JP2020095718A - Linear motor stage control method and control device - Google Patents

Abstract

To provide a control method and control device of a 2-axis linear motor stage (gantry stage) based on NCTF control method easy-to-design the flow and easy-to-adjust a controller capable of high-accuracy and high-speed positioning without requiring special knowledge about control theory.SOLUTION: When positioning with a two-axis linear motor stage (gantry stage) in which two linear motors installed parallel to the surface plate are connected with a table, by means of NCTF control that uses the reference characteristic locus obtained from open loop experiment using input signal to linear motor stage, high frequency vibrations that occur when the table follows the vibration of the surface plate are suppressed by making the table follow the vibrations caused by the surface plate.SELECTED DRAWING: Figure 13

Description

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

The linear motor stage used in industrial machines such as machine tools, measuring instruments, and semiconductor manufacturing equipment plays an important role in the field. Since the motion accuracy of this linear motor stage has a great influence on the quality and characteristics of products, there is an increasing demand for high-accuracy 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 it is difficult to achieve the severe performance requirements of recent years, and it is possible to achieve high performance while maintaining convenience. A method is needed.

Patent No. 5574762

When high-precision positioning is required, it is generally fixed on a surface plate with sufficient rigidity, but the need for high-acceleration motion increases year by year, and the vibration problem of the entire device including the surface plate becomes apparent. And its control is an important issue. As a method of suppressing vibration caused by a surface plate or the like, 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 support. However, there is a problem that the device becomes large and the cost increases, so that it can be used only for a mechanism that allows it. Therefore, as a control measure, control using advanced control (sliding mode control, robust control using a disturbance observer, or the like) is used instead of PID control, which is currently the mainstream. However, it is not widely used because it requires the effort to obtain modeling in advance and also requires sufficient knowledge of the underlying control theory.

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

The present invention has been made in view of the above circumstances, enables easy flow of design and adjustment of a controller, and enables high-accuracy and high-speed positioning without requiring special knowledge about control theory. , NCTF control method based linear motor stage control method and control device.

Another object of the present invention is to reduce the influence of the 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 allow the table to follow the surface plate vibration so that the relative displacement is The 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 linear motor stage control method according to the present invention is a method for controlling the position of a biaxial linear motor stage in which two linear motors installed in parallel to a surface plate are connected by a table. In the process of causing the table to follow the vibration of the surface plate and causing the table to follow the vibration of the surface plate by using NCTF control that performs control based on a reference characteristic locus obtained by an open loop experiment using the input signal of It is characterized by suppressing high-frequency vibrations that occur.

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

According to the present invention, NCTF control is used, and the table is made to follow the vibration of the surface plate, and high frequency vibration generated in the process of making the table follow the vibration of the surface plate is suppressed. The relative movement of the table with respect to the surface plate is not affected by the vibration of the surface plate, the relative positioning time of the table with respect to the surface plate is shortened, and high frequency vibration can be suppressed, so that the two-axis linear motor stage High-accuracy and high-speed positioning is performed in the (gantry stage).

The control method of the linear motor stage according to the present invention is characterized in that the central displacement of the table, which is represented by the average displacement of the biaxial linear motor stages, is fed back and controlled.

A linear motor stage control device according to the present invention includes an adder that adds displacements of biaxial linear motor stages, and a 1/2 unit that obtains 1/2 of the addition result of the adder. It is characterized in that the outputs of the two devices are fed back and controlled.

In the present invention, the center displacement ((x _s1 +x _s2 )/2) of the table, which is represented by the average of the displacements (x _s1 , x _s2 ) of the biaxial linear motor stage, is fed back and controlled, so-called center of gravity. Position control is performed. Therefore, the command value to each linear motor stage is the same, and the configuration is simple.

The linear motor stage control method according to the present invention is characterized in that the high-frequency vibration is suppressed by a differentiator that satisfies F _d (s)=K _c ·s (K _c : gain for adjusting damping performance). To do.

In the linear motor stage controller according to the present invention, the second controller includes a differentiator that satisfies F _d (s)=K _c ·s (K _c : gain for adjusting damping performance). And

In the present invention, in order to suppress the high frequency vibration generated in the process of causing the table to follow the vibration of the surface plate, F _d (s)=K _c s (K _c : gain for adjusting damping performance). Use a differentiator that satisfies. With a simple configuration, the effect of suppressing high frequency vibration can be obtained.

