Flow rate control method, flow rate control system, parameter identification method, and program

Abstract

A purpose of the present invention is to provide a technology capable of realizing high performance in flow rate control. The present invention is a flow rate control method that controls the flow rate of a flow rate control valve by displacing a movable valve body housed in a housing of the flow rate control valve, wherein a disturbance force caused by a pressure difference between the upstream side and the downstream side of the valve body is compensated while displacing the valve body by using feedforward control to input, into the flow rate control valve, a first control input that displaces the valve body in accordance with the mass of the valve body and the viscous friction, a second control input that compensates the steady-state component of the disturbance force caused by the pressure difference, and a third control input that compensates a transient component of the disturbance force.

Description

Flow rate control method, flow rate control system, parameter identification method, and program

[0001] This invention relates to a flow rate control method, a flow rate control system, a parameter identification method, and a program.

[0002] As flow control valves, pneumatic valves are known for controlling the flow rate of gases. Applications of pneumatic valves for precision control include semiconductor manufacturing equipment, liquid crystal manufacturing equipment, pneumatic active vibration isolation tables, and pneumatic cylinders. Since gas flow control in these devices is closely related to the control accuracy and control speed of higher-level equipment, further performance improvements are required.

[0003] Requirements for pneumatic valves in precision control include high-precision flow control and fast-response flow control. However, precise flow control has been difficult because the flow characteristics of pneumatic valves fluctuate due to the pressure difference between the upstream and downstream sides of the valve.

[0004] In relation to methods for controlling flow rate using valves whose valve body position can be measured, for example, Non-Patent Document 1 proposes valve body position feedback (FB) control to compensate for the hysteresis characteristics of the solenoid. Furthermore, Non-Patent Document 2 proposes valve body position feedforward (FF) control to suppress rapid changes in air disturbances when the valve opening is changed rapidly.

[0005] Hattori, K., Ohnishi, W. and Koseki, T.: Mass Flow Rate Control with Compensation of Nonlinearity using Valve Internal Variables, in 2024 IEEE18th International Conference on Advanced Motion Control (AMC), pp. 1-6 (2024) Hattori, K., Ohnishi, W. and Koseki, T.: Compensation of Pressure Dependent Disturbance:Poppet Position Control in a Pneumatic Valve, in 2024IEEE / ASME International Conference on Advanced Intelligent Mechatronics (AIM2024), pp. 1-6 (2024)

[0006] The purpose of the technology disclosed herein is to provide a technology that enables high-performance flow control.

[0007] To solve the above problems, the technology disclosed herein employs the following configuration. In other words, the gist of the technology disclosed herein is as follows.

[0008] (Aspect 1) A flow control method for controlling the flow rate of a flow control valve by displacing a movable valve body housed in the housing of the flow control valve, wherein a first control input for displacing the valve body in accordance with the mass and viscous friction of the valve body, a second control input for compensating the steady-state component of a disturbance force caused by a pressure difference between the upstream and downstream sides of the valve body, and a third control input for compensating the transient component of the disturbance force are input to the flow control valve by feedforward control, thereby compensating for the disturbance force caused by the pressure difference while displacing the valve body. (Aspect 2) The flow rate control method according to aspect 1, wherein the position of the valve body or the flow rate of the flow control valve is used as the first control quantity, the first control input is derived based on a target value of the first control quantity and a relational expression obtained in advance that shows the relationship between the control input and the first control quantity for making the first control quantity follow a predetermined trajectory when there is no pressure difference, the second control input is derived based on the target value of the first control quantity, a measured value of the pressure difference and a steady-state characteristic obtained in advance that shows the relationship between the control input and the first control quantity in a steady state when there is a pressure difference, according to the pressure difference, and the third control input is derived based on the target value of the first control quantity and a relational expression obtained in advance that shows the relationship between the control input and the first control quantity for compensating for the transient component of the disturbance force when making the first control quantity follow a predetermined trajectory when there is a pressure difference. (Aspect 3) The flow rate control method according to aspect 2, wherein the first control quantity is the position of the valve body, and a target value for the position of the valve body, which is the target value of the first control quantity, is derived based on a target value of the flow rate as a second control quantity, a measured value of the pressure difference, a steady-state characteristic obtained in advance that shows the relationship between the flow rate and the position of the valve body according to the pressure difference, and a dead time from the position of the valve body to the flow rate, which has been identified in advance. (Aspect 4) A flow rate control system comprising a flow rate control valve having a housing and a movable valve body housed in the housing, and a control device that controls the flow rate of the flow rate control valve by executing the flow rate control method according to any one of aspects 1 to 3. (Aspect 5) A program that causes a computer to execute the flow rate control method according to any one of aspects 1 to 3.(Aspect 6) A parameter identification method for identifying a parameter for deriving a control input for feedforward control, which compensates for disturbance force resulting from a pressure difference between an upstream side and a downstream side of the movable valve body while displacing the valve body, in flow control that controls a flow rate of a flow control valve by displacing the movable valve body housed in a housing of the flow control valve, wherein: a position of the valve body or a flow rate of the flow control valve is used as a first controlled variable; and the parameter θ is used for deriving a first control input that displaces the valve body in accordance with a mass and viscous friction of the valve body. a comprising the steps of: identifying said parameter; acquiring a steady-state characteristic indicating a relationship between a steady-state component of the disturbance force and the first controlled variable according to the pressure difference, for identifying a second control input that compensates for the steady-state component of the disturbance force resulting from the pressure difference between the upstream side and the downstream side of the valve body; and identifying a parameter θ for deriving a third control input that compensates for a transient component of the disturbance force. ｄ A parameter identification method comprising: (Aspect 7) In the step of identifying the parameter θ ａ , the parameter θ is identified based on a control input f for causing the first controlled variable to follow a predetermined trajectory in a state where there is no pressure difference. ａｃｃ ; in the step of acquiring the steady-state characteristic, the steady-state characteristic is acquired based on a steady-state input u which is a control input in a steady state when the pressure difference exists. ａ ; and in the step of identifying the parameter θ ｓｔａｔｉｃ , the parameter θ ｄ is identified based on a control input d for compensating for the transient component of the disturbance force when causing the first controlled variable to follow the predetermined trajectory in a state where the pressure difference exists. ｄｙｎａｍｉｃ , the parameter identification method according to Aspect 6. (Aspect 8) The control input f ｄ and a control input f for causing the first controlled variable to follow the predetermined trajectory in a state where the pressure difference exists ａｃｃ are acquired as training data; and in the step of identifying the parameter θ ｔｏｔａｌ , the control input f ｄ and the control input f ｔｏｔａｌ and the control input f ａｃｃFrom the difference between the above, a control input d for compensating the disturbance force is obtained, and the control input d and the steady-state input u ｓｔａｔｉｃ From the difference, the control input d for compensating the transient component of the disturbance force is obtained. ｄｙｎａｍｉｃ The parameter identification method described in Embodiment 7, which obtains the control input f ａｃｃ and the control input f ｔｏｔａｌ A parameter identification method according to Embodiment 8 (Embodiment 10) A program that causes a computer to execute the parameter identification method according to any one of Embodiments 6 to 9.

[0009] The technology described herein makes it possible to achieve high performance in flow rate control.

[0010] Figure 1 is a schematic diagram of the fluid supply system 100 according to the embodiment. Figure 2 is a cross-sectional view showing the structure of the flow control valve 2 according to the embodiment. Figure 3 is a diagram showing the hardware configuration of the control device 3 according to the embodiment. Figure 4 is a diagram for explaining the steady-state response of the input current. Figure 5 is a diagram for explaining the transient response of the supply pressure. Figure 6 is a control block diagram of the flow control system 110 according to the embodiment. Figure 7 shows an example of steady-state characteristics stored in the lookup table 30. Figure 8 shows an example of steady-state characteristics stored in the lookup table 40. Figure 9 is a flowchart for explaining the parameter identification process according to the embodiment. Figure 10 is a flowchart for explaining the details of step S2 in Figure 9. Figure 11 is a flowchart for explaining the details of step S4 in Figure 9. Figure 12 is a diagram showing a specific example of the parameter identification method. Figure 13 is a flowchart for explaining the flow control process according to the embodiment. Figure 14 is a diagram showing a specific example of the flow control process. Figure 15 is a control block diagram of the flow control system 110A according to a modified example. Figure 16 is a schematic diagram of the flow control system 110B according to an embodiment. Figure 17 shows the results of Experiment 1. Figure 18 shows the results of Experiment 2. Figure 19 shows the results of Experiment 3. Figure 20 is a mathematical diagram (1) showing the mathematical formulas used to describe the embodiment. Figure 21 is a mathematical diagram (2) showing the mathematical formulas used to describe the embodiment. Figure 22 is a mathematical diagram (3) showing the mathematical formulas used to describe the embodiment. Figure 23 is a mathematical diagram (4) showing the mathematical formulas used to describe the embodiment. Figure 24 is a mathematical diagram (5) showing the mathematical formulas used to describe the embodiment.

[0011] Embodiments of this disclosure will be described below with reference to the drawings. However, this description should not be interpreted as limiting, and will not limit the subject matter described in the claims. Furthermore, various changes, substitutions, and modifications can be made without departing from the spirit and scope of this disclosure. Different embodiments can also be combined as appropriate.

[0012] In the following description, an example of a flow control valve will be described in which the technology described herein is applied to a pneumatic valve for controlling the flow rate of air. However, the scope of application of the technology described herein is not limited to this. The fluid to be controlled by flow control is not limited to air; it may be other fluids. Furthermore, the flow control valve may be, for example, a hydraulic valve.

[0013] Figures 20 to 24 are mathematical diagrams showing the formulas used in describing the embodiments. The following explanation will refer to these figures as appropriate.

[0014] [Overall Configuration] Figure 1 is a schematic diagram of the fluid supply system 100 according to the embodiment. As shown in Figure 1, the fluid supply system 100 includes a compressor 1, a flow control valve 2, a control device 3, a flow meter 4, an upstream pressure sensor 5, a downstream pressure sensor 6, and a pressure control valve 7. The fluid supply system 100 supplies air sent from the compressor 1, which is the fluid supply source, to the downstream equipment 200. In addition, the flow control valve 2, control device 3, flow meter 4, upstream pressure sensor 5, and downstream pressure sensor 6 of the fluid supply system 100 constitute a flow control system 110.

