JPH07121213A - Route control unit - Google Patents

Abstract

PURPOSE:To attain excellent course control over even a controlled system even if the controlled system which has plural control axes has a saturated element. CONSTITUTION:This control unit has the controlled system 3 which physically moves in a target course and has the saturated element, a generating means 1 which generates position command signals by the control axes on the basis of a target course signal, a position command signal storage means 13 which stores the position command signals by the control axes by a finite time, and a control means 2 which controls the controlled system according to the position command signals and the state quantity of the controlled system; and the control means controls the operation of other control axes so that a course error becomes small when one control axis reaches a saturation area.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a machine tool for simultaneously controlling a plurality of axes for free-form surface processing, a zoom lens for moving a plurality of lens groups used in a camera system, and
The present invention relates to a route control device which is applied to a scanning type exposure device or the like that performs exposure by moving axes at the same time, and moves a target route by simultaneously controlling a plurality of control targets.

[0002]

2. Description of the Related Art FIG. 4 shows an example of the configuration of a conventional biaxial path control device (hereinafter referred to as a control system). Such a control system
Conventionally, it is often used in NC devices and the like. The control system of FIG. 4 is a position control system having the same configuration of the control system of each axis and having a speed control system for stabilization as a minor loop.

In this control system, the control input 7a to the first axis is obtained from the target position command value 1a, the position signal 18a and the speed signal 19a, and the control input 7b to the second axis is obtained.
Is calculated from the target position command value 2b, the position signal 18b, and the speed signal 19b, and the two axes are controlled independently of each other. Such a position control system is a control system having a relatively low gain position control loop and a relatively high gain speed control loop inside thereof. The characteristic of this control system is that the rigidity of the control system against disturbances can be set high by the high gain of the speed control loop, and the response of the position control loop that does not give an excessive shock to the mechanical system can be easily obtained because the gain is low. Is.

The target value generating means 1 generates a position target value so that the two axes are along the target path, and commands the position control system for the first axis and the second axis. At this time, the target value signals 1a and 1b are instructed so that the synchronous relationship between the two axes is always maintained. Space 2 for example
When a circular locus is to be drawn on an axis, if a sine wave or a cosine wave is output from the position command signal generating means 1 as a position command value for each axis component, it corresponds to each axis based on the control means. The position of the controlled object is controlled simultaneously. If the X and Y axes completely follow this target value, an accurate circle will be drawn.

[0005]

However, in such a path control system, since each axis is controlled independently, unless the responsiveness of each axis is made the same, the synchronization relationship of each axis is broken and it is good. It is not possible to perform proper route control. Therefore, in such a control system, it is necessary to set the speed control loop gain and the position control loop gain of each axis to be the same, and at least the position control loop to be the same.

Also, there is usually a limit to the control inputs that can be used for control, which can be expressed as a saturation factor. For example, the controlled object in FIG. 4 is assumed to drive a motor by a current source, and in this case, the control input is a current. At this time, the capacity of the current source is limited, and the maximum value is set by various factors such as price, volume, and controllability. Here, 14a and 14b correspond to current sources having saturation characteristics. In this control target, the current value is proportional to the acceleration. Therefore, when the acceleration required for control exceeds the acceleration that can be supplied by the control device, such as when the target command value changes rapidly, the acceleration (current) is saturated in the saturated region by performing appropriate acceleration / deceleration or setting the target speed small. It is necessary to control so as not to reach. Further, since a large acceleration has a large impact on the mechanical system and may damage the mechanical system, it may be necessary to limit the control input at a smaller acceleration than the limitation of the current source.

FIG. 8 is a diagram showing the characteristics of the conventional system.
The locus C0 is a target circular locus. The locus when the X-axis and Y-axis position control loop gains are set to be the same is shown as C1. The locus C1 is a circular locus although the radius is smaller than the target circle except for the start point and the end point of the route. Here, in order to clarify the difference between the target locus and the follow-up locus, the gain of the control system is lowered and the follow-up performance is deteriorated. This tendency is more remarkable as the target speed is higher and the gain of the control system is lower. Further, in the figure, C2 is the response when the gains of the two axes are different. At this time, the following locus is an ellipse, and it can be seen that the synchronism of the two axes is important in the route control.