The control method of the linear motor stage according to the present invention is characterized in that the differential of the displacement difference of the linear motor stage of each axis is locally fed back to suppress the rotational vibration of the table.

In the control device for a linear motor stage according to the present invention, the second control unit has a controller that locally feeds back the differentiation of the displacement difference of the linear motor stage of each axis.

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

The linear motor stage control method according to the present invention uses a bandpass filter (ω _b : angular frequency, ζ ₁ , ζ ₂ : damping coefficient) having a transfer function represented by the equation (6) described later to determine the constant value. The table is made to follow the vibration of the board.

The linear motor stage control device according to the present invention is characterized in that the first control unit is a bandpass filter having a transfer function represented by the following equation (6).

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

The linear motor stage control method according to the present invention is characterized by adding feedforward control to the NCTF control.

The linear motor stage control device according to the present invention is characterized by further including 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, more accurate and high-speed positioning is performed.

In the linear motor stage control method and control device of the present invention, the flow of design and adjustment of the controller are easy, and highly accurate and high-speed positioning can be realized without requiring sufficient knowledge of control theory. it 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.

It is a block diagram which shows the general structure of an NCTF control system. It is a schematic diagram showing the composition of the linear motor stage to which the control method and control device in the present invention are applied. It is a block diagram showing a control system in an embodiment of the present invention. It is a figure which shows the mechanical model of a 1-axis linear motor stage. It is a figure which shows a microscopic model. It is a block diagram which shows the control system which added controller B(s) to the NCTF control system. It is a block diagram showing arrangement of a controller F(s). It is a block diagram which shows an example of the control system which added controller F(s) to the NCTF control system. It is a block diagram which shows the other example of the control system which added controller F(s) to the NCTF control system. It is a block diagram which shows the control system in other embodiment of this invention which incorporated the feedforward controller FF _tiv (t). FIG. 11 is a block diagram showing a control system according to still another embodiment of the present invention applied to a two-axis linear motor stage. It is a block diagram which shows an example of the control system in another embodiment of this invention which incorporated the feedforward controller FF _tiv (t) applied to a 2-axis linear motor stage. It is a block diagram which shows the other example of the control system in other embodiment of this invention which incorporated the feedforward controller FF _tiv (t) applied to a 2-axis linear motor stage.

Hereinafter, the present invention will be described in detail with reference to the drawings showing an embodiment thereof.

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

In the NCTF control system, the nominal characteristic trajectory (NCT) in which the desired damping characteristic is written on the phase plane and the operation of the controlled object (plant) are constrained to the NCT and It is composed of a PI compensator for stopping at the origin. The NCT is created by a simple open loop experiment, and the gain of the PI compensator is determined to be an optimum value by a step response and trajectory control experiment. Therefore, the NCTF control system does not need detailed model parameters and can be easily designed without knowledge of control theory. The open loop experiment is preferably performed by giving a rectangular wave current command to the motor. Further, it is desirable to adjust the magnitude and time of the rectangular wave input so that the table operates in the movable area at a speed exceeding the target maximum speed.

First, an open-loop experiment of actually accelerating and decelerating a controlled object using a rectangular wave signal is performed to obtain an actual operation result of the controlled object (plant). The NCT uses the deceleration region of the open-loop displacement response waveform, and is described on the phase plane with the horizontal axis representing the difference (virtual error) between the final value of the displacement and the transient response, and the vertical axis representing the derivative thereof. In the vicinity of the origin of NCT, linear approximation is further performed with a slope of a point at which the differentiation of the virtual error is equal to or less than a predetermined value.

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

As shown in FIG. 1, u _p is the difference between the differential value of the deviation and the NCT output value at the present time point, u ₀ is the output value of the P controller, and u _i is the I control value. The output value of the device, 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, reference numeral 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 that can be moved by a linear motor is installed on the surface plate 1. The linear motor used is, for example, a coreless linear motor having a mover, which is an electromagnet, and a stator, which is a permanent magnet.