[0015] The compressor 1 delivers compressed air stored in a tank (not shown), for example. The flow path L shown in Figure 1 is composed of pipes, for example, and circulates air from the compressor 1 to the downstream equipment 200.

[0016] Figure 2 is a schematic cross-sectional view showing the structure of a flow control valve 2 according to an embodiment. In Figure 2, a cross-section along the direction of airflow in the flow path L is shown. The flow control valve 2 is installed in the flow path L to control the flow rate of the fluid flowing through the flow path L. The flow control valve 2 is, as an example, a pneumatic valve for controlling the flow rate of air. The flow control valve 2 is configured as, for example, a poppet-type electric valve whose valve body is driven by a linear actuator. As shown in Figure 2, the flow control valve 2 has a housing 21, a valve body 22, a linear actuator 23, and a position sensor 24.

[0017] The housing 21 has an inlet 21a through which air flows in and an outlet 21b through which air flows out. The air supplied to the flow control valve 2 flows into the housing 21 from the flow path L via the inlet 21a and flows out from inside the housing 21 to the flow path L via the outlet 21b. Inside the housing 21, between the inlet 21a and the outlet 21b, a valve chamber 21c is formed. The valve chamber 21c is provided with an inlet port 21d for introducing air into the valve chamber 21c and an outlet port 21e for discharging air from the valve chamber 21c.

[0018] The valve body 22 is housed in the housing 21. Specifically, the valve body 22 is movable and is positioned to be displaceable within the valve chamber 21c. The valve body 22 moves forward and backward relative to the outlet port 21e in response to control by the control device 3, thereby increasing or decreasing the effective cross-sectional area of ​​the flow path from the inlet port 21d to the outlet port 21e. This changes the opening degree of the flow control valve 2, and thus changes the flow rate of air flowing out from the outlet 21b into the flow path L, that is, the flow rate of air supplied to the downstream equipment 200. Therefore, the flow rate of the flow control valve 2 is determined according to the position y of the valve body 22. Hereinafter, the position of the valve body 22 may be referred to as the "valve body position".

[0019] The linear actuator 23 constitutes a linear motor that acts as a drive unit for displacing the valve body 22. The linear actuator 23 has a stator 23a provided on the housing 21 side and a movable element 23b provided on the valve body 22 side. The stator 23a is cylindrical in shape and includes a yoke, an electromagnetic coil, etc. The movable element 23b is composed of a permanent magnet, etc., and is capable of reciprocating inside the stator 23a. The linear actuator 23 is driven by a current (input current) supplied from the control device 3 as a control input (operated amount), and displaces the movable element 23b according to the magnitude of the input current. When the linear actuator 23 is driven, the thrust of the movable element 23b is transmitted to the valve body 22, and the valve body 22 is displaced.

[0020] The position sensor 24 measures the valve body position y. The position sensor 24 outputs the measured value of the valve body position y to the control device 3.

[0021] Furthermore, the flow control valve according to this disclosure is not limited to an electric valve driven by a linear motor using electric current as the control input, but may also be configured as an electromagnetic proportional valve using a proportional solenoid as the drive unit for displacing the valve body. In addition, the flow control valve may be a piezo valve or the like, which is driven by voltage as the control input to displace the valve body. Moreover, the structure of the valve body is not limited to a poppet type, but may be a spool type.

[0022] Returning to Figure 1, the flow meter 4 is installed downstream of the flow control valve 2 in the flow path L and measures the flow rate of air flowing out from the flow control valve 2.

[0023] The upstream pressure sensor 5 is located upstream of the flow control valve 2 in the flow path L, and the pressure P upstream of the flow control valve 2 is measured. ｕ The pressure P is measured. Specifically, in the example shown in Figure 1, the upstream pressure sensor 5 is installed between the compressor 1 and the flow control valve 2; however, the position of the upstream pressure sensor 5 is not limited to this. ｕ The pressure should be any pressure upstream of the valve body 22.

[0024] The downstream pressure sensor 6 is located downstream of the flow control valve 2 in the flow path L, and measures the pressure P downstream of the flow control valve 2. ｄ The pressure P is measured. Specifically, in the example shown in Figure 1, the downstream pressure sensor 6 is installed between the flow meter 4 and the downstream equipment 200; however, the position of the downstream pressure sensor 6 is not limited to this. ｄ The pressure P should be the pressure downstream of the valve body 22. ｄ For example, this could be the internal pressure of the downstream equipment 200, in which case the downstream pressure sensor 6 may be installed inside the downstream equipment 200. Alternatively, the downstream pressure sensor 6 may be installed immediately before the downstream equipment 200, or between the flow control valve 2 and the flow meter 4.

[0025] The pressure control valve 7 is located upstream of the upstream pressure sensor 5 in the flow path L, and controls the pressure of the air flowing into the flow control valve 2 (i.e., pressure P). ｕ ) controls.

[0026] The control device 3 controls the flow rate of the flow control valve 2 by executing the flow rate control method described later. Specifically, the control device 3 performs processing for executing the flow rate control method (hereinafter referred to as the flow rate control processing). In addition, the control device 3 identifies parameters for deriving the control input (input current) to be input to the flow control valve 2 in flow rate control by executing the parameter identification method described later. Specifically, the control device 3 performs processing for executing the parameter identification method (hereinafter referred to as the parameter identification processing).

[0027] Figure 3 shows the hardware configuration of the control device 3 according to the embodiment. The control device 3 is, for example, an electronic device having an electronic circuit. The control device 3 has, for example, the hardware configuration of a general-purpose computer and includes a CPU 301 which is a processor, a memory 302, a communication interface (communication IF) 303, and storage 304. Each part is connected to the others via a bus 305. The control device 3 may also be, for example, a computer board (microcontroller).

[0028] The storage device 304 is an auxiliary storage device having a program storage area (not shown) that stores, for example, a program 10 (flow control program) for performing flow control processing and a program 20 (parameter identification program) for performing parameter identification processing. The storage device 304 also has an information storage area (not shown) that stores various types of information used when performing flow control processing and parameter identification processing. The information storage area of ​​the storage device 304 stores, for example, lookup tables 30 and 40 used in parameter identification processing and parameters (parameter θ) determined by the parameter identification processing. ａ , θ ｄ ) and the like are stored. The storage 304 may be, for example, an HDD (Hard Disk Drive) or an SSD (Solid State Drive).

[0029] Memory 302 is an area for loading programs 10 and 20 stored in storage 304. Memory 302 may also be used as an area for these programs to store data.

[0030] The CPU 301 performs flow rate control processing by executing program 10 loaded from storage 304 into memory 302, for example. The CPU 901 performs parameter identification processing by executing program 20 loaded from storage 304 into memory 302, for example. The CPU 301 may also obtain and execute programs 10 and 20 from other devices, for example, via a communication network.

[0031] The communication IF 303 is a device that communicates with external devices via a communication network such as the Internet. For example, the communication IF 303 communicates with an operation terminal (not shown) that allows an operator of the flow control system 110 to input necessary information via the communication network.

[0032] [Disturbance Forces] Next, with reference to Figures 2 and 20, we will explain the disturbance forces that should be considered in flow control by the flow control valve 2. Let M be the mass of the valve body, D be the coefficient of viscous friction, and K be the constant of electromagnetic force. ｆ If i is the input current (control input) to the flow control valve 2, r is the radius of the valve body 22, and ΔP is the pressure difference between the upstream and downstream sides of the valve body 22, then the basic equation of motion for the valve body 22 is expressed as equation (1) (see Figure 20).

[0033] Here, ΔP is the pressure P on the upstream side of the flow control valve 2 in the initial state when no air is flowing through the flow control valve 2. ｕ and the downstream pressure P ｄ The difference is ΔP ｉｎｉｔ = P ｕ -P ｄ (=ΔP) ０ ) is approximately equal to F. Disturbances caused by the dynamics of ΔP, such as local or instantaneous fluctuations of ΔP, are expressed as F. ｄ Therefore, the equation of motion for the valve body can be expressed as equation (2) (see Figure 20).

[0034] In flow control using a flow control valve 2 with a valve body 22, it is necessary to consider the pressure dependence of the force acting on the valve body 22. When the right-hand side of equation (1) is zero, the position of the valve body 22 does not change, and the opening degree of the flow control valve 2 is maintained at a constant level. In this state, as the pressure difference ΔP between the upstream and downstream sides of the valve body 22 increases, the required input current i increases.

[0035] Figure 4 is a diagram illustrating the steady-state response of the input current. Specifically, in Figure 4, the pressure difference ΔP in the initial state where no air is flowing is shown. ｉｎｉｔ The steady-state response of the input current i is shown when the valve body 22 is displaced at a sufficiently slow speed while maintaining the balance of forces acting on the valve body 22, assuming a pressure of 0.30 MPa. As shown in Figure 4, it can be seen that the current required for force balance decreases as the valve body position rises. This result indicates that the disturbance force F caused by ΔP shown in equation (2) (see Figure 20) corresponds to the opening degree (valve body position) of the flow control valve 2. ｄ This is due to a change in the steady-state component. To increase the speed of the flow response, it is necessary to displace the valve body at high speed, and therefore it is necessary to quickly compensate for the steady-state component of the disturbance force associated with the change in the pressure difference between the upstream and downstream sides of the valve body 22.

[0036] Furthermore, in flow control by the flow control valve 2, it is necessary to consider resonance originating from the compressibility of air. Because the propagation speed of air is slow, rapidly changing the opening degree of the flow control valve 2 induces resonance in the piping that constitutes the flow path L connected to the flow control valve 2. Figure 5 is a diagram illustrating the transient response of the supply pressure. Specifically, Figure 5(a) shows the trajectory of the valve body 22 (time displacement of the valve body position), and Figure 5(b) shows the change in supply pressure when the valve body 22 is displaced rapidly as shown in Figure 5(a). As shown in Figures 5(a) and 5(b), it can be seen that when the valve body 22 is displaced rapidly, resonance occurs instantaneously, and the supply pressure fluctuates. This result indicates that a disturbance force F caused by ΔP shown in equation (2) (see Figure 20) is generated by the rapid change in the opening degree (valve body position) of the flow control valve 2. ｄ This is due to fluctuations in the supply pressure. To achieve a faster flow rate response, it is necessary to displace the valve body at high speed, and therefore it is necessary to quickly compensate for the transient component of the disturbance force associated with instantaneous fluctuations in the supply pressure.

