JP7360124B2 - Gantry stage control method and control device - Google Patents

Description

The present invention relates to a method and apparatus for controlling the position of a gantry stage.

Linear motor stages are widely used at manufacturing sites for industrial products such as machine tools, measuring instruments, semiconductor devices, and display devices. Since the motion accuracy of a linear motor stage has a large effect on the quality and characteristics of a product, there is an increasing demand for high-precision and high-speed positioning. A linear motor stage is constructed by disposing a table movable by a linear motor on a surface plate.

In recent years, for example, as display devices have become larger, it has become necessary to transport large and heavy liquid crystal panels using linear motor stages. Therefore, in order to obtain a large thrust and support and transport heavy products, we have developed a gantry stage that transports products using two linear motion mechanisms arranged in parallel, that is, two linear motor stages arranged in parallel. A gantry stage is used that is connected by a connecting table.

Japanese Patent Application Publication No. 2008-221444 Patent No. 5574762

Conventionally, PID control, which is easy to design and adjust and is easy to handle, has been widely used in precision mechanisms to control general linear motor stages. There is a need for a control method that can achieve high performance while maintaining performance.

When high-precision positioning is required, it is common to fix it to a surface plate with sufficient rigidity, but as the need for high-acceleration motion increases year by year, vibration problems of the entire device, including the surface plate, have become apparent. Therefore, its suppression has become an important issue. As a method of suppressing vibrations caused by a surface plate, etc., there is a method of using an active vibration isolator or a reaction force compensator incorporating an actuator, in addition to a combination of a large-mass surface plate and a highly rigid column. However, since there is a problem that the device becomes larger and the cost increases, it can only be used in a mechanism that allows this. Therefore, as a control measure, control using advanced control (sliding mode control, robust control using a disturbance observer, etc.) is being performed in place of the currently mainstream PID control. However, it has not become widespread because it requires a lot of effort to perform modeling in advance and requires sufficient knowledge of the underlying control theory.

In addition, in gantry stages, it is required to precisely synchronize control of two linear motion mechanisms arranged in parallel, so in conventional technology, control elements such as cross-coupling controllers that are responsible for coordinated movement of two axes are used to control There are also examples where it is incorporated into the system.

By the way, as a control system design method that achieves both high accuracy and ease of use, the NCTF (Nominal Characteristic Trajectory Following) control method is used to design a high-precision positioning control system from simple open-loop experiments and controller parameter adjustment. Are known. However, even with this NCTF control method, the actual situation is that the vibration problem that has become apparent has not been solved.

The present invention has been made in view of the above circumstances, and allows for easy design flow and controller adjustment, and enables high-accuracy and high-speed positioning without requiring special knowledge of control theory. , an object of the present invention is to provide a gantry stage control method and control device based on the NCTF control method.

Another object of the present invention is to reduce the influence of surface plate vibration on the relative displacement between the surface plate and the table, improve the rigidity of the table with respect to the surface plate, and reduce the relative displacement by allowing the table to follow the surface plate vibration. It is an object of the present invention to provide a control method and a control device for a gantry stage based on the NCTF control method, which is not affected by surface plate vibration and can also suppress vibrations caused by table yawing (swing in the rotational direction).

A gantry stage control method according to the present invention is a method for controlling the position of a gantry stage, in which a table is installed on a surface plate, via two linear motors arranged in parallel, and in which input signals to the linear motors are The table is made to follow the vibration of the surface plate using NCTF control based on the reference characteristic locus obtained from the open-loop experiment using the method, and high-frequency vibrations that occur in the process of making the table follow the vibration of the surface plate are suppressed. The present invention is characterized in that the control is performed independently for each of the two linear motors.

A gantry stage control device according to the present invention is a device that controls the position of a gantry stage in which a table is installed on a surface plate via two linear motors arranged in parallel, and which inputs an input signal to the linear motors. an NCTF control system that performs control based on a reference characteristic locus obtained from an open-loop experiment, a first control unit that causes the table to follow the vibrations of the surface plate, and a process that causes the table to follow the vibrations of the surface plate. The linear motor is characterized in that a control system including a second control section for suppressing high-frequency vibrations generated in the linear motor is independently provided for each of the two linear motors.

