JP3286186B2 - Fine movement positioning control device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a fine positioning control device for positioning a positioning object at a predetermined position in a predetermined posture, and in particular, to eliminate the influence of the natural vibration mode of the positioning object and to control the position of another positioning axis. Eliminate the interference between
The present invention relates to a fine-movement positioning control device capable of suppressing the influence of the interference and independently setting control characteristics for each axis.

[0002]

2. Description of the Related Art In recent years, positioning accuracy in the submicron order has been required for positioning in fields such as precision machining, assembly, and adjustment. In particular, in an ultra-precision positioning stage for the purpose of exposing a fine pattern, a linear motor is used as an actuator in order to realize a high driving resolution and a wide frequency response.

FIG. 17 shows a conventional fine-movement positioning apparatus for controlling the positioning of a total of three degrees of freedom, that is, two degrees of freedom in a vertical z-straight direction and a rotational direction about the x and y axes. In the figure, reference numeral 1 denotes a flat plate-shaped substrate to be positioned, which has spring elements 2a, 2b, 2
c elastically supported. Reference numerals 3a, 3b, and 3c denote actuators for generating forces in the vertical direction, and power amplifiers 4-1 to 4-3 for driving the actuators in accordance with commands 4a, 4b, and 4c to the actuators are provided. Position sensors 5a, 5b, and 5c for measuring the displacement of the substrate 1 in the vertical direction are provided near the actuator, and the outputs of the sensors are output from electrical signals 6a, 6b, and 6c by displacement amplifiers 6-1 to 6-3.
Is converted to These will be referred to as a fine movement positioning mechanism. Also, z ₁ axis output mechanism from the command of the actuator 4a to displacement signal 6a of the position sensor, as well as z ₂ axis between 4b-6b, the inter 4c-6c is referred to as z ₃ axes.

[0004] Now, the instruction 4a is added to z ₁ axis. Response of this time the positioning mechanism not only the position sensor 5a of z ₁ axis appears as a displacement in z ₂ axis and z ₃ axes. Similarly, if you make inputs to the z ₂ axis or z ₃ axis appears in response to all axes. That is, there is interference with other axes. This will be described with reference to a Bode diagram.
20 to FIG. Z _ij in the figure indicates the response of the z _i axis when the z _j axis is input. Figure 18 shows the response of z ₁ to z ₃ each axis with respect to the input of the z ₁ axis. In z ₁ axis output (z ₁₁₎ is observed two peaks. These two peaks are vibration modes in the z and ω _x directions. Also there is a peak at about the same height in the z ₂ and z ₃ axis response (z _21, z _31), it can be seen that there is a dynamic interference in the two frequency ranges. In FIGS. 19 and 20, z and ω
A vibration mode of ω _y is recognized between vibration modes of _x ,
Interference exists in the frequency range of the mode of z, ω _x , ω _y . In addition, the difference between the diagonal term and the off-diagonal term of the gain in the low frequency range (for example, the difference between z ₁₁ and z ₂₁ and z ₁₁
The difference) is small in z _31, it can be seen that the interference is present in static.

Conventionally, as shown in FIG. 17, a control system for each axis is independently configured for such a system. A command signal v ₁ to v ₃ of the displacement signals 6a~6c and each axis of each axis are compared by the deviation amplifier 13 a to 13 c, the deviation signal e for each axis
_{1 to} e ₃ are generated. The input signal u ₁ ~u ₃ to each axis generated by the compensator 12a~12c provided for each axis deviation signal based. The input signals u _{1 to} u ₃ are sent to power amplifiers 4-1 to 4-3 and are sent to actuators 3a to 3c.
Is driven.

FIGS. 21 to 23 are Bode diagrams of the closed loop of the control system in the conventional example of FIG. Z _ijc in the figure is a displacement signal (6a) of the z _i axis from the command signal v _j to the z _j axis.
6c). Z ₁ is the response to each axis from the axis input non diagonal terms (z _21c, z _31c) in FIG. 21 the gain of which is smaller than the diagonal terms z _11c, interference is suppressed by the control system . In contrast, we've almost match the frequency range where there is gain and z ₃ axis z ₂ axis in FIG. 22 and FIG. 23. When control is actually performed in such a system, oscillation may occur due to a slight disturbance.

