JP3267314B2 - Positioning control method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a positioning control method using a rolling guide mechanism, and more particularly to a positioning control method used in a semiconductor manufacturing apparatus, an ultra-precision processing apparatus, an ultra-precision measuring apparatus, etc., which require an accuracy of a nanometer unit. About the method.

[0002]

2. Description of the Related Art Conventionally, a positioning control method using a rolling guide mechanism does not consider minute deformation of a rolling guide portion. The displacement of the guide mechanism is several tens of nm
A region I which shows a linear spring characteristic below, a region II which shows a non-linear spring characteristic having a hysteresis of 400 nm or more and 100 μm or less, and a normal rolling characteristic which is moved by a driving force exceeding the saturation frictional force above 100 μm. Indicate area
III, and the high-precision positioning control method includes a coarse positioning control in the region III and a region I,
It was proposed to separately control the fine positioning control in II.

[0003]

The above-described positioning control method according to the prior art is characterized in that the positioning is performed from the region III where the coarse positioning including the rolling is performed to the region I where the displacement of 100 μm or less is performed only by the spring characteristic without the rolling. It takes time to stop the table on which the object is placed, and the external force must be less than several tens of grams to keep the table in the region I. There is a drawback that the spring constant cannot be held and the spring constant must be checked in advance.

SUMMARY OF THE INVENTION It is an object of the present invention to reduce the time for stopping a table from a region III to a region I, to maintain the positioning in the region I even in a system to which a large external force is applied, and to estimate a spring constant. Is to provide a way.

[0005]

According to the positioning control method of the present invention, after the rolling guide table is stopped at a position beyond the target position by the coarse movement positioning, the process is shifted to the fine movement positioning, and the table is stepped at least twice. To the target position, and for each subsequent fine movement of the fine movement positioning, set the spring force of the table from the driving force at each of the two fine movements and the data of the position at that time, The driving force is corrected.

The above control is performed by the following steps.
You . (1) a first step of performing a coarse positioning control to move the table by adding a driving force f ₀ from the positioning starting point x ₀ to the first position x ₁ to slightly beyond the final target position x _r, (2) the table from a first position x _1, the first position x ₁ and the final target position a second position intermediate the x _r x ₂
The first fine movement positioning control in the area II is performed in which the driving force f ₁ = f ₀ −Δf is obtained by subtracting the minute force Δf from the driving force f ₀ at the time of coarse movement positioning, and the position x at this time is second measuring the driving force f ₂ at the moment became x ≧ x ₂
Steps and, (3) the table from the second position x _2, the third position x ₃ intermediate the second position x ₂ and the final target position x _r
A third step of performing a second fine movement positioning control for moving with the driving force f ₁ , and measuring the driving force f ₃ at the moment when the position x at this time becomes x ≧ x ₃ ; (4) ) to the table from the third position x _3, the fourth position x ₄ intermediate the third position x ₃ of the final target position x _r
, K _S4 = (f ₂ −f ₃ ) / (x ₂ −x ₃ ) is a linearized spring constant, and a driving force f = f ₁ + K _S4 * (x ₄₎ when x ₄ <x <x ₃ is satisfied. A fourth step of performing a third fine movement positioning control for moving at -x), and measuring a driving force f ₄ at the moment when the position x at this time becomes x ≧ x ₄ ; (5) Further, the table from position x _n-1 of the n-1, the position x _n-1 and the intermediate position first n of the final target position x _r
To the position _xn , K _Sn = (f _n−2 −f _n−1 ) / (x _n−2 −x _n−1 ) where x _n <x <x _n−1 and f _M to 1
A driving force f = f _M + K _Sn * (x _n −x) when the driving force is the driving force before the moving sample period is set, and the n-th fine positioning is performed, and the position x at this time becomes x ≧ x _n sequentially through the steps of the n measuring the driving force f _n of the moment it became, lapping near to the final target position x _r.

Further, in the near lapping positioning method to the final target position x _r through said n steps, linearization spring constant _{K Sn = (f 3 -f 2} ) / be fixed with (x ₂ -x ₃₎ Also, the driving force f in the fourth and fifth steps is f = f _M + K _Sn * (x _r −x where v is the speed of the table of the rolling guide and K _V is the gain of the speed feedback. ) −K _V * v.