In the present invention, NCTF control is utilized, the table is made to follow the vibration of the surface plate, and high frequency vibrations generated in the process of making the table follow the vibration of the surface plate are suppressed. Further, such control is performed independently on the two linear motors to suppress vibrations caused by yawing of the table due to the gantry. Therefore, highly accurate and high-speed positioning on the gantry stage is achieved.

The gantry stage control method according to the present invention is characterized in that feedforward control is added to the NCTF control.

The gantry stage control device according to the present invention is characterized in that it further includes a feedforward controller that applies feedforward control to the NCTF control system.

In the present invention, feedforward control using learning control is added to NCTF control. Therefore, positioning can be performed with higher precision and higher speed.

The gantry stage control device according to the present invention is characterized in that the first control section is a bandpass filter having a transfer function expressed by equation (3) described below.

In the present invention, the first control section is a bandpass filter having a transfer function expressed by equation (3) described later. Therefore, the configuration of the control system is further simplified.

The gantry stage control device according to the present invention is characterized in that the second control section is a differentiator.

In the present invention, the second control section is a differentiator. Therefore, the configuration of the control system is further simplified.

With the gantry stage control method and control device of the present invention, the design flow and controller adjustment are easy, and high-accuracy and high-speed positioning can be achieved without requiring sufficient knowledge of control theory. . Since the table follows the vibration of the surface plate, the relative movement of the table with respect to the surface plate is not affected by the vibration of the surface plate, and the relative positioning of the table with respect to the surface plate can be completed in a short time. Furthermore, since each of the two linear motors is controlled independently, it is possible to eliminate the influence of yawing of the table due to the use of a gantry.

FIG. 2 is a block diagram showing a general configuration of an NCTF control system. FIG. 2 is a block diagram showing a basic control system used for control of the present invention. FIG. 3 is a diagram showing a dynamic microscopic model of a linear motor stage. FIG. 2 is a block diagram showing a control system in which a controller B(s) is added to the NCTF control system. FIG. 2 is a block diagram showing the arrangement of a controller F(s). FIG. 2 is a block diagram illustrating an example of a control system in which a controller F(s) is added to the NCTF control system. FIG. 3 is a block diagram showing another example of a control system in which a controller F(s) is added to the NCTF control system. 1 is a schematic diagram showing the configuration of a gantry stage to which a control method and a control device according to the present invention are applied. FIG. 2 is a block diagram showing a control system for controlling the center of gravity position of a gantry stage. FIG. 2 is a block diagram showing a control system as an embodiment of the present invention, which aims to control the center of gravity position of a gantry stage and suppress vibrations caused by yawing. It is a figure which shows the presence or absence of yawing of a table. 11 is a graph showing a positional deviation between both plants (linear motors) in the control system shown in FIG. 9 and the control system shown in FIG. 10. FIG. 7 is a block diagram showing a control system in another embodiment of the present invention incorporating a feedforward controller FF _tiv (t).

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described in detail below based on drawings showing embodiments thereof.

First, the NCTF control system as a feedback control system that is the basis of the present invention will be briefly explained. FIG. 1 is a block diagram showing a general configuration of an NCTF control system.

In the NCTF control system, the desired damping characteristics are expressed on the phase plane (Nominal Characteristic Trajectory: NCT), the operation of the controlled object (plant) is constrained to the NCT, and the desired damping characteristics are expressed on the phase plane. It consists of a PI compensator for stopping at the origin. The NCT is created through simple open-loop experiments, and the gain of the PI compensator is determined to an optimal value through step response and trajectory control experiments. Therefore, the NCTF control system does not require detailed model parameters and can be easily designed without knowledge of control theory. It is desirable to perform open-loop experiments by giving a rectangular wave current command to the motor. It is also desirable to adjust the magnitude and duration of the rectangular wave input so that the table moves within the movable region above the target maximum speed.