In the conventional example shown in FIG. 17, when the control system is configured independently for each axis as described above, if the interference between the axes is large, the desired positioning accuracy cannot be achieved when all the axes are simultaneously controlled. In addition, there is a problem that oscillation may occur.

[0008]

SUMMARY OF THE INVENTION The present invention has been made in view of the above-mentioned problems in the prior art, and eliminates the influence of the natural vibration mode of the positioning object and eliminates the interference with other axes. It is an object of the present invention to provide a fine movement positioning control device that eliminates or suppresses the influence of interference and enables control characteristics to be set independently for each axis.

[0009]

[0010]

Means for Solving the Problems] fine positioning control device of the present onset bright order to solve the above problems, a linear motion direction one axis
And said first orthogonal to the axis to and positioned object is <br/> elastically supported movement available-a total of three axial directions of the respective rotation about motion direction biaxial rectilinear direction two axes perpendicular to each other, the positioning Object
At least three actuators for driving the at least three position sensors for measuring the movement distance of the object to be positioned, wherein a displacement amplifier for converting an output of the position sensors in the displacement signal, respectively the displacement signal A deviation amplifier that outputs a deviation signal in comparison with a command signal corresponding to the displacement signal, a compensator that independently compensates for each output of the deviation amplifier, and a low-frequency gain for the output of the compensator. a correction device for generating a command input by correcting matrix of the inverse matrix of, you <br/>, comprising a power amplifier for driving the actuator by the command input.

[0011]

[0012]

[Action] In the control system configuration of the above SL, correction device suppresses static interference, dynamic interference that can not be suppressed by the correction device is suppressed by the compensator provided for each axis.

[0013]

DESCRIPTION OF THE PREFERRED EMBODIMENTS In general, an elastic support is provided so as to be movable in a total of three axial directions, one axial direction of linear motion and two axial directions of rotation about each of two other linear axes orthogonal to the axis. The positioned object to be positioned is modeled as shown in FIG. The coordinates of the center of gravity of the positioning target are x _G and y _G , the position coordinates of each spring element are x _i and y _i (i = 1, 2, 3), and the rigidity value is k _i
(I = 1, 2, 3). The position coordinates of the three actuators are x _ai , y _ai (i = 1, 2, 3), and the generated force is u _i (i = 1, 2, 3). The mass of the positioning target is m, the moment of inertia around the x axis is I _x , and the moment of inertia around the y axis is I _y . The equations of motion in the z, ω _x , and ω _y directions of this system are given assuming that the damping term is 0.

[0014]

(Equation 1) Becomes Where equation (1) is

[0015]

(Equation 2) It is expressed as Adding the attenuation term to equation (2)

[0016]

(Equation 3) Becomes Regardless of the value of C, its generality will not be lost in the following discussion, so that the details are omitted.

[0017]

(Equation 4) It is. The size of A is 6 × 6, and the size of B is 6 × 3.

The position coordinates of the sensor are represented by x _si , y _si (i = 1,
2,3), assuming that the measured value in the z direction is z _i (i = 1, 2, 3), the measured value vector Y = [z ₁ z ₂ z ₃ ] ^T is obtained by using x in the equation (4).

[0019]

(Equation 5) Becomes By combining equations (4) and (5), a state space expression from the input u of each actuator to the output of each sensor

[0020]

(Equation 6) Get.

The necessary and sufficient condition that the equation (6) is controllable is

[0022]

(Equation 7) It is. From equations (4) and (5)

[0023]

(Equation 8) If the rank of the matrix F is 3, the rank of the equation (8) becomes 6, and the equation (6) becomes controllable. The fact that the matrix F has the full rank 3 means that, when physically interpreted, the actuators do not exist on the same straight line. That is, the arrangement of the actuators may form a triangle.

The necessary and sufficient condition that the equation (6) is observable is

[0025]

(Equation 9) It is. From equations (4) and (5)

[0026]

(Equation 10) If the matrix S has the full rank 3, the rank of the equation (10) is 6, which is observable. The physical interpretation at this time is that the sensors do not exist on the same straight line. That is, the arrangement of the sensors may form a triangle. Hereinafter, description will be made assuming that the expression (6) is controllable and observable, that is, both the matrices F and S are regular.

In general, if controllable, the regular transformation matrix Q
Can be converted into a controllable canonical form as shown below.