[0037] As described above, in order to improve the performance of flow control, it is necessary to compensate for (cancel out) the disturbance force (compressibility of air) caused by the pressure difference ΔP. The flow control system 110 according to this embodiment displaces the valve body 22 and compensates for the disturbance force by FF control, which will be described below.

[0038] [Configuration of Flow Control System 110] Figure 6 is a control block diagram of the flow control system 110 according to the embodiment. In Figure 6, the valve body position y is a measured value measured by the flow control valve 2, and the flow rate m dot is a measured value measured by the flow meter 4. Also, the pressure P on the upstream side of the flow control valve 2 ｕ This is a measurement value obtained by the upstream pressure sensor 5, and the pressure P downstream of the flow control valve 2. ｄ This is the measurement value obtained by the downstream pressure sensor 6. Also, ΔP is the upstream pressure P ｕ (Measured value) and downstream pressure P ｄ The difference from (measured value), ΔP = P ｕ -P ｄ ΔP ０ This is ΔP in the initial state where no air is flowing. The flow rate control system 110 will be described below with reference to Figures 6, 21, and 22.

[0039] As shown in Figure 6, the flow control system 110 employs a cascade control method. The flow control system 110 uses the valve body position y as the first control quantity to be compensated by FF control, and the mass flow rate m dot of the flow control valve 2 as the second control quantity, where the mass flow rate m dot is equal to the command value (target value) of the mass flow rate m ｒｅｆ The flow control valve 2 is controlled to follow the dot.

[0040] The control device 3 receives the command value m as the second control variable. ｒｅｆ Based on the dot (t), the command value (target trajectory) of the valve body position is y. ｒｅｆ (t) is calculated. Then, the control device 3 calculates the command value y of the valve body position derived as the first control quantity. ｒｅｆ Based on (t), the control input f to be input to the flow control valve 2 is as follows: ｒｅｆ (In this example, the current i is output.)

[0041] The flow control valve 2 receives a control input f ｒｅｆ The flow rate is adjusted by changing the valve body position according to the value of [a certain parameter]. The flow control valve 2, which is the target of control, has two nominal plants, plant 25 and plant 26, pre-configured.

[0042] Plant 25 controls the control input f of the flow control valve 2. ｒｅｆ This is the nominal plant from the valve body position y. The transfer function G(s) of plant 25 is the product of the second-order lag system and the dead time, as shown in equation (3) (see Figure 21).

[0043] Plant 26 is a nominal plant from valve body position y to flow rate m dot. The transfer function of plant 26 is the pressure difference ΔP ０ Transformation coefficient φ(ΔP) depends on the transformation coefficient. ０ This results in a dead-time system having ). The pressure-dependent conversion coefficient φ(ΔP0) is given as a lookup table based on previously acquired steady-state characteristics, and specifically, it is equivalent to the forward system of steady-state characteristics shown in Figure 7 below.

[0044] The control device 3 includes an FB (feedback) controller 31, an FF (feedforward) controller 32, an FB controller 33, and an FF controller 34 (disturbance compensation FF controller).

[0045] The control device 3 receives the input command value m ｒｅｆ Based on the dot (t), the FB controller 31 and the FF controller 32 set the command value (target trajectory) y of the valve body position. ｒｅｆ Calculate (t).

[0046] Furthermore, the control device 3 sets the command value y of the valve body position. ｒｅｆ Based on (t), the FB controller 33 and the FF controller 34 input the control input f to the flow control valve 2. ｒｅｆ (In this example, the current i is output.)

[0047] The FB controller 31 controls the flow rate command value m ｒｅｆ Based on the measured values ​​of the dot (t) and the flow rate m dot, general PID control is performed on the flow rate m dot.

[0048] The FF controller 32 controls the pressure difference ΔP０ and the command value of the flow rate m ｒｅｆ Based on the dot (t), the target trajectory y is the target value of the first controlled variable. ｒｅｆ By deriving this, FF control is performed for the flow rate m dot. More specifically, the FF controller 32 controls the flow rate command value (target value) m ｒｅｆ Dot (t) and measured pressure difference ΔP ０ Based on the steady-state characteristics showing the relationship between the flow rate m dot and the pressure difference ΔP between the valve body position y, which have been acquired in advance, and the dead time of the nominal plant (plant 26) from the valve body position y to the flow rate m dot, which have been identified in advance, the command value (target trajectory) of the valve body position y is determined. ｒｅｆ Derive (t).

[0049] Figure 7 shows an example of the steady-state characteristics stored in the lookup table 30. The steady-state characteristics shown in Figure 7 represent the relationship between the flow rate m dot and the valve body position y, corresponding to the pressure difference ΔP. As shown in Figure 7, the steady-state characteristics represent the relationship between the flow rate m dot and the valve body position y in the steady state of the flow control valve 2. ｓｔａｔｉｃ (m dot, ΔP) is obtained in advance for each of the multiple pressure differences ΔP through prior measurements or other means.

[0050] The FF controller 32 obtains the pressure difference ΔP from the lookup table 30. ０ y corresponding to ｓｔａｔｉｃ (m dot, ΔP) ０ Refer to the command value m for the flow rate. ｒｅｆ Based on the dot (t) and the pre-identified dead time of the nominal plant (plant 26) from valve position y to flow rate m dot, the command value y for valve position is set. ｒｅｆ The following is derived: The dead time of the nominal plant (plant 26) is τ ｎ Then, y ｒｅｆ This is expressed as shown in equation (4) (see Figure 21). As shown in equation (4), the FF controller 32 controls the dead time τ ｎ This compensates for the loss. This allows the control input to be anticipated and changed earlier than the flow rate command value begins to change, by anticipating the control input to be input to the flow control valve 2.

[0051] The FB controller 33 controls the command value y of the valve body position. ｒｅｆBased on [the target value] and the measured value of the valve element position y, general PID control is performed on the valve element position y. The transfer function C of the FB controller 33 ＦＢ (s) can be expressed as Equation (5) (see Figure 21). In Equation (5), K ｐ is a proportional gain constant, K ｉ is an integral gain, K ｄ is a derivative gain, and τ ｄ is the time constant of the derivative component.

[0052] The FF controller 34 performs feedforward control on the valve element position y by deriving a control input f^(y ０ , ΔP ｒｅｆ , ΔP ０ , θ ａ , θ ｄ ) that can compensate for disturbance force caused by the pressure difference ΔP while displacing the valve element 22.

[0053] Specifically, the FF controller 34 derives a first control input f^ ａｃｃ (y ｒｅｆ , θ ａ ) for displacing the valve element 22 in correspondence with the mass M and viscous friction of the valve element 22, a second control input d^ ０ (y ｓｔａｔｉｃ , ΔP ｒｅｆ , ΔP ０ ) for compensating the steady-state component of the disturbance force caused by the pressure difference ΔP between the upstream side and the downstream side of the valve element 22, and a third control input d^ ｄｙｎａｍｉｃ (y ｒｅｆ , θ ｄ ) for compensating the transient component of the disturbance force, and inputs these to the flow control valve 2. Here, θ ａ and θ ｄ are parameters of a second-order lag system model. Specifically, θ ａ = [M, D, τ]. At this time, M is the mass of the valve element 22, D is the viscous friction coefficient, and τ is the dead time. Further, θ ｄ = [K, ζ, ω ｎ . At this time, K is the gain, ζ is the damping coefficient, and ω ｎ is the natural angular frequency.

[0054] The FF controller 34 obtains the first control input f^ ａｃｃ (y ｒｅｆ , θ ａA first FF controller 341 that outputs ) and a second control input d^ ｓｔａｔｉｃ (y ｒｅｆ ΔP ０ A second FF controller 342 outputs a third control input d^ ｄｙｎａｍｉｃ (y ｒｅｆ , θ ｄ Includes a third FF controller 343 that outputs ) and a control input f^(y ｒｅｆ ΔP ０ , θ ａ , θ ｄ ) can be expressed as shown in equation (6) (see Figure 21).

[0055] The first FF controller 341 receives the first control input f^ ａｃｃ (y ｒｅｆ , θ ａ By outputting the first control input f^, control (acceleration FF control) is performed according to the mass M and viscous friction of the valve body 22. In detail, this viscous friction is the viscous friction acting on the valve body 22 by the inner wall of the housing 21 and the fluid (air). ａｃｃ (y ｒｅｆ , θ ａ The control input for tracking the trajectory of the valve body 22 is a control input corresponding to the mass M of the valve body 22 and the viscous friction, and is a control input for displacing the valve body 22. The first FF controller 341 controls the command value (target trajectory) y of the valve body position. ｒｅｆ Based on (t) and a previously acquired relational expression showing the relationship between the control input (current i) and the control amount (valve position y) for making the valve body position y follow a predetermined trajectory when there is no pressure difference ΔP (ΔP = 0), the first control input f^ ａｃｃ (y ｒｅｆ (t), θ ａ The above relation is derived from a second-order lag system model and can be expressed as equation (7) (see Figure 22). Relation (7) is the control input f when the controlled variable (valve body position y) is made to follow a predetermined trajectory in the absence of a pressure difference ΔP, as will be described later. ａｃｃ Based on this, it is obtained. As shown in equation (7), the first FF controller 341 compensates for the dead time τ. Thus, y ｒｅｆ The first control input f^ starts before (t) begins to change. ａｃｃ (y ｒｅｆ, θ ａ You can enter ).

[0056] Furthermore, the transfer function C of the first FF controller 341 ＦＦ，１ (s) can be expressed as the inverse system of the nominal plant, plant 25, as shown in equation (8) (see Figure 22).

[0057] The second FF controller 342 receives the second control input d^ ｓｔａｔｉｃ (y ｒｅｆ ΔP ０ By outputting ), the pressure difference ΔP ０ Control is performed to compensate for the steady-state component of the disturbance force caused by the second control input d^ ｓｔａｔｉｃ (y ｒｅｆ ΔP ０ ) In the trajectory tracking of the valve body 22, the pressure difference ΔP ０ This is a control input to compensate for the steady-state component of the disturbance force caused by the second FF controller 342. The second FF controller 342 controls the command value (target trajectory) y of the valve body position. ｒｅｆ (t) and the control input (steady state input) u in the steady state when there is a pressure difference ΔP, which has been acquired in advance. ｓｔａｔｉｃ Based on the steady-state characteristics showing the relationship between (t) and the controlled amount (valve position y) according to the pressure difference ΔP, the second control input d^ ｓｔａｔｉｃ (y ｒｅｆ (t), ΔP ０ Derive the following:

[0058] Figure 8 shows an example of the steady-state characteristics stored in the lookup table 40. The steady-state characteristics shown in Figure 8 show the relationship between the control input u (current i in this example) and the pressure difference ΔP between the valve body position y. As shown in Figure 8, the steady-state characteristics are defined as the control input u in the steady state (steady-state input u ｓｔａｔｉｃ The steady-state characteristics showing the relationship between (y, ΔP) and the valve body position y have been acquired in advance for each of the multiple pressure differences ΔP through prior measurements or other means.