FIG. 3 is a block diagram showing a control system in the 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 control target. The first controller 12 and the 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 the vibration of the surface plate 1, and specifically, a bandpass filter (B( having a transfer function represented by Expression (6) described later) (B( s)). The second controller 16 is a controller provided to suppress high-frequency vibration generated in the process of the table 2 following the vibration of the surface plate 1, and specifically, a differentiator (F(s)). Is.

The control system shown in FIG. 3 is based on the NCTF control system 11 capable of designing a highly accurate positioning control system based on a simple open-loop experiment and controller parameter adjustment, and is used to eliminate residual vibrations of the equipment frame that are difficult to remove. A control system in which a band-pass filter (B(s)) having a transfer function represented by the following equation (6) for the 2 to follow and a differentiator (F(s)) for suppressing high frequency vibration are added. Is.

Hereinafter, the design procedure and the adjusting method of the control system as shown in FIG. 3 will be described.

FIG. 4 is a diagram showing a mechanical model of the one-axis linear motor stage. In the following description, a control system design method that uses only qualitative characteristics of an object and does not require a detailed model is used. I will explain. A dynamic model is used to study the control system for reducing the influence of the table vibration when the table 2 moves at high speed on the relative displacement x ₂ −x ₁ of the table 2 with respect to the table 1. Therefore, modeling is performed with a two-inertia system including the surface plate 1. In the modeling, all the parts including the linear guide, the stator, and the like, except for the movable parts, are collectively regarded as a surface plate, and the mass point of mass m ₁ is set. Since the linear ball guide has a non-linear spring characteristic 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 region is represented by the following formula (2), and the equation of motion in the microscopic region is represented by the following formula (3). Note that 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 : The spring coefficient of the surface plate 1, k ₂ : spring coefficient of the non-linear spring, f: Coulomb friction force, p: thrust.

A method of identifying each model parameter will be described.
(A) Coulomb friction force f
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, and slowly move the load cell from the state where the table 2 is stationary at a substantially constant speed to pull the table 2, measure the frictional force at that time with the load cell, and displace the table. Is measured with an encoder.

(B) Viscosity coefficient c _{3 of} Table 2
The viscosity coefficient of Table 2 is an element included in both the macroscopic region and the microscopic region. Since this coefficient tends to increase with decreasing speed, it is treated as a function of speed. Solving the equation of motion of the one-inertia system for the viscosity coefficient gives the following equation (4).

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

The thrust p can be set to 0 when no current is applied. Therefore, an experiment for measuring the displacement from the state where the table 2 is at a predetermined speed until it naturally stops is performed, and the measured displacement in the deceleration region is calculated by the formula (5 ) To derive the viscosity coefficient c ₃ .

(C) Spring constant k _{1 of} surface plate ₁
The spring constant of the surface plate 1 is determined by an open loop experiment with a rectangular wave acceleration/deceleration input. After the deceleration rectangular wave is input, it takes time for the vibration to be attenuated even when the input becomes zero, and this vibration is considered to be caused by the shaking of the surface plate 1. Therefore, this vibration waveform is subjected to FFT analysis to obtain the vibration frequency f _s of the surface plate 1, and the spring constant k ₁ of the surface plate ₁ is derived as follows.
k ₁ =(2πf _s ) ² ·m ₁

(D) the viscosity coefficient of the surface plate 1 c ₁ and the viscosity coefficient of the non-linear spring c ₂ and the spring constant k ₂
Viscosity coefficient c ₂ and the spring constant k ₂ of the remaining viscosity coefficient c ₁ of the surface plate 1 is a parameter and the nonlinear spring, the simulation result is determined by fine adjustment to the fitting using model open loop experiments ..

The above is the method for identifying the parameters of the dynamic model shown in FIG. No parameter identification is required for the present invention.

Hereinafter, the basic idea of the control system and the design procedure for suppressing the influence of the surface plate vibration generated during high-speed motion and improving the control performance will be described.

Examine a control system that is effective in reducing surface plate vibration, which causes control performance deterioration. The dynamic model described above switches between two models during macroscopic movement and during microscopic movement. However, at the stop position, the control target is considered to be in the state of the microscopic model. The control system is derived based on a microscopic model as shown in FIG. In FIG. 5, the same parameters as those in FIG. 4 are designated by the same reference numerals, and d is the disturbance.