[0028]

[Equation 11] According to the procedure for obtaining the regular transformation matrix Q, the equation (6) is transformed into a controllable canonical form. First, the controllable matrix [B AB ···
・ A ^n-1 B], the independent vectors are sequentially numbered n from the left.
(= 6) Take out the book. Since the rank of [B AB] is 6, six lines can be obtained so far.

[0029]

(Equation 12) Arrange as follows. At this time, [d ₁ d ₂ d ₃ ] = [2
22] is called the controllable index. The shape of L is from equation (4)

[0030]

(Equation 13) Becomes Next, L ^-1 is obtained, and two lines, two lines,
Divide into three blocks of two lines, and the bottom line of each block is q
₁ , q ₂ and q ₃ . At this time, from equation (13)

[0031]

[Equation 14] Becomes The transformation matrix Q is

[0032]

(Equation 15) Becomes From this Q, the controllable canonical form of equation (11) is obtained, and each form is

[0033]

(Equation 16) Using these, the transfer matrix expression T (s) = C in equation (6)
(SI-A) ^-1 B is represented as follows.

[0034]

[Equation 17] It turns out that it becomes. B _m is a unit matrix. Therefore, equation (16) is equivalent to the following equation.

[0035]

(Equation 18) Equation (18) is an irreducible decomposition expression T (s) = R (s) P ^-1 (s). Ie

[0036]

[Equation 19] However, the diagonal term of P (s) is a second-order monic polynomial, and the off-diagonal term is a first-order or lower polynomial (monic means that the highest order coefficient is 1).

Since equation (6) is controllable, poles can be arbitrarily arranged by state feedback. Also,

[0038]

(Equation 20) Since the equation (20) is regular, an inverse matrix exists.

Consider the following feedback control law.

[0040]

(Equation 21) Specify the closed-loop characteristic polynomial p _f (s)

[0041]

(Equation 22)

[0042]

(Equation 23)

[0043]

(Equation 24) And Also,

[0044]

(Equation 25) Then the transfer matrix of the closed-loop system is

[0045]

(Equation 26) It can be seen that the closed loop system is made diagonal, that is, decoupling.

Therefore, if the state feedback control law (20) is configured so as to satisfy the expressions (22) and (23), the dynamic characteristics of the positioning target can be made desired, and further, from other axes. And good positioning control is achieved.

[0047]