First, an open-loop experiment is conducted in which the controlled object is actually accelerated and decelerated using a rectangular wave signal, and the actual operation results of the controlled object (plant) are obtained. NCT utilizes the deceleration region of the open-loop displacement response waveform, and is described on a phase plane with the horizontal axis representing the difference (virtual error) between the final displacement value and the transient response, and the vertical axis representing the differential. Near the origin of the NCT, linear approximation is further performed using the slope of the point where the differential of the virtual error is less than or equal to a predetermined value.

Subsequently, the gain of the PI compensator is adjusted. The proportional gain K _p is determined from a step response experiment at a predetermined height using only proportional control. In addition, the integral gain K _I is determined by conducting a trajectory control experiment using the second-order integral of the triangular wave acceleration target value as the target displacement trajectory, and is determined to a value that provides the best trajectory tracking performance near the stop position and maintains stability. . As the integrator, an integrator with a saturation condition that complies with the condition of equation (1) below is used.

As shown in Figure 1, each parameter in equation (1) is as follows: u _p is the difference between the differential value of the deviation at the current moment and the NCT output value, u ₀ is the output value of the P controller, and u _i is the I control Δu _i is the rate of change of u _i , and u _s is the maximum absolute value of the manipulated variable that can be sent to the amplifier.

FIG. 2 is a block diagram showing a basic control system used for control of the present invention. This control system includes an NCTF control system 11 having an NCT, a PI compensator, etc., a first controller 12, a second controller 13, and a plant 14 as a controlled object. The first controller 12 and second controller 13 added to the NCTF control system 11 are characteristic elements of the present invention.

The first controller 12 is a controller provided to make the table follow the vibration of the surface plate, and specifically, the first controller 12 is a bandpass filter (B (s)). The second controller 13 is a controller provided to suppress high-frequency vibrations that occur in the process of the table following the vibrations of the surface plate, and is specifically a differentiator (F(s)). .

The control system shown in Fig. 2 is based on the NCTF control system 11, which allows a highly accurate positioning control system to be designed from simple open-loop experiments and controller parameter adjustments. A control system that includes a bandpass filter (B(s)) having a transfer function expressed by equation (3) described later to follow be.

Below, the basic concept and design procedure of a control system as shown in FIG. 2 for suppressing the influence of surface plate vibration that occurs during high-speed motion and improving control performance will be explained.

We will investigate a control system that is effective in reducing surface plate vibration, which is a factor in deteriorating control performance. A dynamic model is used to study a control system to reduce the effect of surface plate vibration when the table moves at high speed on the relative displacement x ₂ −x ₁ of the table with respect to the surface plate. Since the controlled object is considered to be in the state of a microscopic model at the stop position, the control system of the present invention is derived based on the microscopic model as shown in FIG. In modeling, all parts other than the movable parts, including linear guides and stators, are collectively regarded as a surface plate, and are defined as a mass point of mass m ₁ . Furthermore, the linear ball guide has nonlinear spring characteristics in the microscopic region, which affects microscopic behavior.

The equation of motion in the microscopic region is expressed by the following equation (2). In addition, m ₂ : mass of table, c ₁ : viscosity coefficient of surface plate, c ₂ : viscosity coefficient of nonlinear spring, c ₃ : viscosity coefficient of table, k ₁ : spring coefficient of surface plate, k ₂ : coefficient of nonlinear spring. Spring coefficient, p: thrust.

The reason why surface plate vibration deteriorates position accuracy during high-speed motion is that vibrations are excited in the surface plate by the table's high acceleration/deceleration motion, and even after the table reaches the stop position, the vibrations remain and cause disturbances. This is thought to be due to the effect on the relative displacement of the table with respect to the surface plate. The mass difference between the surface plate and the table is large (for example, the surface plate: about 200 kg, the table: about 2 kg), and it is difficult to remove this residual vibration by controlling the table. Therefore, it is practical to prevent the table from shaking in the same way as the surface plate and to prevent the effect of surface plate vibration from appearing on the relative displacement of the table with respect to the surface plate. In other words, it is practical to make the table follow the vibration of the surface plate.