[0059] The second FF controller 342 calculates the pressure difference ΔP from the lookup table 40. ０ A steady input u compensates for the steady component of the disturbance force caused by ｓｔａｔｉｃ (y, ΔP ０ Refer to the command value y for the valve body position. ｒｅｆBased on (t), the second control input d^ ｓｔａｔｉｃ (y ｒｅｆ (t), ΔP ０ Derive the second control input d^ ｓｔａｔｉｃ (y ｒｅｆ (t), ΔP ０ ) can be expressed as shown in equation (9) (see Figure 22).

[0060] Furthermore, the transfer function of the second FF controller 342 is u ｓｔａｔｉｃ | ΔＰ This is the result.

[0061] The third FF controller 343 receives the third control input d^ ｄｙｎａｍｉｃ (y ｒｅｆ (t), θ ｄ By outputting ), the pressure difference ΔP ０ Control (vibration component control) is performed to compensate for the transient component of the disturbance force caused by the third control input d^ ｄｙｎａｍｉｃ (y ｒｅｆ (t), θ ｄ ) is a control input for compensating for the transient component of the disturbance force in the trajectory tracking of the valve body 22. The third FF controller 343 controls the command value of the valve body position (target trajectory) y ｒｅｆ Based on (t) and a previously acquired relational expression showing the relationship between the control input (current i) and the controlled variable (valve position y) for compensating for the transient component of disturbance force when the valve position y follows a predetermined trajectory in a state where there is a pressure difference ΔP (ΔP≠0), the third control input d^ ｄｙｎａｍｉｃ (y ｒｅｆ (t), θ ｄ The above relation is derived from a second-order lag system model representing damped oscillations, and can be expressed as equation (10) (see Figure 22).

[0062] As will be described later, the control input f when the controlled amount (valve body position y) is made to follow a predetermined trajectory while there is a pressure difference ΔP. ｔｏｔａｌ And, the control input f when the controlled variable is made to follow a predetermined trajectory in the absence of a pressure difference ΔP. ａｃｃ Based on the difference between the two, a control input d is obtained to compensate for the disturbance force caused by the pressure difference ΔP. Then, the control input d and the steady-state input u ｓｔａｔｉｃ Based on the difference, the above relation (10) is obtained.

[0063] Furthermore, the transfer function C of the third FF controller 343 ＦＦ，２ (s) can be expressed as shown in equation (11) (see Figure 22).

[0064] Based on the above, the transfer function C of the FF controller 34 ＦＦ (s) can be expressed as shown in equation (12) (see Figure 22), with the transfer functions of the FF controllers 341, 342, and 343 as compensation terms. In equation (12), the compensation term C of the first FF controller 341 ＦＦ，１ (s) is called the "acceleration-velocity term," and the compensation term u of the second FF controller 342 ｓｔａｔｉｃ | ΔＰ This is called the "steady-state term," and is the compensation term C of the third FF controller 343. ＦＦ，２ (s) is called the "oscillation term".

[0065] [Parameter Identification Method] The parameter identification method for identifying the parameters used to derive the control input f^ will be described below. Parameter identification is performed by the parameter identification program 20 causing the control device 3 to execute the parameter identification process described later.

[0066] Figure 9 is a flowchart illustrating the parameter identification process according to the embodiment. Figure 10 is a flowchart illustrating the details of step S2 in Figure 9. Figure 11 is a flowchart illustrating the details of step S4 in Figure 9. Figure 12 is a diagram showing a specific example of the parameter identification method. Figure 12(a) shows the target trajectory y ｒｅｆ Figure 12(b) shows the trajectory (valve body position y) obtained by (t) and iterative learning control (ILC). ΔＰ (f ａｃｃ , f ｔｏｔａｌ Figure 12(c) shows the control input f when the pressure difference ΔP obtained by the ILC is 0. ａｃｃ This is shown. Figure 12(d) shows the control input d| that compensates for the disturbance force due to the pressure difference ΔP obtained from the ILC results. ΔＰ This is shown. Figure 12(d) shows the control input d^ that compensates for the steady-state component of the disturbance force due to the pressure difference ΔP. ｓｔａｔｉｃ | ΔＰThis is shown. Figure 12(e) shows the control input d^ that compensates for the transient component of the disturbance force due to the pressure difference ΔP obtained from the ILC results. ｄｙｎａｍｉｃ | ΔＰ This is shown below. The explanation will be given with reference to Figures 9 to 12 and Figure 23.

[0067] In the parameter identification process, first, as shown in Figure 9, the control device 3 uses the command value y of the target trajectory of the valve body position, which serves as training data for identifying the parameters. ｒｅｆ (t) is determined (step S1). Specifically, the control device 3 refers to the lookup table 30 for any pressure difference ΔP and the command value m ｒｅｆ The dot (t) and the dead time τ of the nominal plant (plant 26) from the valve body position y to the flow rate m dot, which has been identified in advance. ｎ Based on that, y ｒｅｆ Calculate (t). y ｒｅｆ (t) is expressed as shown in equation (13) (see Figure 23). In Figure 12(a), "reference" is the target trajectory y obtained in step S1. ｒｅｆ An example of (t) is shown. Note that the target trajectory y ｒｅｆ (t) is the command value m of the flow rate. ｒｅｆ As long as the dot (t) matches the rise time and fall time, the step width can be arbitrary, so the pressure difference ΔP referenced from the lookup table 30 can be arbitrarily selected.

[0068] Returning to Figure 9, the control device 3 then receives a first control input f^ corresponding to the mass and viscous friction of the valve body 22. ａｃｃ (y ｒｅｆ , θ ａ ) parameter θ for deriving ａ Identify (Step S2). In Step S2, the control device 3 moves the controlled amount (valve body position y) along a predetermined trajectory (y) when there is no pressure difference ΔP. ｒｅｆ Control input f to make it follow (t) ａｃｃ The following is derived as training data, and the control input f ａｃｃ Based on this, the parameter θ ａ Identify it.

[0069] As shown in Figure 10, in step S2, first the control device 3 receives the control input f which will be used as training data. ａｃｃObtain (step S21). Control input f ａｃｃ As described above, in the state where there is no pressure difference ΔP (ΔP = 0), the valve body position y is moved to the target trajectory y. ｒｅｆ This is a control input to make it follow (t). In step S21, for example, the supply pressure to the flow control valve 2 is made equal to atmospheric pressure, resulting in a state of zero supply pressure (no compressed air). This makes the pressure difference ΔP zero. Then the control device 3 sets the target trajectory y ｒｅｆ By performing iterative learning control (ILC) on (t), the control input f ａｃｃ This will be used as training data.

[0070] Here, ILC is a method of nonparametrically determining the feedforward (FF) input that minimizes the error with respect to the target under those experimental conditions by repeatedly correcting the control input while performing tracking control (trials) with respect to the target trajectory of the controlled object under the same experimental conditions. The control device 3 performs ILC to determine the target trajectory y ｒｅｆ (t) fitted control input f ａｃｃ This can be calculated, provided that the control input f ａｃｃ The method for identifying and acquiring this information is not limited to ILC, but can be selected as appropriate.

[0071] In Figure 12(a), "0.0 MPa" represents the target trajectory y in the state where there is no pressure difference ΔP. ｒｅｆ The trajectory of the valve body position y obtained by ILC for (t) is shown. "0.0 MPa" in Figure 12(b) and "ILC" in Figure 12(c) represent the target trajectory y when there is no pressure difference ΔP. ｒｅｆ The control input f obtained by ILC for (t) ａｃｃ This indicates.

[0072] As shown in Figure 10, in step S2, the control device 3 then controls the control input f ａｃｃ Based on this, the parameter θ ａ Identify = [M, D, τ] (Step S22). Specifically, the control device 3 uses a second-order lag system model from the control input (current i) to the valve body position y, as represented by equation (7) (see Figure 22), and the control input f is the training data. ａｃｃ The parameter θ of the model that provides a control input close to that of the model.ａ The parameter θ is determined by optimization, as shown in equation (14) (see Figure 23). ａ This can be determined using methods other than the least squares method, such as the parameter θ. ａ You may identify it.

[0073] As described above, the parameter θ ａ = By identifying [M, D, τ], the first control input f^ expressed by equation (7) is obtained. ａｃｃ (y ｒｅｆ (t), θ ａ ) becomes possible. In Figure 12(c), "model" is the parameter θ ａ The control input f^ derived by ａｃｃ This indicates.

[0074] Returning to Figure 9, next, the control device 3 controls the pressure difference ΔP ０ A second control input d^ compensates for the steady-state component of the disturbance force caused by the second control input d^ ｓｔａｔｉｃ (y ｒｅｆ (t), ΔP ０ Step S3 is used to determine the steady-state control input u, which is the control input in the steady state when there is a pressure difference ΔP. ｓｔａｔｉｃ Based on this, steady-state characteristics are obtained. For example, the control device 3 measures the control input u (current i in this example) in the steady state when the valve body position y is changed for each of the multiple pressure differences ΔP, and as shown in Figure 8, for each of the multiple pressure differences ΔP, the steady-state control input u (steady-state input u ｓｔａｔｉｃ A steady-state characteristic is obtained that shows the relationship between (y, ΔP) and the valve body position y. The process in step S3 may be performed in advance.

[0075] Next, the control device 3 receives a third control input d^ that compensates for the transient component of the disturbance force. ｄｙｎａｍｉｃ (y ｒｅｆ (t), θ ｄ ) parameter θ for deriving ｄIdentify (step S4). In step S4, the control device 3 moves the control amount (valve body position y) along a predetermined trajectory (y) while there is a pressure difference ΔP. ｒｅｆ Control input f to make it follow (t) ｔｏｔａｌ The following is derived as training data, and the control input f ｔｏｔａｌ Based on this, the parameter θ ｄ Identify it.