Embodiments and Reference Examples Hereinafter, embodiments and reference examples of the present invention will be described with reference to the drawings. First, the present invention will be described.
A reference example serving as a premise for this will be described. [ First Embodiment] FIG. 1 shows a wafer stage z-tilt mechanism control system of a semiconductor exposure apparatus employing a fine movement positioning control device according to a first embodiment of the present invention. A wafer chuck (not shown) is mounted on the substrate 1, which is a positioning object.
The substrate 1 is supported by a radial static pressure bearing 2 on an x stage 9 that can move in the x direction on a Y stage (not shown). With this radial static pressure bearing, the substrate 1 is made of x and y
It is rigidly supported in the axial direction and moves freely in the z direction.
Further, the substrate 1 can move in the ω _x and ω _y directions, which are rotations around the x-axis and the y-axis, by the gap between the static pressure bearings. 3a ~
Reference numeral 3c denotes a linear motor, which generates a force between the x-stage 9 and the substrate 1 by an output from the power amplifier 4. An air spring (not shown) is provided in the linear motors 3a to 3c to compensate for the gravity of the substrate 1. With this gravity compensation mechanism, the substrate 1 is located at the equilibrium point even when the linear motor is not generating a force. If the gravity compensation mechanism is not used, the linear motor must always support the weight of the substrate 1, requiring a large current and increasing the heat generation, which is not preferable. The substrate 1 is elastically supported on the x stage 9 by the radial static pressure bearing 2 and the air spring. Reference numerals 5a to 5c denote displacement sensors using linear encoders, and relative displacements 6a to 6c of the x stage 9 and the substrate 1 in the z direction are obtained by the displacement amplifier 6. 7a to 7c are acceleration sensors from which acceleration signals 8a to 8c are obtained by the accelerometer amplifier 8. Z ₁ axis between input 4a and output 6a, z ₂ axis between 4b-6b and 4c-6c, z
I will call it _three axes. To construct a state feedback control system for this system, a control model in which the characteristics of the system are quantified is required. A spring-mass model is created for an elastically supported structure such as this system, and a mass matrix M, a stiffness matrix K, and a damping matrix C in equation (3) are obtained. A good way is to find a spatial representation. The mass matrix M can be obtained almost accurately by calculation or measurement by design. The stiffness matrix K can be obtained as a theoretical value from the design stiffness value of the spring and the arrangement of the springs, but includes a large number of error factors. For the attenuation, it is easy to input the modal attenuation rate of each motion mode. The input B and the output matrix C of the equation (6) are determined from the thrust constant of the linear motor, the constant of the power amplifier, the geometric arrangement, the characteristics of the linear encoder, the constant of the displacement amplifier, and the geometric arrangement. From now on, the nominal value of the control model [A,
B, C]. As described above, this nominal value is model narrowing combined in the (identification) of the row of cormorants required by experimental values because it contains errors. There are many methods for this, and it is common to measure and identify a time axis response such as a frequency response or a step response. In this system, identification is performed by adjusting the rigidity value and arrangement of the spring. A control system is designed based on the control model (6) thus created. As described above, if the arrangement of the actuator and the position sensor form a triangle, it is controllable and observable. Therefore, a regular transformation matrix Q is obtained, and is transformed into a controllable canonical form (11). From equation (16), the irreducible decomposition expression of the transfer matrix T (s) = R
(S) P ^-1 (s) is determined. The characteristic polynomial of the closed loop to be specified is determined as in equation (22), and (23), (2)
4) The feedback matrix _Fb is obtained by the equation (4). The specified closed loop is determined in consideration of the following characteristic, the attenuation characteristic, and the steady characteristic. In FIG. 1, reference numeral 10 denotes a state quantity extractor, z ₁
And outputs a state quantity signal 10a~10f consisting position and velocity section of each of the to z ₃ axes. Specifically a position signal z ₁ to z ₃ axes 6a~6c filter outputs with no acceleration signal 8a~8c outputs performed once integration. 11
Consists of is a feedback matrix F _b feedback circuit. The compensator 12 calculates the gain matrix G satisfying the expression (25).
Consists of G is such that when the low-frequency gain of the closed-loop transfer matrix equation (26) is a unit matrix, the steady-state position error becomes 0 and follows the position command reference input v of equation (21) without deviation.

[0048] [Reference Example 2] Using the acceleration sensor to determine the speed terms of Reference Example 1, the state quantity. However, obtaining a state quantity including a position and a speed is not limited to this method. Since the relationship among the position, velocity, and acceleration is time differentiation and time integration, if one of them can be detected, the state quantity, that is, the position and velocity, can be obtained. Also, from the viewpoint of cost, it is preferable that the number of sensors used is small. The reference example 2 uses only a position sensor as a sensor. Even though the speed is a time derivative of the position, it is not preferable to actually differentiate the position information. Derivatives, by definition, use future values and are not feasible in practice. Even if the backward difference is used in a simulated manner, the effect of observation noise increases,
The value is not reliable. Therefore, state feedback is performed using a state observer (observer). Further, the state quantity to be estimated does not necessarily have to be the physical quantity of the position and the speed, but may be any equivalent to the physical quantity in the control system. The control system may be configured in a model obtained by equivalently converting the control model (6). That is, the state quantity x
Is fed back. Here, a control system design method in the frequency domain using a low-dimensional observer is used.

From the control model (6), an irreducible decomposition expression T (s) = R (s) P of the transfer matrix in the same manner as in Reference Example 1.
^-1 (s) is obtained. The observable index determined when obtaining the observable canonical form of equation (6) is [2 2 2] in the same manner as when obtaining the controllable index. Furthermore, this maximum value 2
Is referred to as an observable index ν. Now, let q (s) be a ν-1 order monic stable polynomial and Q (s)

[0050]

[Equation 27] And The physical meaning of the zero of det Q (s) is the pole of the low-dimensional observer. The following polynomial matrix equation using P _F (s) that satisfies equation (22)

[0051]

[Equation 28] , A 3 × 3 polynomial matrix solution K (s) having a row order of at most ν-2 and a 3 × 3 polynomial matrix solution H (s) having a row order of at most ν-1 are obtained. The next control law using these

[0052]

(Equation 29) Is used. At this time, from equation (28)

[0053]

[Equation 30] On the other hand, from equation (29)

[0054]

(Equation 31) From equations (30) and (31)

[0055]

(Equation 32) Becomes Since Q (s) is stable and P _F (s) is diagonal, if G is given by equation (25), the closed-loop transfer matrix becomes equation (26) from equation (19). Figure 2 shows a block diagram of Reference Example 2. Portions surrounded by dotted lines in the figure correspond to the state quantity extraction circuit and the feedback circuit.