Therefore, the table needs to be able to move at the frequency of the surface plate vibration, and it is desirable that no resonance points exist. Therefore, in order to improve the followability of the frequency f _s to the target value input, a controller B(s) expressed by the following formula (3) is connected in series to the PI compensator of the NCTF control system, as shown in Figure 4. to improve rigidity at the frequency f _s . Note that in equation (3), ω _b : angular frequency, ζ ₁ , ζ ₂ : damping coefficient.

By arranging the controller B(s) in series with the PI compensator, the target value tracking performance is improved compared to the case where only NCTF control is used. Further, by providing the controller B(s), the gain of the frequency f _s decreases, thereby improving the characteristic of suppressing the influence of disturbance.

The smaller the value of the damping coefficient ζ ₂ is set, the more the damping performance of the controller B(s) can be expected to improve. However, if the value of the damping coefficient ζ ₂ of the controller B(s) is set to a small value, high frequency vibrations due to the nonlinear spring are likely to occur.

Therefore, we will consider control to suppress such high-frequency vibrations. When the equation of motion of the microscopic model expressed by the above equation (2) is subjected to Laplace transform, the following equation (4) is obtained.

Here, for simplicity, it is replaced as shown in equation (5) below.

By rewriting equation (4) using equation (5), the following equation (6) is obtained.

Consider a controller F(s) that improves the damping characteristics of the mechanism by arranging it as shown in FIG. 5 in the mechanism represented by this transfer function. A transfer function including the controller F(s) is expressed by the following equation (7). If the denominator of Equation (7) can be factorized as shown in Equation (8) below, c ₂ +c ₃ and k ₂ including the parameters of the nonlinear spring can be adjusted using the arbitrarily determined parameter G _c . For this purpose, the controller F(s) may be designed as shown in equation (9) below.

In order to improve the damping performance, if G _c =K _c ·s, the denominator of equation (7) can be modified as shown in equation (10) below, and the damping coefficient can be set arbitrarily. The transfer function of the controller F(s) at this time is shown in the following equation (11).

FIG. 6 shows an example of a block diagram in which such a controller F(s) is added to the NCTF control system. When the controller F(s) is placed at the local feedback position as shown in Figure 6, the input to the controller F(s) is the relative displacement x ₂ - x ₁ , and the surface plate displacement x ₁ and the table displacement Since the origin with x ₂ is at the starting position, if the target value changes, the controller F(s) will output a force that attempts to prevent the table from operating. The controller F(s) must output a force that keeps the table at the final stop position, that is, a force that makes the displacement error from the final stop position zero. A controller F(s) should be placed. A block diagram of the control system in this case is shown in FIG.

A block diagram in which the above-mentioned controller B(s) and controller F(s) are added to the NCTF control system is shown in FIG. 2 described above. By using the controller F(s) (second controller 13) together with the gain in the high frequency range that has been increased by adding the controller B(s) (first controller 12), the NCTF control can be increased. It can be lowered to the same level as the case. As a result, by adding controller F(s) to the NCTF control system, high-frequency vibrations caused by nonlinear springs that are likely to occur due to the addition of controller B(s) that causes the table to follow surface plate vibrations can be reduced. It can be suppressed. The attenuation rate of high-frequency vibrations, which was lowered by adding the controller B(s), is improved by using the controller F(s) in combination than in the case of only the NCTF control system. Furthermore, regarding the disturbance characteristics, even when the controller F(s) is used in combination, the effect of the controller B(s) can be maintained. From the above, by using the controller F(s) in combination, the effect of suppressing high-frequency vibrations can be expected without impairing the effect of the controller B(s) in following the surface plate vibrations. The control system shown in FIG. 2 controls the table to follow the vibrations of the surface plate. That is, the object of control is to make the table follow the vibration of the surface plate. Therefore, the relative movement of the table with respect to the surface plate is not affected by the vibration of the surface plate, and the time required for relative positioning of the table with respect to the surface plate is shortened.

By using the controller F(s) in combination, the value of the damping coefficient ζ ₂ can be lowered without generating high-frequency vibrations. The peak of high frequency vibration that appears due to the addition of the controller B(s) disappears by the combined use of the controller F(s), and the high frequency vibration suppressing effect of the controller F(s) is obtained.

