JP6631745B1 - Control method and control device for linear motor stage - Google Patents

Abstract

A method of controlling a linear motor stage based on an NCTF control method, which facilitates the flow of design and adjustment of a controller, enables high-accuracy and high-speed positioning without requiring special knowledge on control theory. And a control device. When positioning with a linear motor stage having a movable table mounted on a surface plate, NCTF control using a reference characteristic trajectory obtained from an open loop experiment using an input signal to the linear motor stage is performed. In addition, the table is made to follow the vibration caused by the surface plate, and the high frequency vibration generated in the process of making the table follow the vibration of the surface plate is suppressed. Feed forward control is added to NCTF control. The present invention is directed to control for suppressing the influence of vibration caused by the surface plate on the relative movement of the table with respect to the surface plate. [Selection diagram] FIG.

Description

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

  A linear motor stage used for an industrial machine such as a machine tool, a measuring instrument, and a semiconductor manufacturing apparatus plays an important role in the field. Since the motion accuracy of the linear motor stage has a great influence on the quality and characteristics of a product, 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. However, it has been difficult to achieve strict required performance in recent years, and control that can achieve high performance while maintaining convenience is achieved. A method is needed.

Patent No. 5574762

  When high-precision positioning is required, it is common to fix the plate to a surface plate with sufficient rigidity.However, the need for high-acceleration motion has increased year by year, and the vibration problem of the entire device including the surface plate has become apparent. 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, since there is a problem that the device becomes large and the cost increases, it can be used only for a mechanism that allows it. Therefore, as a control measure, control using advanced control (such as sliding mode control or robust control using a disturbance observer) instead of PID control which is currently mainstream is performed. However, it has not been widely used because it requires labor to find modeling in advance and requires sufficient knowledge of the underlying control theory.

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

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

  Another object of the present invention is to reduce the influence of surface table vibration on the relative displacement between the surface plate and the table, improve the rigidity of the table relative to the surface plate, and allow the table to follow the surface plate vibration to achieve relative displacement. 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 the surface plate vibration does not appear.

A method for controlling a linear motor stage according to the present invention is a method for controlling a position of a linear motor stage in which a movable table is installed on a surface plate, and an open loop experiment using an input signal to the linear motor stage. Using NCTF control that performs control based on the normative characteristic trajectory obtained from the table, the table is made to follow the vibration of the surface plate by a band-pass filter having a transfer function represented by Expression (6) described below , It is characterized in that high-frequency vibration generated in the process of causing the table to follow the vibration is suppressed.

A control device for a linear motor stage according to the present invention is a device for controlling a position of a linear motor stage in which a movable table is installed on a surface plate, and an open-loop experiment using an input signal to the linear motor stage. An NCTF control system that performs control based on a reference characteristic trajectory obtained from the control table, a first control unit that causes the table to follow the vibration of the surface plate, and a high-frequency vibration generated in a process of causing the table to follow the vibration of the surface plate And a second control unit that suppresses the following : wherein the first control unit is a band-pass filter having a transfer function represented by Expression (6) described below .

  In the present invention, the NCTF control is used, and the table is made to follow the vibration of the surface plate, thereby suppressing the high frequency vibration generated in the process of making the table follow the vibration of the surface plate. Therefore, high-precision and high-speed positioning in the linear motor stage is performed.

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

  The control apparatus for a linear motor stage according to the present invention is further characterized by further comprising a feedforward controller for applying feedforward control to the NCTF control system.

  According to the present invention, feedforward control using learning control is added to NCTF control. Therefore, high-precision and high-speed positioning is performed.

  The control method of the linear motor stage according to the present invention is characterized in that control is performed to cause the table to follow the vibration of the surface plate.

  The control device for a linear motor stage according to the present invention performs control for causing the table to follow the vibration of the surface plate.

  In the present invention, control is performed to cause the table to follow the vibration of the surface plate. That is, according to the present invention, the control is to make the table follow the vibration of the surface plate. Therefore, the relative movement of the table with respect to the base is not affected by the vibration of the base, and the relative positioning time of the table with respect to the base is reduced.

  In the linear motor stage control device according to the present invention, the second control unit is a differentiator.