The reason why the surface plate vibration deteriorates the position accuracy during high-speed movement is that the high acceleration/deceleration motion of the table 2 excites the surface plate 1 to vibrate and the vibration remains after the table 2 reaches the stop position. It is considered that this is because it acts as a disturbance and affects the relative displacement of the table 2 with respect to the surface plate 1. The mass difference between the surface plate 1 and the table 2 is large (for example, surface plate 1:200 kg, table 2:2 kg), and it is difficult to remove this residual vibration by controlling the table 2. Therefore, it is realistic that the table 2 shakes like the surface plate 1 and the influence of the surface plate vibration does not appear on the relative displacement of the table 2 with respect to the surface plate 1. In other words, it is realistic to make the table 2 follow the vibration of the surface plate 1.

Therefore, the table 2 needs to be able to move at the frequency of the platen 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, the controller B(s) represented by the following equation (6) is connected in series to the PI compensator of the NCTF control system as shown in FIG. It is arranged to improve the rigidity at the frequency f _s . In equation (6), ω _{b is the} angular frequency, and ζ ₁ and ζ _{2 are} damping coefficients.

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

The smaller the damping coefficient ζ ₂ is set, the more the damping performance of the controller B(s) can be expected to improve. However, when the value of the damping coefficient ζ ₂ of the controller B(s) is set small, high frequency vibration due to the non-linear spring is likely to occur.

Therefore, a control for suppressing such high frequency vibration will be examined. The following equation (7) is obtained by Laplace transforming the equation of motion of the microscopic model represented by the equation (3).

Here, for simplification, it is replaced by the following equation (8).

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

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

In order to improve the damping performance, if G _c =K _c ·s, the denominator of equation (10) can be transformed into 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 arranged at the local feedback position as shown in FIG. 8, the input to the controller F(s) is the relative displacement x ₂ −x ₁ , and the platen displacement x ₁ and the table displacement. Since the origin of x ₂ is at the start position, when the target value changes, the controller F(s) outputs a force that hinders the operation of the table 2. Since the controller F(s) must output a force for holding the table 2 at the final stop position, that is, a force for making the displacement error from the final stop position zero, the position where the input becomes the displacement error. The controller F(s) should be located at. A block diagram of the control system in this case is shown in FIG.

The block diagram in which the controller B(s) and the controller F(s) as described above are added to the NCTF control system is FIG. 3 described above. By using the gain of the high frequency range raised by adding the controller B(s) (first controller 12) together with the controller F(s) (second controller 13), the NCTF control It can be lowered to the same level as the case. As a result, by adding the controller F(s) to the NCTF control system, the controller B(s) that causes the table 2 to follow the platen vibration is easily added to the controller F(s). Can be suppressed by The damping ratio of the high frequency vibration lowered by adding the controller B(s) is improved by using the controller F(s) together, compared with the case of only the NCTF control system. Regarding the disturbance characteristic, the effect of the controller B(s) can be maintained even when the controller F(s) is used together. As described above, by using the controller F(s) together, the effect of suppressing high frequency vibration can be expected without impairing the effect of the controller B(s) on the vibration of the surface plate.

By using the controller F(s) together, the value of the damping coefficient ζ ₂ can be lowered without generating high frequency vibration. The peak of the high frequency vibration that appears due to the addition of the controller B(s) disappears when the controller F(s) is used together, 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) represented by the equation (14), it is necessary to identify the parameters k ₁ , k ₂ , c ₁ , c ₂ +c ₃ , m ₁ +m ₂ . Here, k ₁ can be estimated from the open loop experiment as described above, and even if it is considered that the masses m ₁ and m ₂ of the mechanism are known, it takes time to identify the remaining parameters. It is possible that the system cannot be designed simply.

Therefore, the controller F(s) for suppressing high frequency vibration is simplified as follows. From the equation (10), the transfer function of the mechanism having the controller F(s) for 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 very large with respect to the mass of the stage movable part including the table. It can be said that the relationship ₁ >>m ₂ holds. When this condition is satisfied, the fractional part included in the first term of the equation (15) can be approximated by the following equation (16) by ignoring the term of m ₂ . At this time, the equation (15) is represented by the following equation (17).