By the way, in order to design the controller F(s) expressed by equation (11), it is necessary to identify parameters k ₁ , k ₂ , c ₁ , c ₂ +c ₃ , m ₁ +m ₂ . Here, k ₁ can be estimated from an open-loop experiment, and even if we assume that the masses m ₁ and m ₂ of the mechanism are known, it takes time to identify the remaining parameters. There may also be situations where the design cannot be carried out.

Therefore, the controller F(s) for suppressing high frequency vibrations is simplified as follows. From equation (7), the transfer function of the mechanism having local feedback with controller F(s) is expressed by equation (12) below.

Although the linear motor stage used in the present invention is installed on a relatively simple surface plate, the mass of the device excluding the movable part is still very large compared to the mass of the stage movable part including the table. It can be said that the relationship ₁ >> m ₂ holds true. When this condition is satisfied, the fractional part included in the first term of equation (12) can be approximated as shown in equation (13) below by ignoring the term m ₂ . At this time, equation (12) is expressed by equation (14) below.

Therefore, in order to improve the damping performance, the controller F(s) only needs to satisfy the following equation (15). The simplified controller F(s) in this case is designated as F _d (s) to distinguish it from Equation (11).
F _d (s)=K _c・s (15)

In this way, if the condition of m ₁ >>m ₂ is satisfied, the second term of equation (11) can be omitted, so the only parameter that needs to be determined is K _c , which is the gain for adjusting the damping performance. Good, there is no need to identify various model parameters. Even in such a case, the effect of suppressing high frequency vibrations is not lost.

Using the control system shown in FIG. 2, design and adjustment are performed in the following order.
(Step 1: Design of NCTF control system 11 and identification of problematic vibration frequency f _s )
First, the basic NCTF control system (see FIG. 1) is designed using the procedure described above. Further, by performing, for example, FFT analysis on the displacement waveform and velocity waveform obtained in an open-loop experiment performed for NCT creation, the vibration frequency f _s that becomes a problem during high-speed motion is experimentally identified.

(Step 2: Design and adjustment of controller B(s) that makes the table follow the surface plate vibration)
In order to suppress the vibration identified in step 1, a controller B(s) (see FIG. 4) placed in series with the PI compensator of the NCTF control system is designed and adjusted. The method of setting each parameter of the controller B(s) is shown below.
(a) ω _b
In order to amplify the output of the PI compensator at the frequency f _b =ω _b /2π, the controller B(s) matches the problematic frequency f _s identified in step 1 with f _b and sets ω _b =2πf _s and set.
(b) ζ ₁ and ζ ₂
The controller B(s) has a larger amplification factor at the frequency f _b as the difference between ζ ₁ and ζ ₂ becomes larger, and a vibration suppressing effect can be expected. However, if ζ ₂ is lowered too much, there is a risk that new high-frequency vibrations will occur, so ζ ₁ and It is necessary to adjust the value with ζ ₂ . Therefore, for example, ζ ₁ =0.9 is set, and control experiments are performed while gradually lowering the value of ζ ₂ (<ζ ₁ ) to obtain an appropriate amplification factor. Note that in this specification, ζ ₁ is set to 0.9. Although ζ ₁ =0.9 is one of the possible values (preferred values) in this control method, it is not limited to this value, and the value of ζ ₁ can be changed as appropriate according to the specifications of the applied control system. Just set it.

(Step 3: Design and adjustment of controller F(s) for high frequency vibration suppression)
If a new high-frequency vibration occurs before a sufficient follow-up effect of the table surface plate vibration is obtained in step 2, or if high-frequency vibration has already occurred, the controller F(s) should be adjusted further. Add (see Figure 2). The simplified F(s) is a differentiator F _d (s), and the only parameter to be adjusted is the gain K _c . Gradually increase K _c and adjust to an appropriate K _c that can suppress high-frequency vibrations.