[0076] As shown in Figure 11, in step S4, first the control device 3 receives the control input f which will be used as training data. ｔｏｔａｌ Obtain (step S41). Control input f ｔｏｔａｌ As described above, when there is a pressure difference ΔP (ΔP≠0), the valve body position y is moved to the target trajectory y. ｒｅｆ This is a control input to make it follow (t). In step S41, for example, compressed air is supplied to the flow control valve 2, and the initial pressure difference ΔP ０ With the flow control valve 2 supplied with the target trajectory y ｒｅｆ By performing ILC on (t), the control input f ｔｏｔａｌ The control device 3 obtains multiple pressure differences ΔP by ILC. ０ Regarding the target trajectory y, ｒｅｆ (t) fitted control input f ｔｏｔａｌ This is obtained as training data. However, the control input f ｔｏｔａｌ The method for identifying and acquiring this information is not limited to ILC, but can be selected as appropriate.

[0077] In Figure 12(a), "0.10 MPa", "0.20 MPa", and "0.30 MPa" represent the initial pressure difference ΔP, respectively. ０ Target trajectory y when the pressure is 0.10 MPa, 0.20 MPa, and 0.30 MPa. ｒｅｆ The trajectory of the valve body position y obtained by ILC for (t) is shown. In Figure 12(b), "0.10 MPa", "0.20 MPa", and "0.30 MPa" represent the initial pressure difference ΔP, respectively. ０ Target trajectory y when the pressure is 0.10 MPa, 0.20 MPa, and 0.30 MPa ｒｅｆ The control input f obtained by ILC for (t) ｔｏｔａｌ This indicates.

[0078] As shown in Figure 11, in step S4, the control device 3 then receives the control input f, which is the training data. ｔｏｔａｌ and control input f ａｃｃ From the difference, a control input d is obtained to compensate for the disturbance force caused by the pressure difference ΔP (step S42). Control input f when there is a pressure difference ΔP ｔｏｔａｌ Control input f when there is no pressure difference ΔP ａｃｃ By taking the difference, it is possible to extract a control input d that compensates only for the disturbance force caused by the pressure difference ΔP in the training data. In Figure 12(d), "0.10 MPa", "0.20 MPa", and "0.30 MPa" represent the initial pressure difference ΔP, respectively. ０ Control input d| compensates for disturbance forces caused by pressure differences ΔP when the pressure is set to 0.10 MPa, 0.20 MPa, and 0.30 MPa. ΔＰ This indicates.

[0079] Here, the control input d| compensates for the disturbance force caused by the pressure difference ΔP. ΔＰ As shown in equation (15) (see Figure 23), the control input d compensates for the steady-state component of the disturbance force caused by the pressure difference ΔP. ｓｔａｔｉｃ | ΔＰ and a control input d that compensates for the transient component of the disturbance force caused by the pressure difference ΔP. ｄｙｎａｍｉｃ | ΔＰ It is the sum of the two.

[0080] As shown in Figure 11, in step S4, the pressure difference ΔP is then calculated based on the steady-state characteristics showing the relationship between the steady-state component of the disturbance force and the controlled variable. ０ Control input d compensates for the steady-state component of the disturbance force caused by ｓｔａｔｉｃ | ΔＰ The control device 3 obtains the pressure difference ΔP by referring to the lookup table 40, for example. ０ Accordingly, in the steady state, the valve body position y is set to the target trajectory y. ｒｅｆ (t) Steady-state input u ｓｔａｔｉｃ (y ｒｅｆ (t), ΔP ０ The control device 3 calculates the steady-state input u obtained thereby. ｓｔａｔｉｃ (t) is the control input d that compensates for the steady-state component of the disturbance force. ｓｔａｔｉｃ | ΔＰ (u ｓｔａｔｉｃ(t) = d ｓｔａｔｉｃ | ΔＰ ).

[0081] As described above, the measured pressure difference ΔP ０ The corresponding steady-state input u ｓｔａｔｉｃ By referring to (y, ΔP), a second control input d^ is expressed by equation (9) (see Figure 22). ｓｔａｔｉｃ (y ｒｅｆ ΔP ０ This makes it possible to derive the following. In Figure 12(e), "0.10 MPa", "0.20 MPa", and "0.30 MPa" represent the initial pressure difference ΔP, respectively. ０ When the control input d^ is set to 0.10 MPa, 0.20 MPa, and 0.30 MPa, ｓｔａｔｉｃ | ΔＰ This indicates.

[0082] As shown in Figure 11, in step S4, the control device 3 then controls the control input d| ΔＰ and control input d^ ｓｔａｔｉｃ | ΔＰ From the difference, the control input d is used to compensate for the transient component of the disturbance force caused by the pressure difference ΔP. ｄｙｎａｍｉｃ | ΔＰ (Step S44) The control input d| compensates for the disturbance force including the steady-state component and the transient component. ΔＰ And, a control input d^ that compensates for the steady-state component of the disturbance force. ｓｔａｔｉｃ | ΔＰ By taking the difference with the control input d, only the transient component of the disturbance force caused by the pressure difference ΔP in the training data is compensated for. ｄｙｎａｍｉｃ | ΔＰ This can be extracted. In Figure 12(f), "0.10 MPa", "0.20 MPa", and "0.30 MPa" represent the initial pressure difference ΔP, respectively. ０ When the control input d^ is set to 0.10 MPa, 0.20 MPa, and 0.30 MPa, ｄｙｎａｍｉｃ | ΔＰ This indicates.

[0083] As shown in Figure 11, in step S4, the control device 3 then controls the control input d ｄｙｎａｍｉｃ | ΔＰ Based on this, the parameter θ ｄ = [K, ζ, ω ｎ] is identified (step S45). Specifically, the control device 3 is based on a second-order lag system model from the control input (current i) to the valve body position y, as represented by equation (11) (see Figure 22), and the training data is the control input d ｄｙｎａｍｉｃ | ΔＰ The parameter θ of the model that provides a control input close to that of the model. ｄ = [K, ζ, ω ｎ The parameter θ is determined by optimization. For example, as shown in equation (16) (see Figure 23), the parameter θ is determined by optimization using the least squares method. ｄ This is what is required. Note that other methods may be used besides the least squares method. Also, in this example, for the sake of simplifying the model, the parameter θ is used. ｄ This is a combination of multiple initial pressure differences ΔP ０ The average value of the parameters calculated for each of the following pressures (0.10 MPa, 0.20 MPa, 0.30 MPa) will be used. However, the parameter θ ｄ The methods for identifying them are not limited to this.

[0084] As described above, the parameter θ ｄ = [K, ζ, ω ｎ By identifying ], a third control input d^ as represented by equation (10) is obtained. ｄｙｎａｍｉｃ (y ｒｅｆ , θ ｄ ) becomes possible to derive. In Figure 12(f), "normal" is the parameter θ ｄ The control input d^ derived by ｄｙｎａｍｉｃ (y ｒｅｆ , θ ｄ ) indicates.

[0085] Through the processing of steps S1 to S4 described above, the control input f^(y) of the FF controller 34 is processed. ｒｅｆ ΔP ０ , θ ａ , θ ｄ ) parameter θ for deriving ａ , θ ｄ It is possible to identify them.

[0086] [Flow Rate Control Method] The flow rate control method for controlling the flow rate of the flow rate control valve 2 will be described below. The flow rate control method is performed by the flow rate control program 10 causing the control device 3 to execute the flow rate control process described later.

[0087] Figure 13 is a flowchart illustrating the flow rate control process according to the embodiment. The following explanation will refer to Figures 13, 21, and 22.

[0088] In the flow rate control process, first, as shown in Figure 13, the control device 3 determines the pressure difference ΔP between the upstream and downstream sides of the flow control valve 2 (specifically, the valve body 22) in the initial state when no air is flowing through the flow control valve 2. ０ The control device 3 obtains the upstream pressure P measured by the upstream pressure sensor 5, for example. ｕ The measured value and the downstream pressure P measured by the downstream pressure sensor 6 ｄ By calculating the difference with the measured value, the pressure difference ΔP ０ Obtain it.

[0089] Next, the control device 3 controls the pressure difference ΔP ０ and the command value of the flow rate m ｒｅｆ Based on the dot (t), the target value (command value) of the first controlled variable is the target trajectory y ｒｅｆ (t) is derived (step S102). Specifically, the FF controller 32 of the control device 3 obtains the pressure difference ΔP from the lookup table 30. ０ y corresponding to ｓｔａｔｉｃ (m dot, ΔP) ０ Refer to the command value m for the flow rate. ｒｅｆ The dot (t) and the dead time τ of the nominal plant (plant 26) from the valve body position y to the flow rate m dot, which has been identified in advance. ｎ Based on this, the command value (target trajectory) of the valve body position y ｒｅｆ Derive (t). As shown in equation (4), y ｒｅｆ (t) = y ｓｔａｔｉｃ (m ｒｅｆ dot (t + τ) ｎ ), ΔP ０ )

[0090] Next, the control device 3 sets the target trajectory y of the valve body position. ｒｅｆ(t) and parameter θ ａ Based on this, a first control input f^ is used to displace the valve body 22 in accordance with the mass M of the valve body 22 and viscous friction. ａｃｃ (y ｒｅｆ (t), θ ａ ) is derived (step S103). Specifically, the first FF controller 341 of the control device 3 determines the target trajectory y of the valve body position. ｒｅｆ Based on (t) and the previously acquired relational equation (7) (see Figure 22) which shows the relationship between the control input (current i) and the control amount (valve position y) for making the valve body position y follow a predetermined trajectory when there is no pressure difference ΔP (ΔP = 0), the first control input f^ ａｃｃ (y ｒｅｆ (t), θ ａ Derive the following:

[0091] Next, the control device 3 controls the pressure difference ΔP ０ and the target trajectory y of the valve body position ｒｅｆ Based on (t), the pressure difference ΔP ０ A second control input d^ to compensate for the steady-state component of the disturbance force caused by the above. ｓｔａｔｉｃ (y ｒｅｆ (t), ΔP ０ ) is derived (step S104). Specifically, the second FF controller 342 of the control device 3 derives the second control input d^ based on the steady-state characteristics obtained in advance, which show the relationship between the control input (current i) and the control amount (valve position y) in a steady state when there is a pressure difference ΔP, according to the pressure difference ΔP. ｓｔａｔｉｃ (y ｒｅｆ (t), ΔP ０ The second FF controller 342 derives the pressure difference ΔP from the lookup table 40. ０ The corresponding steady-state input u ｓｔａｔｉｃ (y, ΔP ０ Refer to the reference and set the valve body position y in the steady state to the target trajectory y ｒｅｆ The control input to make it follow (t) is the second control input d^ ｓｔａｔｉｃ (y ｒｅｆ (t), ΔP ０ It is calculated as follows:

[0092] Next, the control device 3 sets the target trajectory y of the valve body position. ｒｅｆ (t) and parameter θ ｄBased on this, the pressure difference ΔP ０ A third control input d^ to compensate for the transient component of the disturbance force caused by the above. ｄｙｎａｍｉｃ (y ｒｅｆ (t), θ ｄ ) is derived (step S105). Specifically, the third FF controller 343 of the control device 3 determines the target trajectory y of the valve body position. ｒｅｆ Based on (t) and the previously acquired relational expression (10) (see Figure 22) which shows the relationship between the control input (current i) and the control amount (valve position y) for making the valve body position y follow a predetermined trajectory when there is a pressure difference ΔP (ΔP≠0), the third control input d^ ｄｙｎａｍｉｃ (y ｒｅｆ (t), θ ｄ Derive the following:

[0093] Next, the control device 3 sets the valve body position y to the target trajectory y ｒｅｆ (t) while maintaining the pressure difference ΔP ０ Control input f^(y) capable of compensating for disturbance forces caused by external forces ｒｅｆ ΔP ０ , θ ａ , θ ｄ ) is derived (step S106). Specifically, the FF controller 34 of the control device 3 uses the first control input f^ derived in steps S103 to S105. ａｃｃ (y ｒｅｆ (t), θ ａ ) and the second control input d^ ｓｔａｔｉｃ (y ｒｅｆ ΔP ０ ) and the third control input d^ ｄｙｎａｍｉｃ (y ｒｅｆ , θ ｄ ) and are added together as shown in equation (6) (see Figure 21), and the control input f^(y ｒｅｆ ΔP ０ , θ ａ , θ ｄ Derive the following:

[0094] Next, the control device 3 provides the control input f^(y) to the flow control valve 2. ｒｅｆ ΔP ０ , θ ａ , θ ｄ ) is commanded (step S107).

[0095] By processing steps S101 to S107 described above, the pressure difference ΔP ０ The valve body 22 can be displaced while compensating for the disturbance force caused by the flow control valve 2, thereby controlling the flow rate of the flow control valve 2. Figure 14 is a diagram showing a specific example of the flow control process. Figure 14(a) shows the command value m of the flow rate in step S101. ｒｅｆ The dot (t) is shown. Figure 14(b) shows the target trajectory y of the valve body position in step S102. ｒｅｆ (t) is shown. Figure 14(c) shows the first control input f^ derived in steps S103 to S105. ａｃｃ (y ｒｅｆ (t), θ ａ ), second control input d^ ｓｔａｔｉｃ (y ｒｅｆ ΔP ０ ), and the third control input d^ ｄｙｎａｍｉｃ (y ｒｅｆ , θ ｄ ) indicates.

[0096] [Operation and Effects] As described above, the flow rate control method according to the embodiment controls the flow rate of the flow control valve 2 by displacing a movable valve body 22 housed in the housing 21 of the flow control valve 2. In this embodiment, a first control input corresponding to the mass and viscous friction of the valve body 22 and the pressure difference ΔP between the upstream and downstream sides of the valve body 22 are used. ０ A second control input that compensates for the steady-state component of the disturbance force caused by the pressure difference, and a third control input that compensates for the transient component of the disturbance force, are input to the flow control valve 2 via FF control, thereby compensating for the disturbance force caused by the pressure difference while displacing the valve body 22.

[0097] According to this, in flow control, the valve body 22 is displaced at high speed and with high precision while maintaining a pressure difference ΔP ０ By compensating for the resulting disturbance forces (air pressure dynamics) with FF control, the response speed and tracking performance of flow control can be improved. As a result, it becomes possible to achieve high-performance flow control.

[0098] Furthermore, in this embodiment, the first control input is derived based on the target value of the first control variable which is subject to compensation by FF control, and a relational expression obtained in advance that shows the relationship between the control input and the first control variable, which is used to make the first control variable follow a predetermined trajectory when there is no pressure difference ΔP. ０ A second control input is derived based on the measured value and a previously acquired steady-state characteristic showing the relationship between the control input and the first control variable in a steady state with a pressure difference ΔP, corresponding to the pressure difference ΔP. Then, in this embodiment, a third control input is derived based on the target value of the first control variable and a previously acquired relational expression showing the relationship between the control input and the first control variable for compensating for the transient component of disturbance force when the first control variable follows a predetermined trajectory with a pressure difference ΔP.

[0099] This provides a first control input that displaces the valve body 22 in response to the mass and viscous friction of the valve body 22, and a pressure difference ΔP ０ A second control input that compensates for the steady-state component of the disturbance force caused by the disturbance, and a third control input that compensates for the transient component of the disturbance force can be derived.

[0100] Furthermore, in this embodiment, the valve position is the first control variable that is subject to compensation by FF control, and the target value of the flow rate is the second control variable, and the pressure difference ΔP ０ The measured values, the steady-state characteristics showing the relationship between flow rate and the pressure difference ΔP between the valve body position (which were obtained in advance), and the dead time τ from the valve body position to the flow rate (which were identified in advance) ｎ Based on this, the target value of the first control variable (the target trajectory of the valve body position) is derived.

[0101] According to this, the target value of the valve body position can be derived from the target value of the flow rate (command value), and the valve body position can be controlled. Also, the time τ from the valve body position to the flow rate can be controlled. ｎ By compensating for this, the control input to be input to the flow control valve 2 can be anticipated, and the control input can be changed earlier than when the flow command value starts to change. As a result, more accurate flow control becomes possible.

[0102] Furthermore, in this embodiment, the valve body position is measured, and feedback control is performed based on the measured value of the valve body position. This makes it possible to achieve high performance and robustness of flow control. However, the technology according to this disclosure does not require measuring the valve body position, and feedback control of the valve body position is not essential.

[0103] Furthermore, the flow control system 110 according to the embodiment includes a flow control valve 2 having a housing 21 and a movable valve body 22 housed in the housing 21, and a control device that controls the flow rate of the flow control valve 2 by executing the flow control method described above.

[0104] The flow rate control system 110 can improve the response speed and tracking performance of flow rate control by implementing the flow rate control method described above.

[0105] Furthermore, the parameter identification method according to the embodiment identifies parameters for deriving a control input in flow control, which controls the flow rate of the flow control valve 2 by displacing a movable valve body 22 housed in the housing 21 of the flow control valve 2. The parameter identification method takes the valve body position or flow rate as a first control quantity that is subject to compensation by FF control, and derives a parameter θ for deriving a first control input that displaces the valve body in accordance with the mass and viscous friction of the valve body 22. ａ Steps to identify and pressure difference ΔP ０ The steps include obtaining a steady-state characteristic that shows the relationship between the steady-state component of the disturbance force and the pressure difference ΔP between the first control variable and a second control input that compensates for the steady-state component of the disturbance force caused by the disturbance, and deriving a parameter θ for a third control input that compensates for the transient component of the disturbance force. ｄ The steps include identifying and

[0106] According to this, in flow rate control, the pressure difference ΔP ０ By using FF control, it is possible to derive a control input that can compensate for the disturbance force caused by the external forces. As a result, it becomes possible to achieve high performance in flow control.

[0107] Furthermore, in the parameter identification method according to the embodiment, the parameter θ ａ In the step of identifying the control input f, the control input f is used to make the first control variable follow a predetermined trajectory when there is no pressure difference ΔP.ａｃｃ Based on this, the parameter θ ａ In the step of identifying and obtaining steady-state characteristics, the steady-state input u is the control input in the steady state when there is a pressure difference ΔP. ｓｔａｔｉｃ Based on this, the steady-state characteristics are obtained, and the parameter θ ｄ In the step of identifying the first control variable, a control input d is used to compensate for the transient component of the disturbance force when the first control variable is made to follow a predetermined trajectory while there is a pressure difference ΔP. ｄｙｎａｍｉｃ (=d ｄｙｎａｍｉｃ | ΔＰ Based on the parameter θ, ｄ Identify it.

[0108] According to this, the parameter θ ａ and parameter θ ｄ By individually identifying these parameters, the accuracy of the parameters can be improved. As a result, flow control can be made more efficient.

[0109] Furthermore, in the parameter identification method according to the embodiment, for example, the control input f is identified by ILC. ａｃｃ And, in the state of a pressure difference ΔP, the control input f is used to make the first control variable follow a predetermined trajectory. ｔｏｔａｌ The following are obtained as training data. Also, the parameter θ ｄ In the step of identifying the control input f ｔｏｔａｌ and control input f ａｃｃ From the difference between the two, a control input d is obtained to compensate for the disturbance force, and the control input d and the steady-state input u are used. ｓｔａｔｉｃ From the difference, the control input d to compensate for the transient component of the disturbance force is obtained. ｄｙｎａｍｉｃ Obtain it.

[0110] According to this, the control input f is used to make the first control variable follow a predetermined trajectory when there is a pressure difference ΔP. ｔｏｔａｌ Control input d to compensate for the transient component of the disturbance force ｄｙｎａｍｉｃ It is possible to extract the parameter θ ｄ They can be identified independently.

[0111] In the parameter identification method according to the embodiment, by performing ILC, the control input f ａｃｃ and control input f ｔｏｔａｌTo obtain the following.

[0112] According to this, the control input f obtained by the ILC ｔｏｔａｌ By using this as training data for parameter identification, the accuracy of the parameters can be improved.

[0113] [Modifications] Modifications of the embodiment will be described below, with reference to Figure 24 as necessary.

[0114] In the above embodiment, the first control input f^ ａｃｃ (y ｒｅｆ , θ ａ ) parameter θ for deriving ａ Based on a second-order lag system model, θ ａ = [M, D, τ], but the parameter θ ａ This is not limited to the parameter θ. ａ For example, Coulomb friction can be added, with parameter θ ａ The model used to identify it can be selected as appropriate.