By the way, a route control system is required to have high-speed and highly accurate route control characteristics. In order to realize a highly accurate path control system, it is necessary to set the position loop gain high. In addition, the target speed becomes high for high-speed route control. Both of these require high acceleration. However, since a large acceleration requires a large current, it can be used only just before the saturation region. If the control is performed using the saturation region, the two axes will not be synchronized with each other, so that good path control cannot be performed. For this reason, the conventional method has taken measures such as setting a limit on the target command value so that the control input does not reach the saturation region, or reducing the gain of the control system to reduce the maximum acceleration.

For example, in the example of the arc described above, a large acceleration is required at the start point and the end point of the arc, so acceleration / deceleration is performed on the target command value. However, in order to accelerate or decelerate the target command value, it takes a lot of time to calculate the target command value. Further, in the case of a complicated path curve, there arises a problem that it is difficult to create an appropriate acceleration / deceleration pattern. In terms of performance, the saturation region should be effectively used and the response should be as fast as possible, but such usage is difficult. Further, if the gain of the control system is lowered, the following capability of the control system is deteriorated, which is not desirable, and various problems occur.

In order to investigate this saturation problem, the maximum value of the control input is limited and the path control is performed. In FIG. 9 (A),
The locus at this time is shown as C1. FIG. 9B shows acceleration response waveforms on the X-axis and the Y-axis at this time. In this example, the Y axis has not reached the saturation region at the start end and the stop end, but X
It can be seen that the axis has reached the saturation region. As is clear from FIG. 9A, the locus C1 is a locus largely deviated from the target circle. From this example, the difficulty of route control when the saturation region is reached is understood.

The present invention has been made in view of the above circumstances, and an object thereof is to provide a route control device capable of performing good route control even for a control target having a saturation element. .

[0012]

In order to achieve the above-mentioned object, in the present invention, the control target having a saturation element is controlled so that the target values of the respective axes interfere with each other. ing. Therefore, in the present invention, the inventor of the present application first discloses Japanese Patent Application Nos. 4-311143 and 4-311.
The route control system indicated by No. 144 is applied to a control target having a saturation element. This makes it possible to perform good path control even when the saturation region is reached.

Further, by intentionally inserting a saturation element having a saturation region smaller than the saturation element naturally possessed by the controlled object (claim 2), good path control can be performed while changing the acceleration limit according to the situation. to enable. In the present invention, 2
Since the axes are controlled in a coordinated manner, even when one of the axes reaches the saturation region, the other axis compensates for the movement, thereby performing the excellent path control so as not to break the synchronous relationship between the two axes. be able to.

In order to configure the control system, the present invention does not form a control loop independently for each axis to be controlled as in the conventional system, but rather sets the state quantity and the target value not only for the target axis but also for other axes. A control loop is formed by using the state quantity of the axis and the target value. For this purpose, an evaluation function is determined, and a route control is performed by configuring a control system that optimizes this evaluation function. In order to configure a control system, an evaluation function such as the expression of (Claim 5) including the evaluation terms shown in (Claim 6) is defined, and the optimum control input that minimizes this function is controlled. It is realized by sequentially obtaining from the state quantity and the target value by a computer and sequentially instructing this control input to the control target.
That is, configuring the control system involves calculating the optimum control input that minimizes the evaluation function of such an equation.
A configuration diagram at this time is shown in FIG. An optimum control input that minimizes this evaluation function is, for example, DP (Dynamic
Programing) method and the like.

[0015]

【Example】

(Embodiment 1) FIG. 1 shows an embodiment of the present invention. This figure shows an example in which the route control system of the present invention is configured for the same controlled object 3 as the example shown in FIG. Here the state quantity 8
Although a and 8b are shown by one line, this is a vector quantity and is a state vector representing a plurality of information. The other lines are vector quantities as well. The controlled object 3 is the same as the controlled object shown in FIG. 4, so that the state quantities 8a and 8b respectively represent the position and speed signals of the first and second axes. Further, the control inputs 7a and 7b are current values, which are proportional to the acceleration of the controlled object 3 when no disturbance is applied.

The characteristic of the controlled object 3 is represented by a state equation. Equation 1 is a transformation of this equation of state into a discrete time system equation. Here, Φ and G are matrices representing the characteristics of the system.