(Step 4: Redesign of controller F(s) (differentiator F _d (s)))
By adding the controller F(s) (differentiator F _d (s)) and adjusting its parameters, the occurrence of high-frequency vibrations can be suppressed, and ζ ₂ of the controller B(s) can be further lowered. can. Adjust ζ ₂ again until the target performance is achieved.

By sequentially executing the above four steps, the design and adjustment of the control system for vibration suppression during high-speed motion is completed.

Hereinafter, a mode in which the gantry stage is controlled using a control system in which a controller B(s) and a controller F(s) are added to the NCTF control system as described above will be described.

FIG. 8 is a schematic diagram showing the configuration of a gantry stage to which the control method and control device of the present invention are applied. In FIG. 8, 1 is a surface plate, and the surface plate 1 has a plurality of legs 1a and is grounded by an adjuster 1b. On the surface plate 1, two linear motors 2a and 2b, which are coreless linear motors having, for example, a mover that is an electromagnet and a stator that is a permanent magnet, are provided in parallel. A connecting table 3 is provided so as to straddle the two linear motors 2a, 2b, and the table 3 is fixed to the mover of each linear motor 2a, 2b. A product to be transported is placed on a table 3, and the table 3 is moved together with a movable member by two linear motors 2a and 2b.

FIG. 9 is a block diagram showing a control system aimed at controlling the center of gravity position of the gantry stage, and FIG. 10 is a block diagram showing the implementation of the present invention aimed at controlling the center of gravity position of the gantry stage and suppressing vibrations caused by yawing. It is a block diagram showing a control system as a form. In FIGS. 9 and 10, elements similar to those in FIG. 2 are denoted by the same reference numerals, and explanations thereof will be omitted. The control system shown in FIGS. 9 and 10 includes two plants 14a and 14b to be controlled corresponding to the gantry stage, and includes an adder 21 and a 1/2 unit 22. Further, the control system shown in FIG. 9 further includes a controller 23.

In the example shown in FIG. 9, the two plants 14a, 14b (linear motors 2a, 2b) are controlled by one control system having the configuration shown in FIG. 2 common to them. In the control system shown in FIG. 9, a controller 23 is used to locally feed back the differential of the displacement difference x _s1 -x _s2 of each axis. Also, the center displacement x _c (=(x _s1 + x _s2 )/2) of the connection table 3 calculated from the average value of the encoder output of each linear motor 2a, 2b follows the target value x _r . Therefore, the command value to each plant 14a, 14b is the same.When controlling the center of gravity position of the gantry stage, the control system shown in FIG. 9 is sufficient, but when the yawing is large, the control system shown in FIG. Position control may not be possible.

On the other hand, in the embodiment shown in FIG. 10, one control system having the configuration shown in FIG. 2 is provided for each of the two plants 14a, 14b (linear motors 2a, 2b), and are independently controlled. Position control is performed by feeding back encoders provided for each axis, and the average value (=((x _s1 + x _s2 )/2) of x _s1 and x _s2 that are independently controlled is used as the output x _c . There is.

In controlling the gantry stage, it is necessary to consider the generation of new vibrations due to the yawing of the connecting table 3 due to the gantry. 11A and 11B are diagrams showing the presence or absence of yawing of the table 3. FIG. 11A shows a state in which yawing does not occur, and FIG. 11B shows a state in which yawing occurs. The white arrows in FIGS. 11A and 11B indicate the traveling direction of the table 3 (mover), and the arrows in FIG. 11B indicate the yawing direction of the table 3.

A comparison of control performance between the control system shown in FIG. 9 and the control system (embodiment) shown in FIG. 10 will be described. FIG. 12 is a graph showing the positional deviation between both plants 14a, 14b (linear motors 2a, 2b) in the control system shown in FIG. 9 and the control system shown in FIG. In FIG. 12, the horizontal axis shows the time [seconds] from the start of control, and the vertical axis shows the positional deviation x _s1 −x _s2 [μm]. Moreover, in FIG. 12, (a) shows the results in the control system shown in FIG. 9, and (b) shows the results in the control system (embodiment) shown in FIG.