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

  In the control method and the control device of the linear motor stage of the present invention, the flow of the design and the adjustment of the controller are easy, and high-precision and high-speed positioning can be realized without requiring sufficient knowledge of the control theory. it can. Since the table follows the vibration of the base, the relative movement of the table with respect to the base is not affected by the vibration of the base, and the relative positioning of the table with respect to the base can be completed in a short time.

FIG. 2 is a block diagram showing a general configuration of an NCTF control system. It is a schematic diagram showing the composition of the linear motor stage to which the control method and the control device in 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 illustrating a mechanical model of a one-axis linear motor stage. It is a figure showing a microscopic model. It is a block diagram which shows the control system which added the controller B (s) to the NCTF control system. It is a block diagram which shows arrangement | positioning of the controller F (s). It is a block diagram which shows an example of the control system which added the controller F (s) to the NCTF control system. It is a block diagram which shows the other example of the control system which added the controller F (s) to the NCTF control system. FIG. 11 is a block diagram showing a control system according to another embodiment of the present invention incorporating a feedforward controller FF _tiv (t). It is a block diagram showing a control system in still another embodiment of the present invention applied to a two-axis linear motor stage. It is a block diagram showing an example of a control system in _yet another embodiment of the present invention incorporating a feedforward controller FF _tiv (t) applied to a two-axis linear motor stage. FIG. ₁₆ is a block diagram showing another example of a control system according to _still another embodiment of the present invention, incorporating a feedforward controller FF _tiv (t) applied to a two-axis linear motor stage.

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

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

  In the NCTF control system, a reference characteristic trajectory (Nominal Characteristic Trajectory: NCT) in which desired attenuation characteristics are expressed on a phase plane and an operation of a control target (plant) are constrained to the NCT, and And 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 require detailed model parameters and can be easily designed without knowledge of control theory. The open loop experiment is desirably performed by giving a rectangular wave current command to the motor. Also, it is desirable to adjust the magnitude and time of the rectangular wave input so that the table operates at a speed exceeding the target maximum speed in the movable area.

  First, an actual operation result of the control target (plant) is obtained by performing an open loop experiment in which the control target is actually accelerated / decelerated using the rectangular wave signal. NCT uses the deceleration region of the open-loop displacement response waveform, and is described on a phase plane with the horizontal axis representing the difference between the final value of the displacement and the transient response (virtual error) and the vertical axis representing its derivative. In the vicinity of the origin of the NCT, a linear approximation is further performed using the slope of a point at which the derivative of the virtual error becomes a predetermined value or less.

Subsequently, the gain of the PI compensator is adjusted. The proportional gain _Kp is determined from a step response experiment at a predetermined height using only the proportional control. Further, the integral gain K _I, as a target displacement trajectory second-order integration of the triangular wave acceleration target value, performs trajectory control experiments, best trajectory tracking performance in the vicinity of the stop position is determined to a value that stability is maintained . As the integrator, an integrator with a saturation condition according to the following equation (1) is used.

Each parameter of the formula (1), as shown in FIG. 1, u _p is the difference between the differential value and the NCT output value of the deviation at the present time, u ₀ is the output value of the P controller, u _i is I Control output value of the vessel, Delta] u _i denotes the maximum absolute value of u _i change rate, u _s is the operation amount be sent to the amplifier.

  FIG. 2 is a schematic diagram showing a configuration of a linear motor stage to which the control method and the control device according to the present invention are applied. In FIG. 2, reference numeral 1 denotes 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, a table 2 movable by a linear motor is provided. The linear motor to be used is, for example, a coreless linear motor having a mover which is an electromagnet and a stator made of a permanent magnet.

  FIG. 3 is a block diagram illustrating a control system according to the embodiment of the present invention. This control system includes an NCTF control system 11 having an NCT, a PI compensator and the like, 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 more specifically, a band-pass filter (B () having a transfer function represented by the following equation (6). s)). The second controller 16 is a controller provided to suppress high-frequency vibration generated in a process in which the table 2 follows the vibration 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 can design a high-precision positioning control system based on simple open-loop experiments and controller parameter adjustment. A control system in which a band-pass filter (B (s)) having a transfer function represented by the following equation (6) and a differentiator (F (s)) for suppressing high-frequency vibration are added. It is.

