention can be embodied as a gas-pressure-driven apparatus including a bellows pump in place of the pump  13  of  FIG. 1 . In this case as well, like the second embodiment, the displacement amount of the bellows (i.e., the movable member) can be calculated by dividing the volume change amount ΔV(n+1) by the cross-sectional area of the bellows.   As shown in  FIG. 9 , the present invention can be embodied as a gas-pressure-driven apparatus including an air cylinder  213  which works for a load F. Members identical with those of the second embodiment are denoted by the same symbols and their description will be omitted. In the case where the piston  123  (i.e., the movable member) stops in a state in which the volume of the working chamber  126  can be changed, the force acting on the piston  123  from the working chamber  126  side balances with the force acting on the piston  123  from the spring chamber  127  side (i.e., the side opposite the working chamber  126 ). In this state, the load F in the direction of movement of the piston  123  acts on the piston  123 . The higher the pressure applied to the piston  123 , the larger the force acting on the piston  123  due to the pressure. Accordingly, by controlling the supply and discharge section such that the piston  123  stops and calculating the load F such that the calculated load F increases with the pressure detected by the pressure sensor  72  in the state in which the piston  123  stands still, the load F can be calculated properly. Notably, in the case of the air cylinder  213 , the state in which the volume of the working chamber  126  cannot be changed may be created by mechanically fixing the piston  123 .       

     Notably, the above-described embodiments may be modified as follows.
         The pressure sensor  72  may be one which detects the pressure of the working chamber.   In the above-described embodiments, operation air is used as the working gas supplied to and discharged from the working chamber. However, a gas other than air, such as nitrogen, may be used as the working gas.   In a state in which the volume of the working chamber is made unchangeable for calculation of the initial volume V( 0 ) of the working chamber, the controller  70  (i.e., the control section) calculates the temperature of the working chamber such that the calculated temperature increases with the increase of the pressure detected by the pressure sensor  72 . In the state in which the volume of the working chamber is made unchangeable for calculation of the initial volume V( 0 ) of the working chamber, the ratio between the pressure and the temperature becomes constant according to the Boyle-Charles&#39; law. Therefore, the temperature of the working chamber can be calculated properly by calculating the temperature of the working chamber such that the calculated temperature increases with the increase of the pressure detected by the pressure sensor  72 .   The controller  70  (the control section) calculates the temperature of the working chamber on the basis of the preset relation among the volume, pressure, and temperature of the working chamber, the initial volume V( 0 ) of the working chamber, and the pressure detected by the pressure sensor  72  in the state in which the volume of the working chamber is made unchangeable for calculation of the initial volume V( 0 ) of the working chamber. The Boyle-Charles&#39; law determines the relation among the volume, pressure, and temperature of the working chamber. Therefore, the relation among the volume, pressure, and temperature of the working chamber can be set in advance on the basis of the results of an experiment or design value. Therefore, according to the above-described configuration, the temperature of the working chamber can be calculated through use of the control for calculation of the initial volume V( 0 ) of the working chamber.   When the post-change volume V(n+1) of the working chamber is calculated on the basis of the initial volume V( 0 ) and the integrated flow rate, the pressure change corresponding flow rate QP(n+1) can be considered to be 0. In this case as well, since the integrated flow rate correlates with the volume change amount of the working chamber, the post-change volume V(n+1) of the working chamber can be calculated although the accuracy lowers.