JP7363428B2 - Control method and control device for linear motor stage - Google Patents

Description

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

Linear motor stages used in industrial machinery such as machine tools, measuring instruments, and semiconductor manufacturing equipment play an important role in the field. The motion accuracy of this linear motor stage has a large effect on the quality and characteristics of products, so there is an increasing demand for high-precision and high-speed positioning.

Conventionally, PID control, which is relatively easy to design and adjust and is easy to handle, has been widely used for precision mechanisms, but in recent years it has been difficult to achieve the strict performance requirements, so there is a need for control that can achieve high performance while maintaining convenience. A method is needed.

Patent No. 5574762 specification

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.

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 control method and a control device for a linear motor stage 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. An object of the present invention is to provide a control method and a control device for a linear motor stage based on the NCTF control method, in which the influence of surface plate vibration does not appear.

A method for controlling a linear motor stage according to the present invention is a method for controlling the position of a two-axis linear motor stage in which two linear motors installed parallel to a surface plate are connected by a table. NCTF control performs control based on a reference characteristic locus obtained from an open-loop experiment using an input signal; first control causes the table to follow the vibration of the surface plate; It is characterized by using a second control that suppresses high-frequency vibrations generated in the process of following the .

A linear motor stage control device according to the present invention is a device for controlling the position of a two-axis linear motor stage in which two linear motors installed parallel to a surface plate are connected by a table, and the linear motor stage is connected to the linear motor stage. an NCTF control system that performs control based on a reference characteristic locus obtained from an open-loop experiment using an input signal; a first control section that causes the table to follow the vibration of the surface plate; and a second control section that suppresses high-frequency vibrations generated in the process of following the .

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. The relative movement of the table to the surface plate is no longer affected by the vibrations of the surface plate, the time required to position the table relative to the surface plate is shortened, and high frequency vibrations can be suppressed, making it possible to use a two-axis linear motor stage. High-accuracy and high-speed positioning at the (gantry stage) is performed.

The method for controlling a linear motor stage according to the present invention is characterized in that the center displacement of the table, which is represented by the average displacement of the two-axis linear motor stage, is controlled by feedback.

A control device for a linear motor stage according to the present invention includes an adder that adds displacements of a two-axis linear motor stage, and a 1/2 unit that calculates 1/2 of the addition result of the adder, the 1/2 The feature is that the outputs of the two devices are fed back for control.

In the present invention, the so-called center of gravity is controlled by feedback of the center displacement ((x _s1 +x _s2 )/2) of the table, which is represented by the average displacement (x _s1 , x _s2 ) of the two-axis linear motor stage. Perform position control. Therefore, the command value to each linear motor stage is the same, and the configuration is simple.

In the method for controlling a linear motor stage according to the present invention, the second control suppresses the high-frequency vibration using a differentiator that satisfies F(s)=Kc·s (Kc: gain for adjusting damping performance). It is characterized by

The linear motor stage control device according to the present invention is characterized in that the second control section includes a differentiator that satisfies F _d (s) = K _c ·s (K _c : gain for adjusting damping performance). shall be.

In the present invention, in order to suppress high-frequency vibrations that occur during the process of making the table follow the vibrations of the surface plate, F _d (s) = K _c · s (K _c : gain for adjusting damping performance). Use a differentiator that satisfies the following. The simple configuration provides the effect of suppressing high frequency vibrations.

A method for controlling a linear motor stage according to the present invention is characterized in that rotational vibration of the table is suppressed by locally feeding back the differential of the displacement difference of the linear motor stage for each axis.

The linear motor stage control device according to the present invention is characterized in that the second control section includes a controller that locally feeds back the differential of the displacement difference of the linear motor stage for each axis.

In the present invention, in order to suppress rotational vibration of the table, the differential of the displacement difference of the linear motor stage of each axis is locally fed back. To efficiently suppress rotational vibration of the table due to out-of-synchronization of each axis.