X (k + 1) = ΦX (k) + GU (k) (Equation 1) X state vector U control input vector

The evaluation function is

[0019]

[Outside 3] Here, R target value vector, y = CX output vector X state vector, U control input vector k time, M integration time Q weight function, H weight function. Further, the evaluation function is as follows: S1 _k = e _k ^T q _k e _k (Equation 3) S2 _k = e _k ^T q _{k + 1} e _k (Equation 4)

[0020]

[Outside 4] Evaluation items such as This item is S1 in FIG.
It represents the area of a closed region formed by two curves of the target position command value and the follow-up value as indicated by k and S2k, and is called an area evaluation term. Either or both of S1 _k and S2 _{k in} FIG. 7 are used as the evaluation term. Both will be used in this embodiment. Therefore, the weighting function of the above (Equation 2) is expressed as follows.

Qi = q ₀ + q ₁ * q _i + q ₂ * q _{i + 1} q ₀ constant matrix, q ₁ , q ₂ constants

The model of the actual controlled object is 2 as shown in FIG.
The following inertial system is used. The optimum control input U _k that minimizes the evaluation function of (Equation 2) is obtained as follows. The control system can be realized by calculating this equation in real time.

[0023]

[Outside 5] F ₀ = -B _M G ^T S _M-1 Φ F ₁ = B _M G ^T C ^T Q _{k + 1} F _i = B _M G ^T P _{M + 1-i} ^T ... P _M-1 ^T C ^T Q _{k + i} B _Mj = [G ^T S _Mj-1 G + H _{k + j} ] ^-1 P _Mj = [I-GB _Mj G ^T S _Mj-1 ] Φ S _Mj = Φ ^T S _Mj-1 P _Mj + C ^T Q _{k + j} C S ₀ = C ^T Q _{k + M} C

As described above, by introducing the area evaluation term, the control system that minimizes the evaluation function of the above (Equation 2) becomes a control system in which the state quantities of the independent controlled objects interfere with each other. . At this time, the target position command value uses not only the current value but also a value after a finite time. This value is obtained from the target position command value storage means 13. That is, the control input 7a to the first axis is obtained from the target position command values (signals) 6a and 6b to the first and second axes and the position and speed signals of the first axis. Similarly, the control input 7b to the second axis is the target position command value (signal) 6a, 6b for the first axis and the second axis.
And the position and velocity signals of the second axis.

As described above, in the control system of this embodiment, the target values of the first axis and the second axis interfere with each other to perform control. That is, by configuring a control system that optimizes the evaluation function represented by (Equation 2) including the evaluation terms represented by (Equation 3) and (Equation 4), the control device in which the target values interfere with each other Can be made. Further, although the saturation elements 14a and 14b are assumed to be included in the controlled object 3 here, this is similarly effective even on the control means (device) 2 side.
When it is on the control device 2 side, its maximum value can be changed according to the purpose of use of the designer. For example, the maximum acceleration is not a value determined by the maximum value of the current amplifier which is the controlled object 3, but can be used when it is desired to set the maximum acceleration smaller than the maximum value due to mechanical strength. A configuration example of the control system at this time is shown in FIG.

In FIG. 10, the saturation value of the control input is set to 250 (acceleration saturation value 5000), and the first axis and the second axis are set.
This is a locus when the two axes are controlled so that the axes move along an arcuate trajectory. In the figure, C0 indicates the target locus, and C2 indicates the following locus of this control system. Since the path error is small in the control method of the present embodiment, the path error is magnified 20 times in the radial direction and displayed. The follow-up trajectory of the conventional method for the same target value and saturation value is shown as C1 in FIG. The actual maximum radius error is 1.448 mm in the conventional method and 0.25 in this control method.
It is 8 mm. As described above, the control system according to the present control system can maintain a good synchronization relationship between the two axes even when saturation occurs, as compared with a system in which each axis is controlled independently.

(Second Embodiment: Disturbance Estimation) The control system of the first embodiment described above does not consider the case where a disturbance is applied. For this reason, the influence cannot be suppressed sufficiently. In this case, there is a large position error in the steady state. In the present embodiment, the disturbance is estimated by the disturbance estimators (means) 5a and 5b, and the value W1 is suppressed by using the following (Equation 7). Where W1 is the output of the disturbance estimator 10
a and 10b.