[0056] As described above, at the same time the dynamic characteristic of the positioning mechanism be constructed of a control system of Reference Example 1 and Reference <br/> Example 2 can be the desired one, completely eliminating the interference between the axes And good positioning control is achieved.

[ Embodiment 1] FIG. 4 shows a wafer stage z-tilt mechanism control system of a semiconductor exposure apparatus employing a fine movement positioning control apparatus according to an embodiment of the present invention. A wafer chuck (not shown) is mounted on the substrate 1, which is an object to be positioned.
The substrate 1 is supported by a radial static pressure bearing 2 on an x stage 9 that can move in the x direction on a Y stage (not shown). With this radial static pressure bearing, the substrate 1 is made of x and y
It is rigidly supported in the direction and can move freely in the z direction.
Further, the substrate 1 can move in the ω _x and ω _y directions, which are rotations around the x-axis and the y-axis, by the gap between the static pressure bearings. 3a ~
Reference numeral 3c denotes a linear motor, which generates a force between the x stage 9 and the substrate 1 based on outputs from the power amplifiers 4-1 to 4-3. An air spring (not shown) is provided in the linear motors 3a to 3c to compensate for the gravity of the substrate 1. With this gravity compensation mechanism, the substrate 1 is located at the equilibrium point even when the linear motor is not generating a force. If the gravity compensation mechanism is not used, the linear motor must always support the weight of the substrate 1, requiring a large current and increasing the heat generation, which is not preferable. The substrate 1 is a radial hydrostatic bearing 2
And the air spring elastically supports the x stage 9. Reference numerals 5a to 5c denote displacement sensors using linear encoders, and relative displacements 6a to 6c in the z direction of the x stage 9 and the substrate 1 are obtained by displacement amplifiers 6-1 to 6-3. Input 4a- outputs 6a between the z ₁ axis, similarly 4b-6
b, and between 4c-6c it will be referred to as a z ₂ axis, z ₃ axes. This structure can be represented by a spring mass model having one mass element and three spring elements as shown in FIG. The substrate 1 is positioned the object as a mass element and the center of gravity coordinates x _G, and y _G. The position coordinates of each spring element are defined as x _i , y _i (i = 1, 2,
3), and the stiffness value is k _i (i = 1, 2, 3). The position coordinates of the linear motors 3a to 3c of the actuator are x _ai ,
y _ai (i = 1,2,3), the force generated u _{i (i} = 1,
2, 3). The mass of the object to be positioned m, the moment of inertia about the x-axis and I _y. Z, ω _x , ω _{y of} this system
Assuming that the damping term is 0 in the equation of motion in the direction, the above (1) to
Equation (4) is obtained. In the equation (4), the size of A is 6 × 6, and the size of B is 6 × 3. K is positive definite unless all of the spring constants are 0, and is also regular since it is also a Hermitian matrix. Here, it is assumed that the spring constant is non-zero, that is, K is regular.

[0058] Linear encoders 5a to 5
Assuming that the position coordinate of 5c is x _si , y _si (i = 1, 2, 3) and the measured value in the z direction is z _i (i = 1, 2, 3), the measured value vector Y = [z ₁ z ₂ z ₃ ] ^T is expressed by equation (5) using x in equation (4). By combining equations (4) and (5), a state space expression from the input u of each actuator to the output of each sensor

[0059]

[Equation 33] Get. The mass matrix M can be obtained almost exactly from design calculated values and experimental values. The matrices F and S can be accurately obtained from the information on the characteristics and positions of the actuator and the sensor. The stiffness matrix K and the damping matrix C can be obtained from design values. From these values, the nominal value [A, B, C] of the control model can be calculated. However, since the stiffness matrix and the damping matrix obtained from the design values contain many errors, the control models [A, B,
C] must be matched (identified). There are many methods for this, and identification is generally performed from the frequency response or the time axis response. Now, if equation (33) is expressed as a transfer matrix,

[0060]

(Equation 34) Becomes The low frequency gain G ₀ can be obtained by setting s to 0.