In the linear motor stage control method according to the present invention, the first control includes a bandpass filter (ωb: angular frequency, ζ1, ζ2: damping coefficient) having a transfer function expressed by equation (6) described below. Accordingly, the table is made to follow the vibration of the surface plate.

The linear motor 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 (6) described below.

In the present invention, in order to cause the table to follow the vibration of the surface plate, a bandpass filter having a transfer function expressed by equation (6) described later is used. Therefore, the configuration of the control system is further simplified.

A method for controlling a linear motor stage according to the present invention is characterized in that feedforward control is added to the NCTF control.

The linear motor 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.

With the linear motor stage control method and control device of the present invention, the design flow and controller adjustment are easy, and high-precision and high-speed positioning can be achieved without requiring sufficient knowledge of control theory. can. 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.

FIG. 2 is a block diagram showing a general configuration of an NCTF control system. 1 is a schematic diagram showing the configuration of a linear motor stage to which a control method and a control device according to the present invention are applied. It is a block diagram showing a control system in an embodiment of the present invention. FIG. 3 is a diagram showing a mechanical model of a 1-axis linear motor stage. FIG. 3 is a diagram showing a microscopic model. 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. FIG. 7 is a block diagram showing a control system in another embodiment of the present invention incorporating a feedforward controller FF _tiv (t). FIG. 7 is a block diagram showing a control system in still another embodiment of the present invention applied to a two-axis linear motor stage. FIG. 7 is a block diagram showing an example of a control system in still another embodiment of the present invention incorporating a feedforward controller FF _tiv (t) applied to a two-axis linear motor stage. FIG. 7 is a block diagram showing another example of a control system in still another embodiment of the present invention incorporating a feedforward controller FF _tiv (t) applied to a two-axis linear motor stage.

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 schematic diagram showing the configuration of a linear motor stage to which the control method and control device of the present invention are applied. In FIG. 2, 1 is a surface plate, and the surface plate 1 has a plurality of legs 1a and is grounded by an adjuster 1b. A table 2 is installed on the surface plate 1 and is movable by a linear motor. The linear motor used is, for example, a coreless linear motor that has a mover that is an electromagnet and a stator that is a permanent magnet.

FIG. 3 is a block diagram showing a control system in an embodiment 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 suppress vibration of the surface plate 1, and specifically, a bandpass filter (B( s)). The second controller 16 is a controller provided to suppress high-frequency vibrations generated in the process of the table 2 following the vibrations of the surface plate 1, and specifically, a differentiator (F(s)). It is.

The control system shown in Fig. 3 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 band-pass filter (B(s)) having a transfer function expressed by Equation (6) described later for tracking by 2 and a differentiator (F(s)) for suppressing high-frequency vibrations. It is.

The design procedure and adjustment method for a control system as shown in FIG. 3 will be described below.

FIG. 4 is a diagram showing a mechanical model of a 1-axis linear motor stage. In the following explanation, we will discuss a control system design method that uses only the qualitative characteristics of the target and does not require a detailed model, but when explaining the present invention, we will also explain the parameter identification method in the dynamic model shown in Figure 4. Let me explain. A dynamic model is used to study a control system to reduce the influence of surface plate vibration when table 2 moves at high speed on the relative displacement x ₂ −x ₁ of table 2 with respect to surface plate 1. Therefore, modeling is performed using a two-inertial system including the surface plate 1. 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 . In addition, since the linear ball guide has nonlinear spring characteristics in the microscopic region and affects the microscopic behavior, the model is switched between the macroscopic region (a) and the microscopic region (b).

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

We will explain how to identify each model parameter.
(a) Coulomb friction force f
The Coulomb friction force of the linear guide is measured using a load cell. Attach the load cell to the guide, connect it to the table 2 with a vinyl string, move the load cell slowly at a nearly constant speed from a stationary state to pull the table 2, measure the frictional force at that time with the load cell, and measure the table displacement. is measured with an encoder.