X (k + 1) = A (k) X (k) + B (k) U (k) + W1 (k) (Equation 7) X state vector U control input vector W1 estimated disturbance vector

There are various types of disturbance estimators, but here, a Kalman filter as shown in FIG. 5 is used. The model of the actual controlled object 3 is a secondary inertial system as shown in FIG. 6, and the disturbance generation model is a primary system and the disturbance estimator (means) 5 is used.
a and 5b are formed. A disturbance estimation value output from the disturbance estimator is used to configure a control system that minimizes an evaluation function similar to that in the first embodiment.

FIG. 3 shows the second embodiment and the following third and fourth embodiments.
It is the figure which showed the structure of 5 and 6 collectively. In this embodiment, from FIG. 3, the virtual controlled object 3c and the disturbance measuring means 11a, 11
It is constructed by removing b. FIG. 11 shows a follow-up locus when the step disturbance is applied to the first axis at point D by controlling the two axes so that the first axis and the second axis move in an arcuate trajectory as in the first embodiment. In the figure, C0 indicates a target locus, and C3 indicates a follow-up locus of the control system of this embodiment. C3 has a steady position deviation with respect to the step disturbance. Although not shown in the figure, the following trajectory of the first embodiment is substantially the same as the following trajectory. However, the position deviation at the stop end is 78 in the first embodiment.
[um], 16 [um] in this embodiment. As described above, the control system of the present embodiment can realize a control system having high rigidity against disturbance as compared with the first embodiment.

(Third Embodiment: Virtual Axis) In the first embodiment, a large overshoot may occur at the trailing end of the track. A virtual axis (control target) 3c is introduced in order to suppress this overshoot. Virtual axis 3c
Considers a virtual control axis in addition to the existing control target axes 3a and 3b, and includes this axis as a control target to configure a control system as in the first or second embodiment. FIG. 3 shows the configuration of the control system when the virtual axis is used. The characteristics of the first and second axes to be controlled and the target position value are the same as in the first embodiment.

Here, it is assumed that the characteristics of the virtual axis are the same as those of the first axis, and the position target value signal for the virtual axis moves at a constant speed after the movement of the two axes is stopped. C2 in FIG. 12 is the response of this system, and C0 is the target route. Comparing FIG. 10 that does not use the virtual axis with FIG. 12 that uses the virtual axis, the overshoot at the terminal end portion is small in this embodiment, which shows the effectiveness of this embodiment.

(Embodiment 4) Prediction of Disturbance In Embodiment 2, a configuration is shown in which the disturbance cannot be known in advance. However, when the torque disturbance or the like corresponding to the target position is known in advance, better control can be performed by performing control using this information. In this case, the characteristics of the controlled object 3 are expressed as in the following (Equation 8) to form a control system. Here, W1 is an estimated value of the disturbance estimator used in the second embodiment, and W2 is a known disturbance known in advance. The configuration of this system is also shown in FIG.

X (k + 1) = A (k) X (k) + B (k) U (k) + W1 (k) + W2 (k) (Equation 8) FIG. This is the configuration of the control system when all are included. The position target value and the disturbance similar to those in the second embodiment are applied to the control system thus configured. The response when the disturbance is known in advance is shown in C2 of FIG. Also,
C0 in the figure is a target position locus. C2 and C3
Comparing with, it can be seen that the fluctuation due to the disturbance is smaller in C2 when the disturbance is known in advance.

(Fifth Embodiment: Zoom Lens) The present invention is applied to a zoom lens. FIG. 13 is a block diagram at this time. Here, the case where two lens groups, that is, the first group variator and the second group compensator are controlled is considered. In this case, the second group performs route control in the XY plane with the first axis as the X axis and the second axis as the Y axis. The target path is a lens group 21a of two groups, a bally eater and a compensator, which are optically determined so that the focus is not shifted while zooming.
It is assumed that the position of 21b is obtained in advance.

As an example showing the response of this embodiment, the target route is a circular route here. It is not the case that it is the proper target path that the actual ballyator and compensator draw a circular path, but it can be considered as an example. In this case, the configuration of the control system is exactly the same as that shown in the fourth embodiment (FIG. 3), the response is the same, and the response when the disturbance is applied is C2 in FIG. 11 when the disturbance is known in advance.
become that way.