[0061]

(Equation 35) It is. Here, the existence of the inverse matrix of the matrix A is considered. Since A is expressed by equation (4),

[0062]

[Equation 36] Since K is assumed to be regular, A ^{-1 in the} equation (36) exists. Expression (35) is obtained by using expression (36).

[0063]

(37) Becomes Next, consider the regularity of the matrices F and S. Matrix F
Is regular from Equation (1) unless the actuators are arranged on the same straight line. Similarly, the matrix S is regular if the arrangement of the sensors is not on the same straight line from the equation (5). These conditions are also the necessary and sufficient conditions for controllability and observability of the equation (6). Here, it is assumed that the matrices F and S are both regular. At this time, equation (37) becomes regular and the inverse matrix

[0064]

(38) Exists. The correction system shown in FIG. 5 is created using the correction device 14 expressed by the equation (38). The Bode diagrams of the open loop of this correction system are as shown in FIGS. 6 to 8 (the characteristics before correction are the same as those shown in FIGS. 18 to 20). 6 z ₁ axis input, 7 z ₂ axis input, 8 upon input of z ₃ axis shows the response of each axis.

Referring to FIGS. 6 to 8, since the correction system aims at decoupling in the low frequency range, the gain of the non-diagonal term is lowered in the low frequency range. However, z, ω
_x, dynamic interference of the mode of ω _y is not achieved. Also, z
_2-axis, interference between z ₃ axes effect is obtained that the difference in the gain is greater at higher frequency range than the dynamic interference mode. This is z
Between the _two axes, z ₃ axes, the relationship between the gain and phase in the high frequency range is due to be nearly the same as the low frequency range. That is,
With the correction device using the equation (38), it is possible to suppress the interference in a region other than the limited frequency region of the dynamic interference. For this correction system, a control system having a compensator provided for each axis as shown in FIG. 4 is configured. Deviation amplifier 13a ~
Deviation signal e ₁ to e ₃ for each axis are compared with the command signal v ₁ to v ₃ of the displacement signals 6a~6c and each axis of each axis is generated by 13c. A compensator 1 provided on each axis based on the deviation signal
Input signals u _{1 to} u ₃ to each axis are generated by 2a to 12c. The input signal u ₁ ~u ₃ is corrected input signal u _c1 ~u _c3 becomes the correction device 14, the linear motor is an actuator is transmitted to the power amplifier 4-1 to 4-3 are driven.
The Bode diagrams of the closed loop from the command signal to the displacement signal at this time are as shown in FIGS. During the z ₂ axis and z ₃ axes,
Z _23c and z _33c in z _22c and z _{32 c} and 11 in FIG. 10
It can be seen that interference is suppressed since the gain diagrams of FIG. Figure 9, z _11c and z _21c and z _{31 c}
Although the gain diagram is quite close, it is not a problematic level. As described above, when the control system according to the present embodiment is configured, interference between the axes is suppressed, and excellent positioning control is achieved.

[0066] was performed correction for all axes of Example 2 In Example 1, z ₁ to z _3. However, there are cases where the effect is small as shown in FIG.
This is because originally had less interference with the z ₁ axis and z ₂ axis and z ₃ axes. Therefore, corrects only for strong inter-z ₂ axis -z _3-axis interference. FIG. 12 shows the second embodiment, and FIG. 13 shows the concept of the correction system in the second embodiment. The correction device 14 is constituted by an inverse matrix of the low frequency gains of the z ₂ axis and the z ₃ axis (the second and third rows and the second and third columns of G _{0 in} the equation (35) are extracted). . Input signals u ₁ generated by the compensator 12a is applied directly to the power amplifier 4-1 without going through a correction device 14. Compensator 12b,
Input signal u ₂ generated by 14c, u ₃ is the correction device 14 through to the correction input signal u _c2, u _c3 next power amplifier 4-2,4
Applied to -3. The Bode diagram of the closed loop at this time is shown in FIG.
4 to 16, it can be seen that the gain of the off-diagonal term is greatly reduced and interference is suppressed. in this way,
The correction device of the present embodiment is not performed for all axes,
The present invention may be applied only between axes having strong interference.