After coarse positioning, high-precision positioning can be performed by switching to reciprocating movement of fine displacement by fine positioning in the area II near the target position and gradually moving to fine positioning in the area I by the gradual spring characteristic. Alternatively, a spring constant may be obtained from the driving force during the reciprocating movement of the minute displacement and the vibration of the displacement, and the minute displacement may be performed by adding an optimal driving force to the spring constant.

After entering the region II of the minute displacement, the driving force of the second stage is applied to the displacement generated by the driving force of the first stage by using the driving force of the two stages. It is also possible to control to stop.

[0010]

[Function] In the coarse movement positioning, the control for temporarily stopping slightly beyond the target position and then performing the fine movement positioning of the table in a stepwise manner toward the target position is performed in an area II in which the rolling displacement is proportional to the force. Therefore, the time can be reduced as compared with the case where the positioning is repeated in the region III, and the range of the force is orders of magnitude larger than that in the region I. Therefore, the positioning can be performed even in a system where a large external force is applied. After that, fine movement positioning in the region I can be performed.

[0011]

Next, embodiments of the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram of a main part of an apparatus for executing a first embodiment of a positioning control method according to the present invention, FIG. 2 is a flowchart of the positioning control method, and FIG. 3 shows characteristics of a rolling friction force. FIGS. 4 and 5 are explanatory diagrams showing the relationship between the driving force and the frictional force for the coarse movement positioning of the rolling guide mechanism, FIG. 5 is a diagram showing the relationship between the frictional force and the displacement in the positioning control of FIG. 1, and FIG. FIG. 4 is a diagram illustrating a relationship between a positioning driving force and a displacement.

The main parts related to the positioning control of this device are a command generator 1, a position control controller 2, a force control controller 3, a switch 4, a power amplifier 5, a motor fixing part 6, a motor movable part. 7, a movable table 8,
It has a position detector 9. The command generator 1 issues a position command for the movable table 8. The position controller 2 controls coarse positioning. The force control controller 3 controls fine movement positioning. The switch 4 switches between coarse positioning and fine positioning. The power amplifier 5 amplifies the control current from the position control controller 2 and the force control controller 3 and outputs the amplified control current as the operating current of the motor fixing unit 6. The motor fixing unit 6 is a fixed field coil of a linear motor, and the motor movable unit 7 moves by a change in the current of the motor fixing unit 6. The movable table 8 is a table on which the positioning target is placed. Position detector 9
Detects the position of the movable table 9 and continuously outputs the detection result to the position controller 2 and the force controller 3.

[0014] The rolling friction force in the rolling guide mechanism is:
Usually, it is considered that the characteristics are as shown in FIG. 3, and the dynamic model of the movable table shown in FIG. 1 is approximated to a simple mass system as shown in FIG. Here, x represents a position, f represents a driving force, F represents a frictional force, Fs represents a saturated frictional force, M represents a mass of a table, v represents a speed, r represents a target position, and K _P and K _V. Where f = K _P * (r−x) −K _V * v (1), and a stable position control can be performed by feeding back the position x and the velocity v. Here, the speed v can be directly measured by a speed detector or calculated from a position signal.

However, when the properties of the rolling guide are examined in detail, as described in detail in JP-A-3-73007,
It is known that the displacement is dependent on the driving force in a fine displacement region (for example, a paper, Koizumi et al .: Research on Rolling Friction-Behavior of Rolling Displacement-, "Lubrication", Vol. 27, No. 9, 690/696 (1982)). FIG. 5 shows such a property in a simplified manner, and shows the relationship between the displacement and the frictional force, with the position at the equilibrium in the absence of the driving force and the external force being the origin. Initially, the frictional force F monotonically increases with respect to the displacement and saturates with the steady frictional force Fs. X in the saturated state
After moving to ₁ , returning to the opposite direction in the region II, the elastic deformation that occurred first is released, and hysteresis occurs as shown in FIG. 5, and the frictional force decreases. In the region I where the frictional force depends on the displacement, the displacement and the frictional force are localized, and the same characteristics can be obtained regardless of whether the input is a displacement or a driving force (= frictional force). The present invention provides a control method for performing positioning in the vicinity of a considerably large frictional force, which is about half the saturation frictional force Fs, instead of the frictional force being near zero.