As described above, the control system that minimizes the evaluation function of (Equation 2) is essentially a control system in which the position signals of the control targets that are independent of each other interfere with each other, and also the velocity signal is used. Good path control performance is obtained. At this time, the target position command value uses not only the current value but also a value after a finite time. This value is obtained from the target position command value storage means 13. That is, the control input 7a for the first axis is the target position command values 6a, 6b for the first and second axes, the position signals 18a, 18b for the first and second axes, and the speed signal 19a,
19b. Similarly, the control input 7b to the second axis is the target position command value 6 to the first and second axes.
a, 6b and position signals 18a, 1 for the first and second axes
8b and speed signals 19a and 19b.

As described above, in the control system of the present invention, the target values and the state quantities of the first axis and the second axis interfere with each other for control. That is, by configuring a control system that optimizes the evaluation function of (Expression 2) including the evaluation terms shown in (Expression 3) and (Expression 4), the target values interfere with each other and It is possible to create a path control device in which the other axis corrects the movement when saturated and the path is well controlled. As described above, by applying the present invention to a zoom lens, it is possible to make a zoom lens with a small focus shift and capable of high-speed zooming.

(Embodiment 6: Scanning type exposure apparatus) The present invention is applied to a scanning type exposure apparatus. FIG. 14 is a block diagram at this time. Here, as the first axis, the reticle drive means 33b,
Consider a case where two axes of the wafer driving means 33a are controlled as the second axis. In this case, the two axes perform path control in the XY plane. Further, since the two axes move in a fixed direction in synchronization, the target route becomes a straight line. In this case, the configuration of the control system is exactly the same as that shown in the fourth embodiment, and the response is as shown in FIG. Here, FIG. 15a shows the path following characteristic, C1 is the conventional method shown in FIG. 4, and C2 is the following characteristic of the present control method. Further, FIG. 15b shows the X-axis and Y-axis acceleration waveforms of the conventional method and the present control method at this time, the subscript 1 being the conventional method and the subscript 2 being the present control method.

From FIG. 15b, the X axis reaches the saturation region in both control methods. Therefore, the response C1 of the conventional method is the X-axis and the Y-axis.
The axis synchronism is lost and a large path error occurs.
On the other hand, the response C2 of the present invention moves on the straight line which is the target route with almost no route error. As described above, according to the path control method of the present invention, when one axis is saturated, the other axis performs the correction operation and the synchronous relationship between the two axes does not collapse. Therefore, by applying the present invention to a scanning exposure apparatus, it is possible to make the best use of the capacity of the current source and to make a high-speed and high-precision scanning exposure apparatus.

Example 7: Others 1. In the present application, an example in which the number of control axes is two has been described, but the number of axes is not limited, and the system can be configured with any N axes. 2. It is also possible to calculate the speed signal from the position signal and configure the control system by using the calculated value as the speed signal. 3. Although the characteristic of the virtual axis is set to be the same as that of the first axis in the third embodiment, this characteristic may be any convenient one. 4. The fourth embodiment has shown the control system when the disturbance signal is known. The known disturbance signal may be determined by the target position command value, or may be obtained by providing a disturbance signal detecting means. 5. Here, the case where the saturation element of the control target is in the control input part is shown, but the saturation element is not limited to this part and is the same in any part of the control target.

[0042]

According to the present invention, good route control can be performed even when the saturation region is reached.

[Brief description of drawings]

FIG. 1 is a block diagram showing an outline of an embodiment of the present invention.

FIG. 2 is a block diagram showing an outline of another embodiment of the present invention.

FIG. 3 is a block diagram showing the outline of still another embodiment of the present invention.

FIG. 4 is a block diagram showing an outline of a conventional example.

FIG. 5 is a block diagram showing the configuration of an observer.

FIG. 6 is a block diagram showing a configuration of a controlled object and a disturbance generation model.

FIG. 7 is a diagram illustrating an area term.

FIG. 8 is a diagram showing a problem of the conventional example.

FIG. 9 is a diagram showing characteristics (A: tracking locus, B: acceleration waveform) at saturation of the conventional example.

FIG. 10 is a diagram showing trackability (A: tracking trajectory, B: acceleration waveform) of a system of the present invention with respect to a circular trajectory.

FIG. 11 is a diagram showing the effect of disturbance estimation.