In the control system shown in FIG. 9, the vibrations of the surface plate 1 and the high frequency vibrations of the table 3 can be sufficiently suppressed, but the vibrations accompanying the yawing of the table 3 cannot be suppressed. In contrast, in the control system (embodiment) shown in FIG. 10, not only the vibration of the surface plate 1 and the high-frequency vibration of the table 3, but also the vibration accompanying the yawing of the table 3 can be sufficiently suppressed. . In the control system of the embodiment shown in FIG. 10, both plants 14a and 14b (linear motors 2a and 2b) feed back encoders provided for each axis, and perform position control independently. Therefore, it is possible to control the position of the center of gravity while suppressing vibration in the yawing direction.

In the above embodiment, the desired target setting is achieved by using a control system (see FIG. 10) that performs independent control using two control systems having the configuration shown in FIG. 2, designed and adjusted as described above. It was possible to converge the position within a desired target settling width (for example, ±50 nm) within a time (for example, 150 ms).

Other embodiments of the present invention in which feedforward control is incorporated into the feedback control in the embodiments described above will be described below. This embodiment adds a feedforward controller to the NCTF control system.

In order to improve trajectory tracking performance until reaching the stop position, we design a feedforward controller using learning control. Using the output of the feedback controller as an evaluation index, learning is performed so that the output converges to zero by repeatedly performing a predetermined movement. A feedforward controller is designed based on the output of the learning controller when the tracking error becomes sufficiently small by repeating learning multiple times.

FIG. 13 is a block diagram showing a control system in another embodiment of the present invention incorporating a feedforward controller. In FIG. 13, elements similar to those in FIG. 10 are denoted by the same reference numerals, and explanations thereof will be omitted. The control system shown in FIG. 13 has a configuration in which a feedforward controller 31 is added to the control system shown in FIG. 10, and is a control system that performs feedback control and feedforward control. The feedforward controller 31 in FIG. 13 is a controller designed based on learning control as described above.

Since the feedforward controller 31 is added to incorporate feedforward control, the trajectory tracking performance near the stop position can be improved, and the accuracy of reaching the stop position without falling behind the target displacement trajectory can also be improved. In this embodiment, the position could be converged within a desired target settling width (for example, ±50 nm) within a desired target settling time (for example, 50 ms).

The disclosed embodiments should be considered to be illustrative in all respects and not restrictive. The scope of the present invention is indicated by the claims rather than the above description, and it is intended that all changes within the meaning and range equivalent to the claims are included.

1 Surface plate 2a, 2b Linear motor 3 Table 11 NCTF control system 12 First controller 13 Second controller 14a, 14b Plant 21 Adder 22 1/2 unit 31 Feedforward controller

Claims (4)

A method for controlling the position of a gantry stage in which a table is installed on a surface plate via two linear motors arranged in parallel, the method comprising:
NCTF control based on a reference characteristic locus obtained from an open-loop experiment using an input signal to the linear motor; a first control that causes the table to follow the vibration of the surface plate; A second control for suppressing high-frequency vibrations generated in the process of making the table follow the table is independently performed on each of the two linear motors, and
The first control is performed using a bandpass filter having a transfer function represented by B(s) below (ω _b : angular frequency, ζ ₁ , ζ ₂ : damping coefficient),
The second control is performed using a differentiator.
A gantry stage control method characterized by:

2. The method of controlling a linear motor stage according to claim 1, further comprising adding feedforward control to said NCTF control. A device that controls the position of a gantry stage in which a table is installed on a surface plate via two linear motors arranged in parallel,
an NCTF control system that performs control based on a reference characteristic locus obtained from an open-loop experiment using an input signal to the linear motor; a first control section that causes the table to follow vibrations of the surface plate; A control system comprising: a second control unit that suppresses high-frequency vibrations generated in the process of causing the table to follow vibrations;
provided independently for each of the two linear motors ,
The first control unit is a bandpass filter having a transfer function represented by B(s) below (ω b _: angular frequency, ζ ₁ , ζ ₂ : damping coefficient),
The second control section is a differentiator.
A gantry stage control device characterized by:

The gantry stage control device according to claim 3, further comprising a feedforward controller that applies feedforward control to the NCTF control system.

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