Next, the control method of this embodiment will be described with reference to FIG.
This will be described with reference to the flowchart of FIG.

The switch 4 selects the position controller at the start of the positioning control, and switches to the force controller at the end.

The symbols used in the following description have the following meanings.

X ₀ : Positioning start position x ₀ , x ₁ , x ₂ , x ₃ : Position x _r : Positioning target position f: Driving force f ₀ , f ₁ , f ₂ , f ₃ : Each position x ₀ , Driving force at x ₁ , x ₂ , x ₃ K _S : Linearized spring constant T _S : Sample period of control Normal positioning control is performed from start point x ₀ to x ₁ . At this time, the motor driving force is generated as shown in equation (1) (step 51). Here, x ₁ = x ₀ + δ ₁ (2). [delta] ₁ is a small displacement with.

[0020] After completing the positioning of the step 51 (decision of the positioning in this control may be much more gradual than conventional), from the position x ₁ to x _2, each control sampling period, the driving force as follows Control.

For the current position x, it is determined that x ₂ <x <x ₁ (3) (step 52). When this condition is satisfied, f ₁ = f ₀ −Δf (4) is set (step 53). Here, f _M is the driving force one sample cycle before, and Δf is a certain minute force.

When the driving force is reduced, the position x returns and decreases according to the characteristics shown in FIG.

The driving force at the position x = x _{2 at} the moment when the condition (3) is not satisfied is set to f _2, and the process proceeds to the next step (step 52).

For the current position x, it is determined that x ₃ <x <x ₂ (5) (step 54). Here, x ₂ = x ₁ −δ ₂ (6) where δ ₂ is a minute displacement.

When this condition is satisfied, the driving force is reduced as represented by equation (4) (step 55). The condition (5) at the moment becomes the position x = x ₂ that is no longer satisfied driving force and f _3, and the process proceeds to the next step (Step 54).

Using the data thus far, an approximate linearized spring constant K _S4 is calculated by K _S4 = (f ₂ −f ₃ ) / (x ₂ −x ₃ ) (7) (step 56).

At each sample period, the driving force f is given by f = f_M + K_Sn * (X₁ −x) (8) (Step 57). Repeat this step
And finally the target position x _r Is positioned.

It should be noted that K _Sn is not fixed as described above, and the data of the previous and previous times, f _n−1 , f _n−2 , x _n−1 , x
K _Sn may be determined using _n-2 .

In some cases, it is effective to add speed feedback to enhance the stability of positioning control. In this case, f = f _M + K _Sn * (x _r −x) −K _V * v (9) Here, K _V is the gain of the speed feedback.

FIG. 7 is a block diagram of a main part relating to positioning control of an apparatus in which a second embodiment of the positioning control method according to the present invention is executed. FIG. 8 (a) shows a driving force, a frictional force, and a displacement in the positioning control. 8 (b) is an enlarged view of the fine movement positioning portion, FIG. 9 is a diagram showing the movement of the table when switching from the coarse movement positioning operation to the fine movement positioning operation, and FIG. 10 is a rolling guide area. FIG. 11 is a diagram showing a characteristic of displacement with respect to force in II, FIG. 11 is a diagram showing a characteristic of displacement with respect to force in a region I of the rolling guide,
(B) is a diagram showing a model of the relationship between the force and the frictional force in the rolling guide regions III and I, respectively.

The main part of the positioning control related in this device, the command generator 21, coarse control device 22, fine movement control unit 23, a sine wave generator 24, the switch SW _1, the hold circuit 26, the switch SW _2, divided Unit 26, adder 27,
It has a power amplifier 28, a motor 29, and a position detector 30. Command generator 21 issues a coarse position command r _c and fine movement position command r _f. Coarse controller 22 outputs a control current T _rc performs coarse control of the table by the detection information of the position detector 30 based on the coarse position command r _c. Fine movement control device 23
Performs fine motion control of the table by the detection information of the position detector 30 based on the fine movement position command r _f. The sine wave generator 24 outputs a sine wave signal _Trs . Switch SW ₁ performs the ON / OFF of the hold signal S _h. The switch SW ₂ connects the sine wave signal _{Trs to} the adder 27 and the fine movement control device 2
3 for connecting to the adder 27 the output T _rf. Divider 2
6 to calculate the spring constant _{K = f b k t / x} b at small displacement amplitude of the displacement and the amplitude of the driving force. After coarse movement positioning, the adder 27 superimposes a sine wave on the force command, and thereafter switches to fine movement control. The power amplifier 28 amplifies the control current to the motor 29. The motor 29 is an AC linear motor, which is driven by a drive current from the power amplifier 28 and rolls and guides the table on which the positioning target is placed in a non-contact manner. The position detector 30 is a sensor and continuously outputs table position information.