(b) Viscosity coefficient c ₃ in Table 2
The viscosity coefficients in Table 2 are elements included in both the macroscopic area and the microscopic area. Since this coefficient tends to increase as the speed decreases, it is treated as a function of speed. When the equation of motion of a one-inertia system is solved for the viscosity coefficient, the following equation (4) is obtained.

The discrete system of equation (4) is expressed by equation (5) below using the backward difference method. The subscript j is the sampling number, and T _s is the sampling period.

Since the thrust force p can be set to 0 when no current is applied, an experiment was conducted to measure the displacement of the table 2 from a predetermined speed until it stops naturally, and the measured displacement in the deceleration region was calculated using the formula (5 ) to derive the viscosity coefficient _c3 .

(c) Spring constant k 1 of surface plate ₁
The spring constant of the surface plate 1 is determined by an open loop experiment using rectangular wave acceleration/deceleration input. After inputting the deceleration rectangular wave, it takes time for the vibration to attenuate even when the input becomes zero, and this vibration is thought to be caused by the shaking of the surface plate 1. Therefore, this vibration waveform is subjected to FFT analysis to determine the vibration frequency f _s of the surface plate 1, and the spring constant k ₁ of the surface plate 1 is derived as shown below.
k ₁ = (2πf _s ) ²・m ₁

(d) Viscosity coefficient c ₁ of surface plate 1, viscosity coefficient c ₂ and spring constant k ₂ of nonlinear spring
The remaining parameters, the viscosity coefficient c ₁ of the surface plate 1, the viscosity coefficient c ₂ and the spring constant k ₂ of the nonlinear spring, are determined by fine adjustment so that the simulation results using the model fit the open-loop experimental results. .

The above is the method for identifying parameters of the dynamic model shown in FIG. 4. For the present invention, parameter identification is not required.

Below, we will explain the basic concept of a control system and its design procedure for suppressing the effects of surface plate vibration that occurs during high-speed motion and improving control performance.

We will investigate a control system that is effective in reducing surface plate vibration, which is a factor in deteriorating control performance. The above-mentioned mechanical model switches between two models during macroscopic movement and microscopic movement, but since the controlled object is considered to be in the state of the microscopic model at the stop position, the present invention The control system is derived based on a microscopic model as shown in FIG. Note that in FIG. 5, the same parameters as in FIG. 4 are given the same symbols, and d: disturbance.

The reason why surface plate vibration deteriorates positional accuracy during high-speed motion is that vibrations are excited in surface plate 1 due to the high acceleration and deceleration motion of table 2, and the vibrations remain even after table 2 reaches the stop position. This is thought to be because it acts as a disturbance and affects the relative displacement of the table 2 with respect to the surface plate 1. The difference in mass between the surface plate 1 and the table 2 is large (eg, approximately 200 kg for the surface plate 1 and 2 kg for the table 2), and it is difficult to remove this residual vibration by controlling the table 2. Therefore, it is practical to prevent the table 2 from shaking in the same way as the surface plate 1 and to prevent the effect of surface plate vibration from appearing on the relative displacement of the table 2 with respect to the surface plate 1. In other words, it is practical to make the table 2 follow the vibrations of the surface plate 1.

Therefore, the table 2 needs to be able to move at the frequency of the surface plate vibration, and it is desirable that there is no resonance point. 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 (6) is connected in series to the PI compensator of the NCTF control system, as shown in Figure 6. to improve rigidity at the frequency f _s . In Equation (6), 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 the disturbance d.

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 (3) is subjected to Laplace transform, the following equation (7) is obtained.

Here, for simplicity, it is replaced as shown in equation (8) below.

By rewriting the equation (7) using the equation (8), the following equation (9) is obtained.