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

FIG. 4 is a diagram showing a mechanical model of a one-axis linear motor stage. In the following description, a control system design method using only qualitative characteristics of an object and not requiring a detailed model will be described. However, in the description of the present invention, a method for identifying parameters in a dynamic model shown in FIG. I will explain. A dynamic model is used for a control system study for reducing the influence of the vibration of the table 2 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 using a two-inertia system including the surface plate 1. In modeling, including linear guide and stator etc., regarded as platen together all the components other than the movable portion, and the mass point of mass m _1. Further, since the linear ball guide has a non-linear spring characteristic in a 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 area is represented by the following equation (2), and the equation of motion in the microscopic area is represented by the following equation (3). Incidentally, m _1: mass of the surface plate 1, m _2: mass of the table 2, c _1: viscosity coefficient of the surface plate 1, c _2: viscosity coefficient of non-linear spring, c _3: viscosity coefficient of table 2, k _1: the spring coefficient of the surface plate 1, k _2: spring constant of the non-linear spring, f: Coulomb friction, p: a thrust.

A method for identifying each model parameter will be described.
(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 the table 2 with a vinyl string, slowly move the load cell at a substantially constant speed from a state where the table 2 is stationary, 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 in 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. The following equation (4) is obtained by solving the equation of motion of the one inertial system with respect to the viscosity coefficient.

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

In the state where no current is applied, the thrust can be set to p = 0. Therefore, an experiment for measuring the displacement of the table 2 from the state of the predetermined speed to the spontaneous stop is performed, and the measured displacement in the deceleration region is calculated by the formula (5) ) it is applied to, to derive the viscosity coefficient c _3.

(C) Spring constant k _{1 of} surface plate ₁
The spring constant of the platen 1 is determined from 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 attenuate even if the input becomes zero, and this vibration is considered to be caused by the swing of the surface plate 1. Therefore, we obtain the vibration frequency f _s of the platen 1 the vibration waveform by FFT analysis, to derive the spring constant k ₁ of the surface plate 1 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. For the present invention, parameter identification is not required.

  Hereinafter, a basic concept of a control system for suppressing the influence of surface plate vibration generated at the time of high-speed motion and improving control performance and a design procedure thereof will be described.

  Investigate a control system that is effective for reducing the surface plate vibration which is a cause of control performance degradation. Although the above-described dynamic model switches between the two models at the time of macroscopic movement and at the time of microscopic movement, the controlled object is considered to be in the state of the microscopic model at the stop position. 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 denoted by the same reference numerals, and d is a disturbance.

  The reason why the vibration of the base plate during high-speed movement causes deterioration of the positional accuracy is that the vibration is excited on the base plate 1 by the high acceleration / deceleration movement of the table 2 and the vibration remains even after the table 2 reaches the stop position. This is considered to be due to the fact that it acts in a disturbance manner 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, approximately 200 kg for the surface plate and about 2 kg for the table 2), and it is difficult to remove the residual vibration by controlling the table 2. Therefore, it is realistic that the table 2 swings in the same manner as the surface plate 1 so that 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 base 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. In order to improve the followability to the target value input of the frequency f _s, the controller B (s) represented by the following formula (6) to the PI compensator NCTF control system as shown in FIG. 6 in series arrangement, and improve the 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 as compared with the case where only the NCTF control is used. In addition, 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.

As setting a small value of the attenuation coefficient zeta _2, it can be expected to improve the damping performance of the controller B (s). However, if you set the value of the attenuation coefficient zeta ₂ controllers B (s) smaller, due to the non-linear spring, the high-frequency vibration is likely to occur.

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

  Here, for simplicity, the following equation (8) is used.

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

A controller F (s) that improves the damping characteristics of the mechanism by arranging it in the mechanism represented by this transfer function as shown in FIG. 7 will be studied. The transfer function including the controller F (s) is represented by the following equation (10). If the denominator of the equation (10) can be factorized as shown in 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 this purpose, the controller F (s) may be designed as in the following equation (12).