The dynamic characteristics of the table of the rolling guide mechanism become the characteristics shown by the models in FIGS. 7A and 7B due to the displacement.

Next, a positioning control method according to the second embodiment will be described. (1) the switch SW ₁ off, the switch SW ₂ of
connected to f contact a, as coarse position command r _c = x _1, normal positioning from the departure position x ₀ to the position x _1, i.e. 8
Coarse motion control as position control of the model shown in FIG. The displacement at this time is x ₁ = x ₂ + dx, where x ₂ is the coarse movement positioning target position and the minute displacement is dx. (2) Next, the coarse positioning from position x ₁ as coarse position command r _c = x ₂ to the position x _2. (3) When it is coarse positioning to position x _2, the switch SW ₁ and on, the hold signal S _h to hold circuit 25
Connect to Table is maintained displacement at a position very close to the target position x ₂ by hold circuit 25. That is, by a two-step displacement through the position x ₁ and stopped at the position x ₂ is performed, the characteristics of the table becomes elastic characteristics shown in FIG. 8 (b), the displacement force command is command force is proportional The maintenance will maintain the displacement. (4) Next, connect the switches SW ₂ to the contact b (sinusoidal connection), the superimposed sinusoidal T _rs = Asinωt the force command,
Accordingly table performs a small reciprocating movement in the vicinity of the position x _2. (5) Following this reciprocating motion, the divider 26 identifies the spring constant K at the time of a minute displacement expressed by the following equation from the amplitude f _b of the driving force of the reciprocating motion and the amplitude x _{b of the} displacement.

[0034] _{K = f b k t / x} b (6) FIG. 8 (b) is set in accordance with the control parameters applicable fine motion control in a position control model on a spring constant K obtained in the previous section (5). (7) Next, switching to fine motion control control by connecting a switch SW ₂ to the contact C, and controls the high accuracy.

FIGS. 13 (a) and 13 (b) are diagrams showing the displacement corresponding to the driving force of the spring system and the phase plane in the fine movement control stage of the third embodiment of the positioning control method of the present invention, and FIGS.
FIGS. 4 (a) and 4 (b) show the case where there is attenuation by the control method of FIG. 13, and FIGS. 15 (a) and 15 (b) show the displacement by the positive cast control of the third embodiment and its phase plane. FIG. 16
(A) and (b) show the measurement of the response to a 2N step input, and show the temporal displacement and speed change of the table and the phase change, respectively, and FIGS. 17 (a), (b),
(C) is a specific example when positioning by 1 mm by the positive cast control of the third embodiment, and is a diagram showing a force command waveform, a temporal change of a table, and a change on a phase plane.

This embodiment has the same configuration as that of the first embodiment, but uses a driving force having a two-stage step-like waveform.

Next, a control method according to this embodiment will be described.

After the table is stopped in the range of the area II by the coarse movement control, when the first stage force f _S is applied as a step input, the displacement of the table becomes the spring constant k, the natural frequency ω
As a response of the spring system, a vibration as shown in FIG. 13 (a) is generated with respect to the force f _{s around} the stable point x _s = f _s / k (10). Also,
In the phase plane the track to rotate a circle of radius x _s centered at x _s, as shown in FIG. 13 (b) clockwise. Here the input to the moment it reaches the maximum overshoot point P (2x _s, 0) from f _s, switching to 2f _s as a force of the second stage, the track will be switched to circle around the P, The trajectory stops at this point due to the zero radius circle. Therefore, when performing the positioning where x = u ₀ ,
_{First, f 1 = u 0 / (} 2k) ... (11) comprising a first stage of force giving step instructions to add (step input), the time reaches the maximum overshoot point _{t = t p = π / ω} ... (12 By switching to the second stage force (step input) f ₂ = k · u ₀ (13), positioning without residual vibration is possible.