Therefore, in order to improve the damping performance, the controller F(s) may satisfy the following expression (18). _Let the simplified controller F(s) in this case be F _d (s) to distinguish it from equation (14).
F _d (s)=K _c ·s (18)

As described above, when the condition of m ₁ >>m ₂ is satisfied, the second term of the equation (14) can be omitted. Therefore, if the parameter K _c, which is the gain for damping performance adjustment, is determined. Well, there is no need to identify various model parameters. Even in such a case, the effect of suppressing high frequency vibration 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 specification of problematic vibration frequency f _s )
First, the basic NCTF control system (see FIG. 1) is designed by the procedure described above. Further, the displacement frequency and the velocity waveform obtained in the open loop experiment for making the NCT are subjected to, for example, FFT analysis to experimentally identify the vibration frequency f _s which is a problem during high speed motion.

(Step 2: Design and adjustment of the controller B(s) that causes the table 2 to follow the surface plate vibration)
The controller B(s) (see FIG. 6) arranged in series with the PI compensator of the NCTF control system in order to suppress the vibration identified in step 1 is designed and adjusted. The setting method of each parameter of the controller B(s) is shown below.
(A) ω _b
Since the controller B (s) is to amplify the output of the PI compensator at frequency f _b = _{ω b} / 2π, it is matched with the frequency f _s and f _b of interest identified in step 1 ω _b = 2πf _s And set.
(B) ζ ₁ and ζ ₂
In the controller B(s), the larger the difference between ζ ₁ and ζ ₂ , the larger the amplification factor at the frequency f _b , and the vibration suppression effect can be expected. However, since there is a possibility that new frequency vibration excessively lowered zeta ₂ is generated, to the extent that a new vibration does not occur, the zeta ₁ so as to be able to sufficiently suppress the influence of the surface plate vibration It is necessary to adjust the value of ζ ₂ . Therefore, for example, ζ ₁ =0.9 is set, and a control experiment is performed while gradually reducing the value of ζ ₂ (<ζ ₁ ), and adjustment is performed so that an appropriate amplification factor is obtained. In this specification, ζ ₁ =0.9 is set. ζ ₁ =0.9 is _one of the influential values (preferred value) in this control method, but it is not limited to this value, and the value of ζ ₁ can be set appropriately according to the specifications of the control system to be applied. Just set it.

(Step 3: Design and adjustment of controller F(s) for suppressing high frequency vibration)
If new high frequency vibration is generated before the sufficient effect of following the surface plate vibration of the table 2 is obtained in step 2, or if high frequency vibration is already generated, the controller F(s) is set. Add more (see FIG. 3). The simplified F(s) is the differentiator F _d (s), and the only parameter to be adjusted is the gain K _c . The K _c gradually increased, it is adjusted to a suitable K _c which 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, it is possible to suppress the generation of high-frequency vibration and further reduce ζ ₂ of the controller B(s). it 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 suppressing vibration during high-speed motion are completed.

In the present embodiment, by using the control system having the configuration shown in FIG. 3 designed and adjusted as described above, within a desired target settling time (for example, 150 ms) and within a desired target settling range (for example, ± The position could be converged to 50 nm).

Another embodiment of the present invention in which the feed-forward control is incorporated in the feedback control in the above-described embodiment will be described below. In this embodiment, a feedforward controller is added to the NCTF control system.

In order to improve the trajectory tracking performance until reaching the stop position, we design a feedforward controller using learning control. The output of the feedback controller is used as an evaluation index, and a predetermined motion is repeated to learn to converge the output to zero. A feedforward controller is designed from the output of the learning controller when the tracking error becomes sufficiently small by repeating learning a plurality of times.

FIG. 10 is a block diagram showing a control system according to another embodiment of the present invention in which a feedforward controller is incorporated. 10, the same elements as those of FIG. 3 are designated by the same reference numerals and the description thereof 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 the learning control as described above.

Since the feedforward controller 21 is added to incorporate the feedforward control, the trajectory following performance in the vicinity of the stop position can be improved, and the accuracy of reaching the stop position without delaying the target displacement trajectory can also be improved. In this embodiment, the position could be converged within the desired target settling time (for example, ±50 nm) within the desired target settling time (for example, 50 ms).