Consider a controller F(s) that improves the damping characteristics of the mechanism by arranging it as shown in FIG. 7 in the mechanism represented by this transfer function. A transfer function including the controller F(s) is expressed by the following equation (10). If the denominator of equation (10) can be factorized as shown in equation (11) below, then c ₂ +c ₃ and k ₂ including the parameters of the nonlinear spring can be adjusted by the arbitrarily determined parameter G _c . For this purpose, the controller F(s) may be designed as shown in equation (12) below.

In order to improve the damping performance, if G _c =K _c ·s, the denominator of equation (10) can be modified as shown in equation (13) 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 (14).

FIG. 8 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 8, 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 2 from operating. The controller F(s) must output a force that keeps the table 2 at the final stop position, that is, a force that makes the displacement error from the final stop position zero, so the controller F(s) must output a force that keeps the table 2 at the final stop position, that is, a force that makes the displacement error from the final stop position zero. The controller F(s) should be placed at . A block diagram of the control system in this case is shown in FIG.

The above-mentioned FIG. 3 is a block diagram in which the above-mentioned controller B(s) and controller F(s) are added to the NCTF control system. 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, adding controller F(s) to the NCTF control system eliminates high-frequency vibrations caused by nonlinear springs that are likely to occur by adding controller B(s) that causes table 2 to follow vibrations of the surface plate. can be suppressed by 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.

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 (14), 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 as described above, and even if we assume that the masses m ₁ and m ₂ of the mechanism are known, identifying the remaining parameters is time-consuming, so the control There may also be situations where a simple design of the system cannot be performed.

Therefore, the controller F(s) for suppressing high frequency vibrations is simplified as follows. From the equation (10), the transfer function of the mechanism having the controller F(s) as local feedback is expressed by the following equation (15).

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 (15) can be approximated as shown in equation (16) below by ignoring the term m ₂ . At this time, equation (15) is expressed by equation (17) below.

Therefore, in order to improve the damping performance, the controller F(s) should satisfy the following equation (18). The simplified controller F(s) in this case is designated as F _d (s) to distinguish it from Equation (14).
F _d (s)=K _c・s (18)

In this way, if the condition of m ₁ >> m ₂ is satisfied, the second term of equation (14) 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. 3, 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 causes table 2 to follow surface plate vibration)
In order to suppress the vibration identified in step 1, a controller B(s) (see FIG. 6) 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 to the surface plate vibration of the table 2 is obtained in step 2, or if high-frequency vibration has already occurred, the controller F(s) should be adjusted. Add more (see Figure 3). 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.

In this embodiment, by using the control system having the configuration shown in FIG. 3 designed and adjusted as described above, the desired target settling time (for example, 150 ms) or less and within the desired target settling width (for example, ± 50 nm).

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. 10 is a block diagram showing a control system in another embodiment of the present invention incorporating a feedforward controller. In FIG. 10, elements similar to those in FIG. 3 are designated by the same reference numerals, and their explanations will be omitted. The control system shown in FIG. 10 has a configuration in which a feedforward controller 21 is added to the control system shown in FIG. 3, and is a control system that performs feedback control and feedforward control. The feedforward controller 21 in FIG. 10 is a controller designed based on learning control as described above.

Since the feedforward controller 21 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).

In the embodiment described above, the target is a single-axis linear motor stage, but a two-axis linear motor stage (gantry) in which two linear motor stages installed in parallel are connected by a connecting table is also applicable. The present invention is also applicable to stages). Still other embodiments of the present invention applied to a two-axis linear motor stage will be described below.

FIG. 11 is a block diagram showing a control system in still another embodiment of the present invention applied to a two-axis linear motor stage. In FIG. 11, elements similar to those in FIG. 3 are denoted by the same reference numerals, and explanations thereof will be omitted. The control system shown in FIG. 11 includes two plants 14a and 14b to be controlled corresponding to two-axis linear motor stages, and further includes an adder 31 and a 1/2 unit 32.

In the control system shown in Fig. 11, the center displacement x _c (=(x _s1 + x _s2 )/2) of the connection table calculated from the average value of the encoder output of each linear motor stage is the target value x _r . Control is performed so as to follow. Therefore, the command value to each plant 14a, 14b is the same.