[0115] In the above embodiment, the third control input d^ ｄｙｎａｍｉｃ (y ｒｅｆ , θ ｄ ) parameter θ for deriving ｄ Based on a second-order lag system model, θ ｄ = [K, ζ, ω ｎ ] However, the parameter θ ｄ This is not limited to the parameter θ. ｄ For example, a dead time τ can be added, and the parameter θ ｄ The model for identifying the parameter can be selected as appropriate. ｄ A dependency on the pressure difference ΔP is assigned to it, and the parameter θ ｄ (ΔP) may also be used.

[0116] In the above embodiment, steady input u ｓｔａｔｉｃ The steady-state characteristics showing the relationship between (t) and the pressure difference ΔP between the valve body position y are stored in the lookup table 40, and the pressure difference ΔP ０ The corresponding steady-state input u ｓｔａｔｉｃ (y, ΔP ０Although it is assumed that the steady-state characteristics stored in the lookup table are to be referenced, the steady-state characteristics stored in the lookup table are not limited to the above, and the steady-state input may use other variables. For example, the steady-state characteristics are the steady-state input u ｓｔａｔｉｃ (t) may also be shown as a relationship corresponding to the pressure difference ΔP between the flow rate m dot, and the steady input u with flow rate m dot as a variable ｓｔａｔｉｃ (m dot, ΔP) may also be referenced. Furthermore, the steady-state characteristics are, for example, based on the steady-state input u ｓｔａｔｉｃ The relationship between (t), valve position y, and temperature T, and the pressure difference ΔP, may also be shown, and the steady-state input u with temperature T as a variable ｓｔａｔｉｃ You may also refer to (y, ΔP, T). Also, the steady-state input u ｓｔａｔｉｃ This can be obtained not from a lookup table, but by applying filtering or other processing to the control input d that compensates for the disturbance force caused by the pressure difference ΔP.

[0117] In the above embodiment, the parameter θ ａ , θ ｄ Although this is set as a fixed value, it may also be variable. Specifically, the parameter θ ａ , θ ｄ As a first method in which the parameter θ is variable, for example, ａ , θ ｄ The command value of the flow rate m ｒｅｆ θ with dot (t) and pressure difference ΔP as variables ａ (m ｒｅｆ dot (t, ΔP) and θ ｄ (m ｒｅｆ The dot (t), ΔP) may be stored in the lookup table. In that case, when the control device 3 derives the control input, the command value m of the flow rate is used. ｒｅｆ Dot (t) and pressure difference ΔP ０ Based on this, the parameter θ is obtained from the lookup table. ａ , θ ｄ You may also refer to [this]. Also, the parameter θ ａ , θ ｄ As a second method to make the command value m variable, for example, ｒｅｆ dot (t) or pressure difference ΔP ０ Based on the measured values, the parameter identification method described above is performed to determine the parameter θ ａ , θ ｄThis may be updated in real time. Furthermore, by combining the first and second methods described above, the parameter θ ａ , θ ｄ This may be made variable.

[0118] In the above embodiment, the control input f is used to make the first control variable follow a predetermined trajectory when there is a pressure difference ΔP. ｔｏｔａｌ By decomposing it into elements corresponding to the mass of the valve body, viscous friction, and the steady and transient components of the disturbance force, the parameter θ ａ and parameter θ ｄ Although we identified them individually, the control input f ｔｏｔａｌ Without decomposing the parameter θ ａ , θ ｄ The parameter θ may be identified by optimization using the least squares method, for example, as shown in equation (17) (see Figure 24). ａ , θ ｄ It is also possible to obtain the control input f in the parameter identification method by performing iterative learning control (ILC) without a pressure difference ΔP. ａｃｃ The process of obtaining (step S21) becomes unnecessary.

[0119] In the above embodiment, the valve body position y was set as the first control amount to be compensated for by the disturbance force using FF control, but the flow rate m dot may be set as the first control amount. In that case, measurement of the valve body position y becomes unnecessary, and the flow control valve 2 does not need to have a position sensor 24. Figure 15 is a control block diagram of a modified flow control system 110A. When the flow rate m dot is to be compensated for by FF control, for example, the flow control system 110A may be configured as shown in Figure 15. The modified flow control system 110A differs from the flow control system 110 described in Figure 6 in that it does not have an FB controller 31 and an FF controller 32, and controls the flow rate using an FB controller 33 and an FF controller 34. That is, the flow control system 110A controls the flow rate m dot without using a measured value of the valve body position y.

[0120] The first FF controller 341 of the flow rate control system 110A receives the first control input f^ ａｃｃ (m dot) ｒｅｆ , θ ａThe first control input f^ is used to perform acceleration FF control. ａｃｃ (m dot) ｒｅｆ , θ ａ ) can be expressed as shown in equation (18) (see Figure 24).

[0121] The second FF controller 342 of the flow control system 110A receives the second control input d^ ｓｔａｔｉｃ (m dot) ｒｅｆ ΔP ０ The steady-state component is controlled by outputting the second control input d^ ｓｔａｔｉｃ (m dot) ｒｅｆ ΔP ０ ) is the dead time τ of the nominal plant (plant 26) from valve body position y to flow rate m dot. ｎ Taking this into consideration, it can be expressed as in equation (19) (see Figure 24). This results in the dead time τ ｎ This will be compensated.

[0122] The third FF controller 343 of the flow control system 110A receives the third control input d^ ｄｙｎａｍｉｃ (m dot) ｒｅｆ , θ ｄ The vibration component is controlled by outputting ). Third control input d^ ｄｙｎａｍｉｃ (m dot) ｒｅｆ , θ ｄ ) can be expressed as shown in equation (20) (see Figure 24).

[0123] Control input f^(m dot) of the FF controller 34 of the flow control system 110A ｒｅｆ ΔP ０ , θ ａ , θ ｄ ) can be expressed as shown in equation (21) (see Figure 24).

[0124] In the flow rate control system 110A, for example, as shown in equation (17) above (see Figure 24), the parameter θ is optimized using the least squares method. ａ , θ ｄ You may also request this.

[0125] In the flow control system 110 described in Figure 6, the valve body position was controlled by the FB controller 33, but FB control of the valve body position is not required. However, by controlling the valve body position, it is possible to improve the performance and robustness of the flow control.

[0126] Furthermore, for example, if the steady-state characteristics of flow control deteriorate due to friction inside the flow control valve 2, a dither signal to reduce friction may be applied to the flow control valve 2 in addition to the input signals from FB control and FF control.

[0127] <Applicable Subjects> The scope of application of the technology described herein is not particularly limited, but the high-speed, high-precision, and reproducible gas control realized by the technology described herein can be suitably used for the subjects exemplified below.

[0128] [Mass Flow Controller] For example, the FF control according to this disclosure can be applied to a mass flow controller that controls the gas in semiconductor manufacturing equipment (such as etching equipment and film deposition equipment).

[0129] [Medical Field] High-precision and reproducible gas control required for the operation of pharmaceuticals and medical devices can be achieved by the technology described in this disclosure.

[0130] [General-purpose pneumatic equipment] For example, the technology relating to this disclosure can be applied to general-purpose pneumatic equipment such as active pressure regulators used in factory automation (FA).

[0131] [Pneumatic Active Vibration Isolation Table] A pneumatic active vibration isolation table is used, for example, as the base of a stage in an exposure apparatus. By applying the technology described herein to a pneumatic active vibration isolation table, vibrations caused by high-speed operation of the stage can be canceled by the high-speed response of pneumatics through FF control.

[0132] [Precision pneumatic cylinder] This cylinder can be suitably used for precise stage position control in situations where magnetic force cannot be used, such as in electron beam exposure machines.

[0133] [Hydrogenic Bearings] The technology described herein can be applied to air guides used to prevent friction in hydrostatic bearings. For example, by varying the pressure in the Z direction in synchronization with the drive of a linear motor in the translational direction, pitching of the hydrostatic bearing can be suppressed.

[0134] [Compensation for Interference of Multiple Valves] For example, the technology of this disclosure can also be applied when multiple valves are used in the semiconductor manufacturing equipment and pneumatic active vibration isolation tables described above. For example, when multiple valves interfere with each other, the effects of interference can be compensated for in flow rate control by identifying the parameters of FF control using training data obtained by performing ILC under the influence of interference.

[0135] The present invention will be described in more detail below with reference to examples, but the present invention is not limited to the following examples without departing from its essence.

[0136] Figure 16 is a schematic diagram of the flow control system 110B according to an embodiment. In this embodiment, no other system is placed downstream of the flow control system 110B, and the downstream side of the flow control valve 2 is open to the atmosphere. Therefore, the pressure P on the downstream side of the flow control valve 2 ｄ This is equal to atmospheric pressure. Therefore, in this embodiment, the atmospheric pressure is measured by the downstream pressure sensor 6 and this is used as pressure P. ｄ That's what I decided.

[0137] A linear DC motor valve (SMC, PFCQ) was used for the flow control valve 2, pressure sensors (VALCOM, VPRT) were used for the upstream pressure sensor 5 and the downstream pressure sensor 6, and a flow meter (Keyence, FD-V40A, FD-A250) was used for the flow meter 4. The control device 3 consisted of a controller (Beckhoff, CX5240) and a current controller (Copley Controls, Accelnet BEL-090-06). The controller calculated the valve energizing current based on the command value and measured value of the valve body position and input the corresponding signal to the current controller. The sampling period of the controller was set to 62.5 μs, meaning the sampling frequency was 16 kHz.

[0138] The control system of the embodiment was configured as shown in Figure 6. In the embodiment, the FB controller 31 for flow rate m dots was a PID controller as shown in equation (5) (see Figure 21). The FB controller 33 for valve body position y was a PID controller as shown in equation (5) (see Figure 21). If the bandwidth, which is an indicator of the performance of the closed-loop system, is defined as the frequency at which the absolute value of the sensitivity function first exceeds -3 dB, then the bandwidth of the designed FB controller 31 is 16 Hz, and the bandwidth of the FB controller 33 is 60 Hz.

[0139] In the embodiment, the FF controller 32 for flow rate m dots was a controller as shown in formula (4) (see Figure 21). The FF controller 34 for valve body position y was a controller as shown in formula (12) (see Figure 22), which is a unique feature of the present invention.

[0140] The first FF controller 341 is an inverse system of plant 25, which is a nominal plant of a second-order lag system, as shown in equation (8) (see Figure 22). The first control input f^ ａｃｃ (y ｒｅｆ , θ ａ θ to derive ) ａ The mass of valve body 22, M = 2.28 × 10⁻⁶. －３ , viscous friction coefficient D = 1.65, dead time τ = 0.938 × 10 －３ That's what happened.