In the above-described embodiment, a single-axis linear motor stage is targeted, but a two-axis linear motor stage (gantry) in which two linear motor stages installed in parallel are connected by a connecting table. The present invention can also be applied to a stage). Still another embodiment 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 applied to a biaxial linear motor stage according to still another embodiment of the present invention. In FIG. 11, elements similar to those in FIG. 3 are assigned the same reference numerals and explanations thereof will be omitted. The control system shown in FIG. 11 has two plants 14a and 14b to be controlled corresponding to a two-axis linear motor stage, 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 connecting table calculated from the average value of the encoder output of each linear motor stage is the target value x _r . The control is performed so as to follow, so the command values to the plants 14a and 14b are the same.

12 and 13 are block diagrams showing a control system according to still another embodiment of the present invention, which incorporates a feedforward controller applied to a two-axis linear motor stage. 12 and 13, elements similar to those in FIGS. 10 and 11 are designated by the same reference numerals, and description thereof will be omitted. The control system shown in FIGS. 12 and 13 is a control system which has a configuration in which a feedforward controller 21 is added to the control system shown in FIG. 11 and performs feedback control and feedforward control. Further, the control system shown in FIG. 13 is further provided with a controller 41 to suppress the displacement difference x _s1 -x _s2 of each linear motor stage in order to suppress the rotational vibration of the connecting table due to the synchronization deviation of each axis. The differential is locally fed back. 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 in the case of a two-axis linear motor stage (in the case of a gantry stage), the influence of the platen vibration can be sufficiently suppressed, and the desired target can be obtained. Within the settling time (for example, 50 ms), the position could be converged within the desired target settling width (for example, ±50 nm).

The disclosed embodiments are to be considered in all respects as illustrative and not restrictive. The scope of the present invention is shown not by the above description but by the scope of the claims, and is intended to include meanings equivalent to the scope of the claims and all modifications within the scope.

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 biaxial linear motor stage in which two linear motors installed in parallel to a surface plate are connected by a table,
Using 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, the table is made to follow the vibration of the surface plate, and the table is made to follow the vibration of the surface plate. A method for controlling a linear motor stage, which is characterized in that high-frequency vibrations generated in the process of following are controlled. The method of controlling the linear motor stage according to claim 1, wherein the center displacement of the table, which is represented by the average of the displacements of the biaxial linear motor stage, is fed back and controlled. The linear motor stage according to claim 1, wherein the high-frequency vibration is suppressed by a differentiator that satisfies F _d (s)=K _c ·s (K _c : gain for adjusting damping performance). Control method. 4. The method of controlling a linear motor stage according to claim 1, wherein the differential vibration of the displacement of the linear motor stage of each axis is locally fed back to suppress the rotational vibration of the table. The table is made to follow the vibration of the surface plate by a bandpass filter (ω _b : angular frequency, ζ ₁ , ζ ₂ : damping coefficient) having a transfer function represented by B(s) below. The method for controlling a linear motor stage according to claim 1, wherein

The method of controlling a linear motor stage according to claim 1, wherein feedforward control is added to the NCTF control. A device for controlling the position of a biaxial linear motor stage in which two linear motors installed in parallel to a surface plate are connected by a table,
An NCTF control system that performs control based on a reference characteristic locus obtained by an open loop experiment using an input signal to the linear motor stage, a first control unit that causes the table to follow the vibration of the surface plate, and the surface plate Control unit for a linear motor stage, comprising: a second control unit that suppresses high-frequency vibrations that occur in the process of causing the table to follow the vibrations of 1. An adder for adding the displacements of the two-axis linear motor stages and a 1/2 unit for obtaining 1/2 of the addition result of the adder are provided, and the output of the 1/2 unit is fed back and controlled. The control device for the linear motor stage according to claim 7, wherein 9. The linear motor according to claim 7, wherein the second control unit has a differentiator that satisfies F _d (s)=K _c ·s (K _c : gain for adjusting damping performance). Stage control device. 10. The control device for a linear motor stage according to claim 7, wherein the second control unit has a controller that locally feeds back the differential of the displacement difference of the linear motor stage of each axis. The first control unit is a bandpass filter having a transfer function represented by the following B(s) (ω _b : angular frequency, ζ ₁ , ζ ₂ : damping coefficient). 10. The control device for the linear motor stage according to any one of 10.

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

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