According to the control system configuration of the first or second embodiment,
Good positioning control is achieved because static interference can be suppressed by a simple configuration of a correction device consisting of an inverse matrix of low-frequency gain, and dynamic interference can be suppressed by a compensator provided for each axis. Is done.

[0068]

[0069]

As described in the foregoing, according to the control system configuration of the present invention, it is possible to suppress the static interference by a simple structure only provided a correction device consisting of a inverse matrix of the low-frequency gain,
Since dynamic interference can be suppressed by the compensator provided for each axis, good positioning control is achieved.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration of a z-tilt fine movement positioning control system according to a first reference example of the present invention.

FIG. 2 is a block diagram of a control system according to a second reference example of the present invention.

FIG. 3 is a diagram showing a dynamic model of a positioning mechanism in the block diagram of FIG. 1;

FIG. 4 is a block diagram showing a configuration of a z-tilt fine movement positioning control system according to the first example of the present invention.

FIG. 5 is a block diagram showing the concept of a correction system in the first embodiment.

FIG. 6 is a Bode diagram of an open loop of the correction system in the first embodiment.

FIG. 7 is a Bode diagram of an open loop of the correction system in the first embodiment.

FIG. 8 is a Bode diagram of an open loop of the correction system in the first embodiment.

FIG. 9 is a Bode diagram of a control system closed loop in the first embodiment.

FIG. 10 is a Bode diagram of a control system closed loop in the first embodiment.

FIG. 11 is a Bode diagram of a control system closed loop in the first embodiment.

FIG. 12 is a block diagram illustrating a configuration of a z-tilt fine movement positioning control system according to a second embodiment of the present invention.

FIG. 13 is a block diagram showing the concept of a correction system in the second embodiment.

FIG. 14 is a Bode diagram of a control system closed loop in the second embodiment.

FIG. 15 is a Bode diagram of a control system closed loop in the second embodiment.

FIG. 16 is a Bode diagram of a control system closed loop in the second embodiment.

FIG. 17 is a block diagram showing a configuration of a conventional positioning control system.

FIG. 18 is a Bode diagram of an open loop of the fine movement positioning mechanism of FIG. 17;

FIG. 19 is a Bode diagram of an open loop of the fine positioning mechanism of FIG. 17;

20 is a Bode diagram of an open loop of the fine movement positioning mechanism of FIG. 17;

FIG. 21 is a Bode diagram of a closed loop of the positioning control system of FIG. 17;

FIG. 22 is a Bode diagram of a closed loop of the positioning control system of FIG. 17;

FIG. 23 is a Bode diagram of a closed loop of the positioning control system of FIG. 17;

[Explanation of symbols]

1: substrate, 2: radial static pressure bearing, 3a to 3c: linear motor, 4, 4-1 to 4-3: power amplifier, 5a to 5c: displacement sensor, 6, 6-1 to 6-3: displacement amplifier , 7a-7c:
Acceleration sensor, 8: accelerometer amplifier, 9: x stage,
10: state quantity extractor, 10a to 10f: state quantity signal, 1
1: feedback circuit, 12, 12a to 12c: compensator, 13a to 13c: deviation amplifier, 14: correction device.

Continuation of the front page (58) Field surveyed (Int. Cl. ⁷ , DB name) G05D 3/00-3/20 G05B 11/00-13/04 H01L 21/68

Claims (2)

(57) [Claims] 1. A position which is elastically supported so as to be movable in a total of three axial directions of one linear movement direction and two rotational movement directions about two linear movement directions orthogonal to each other and orthogonal to each other. An object; at least three actuators for driving the positioning object; and at least three actuators for measuring a moving distance of the positioning object
Position sensors, a displacement amplifier that converts an output of each of the position sensors into a displacement signal, a deviation amplifier that compares the electric displacement signal with a command signal corresponding to each displacement signal and outputs a deviation signal, A compensator that independently compensates for each output of the deviation amplifier; a correction device that multiplies the output of the compensator by a correction matrix composed of an inverse matrix of a low-frequency gain to generate a command input; Power to drive the actuator by input
Fine positioning control device, characterized in that it comprises a the amplifier. 2. The correction device according to claim 1, wherein only the axis having strong interference is provided.
And compensating the output of the compensator.
Dynamic positioning control device.