FIG. 12 is a diagram showing the effect of a virtual axis.

FIG. 13 is a block diagram showing an outline of the configuration of a zoom lens.

FIG. 14 is a block diagram showing an outline of the configuration of a scanning exposure apparatus.

FIG. 15 is a diagram showing effectiveness (A: tracking locus, B: acceleration waveform) when the present invention is applied to a scanning exposure apparatus.

[Explanation of reference numerals] 1 position target command value generating means (lens group position calculating means) 1a 1st axis position target command value generating means 1b 2nd axis position target command value generating means 1c Virtual axis position target command value generating means 2 Control Means 2a First axis position control means 2b Second axis position control means 3 Control object 3a First axis control object 3b Second axis control object 3c Virtual axis control object 4 Controller (lens group position control means) 5 Disturbance estimation means 5a First axis disturbance estimating means 5b Second axis disturbance estimating means 6 Target value signal 6a First axis target value signal (lens group position command value; wafer position command value) 6b Second axis target value signal (lens group position command value; Position command value) 7 control input 7a 1st axis control input (lens group control input; wafer control input) 7b 2nd axis control input (lens group control input; reticle control input) 7c Virtual axis control input 8 Measurement state quantity signal 8a First axis state quantity signal 8b Second axis state quantity signal 8c Virtual axis state quantity signal 9 Disturbance signal 9a First axis disturbance signal 9b Second axis disturbance signal 10 Estimated disturbance signal 10a First axis estimated disturbance signal 10b Second axis estimated disturbance signal 11 Disturbance measuring means 11a Disturbance measuring means 11b Second axis disturbance measuring means 12 Measurement disturbance signal 12a First axis measurement disturbance signal 12b Second axis measurement disturbance signal 13 Position command value storage means (lens group position) Storage means) 14a 1st axis saturation element 14b 2nd axis saturation element 15a 1st axis design saturation element 15b 2nd axis design saturation element 18 Position signal 18a 1st axis position signal (lens group position signal; wafer position signal) 18b 2-axis position signal (lens group position signal; reticle position signal) 19a 1st axis velocity signal (lens group velocity signal) 19b 2nd axis velocity signal (reticle position signal) Lens group speed signal) 20a, 20b lens group driving means 21a, 21b lens group 22a lens group position detecting means (wafer position detecting means) 22b lens group position detecting means (reticle position detecting means) 23a, 23b lens group speed detecting means 30 Projection means 33a Wafer drive means 33b Reticle drive means 40 Disturbance signal generation model 42 Kalman gain

Claims (9)

[Claims] 1. A controlled object that physically moves along a target path and has a saturation element, a generation means that generates a position command signal for each control axis based on the target path signal, and a position command signal for each control axis. Is stored for a finite time, and has a control means for controlling the controlled object from the position command signal and the state quantity of the controlled object, wherein the control means has one of the control axes in a saturation region. A path control device characterized by controlling the operation of another control axis so that the path error becomes small when it reaches. 2. The route control device according to claim 1, wherein a use range of the control input is changed by inserting a saturation element into the control input. 3. The control means generates a drive signal for each controlled object using not only the position signals of the corresponding controlled objects but also the position signals of other controlled objects. , 2. The route control device according to any one of 1. 4. A speed detecting means for detecting the speed of each controlled object, wherein the control means determines a control input signal using these speed signals. 3. The route control device according to any one of 3 above. 5. The control signal output by the control means is: Here, R target value vector, y = CX output vector X state vector, U control input vector k time, M integration time Q weighting function, H weighting function J _(k) determined to be minimized The path control device according to claim 1, 2, 3, or 4. 6. The evaluation function is as follows: S1 _k = e _k ^T q _k e _k S2 _k = e _k ^T q _{k + 1} e _k The route control device according to claim 5, further comprising area evaluation terms S1 _k and S2 _{k represented} by 7. The route control device according to claim 5, wherein the disturbance applied to the controlled object is estimated, and the control means also uses the estimated disturbance. 8. The path according to claim 5, wherein a virtual axis that does not physically exist as the control target and a target position command value for the virtual axis are newly added. Control device. 9. The path control device according to claim 5, wherein the disturbance applied to the control target is detected in advance, and the control means also uses the known disturbance. .