In order to improve the damping performance, if G _c = K _c · s, the denominator of the equation (10) can be modified as in the following equation (13), 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 position of the local feedback as shown in FIG. 8, the input to the controller F (s) is a relative displacement x ₂ −x ₁ , and the surface plate displacement x ₁ and the table displacement since the origin of the x ₂ is in the starting position, when the target value is changed, the controller F (s) would output a force to to obstruct 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 eliminating a displacement error from the final stop position, a position at which the input becomes a displacement error. Controller F (s). FIG. 9 shows a block diagram of the control system in this case.

  FIG. 3 is a block diagram in which the controller B (s) and the controller F (s) as described above are added to the NCTF control system. The gain in the high-frequency range raised by adding the controller B (s) (the first controller 12) can be used for the NCTF control by using the controller F (s) (the second controller 13) together. It can be reduced to the same extent as in the case. As a result, by adding the controller B (s) that causes the table 2 to follow the platen vibration to the NCTF control system, the controller F (s) reduces the high frequency vibration caused by the non-linear spring which is likely to be generated. Can be suppressed. By adding the controller B (s), the attenuation rate of the high-frequency vibration reduced is improved by using the controller F (s) together with the case where only the NCTF control system is used. Regarding the disturbance characteristics, 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, an effect of suppressing the high-frequency vibration can be expected without impairing the effect of the controller B (s) following the platen vibration.

Without generating a high-frequency vibrations by a combination of controller F (s), it can be lowered value of the attenuation coefficient zeta _2. The peak of the high-frequency vibration appearing due to the addition of the controller B (s) disappears due to the combined use of the controller F (s), and the effect of suppressing the high-frequency vibration by 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 parameters k ₁ , k ₂ , c ₁ , c ₂ + c ₃ , and m ₁ + m ₂ . Here, k ₁ can be estimated from an 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. There may be situations where simple design of the system cannot be performed.

  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) as the local feedback is represented 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 apparatus excluding the movable part is very large relative to the mass of the stage movable part including the table. It can be said that the relationship of ₁ >> m ₂ holds. When this condition is satisfied, the fractional part included in the first term of Expression (15) can be approximated by Expression (16) by ignoring the term of m ₂ . At this time, the expression (15) is represented by the following expression (17).

Therefore, in order to improve the damping performance, the controller F (s) should satisfy the following expression (18). In this case, the simplified controller F (s) is denoted by F _d (s) in order to distinguish it from Expression (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 determines only K _c which is a gain for adjusting the damping performance, 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.

Design and adjustment are performed in the following order using the control system shown in FIG.
(Step 1: NCTF specific oscillation frequency f _s to be designed and problems of the control system 11)
First, a basic NCTF control system (see FIG. 1) is designed according to the procedure described above. In addition, by displacement waveform and FFT velocity waveform example analysis obtained in an open-loop experiment performed for NCT created experimentally identifies the vibration frequency f _s which is a problem during high-speed movement.

(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 specified in step 1 is designed and adjusted. The setting method of each parameter of the controller B (s) will be described 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
Controller B (s) is larger amplification factor at higher frequency f _b is a large difference between the ₂ and the zeta ₁ zeta, it can be expected vibration suppressing effect. 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値 The value of ₂ needs to be adjusted. Therefore, for example, ζ ₁ is set to 0.9, and a control experiment is performed while gradually lowering the value of ζ ₂ (<ζ ₁ ), so that an appropriate amplification factor is obtained. In this specification, ζ ₁ = 0.9. ζ ₁ = 0.9 is _one of the influential values (preferred values) in the present control method, but is not limited to this value, and the value of ζ ₁ is appropriately set in accordance with the specifications of the applied control system. Just set it.

(Step 3: Design and adjustment of controller F (s) for suppressing high frequency vibration)
If a new high-frequency vibration is generated before the sufficient effect of following the table-plate vibration of the table 2 in step 2 is obtained, or if high-frequency vibration has already been generated, the controller F (s) is turned off. Add more (see FIG. 3). The simplified F (s) is the differentiator F _d (s), and the only parameter to adjust 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 a controller F (s) (differentiator F _d (s)) and adjusting its parameters, generation of high-frequency vibration is suppressed, and ζ ₂ of the controller B (s) can be further reduced. it can. Until we achieve the target performance, to adjust the ₂ again ζ.