[0141] The third FF controller 343 was modeled as a second-order lag system, as shown in equation (11) (see Figure 22). The third control input d^ was determined by the parameter identification method described above. ｄｙｎａｍｉｃ (y ｒｅｆ θ to derive θ) ｄ = [K, ζ, ω ｎ The parameter θ was identified. ｄ The coefficient of force remained constant regardless of the pressure difference, resulting in a gain K = 233, a damping coefficient ζ = 0.24, and a natural angular frequency ωn = 336. The FF controller 34 is constructed by adding the compensation term of the second FF controller 342 to the compensation terms of the first FF controller 341 and the third FF controller 343, which are LTI systems.

[0142] The performance of the flow control system according to the example was evaluated by conducting experiments 1 to 3, described below, and comparing the example with the comparative example.

[0143] In Experiment 1, the response speed and generalization performance of valve body position control were evaluated by comparison with Comparative Example 1. Comparative Example 1 differs from the embodiment in that it does not have a second FF controller 342 and a third FF controller 343 for compensating for disturbance forces (air disturbances) caused by the pressure difference ΔP. The FF controller for valve body position y in Comparative Example 1 has only a first FF controller 341. In other words, Comparative Example 1 performs only control (acceleration FF control) corresponding to the mass M and viscous friction of the valve body 22 in FF control of valve body position y.

[0144] Experiment 1 involved conducting Experiments 1-1 to 1-3. In Experiment 1-1, flow rate control was performed under the same conditions as the training data obtained by ILC. Specifically, in Experiment 1-1, the flow rate step size was set to 100 L / min, and the supply pressure (pressure difference ΔP) was controlled. ０ In Experiment 1-2, the flow rate step was halved to 50 L / min, and the supply pressure was set to 0.30 MPa for flow rate control. In Experiment 1-3, the flow rate step was 100 L / min, and the supply pressure was set to 0.15 MPa for flow rate control.

[0145] Figure 17 shows the results of Experiment 1. Figure 17(a) shows the results of Experiment 1-1, Figure 17(b) shows the results of Experiment 1-2, and Figure 17(c) shows the results of Experiment 1-3. The graph in Figure 17 represents the trajectory tracking results of the valve body position. In Figure 17, "Reference" shows the target trajectory of the valve body position, "ILC" shows the training data acquired by ILC, "Proposed FF" shows the example, and "Acc FF" shows Comparative Example 1.

[0146] Experiment 1-1 showed that the 2-norm of the tracking error was 0.215 mm in the example and 1.573 mm in Comparative Example 1. The 2-norm of the tracking error in the ILC, which was used as training data, was 0.173 mm. This indicates that the example exhibits tracking performance not significantly different from that of the ILC. Experiment 1-2 showed that the 2-norm of the tracking error was 0.403 mm in the example and 0.760 mm in Comparative Example 1. This indicates that the example exhibits high tracking performance even when the step width of the target trajectory is halved. Experiment 1-3 showed that the 2-norm of the tracking error was 0.371 mm in the example and 1.943 mm in Comparative Example 1. This indicates that the example exhibits high tracking performance even when the supply pressure is halved.

[0147] In Experiment 2, the response speed and generalization performance of flow rate control were evaluated by comparison with Comparative Example 1. Experiment 2 consisted of Experiments 2-1 and 2-2. In Experiment 2-1, flow rate control was performed when the flow rate increased at the target flow rate trajectory (target value). In Experiment 2-2, flow rate control was performed when the flow rate decreased at the target flow rate trajectory (target value).

[0148] Figure 18 shows the results of Experiment 2. Figure 18(a) shows the results of Experiment 2-1, and Figure 18(b) shows the results of Experiment 2-2. In Figure 18, the "Input" graph shows the input current (control input) for FF control, and the "Flow rate" graph shows the flow rate trajectory. Also in Figure 18, "Reference" shows the target flow rate trajectory (target value), "Proposed FF" shows an example, and "Acc FF" shows Comparative Example 1.

[0149] The results of Experiments 2-1 and 2-2 showed that the flow rate fluctuations were suppressed in the example compared to Comparative Example 1. This indicates that the example can compensate for the effects of air compressibility.

[0150] In Experiment 3, the response speed and generalization performance of the flow control were evaluated by comparison with Comparative Example 2. The flow control system in Comparative Example 2 differs from the embodiment in that it does not perform FB control and FF control of the valve body position, nor FF control of the flow rate. In other words, Comparative Example 2 only performs FB control of the flow rate m dot.

[0151] In Experiment 3, Experiments 3-1 to 3 were conducted under the same conditions as Experiments 1-1 to 3. In Experiment 3-1, the conditions were the same as those for the training data obtained by ILC, with a flow rate step size of 100 L / min and a supply pressure (pressure difference ΔP ０ In Experiment 3-2, the flow rate was controlled with a supply pressure of 0.30 MPa. In Experiment 3-3, the flow rate was controlled with a step size of 100 L / min and a supply pressure of 0.15 MPa.

[0152] Figure 19 shows the results of Experiment 3. The graph in Figure 19 shows the flow rate trajectory. Figure 19(a) shows the results of Experiment 3-1, Figure 19(b) shows the results of Experiment 3-2, and Figure 19(c) shows the results of Experiment 3-3. In Figure 19, "Reference" shows the target flow rate trajectory (target value), "Proposed" shows an example, and "Conventional" shows Comparative Example 2.

[0153] Experiment 3-1 showed that the flow rate control settling time was 8 ms in the example and 490 ms in comparative example 2. Experiment 3-2 showed that the flow rate control settling time was 43 ms in the example and 446 ms in comparative example 2. Experiment 3-3 showed that the flow rate control settling time was 10 ms in the example and 604 ms in comparative example 2. From this, it was found that the example can shorten the flow rate control settling time without significantly impairing the generalization performance of the flow rate control.

[0154] 1: Compressor 2: Flow control valve 21: Housing 22: Valve body 23: Linear actuator 24: Position sensor 3: Control device 31: FB controller 32: FF controller 33: FB controller 34: FF controller 4: Flow meter 5: Upstream pressure sensor 6: Downstream pressure sensor 100: Fluid supply system 110: Flow control system

Claims

1. A flow control method for controlling the flow rate of a flow control valve by displacing a movable valve body housed in the housing of the flow control valve, wherein a first control input for displacing the valve body in accordance with the mass and viscous friction of the valve body, a second control input for compensating the steady-state component of a disturbance force caused by a pressure difference between the upstream and downstream sides of the valve body, and a third control input for compensating the transient component of the disturbance force are input to the flow control valve by feedforward control, thereby compensating for the disturbance force caused by the pressure difference while displacing the valve body.

2. A flow rate control method according to claim 1, wherein the position of the valve body or the flow rate of the flow control valve is used as the first control quantity, the first control input is derived based on a target value of the first control quantity and a previously acquired relational expression showing the relationship between a control input and the first control quantity for making the first control quantity follow a predetermined trajectory when there is no pressure difference, the second control input is derived based on the target value of the first control quantity, a measured value of the pressure difference, and a previously acquired steady-state characteristic showing the relationship between the control input and the first control quantity in a steady state when there is a pressure difference, according to the pressure difference, and the third control input is derived based on the target value of the first control quantity and a previously acquired relational expression showing the relationship between a control input and the first control quantity for compensating for the transient component of the disturbance force when making the first control quantity follow a predetermined trajectory when there is a pressure difference.

3. The flow rate control method according to claim 2, wherein the first control quantity is the position of the valve body, and a target value for the position of the valve body, which is the target value of the first control quantity, is derived based on a target value of the flow rate as a second control quantity, a measured value of the pressure difference, a steady-state characteristic obtained in advance that shows the relationship between the flow rate and the position of the valve body in accordance with the pressure difference, and a dead time determined in advance from the position of the valve body to the flow rate.

4. A flow control system comprising: a flow control valve having a housing and a movable valve body housed in the housing; and a control device that controls the flow rate of the flow control valve by performing the flow control method described in any one of claims 1 to 3.

5. A program that causes a computer to execute the flow rate control method described in any one of claims 1 to 3.

6. A parameter identification method for identifying parameters for deriving a feedforward control input that compensates for disturbance forces caused by a pressure difference between the upstream and downstream sides of a flow control valve while displacing the valve body in a flow control valve housing, wherein the position of the valve body or the flow rate of the flow control valve is defined as a first control quantity, and the parameter θ is used to derive a first control input that displaces the valve body in accordance with the mass and viscous friction of the valve body. ａ Steps include: identifying a first control variable; obtaining steady-state characteristics showing the relationship between the steady-state component of the disturbance force and the first control variable in accordance with the pressure difference, for identifying a second control input that compensates for the steady-state component of the disturbance force caused by the pressure difference between the upstream and downstream sides of the valve body; and deriving a parameter θ for a third control input that compensates for the transient component of the disturbance force. ｄ A parameter identification method comprising the steps of identifying a parameter.

7. Said parameter θ ａ in the identifying step, the control input f for causing said first controlled variable to follow a predetermined trajectory when there is no pressure difference ａｃｃ based on which, said parameter θ ａ is identified, and in the step of obtaining said steady-state characteristic, steady-state input u which is a control input in a steady-state when there is a pressure difference ｓｔａｔｉｃ based on which, said steady-state characteristic is obtained, and in the step of identifying said parameter θ ｄ , the control input d for compensating a transient component of said disturbance force when causing said first controlled variable to follow said predetermined trajectory in a state where there is a pressure difference ｄｙｎａｍｉｃ based on which, said parameter θ ｄ is identified, the parameter identification method according to claim 6.

8. The control input f ａｃｃ And, in the state of the pressure difference, the control input f is used to make the first control amount follow the predetermined trajectory. ｔｏｔａｌ The following are obtained as training data, and the parameter θ ｄ In the step of identifying the control input f ｔｏｔａｌ and the control input f ａｃｃ From the difference between the above, a control input d for compensating the disturbance force is obtained, and the control input d and the steady-state input u ｓｔａｔｉｃ From the difference, the control input d for compensating the transient component of the disturbance force is obtained. ｄｙｎａｍｉｃ A parameter identification method according to claim 7, which obtains the following.

9. By performing iterative learning control (ILC), the control input f ａｃｃ and the control input f ｔｏｔａｌ A parameter identification method according to claim 8, which obtains the following.

10. A program that causes a computer to perform the parameter identification method described in any one of claims 6 to 9.

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