Next, when the response shown in FIG. 14 has an attenuation ζ, the overshoot point x _p

[0040]

(Equation 1) Therefore, when performing the positioning of x = u ₀ , first,

[0041]

(Equation 2) Time when the maximum overshoot point is reached

[0042]

(Equation 3) By switching to the second stage force f ₂ = k · u ₀ (17), desired positioning can be realized. FIGS. 15A and 15B show the response by the positive cast control and the trajectory on the phase plane, respectively.

[0043] Further, in the actual positioning command value measures the step response of the system, the spring constant k, the peak value x _p of the _{displacement,} the final value x _s, overtravel time t _p determined, (1
5), (17) and

[0044]

(Equation 4) Is determined experimentally from the relationship For example, FIG. 16 shows a result of measuring a response to a 2N step input. From this result, it is _{k = 1.8N / μm x s =} 1.2μm x p = 1.8μm t p = 8.8ms.

When a command value for positioning at a displacement of 1 μm is obtained by the positive cast control, f ₂ = k · 1 μm = 1.8 N f ₁ = f ₂ · x _s / x _p = 1.2 N FIGS. 17A, 17B and 17C show the results of measuring the response of the system when the step command is given. According to this, there is almost no residual vibration, and the required time is 10 ms.
It can be seen that the following high-speed positioning is realized.

[0046]

As described above, according to the present invention, the coarse motion control is stopped in the region II of the non-linear spring characteristic of the rolling guide mechanism, and thereafter, the coarse motion control is calculated for each step after the spring control has passed in the fine motion control stage. Progressing positioning gradually while updating,
Also, stop and hold the coarse motion control near the target position,
Sine wave is superimposed in the fine control and the spring constant is calculated for each cycle to advance the positioning while updating the driving force, or the fine response control calculates the spring constant by measuring the table response frequency to the step input. By measuring the time to the maximum overshoot point on the phase plane of the vibration and applying a driving force that becomes a circle having a radius of 0 of the phase trajectory to stop the fine movement, the required time can be shortened, and a large external force can be obtained. There is an effect that high-precision positioning becomes possible even in a system in which is added.

[Brief description of the drawings]

FIG. 1 is a block diagram of a main part of an apparatus in which a first embodiment of a positioning control method according to the present invention is executed.

FIG. 2 is a flowchart of a positioning control method performed in FIG.

FIG. 3 is a diagram showing characteristics of a rolling friction force.

FIG. 4 is an explanatory diagram showing a relationship between a driving force and a frictional force for coarse movement positioning of the rolling guide mechanism.

FIG. 5 is a diagram showing a relationship between frictional force and displacement in the positioning control of FIG. 1;

FIG. 6 is a diagram showing a relationship between a driving force and a displacement for fine movement positioning.

FIG. 7 is a block diagram of a main part related to control of an apparatus in which a second embodiment of the positioning control method of the present invention is executed.

8A is a diagram showing a relationship between a driving force, a friction force, and a displacement in the positioning control, and FIG. 8B is an enlarged view of a fine movement positioning portion.

FIG. 9 is a diagram showing the movement of the table when switching from the coarse positioning operation to the fine positioning operation.

FIG. 10 is a diagram showing characteristics of displacement with respect to a force in a region II of the rolling guide.

FIG. 11 is a diagram showing characteristics of displacement with respect to a force in a region I of the rolling guide.

FIGS. 12 (a) and (b) are areas of rolling guidance, respectively.
It is a figure which shows the model of the relationship of the force and frictional force in III and I.

FIGS. 13A and 13B are diagrams showing a displacement and a phase plane corresponding to a driving force of a spring system in a fine movement control stage of a third embodiment of the positioning control method according to the present invention, respectively.

14 (a) and (b) are diagrams when there is attenuation in the control of FIG.

FIGS. 15 (a) and (b) are diagrams showing a displacement and a phase plane by the positive cast control of the third embodiment, respectively.