12 and 13 are block diagrams showing a control system in still another embodiment of the present invention incorporating a feedforward controller applied to a two-axis linear motor stage. In FIGS. 12 and 13, elements similar to those in FIGS. 10 and 11 are denoted by the same reference numerals, and explanations thereof will be omitted. The control system shown in FIGS. 12 and 13 has a configuration in which a feedforward controller 21 is added to the control system shown in FIG. 11, and is a control system that performs feedback control and feedforward control. In addition, the control system shown in FIG. 13 further includes a controller 41 to control the displacement difference x _s1 −x _s2 of each linear motor stage in order to suppress rotational vibration of the coupling table due to synchronization of each axis. The configuration is such that the differential is locally fed back. Note that the proportionality of the displacement difference x _s1 −x _s2 may be locally fed back.

By using the control system shown in Figs. 12 and 13, even for a two-axis linear motor stage (gantry stage), the influence of surface plate vibration can be sufficiently suppressed, and the desired goal can be achieved. The position could be converged within a desired target settling width (for example, ±50 nm) within the 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 2 Table 11 NCTF control system 12 First controller 13 Second controller 14, 14a, 14b Plant 21 Feedforward controller 31 Adder 32 1/2 unit 41 Controller

Claims (12)

A method for controlling the position of a two-axis linear motor stage in which two linear motors installed parallel to a surface plate are connected by a table, the method comprising:
NCTF control that performs control based on a reference characteristic locus obtained from an open-loop experiment using an input signal to the linear motor stage; first control that causes the table to follow vibrations of the surface plate; and and second control for suppressing high-frequency vibrations generated in the process of causing the table to follow the vibrations of the linear motor stage. 2. The method of controlling a linear motor stage according to claim 1, wherein the control is performed by feedback of the center displacement of the table, which is represented by the average displacement of the two-axis linear motor stage. 3. The second control suppresses the high-frequency vibration using a differentiator that satisfies Fd(s)=Kc·s (Kc: gain for adjusting damping performance). How to control a linear motor stage. 4. The method of controlling a linear motor stage according to claim 1, wherein rotational vibration of the table is suppressed by locally feeding back differentials of displacement differences of the linear motor stage for each axis. The first control causes the table to follow the vibration of the surface plate using a bandpass filter (ωb: angular frequency, ζ1, ζ2: damping coefficient) having a transfer function expressed by B(s) below. A method for controlling a linear motor stage according to any one of claims 1 to 4.

6. The method for controlling a linear motor stage according to claim 1, further comprising adding feedforward control to said NCTF control. A device for controlling the position of a two-axis linear motor stage in which two linear motors installed parallel to a surface plate are connected by a table,
an NCTF control system that performs control based on a reference characteristic locus obtained from an open-loop experiment using input signals to the linear motor stage; a first control unit that causes the table to follow vibrations of the surface plate; and the surface plate. A control device for a linear motor stage, comprising: a second control section that suppresses high-frequency vibrations generated in the process of causing the table to follow the vibrations of the linear motor stage. It is equipped with an adder that adds the displacement of a two-axis linear motor stage, and a 1/2 unit that calculates 1/2 of the addition result of the adder, and is controlled by feeding back the output of the 1/2 unit. The linear motor stage control device according to claim 7, characterized in that: The linear motor according to claim 7 or 8, wherein the second control section includes a differentiator that satisfies F _d (s) = K _c ·s (K _c : gain for adjusting damping performance). Stage control device. 10. The linear motor stage control device according to claim 7, wherein the second control section includes a controller that locally feeds back differentials of displacement differences of the linear motor stage for each axis. From claim 7, wherein 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). 11. The linear motor stage control device according to claim 10.

12. The linear motor stage control device according to claim 7, further comprising a feedforward controller that applies feedforward control to the NCTF control system.

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