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

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

  Another embodiment of the present invention in which feed-forward control is incorporated into feedback control in the above-described embodiment will be described below. This embodiment is obtained by adding a feedforward controller to the NCTF control system.

  In order to improve the trajectory following performance until reaching the stop position, a feedforward controller is designed using learning control. The output of the feedback controller is used as an evaluation index, and learning is performed such that predetermined output is repeatedly performed so that the output converges to zero. By repeating learning a plurality of times, a feedforward controller is designed from the output of the learning controller when the tracking error becomes sufficiently small.

  FIG. 10 is a block diagram showing a control system according to another embodiment of the present invention incorporating a feedforward controller. In FIG. 10, the same elements as those in FIG. 3 are denoted by the same reference numerals, and 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 near the stop position can be improved, and the accuracy of reaching the stop position without delaying the target displacement trajectory can be improved. In this embodiment, the position can be converged within a desired target settling width (for example, ± 50 nm) within a desired target settling time (for example, 50 ms).

  Although the above-described embodiment is directed to a one-axis linear motor stage, a two-axis linear motor stage (a gantry) in which two linear motor stages installed in parallel are connected by a connection table. The present invention is also applicable to (stage). 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 according to still another embodiment of the present invention applied to a two-axis linear motor stage. In FIG. 11, the same elements as those in FIG. 3 are denoted by the same reference numerals, and description thereof will be omitted. The control system shown in FIG. 11 includes two plants 14 a and 14 b to be controlled corresponding to a two-axis linear motor stage, and further includes an adder 31 and a half 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 corresponds to the target value x _r . The control is performed so as to follow, so that the command values to the plants 14a and 14b are the same.

FIGS. 12 and 13 are block diagrams showing a control system according to still another embodiment of the present invention incorporating a feedforward controller applied to a two-axis linear motor stage. 12 and 13, the same elements as those in FIGS. 10 and 11 are denoted by the same reference numerals, and description 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. Further, the control system shown in FIG. 13 is further provided with a controller 41 to reduce the displacement difference x _s1 −x _s2 of each linear motor stage in order to suppress the rotational vibration of the connection table due to the synchronization deviation of each axis. The configuration is such that the derivative 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 in the case of a two-axis linear motor stage (in the case of a gantry stage), it is possible to sufficiently suppress the influence of platen vibration, and to achieve a desired target. 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 are to be considered in all respects as illustrative and not restrictive. The scope of the present invention is defined by the terms of the claims, rather than the description above, and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims.

Reference Signs List 1 surface plate 2 table 11 NCTF control system 12 first controller 13 second controller 14, 14a, 14b plant 21 feedforward controller

Claims (7)

A method for controlling the position of a linear motor stage in which a movable table is installed on a surface plate,
A band-pass filter (ω _b ) having a transfer function represented by the following B (s) using NCTF control that performs control based on a reference characteristic trajectory obtained from an open-loop experiment using an input signal to the linear motor stage : Angular frequency, ζ ₁ , ζ ₂ : damping coefficient) causes the table to follow the vibration of the surface plate, and suppresses high frequency vibration generated in the process of following the table to the vibration of the surface plate. To control the linear motor stage.

  The control method of a linear motor stage according to claim 1, wherein feedforward control is added to the NCTF control.   3. The control method for a linear motor stage according to claim 1, wherein control is performed to cause the table to follow the vibration of the surface plate. A device that controls the position of a linear motor stage on which a movable table is installed on a surface plate,
An NCTF control system that performs control based on a reference characteristic trajectory obtained from 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 And a second control unit that suppresses high-frequency vibration generated in a process of causing the table to follow the vibration of the first control unit. The first control unit is a band-pass filter having a transfer function represented by the following B (s) ( ω _b : angular frequency, ζ ₁ , ζ ₂ : damping coefficient) .

  The control device for a linear motor stage according to claim 4, further comprising a feedforward controller that applies feedforward control to the NCTF control system.   The control device for a linear motor stage according to claim 4 or 5, wherein control is performed to cause the table to follow the vibration of the surface plate. Control system for a linear motor stage according to any one of 6 from claim 4 wherein the second controller is characterized by a differentiator.

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