FIGS. 16 (a) and (b) are diagrams showing measured values of a response to a 2N step input, showing a temporal displacement and a change in speed of a table, respectively.

17 (a), (b), and (c) are specific examples when positioning with a displacement of 1 mm is performed by the positive cast control of the third embodiment, a force command waveform, a time change of a table, and a phase plane. It is a figure showing a change.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Command generator 2 Position controller 3 Force controller 4 Switch 5 Power amplifier 6 Motor fixed part 7 Motor movable part 8 Movable table 9 Position detector 21 Command generator 22 Coarse movement controller 23 Fine movement controller 24 Sine wave generator 25 Hold circuit 26 Divider 27 Adder 28 Power amplifier 29 Motor 30 Position detector

────────────────────────────────────────────────── ─── Continuation of the front page (56) References JP-A-3-73007 (JP, A) JP-A-1-239609 (JP, A) JP-A-48-15534 (JP, A) (58) Field (Int.Cl. ⁷ , DB name) G05D 3/00-3/20

Claims (3)

(57) [Claims] An area III in which a table on which an object to be positioned is mounted is moved by a rolling guide mechanism driven by a motor with rolling against saturated friction.
Coarse positioning, and fine positioning of the area II in which the table makes a displacement dependent on the force applied against the frictional force, and area I in which the displacement of the table is proportional to the linear driving force due to the spring characteristic. In the positioning control method using the fine movement positioning together, after the table is stopped at a position slightly beyond the target by the coarse movement positioning, the process is shifted to the fine movement positioning in the area II and the area I, and the table is stepwise at least twice. Then, the spring force of the table is set from the driving force during the previous two fine movements and the data of the position at that time, and the driving force to be applied is corrected based on the spring constant. a positioning control method for, the procedure is, (1) the final target position x _r Owazu from the positioning starting point x ₀
A driving force f ₀ is applied to the first position x ₁ that has exceeded
First step for performing coarse positioning control for moving the cable
And-up, (2) the table from a first position x _1, the first position
a second position x ₂ intermediate between x ₁ and the final target position x _r
To the small force Δf from the driving force f ₀ during coarse movement positioning.
Driving force f ₁ = f ₀ −Δf
Performs the first fine positioning control in the area II to be moved
Also, the drive at the moment when the position x ≧ x ₂ at this time
A second step of measuring the force f ₂ , (3) moving the table from a second position x ₂ to a second position
a third position x ₃ intermediate between x ₂ and the final target position x _r
To a second fine positioning control to move by the driving force f ₁
And the third position x at this time becomes x ≧ x ₃ .
A third step of measuring the driving force f ₃ at the instant when the table is moved, and (4) moving the table from a third position x ₃ to a third position.
fourth position of x is in the middle of the x ₃ and the final target position x _r
to x _4, K _S4 = a _{(f 2 -f 3) / (} x 2 -x 3) and linearized spring constant, drive a section of the x ₄ <x <x ₃
Third fine movement to move with power f = f ₁ + K _S4 * (x ₄ -x)
Performs positioning control, position x at this time is the x ≧ x ₄
A fourth step of measuring the driving force f ₄ at the moment of the change , and (5) further determining whether the table is at the n−1th position x _n−1 .
Et al., Intermediate position the n between the position x _n-1 and the final target position x _r
To the position _xn , K _Sn = (f _n−2 −f _n−1 ) / (x _n−2 −x _n−1 ) as a linearized spring constant, x _n <x <x _n−1 , and the f _M
The n-th fine movement positioning for moving with the driving force f = f _M + K _Sn * (x _n −x) when the driving force is the driving force one sample period before movement is performed.
Measuring a driving force f _n of the instantaneous position x becomes x ≧ x _n when
Sequentially through the steps of the n of the constant, the final target position x _r
A positioning control method characterized by bringing closer. 2. The positioning control method according to claim 1, wherein the linearized spring constant K _Sn is K _Sn = (f ₂ −f ₃ ) / (x ₂ −x ₃ ). 3. A fourth and driving force of the fifth step is, the speed of the guide of the table rolling v, driving force when the gain of the speed feedback the _{K V f = f M + K} Sn * (x r -x) -K _v * _v positioning control method according to claim 1 or 2 is.