Control device, positioning device, lithography device, and method for manufacturing articles

Abstract

This technology offers advantages in improving control accuracy through feedforward control, even in environments containing disturbances with low reproducibility. [Solution] The control device includes a determination unit that determines the gain of the feedforward controller based on a control deviation data sequence showing the change in the control deviation of the controlled object and a response data sequence showing the response characteristics of the controlled object when a specific manipulated variable is applied to the controlled object. The determination unit generates a representative value data sequence consisting of representative values ​​of the control deviation of the controlled object at each time based on a plurality of control deviation data sequences acquired multiple times, and determines the gain based on the representative value data sequence and the response data sequence.

Description

[Technical Field]

[0001] The present invention relates to a control device, a positioning device, a lithography device, and a method for manufacturing articles. [Background technology]

[0002] In control systems, such as two-degree-of-freedom control systems, the response performance to a target value depends on the accuracy of the modeling of the controlled object. However, although various modeling methods have been attempted, none have been able to achieve perfectly accurate modeling, and therefore modeling errors have not been eliminated. Furthermore, the higher the performance required of the control system, the more accurate the modeling of the controlled object becomes necessary, which places a great burden on the modeling process. Patent Document 1 describes a method for realizing highly accurate feedforward control without requiring modeling of the controlled object. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2013-218496 [Overview of the project] [Problems that the invention aims to solve]

[0004] Feedforward control, which uses prediction-based control, can be expected to improve control accuracy in highly reproducible disturbance environments. On the other hand, in environments where predictions are likely to be significantly inaccurate, i.e., disturbance environments containing low reproducibility disturbances, it is difficult to maintain the improvement effect.

[0005] In the method described in Patent Document 1, by determining the feedforward operation amount based on the relationship between the operation amount applied to the controlled object and the output response and the control deviation of the controlled object, high-precision control can be achieved without requiring modeling of the controlled object. However, in an environment including disturbances with low reproducibility, since the reproducibility of the control deviation of the controlled object used to determine the feedforward operation amount is low, the feedforward operation amount calculated by the method described in Patent Document 1 may not be optimal.

[0006] An object of the present invention is to provide an advantageous technique for improving control accuracy by feedforward control even in an environment including disturbances with low reproducibility.

Means for Solving the Problems

[0007] One aspect of the present invention relates to a control device that controls a controlled object based on a feedforward operation amount generated by a feedforward controller. The control device includes a determination unit that determines a gain of the feedforward controller based on a control deviation data sequence indicating a change in the control deviation of the controlled object and a response data sequence indicating a response characteristic of the controlled object when a specific operation amount is applied to the controlled object. The determination unit generates a representative value data sequence composed of representative values of the control deviation of the controlled object for each time based on a plurality of control deviation data sequences acquired over a plurality of times, and determines the gain based on the representative value data sequence and the response data sequence.

Effects of the Invention

[0008] According to the present invention, an advantageous technique for improving control accuracy by feedforward control is provided even in an environment including disturbances with low reproducibility.

Brief Description of the Drawings

[0009] [Figure 1] A schematic diagram showing the configuration of an exposure apparatus according to an embodiment. [Figure 2]Figures showing a first configuration example (a) and a second configuration example (b) of a control device that controls a controlled object based on a feedforward manipulated variable. [Figure 3A] A diagram illustrating the gain determination process for determining the gain of a feedforward controller. [Figure 3B] A diagram illustrating the gain determination process for determining the gain of a feedforward controller. [Figure 3C] A diagram illustrating the gain determination process for determining the gain of a feedforward controller. [Figure 4] This figure shows an example of the moving standard deviation of the control deviation of the master plate stage mechanism when a feedforward operation amount is applied to the master plate stage mechanism of the exposure apparatus. [Figure 5] A graph showing the time-series reproducibility of the control deviation of the master plate stage mechanism from time 0 to time 1000 during the exposure process. [Figure 6] A diagram showing an example configuration of the control device according to the first embodiment. [Figure 7] A flowchart illustrating the procedure for determining the gain of a feedforward controller. [Figure 8] A flowchart illustrating the details of the process for acquiring a representative value data sequence of the control deviation in the first embodiment. [Figure 9] A flowchart illustrating the details of the process for determining the number of accumulated control deviation data sequences in the first embodiment. [Figure 10] A flowchart illustrating the details of the process for acquiring the response data sequence in the first embodiment. [Figure 11] This figure illustrates the moving standard deviation of the control error of the master plate stage mechanism when a feedforward control amount gnΔf(t+tn) is applied to the master plate stage mechanism of the exposure apparatus. [Figure 12] A diagram showing an example configuration of the control device according to the second embodiment. [Figure 13] A flowchart illustrating the details of the process for acquiring a representative data sequence of response characteristics in the second embodiment. [Figure 14] A diagram showing an example configuration of the control device according to the third embodiment. [Figure 15] A flowchart illustrating the details of the process for acquiring a representative value data sequence of the control deviation in the third embodiment. [Figure 16] A diagram showing an example configuration of the control device according to the fourth embodiment. [Figure 17] A flowchart illustrating the details of the process for acquiring a representative value data sequence of the control deviation in the fourth embodiment. [Modes for carrying out the invention]

[0010] The embodiments will be described in detail below with reference to the attached drawings. Note that the following embodiments do not limit the invention as defined in the claims. While the embodiments describe multiple features, not all of these features are essential to the invention, and the features may be combined in any way. Furthermore, in the attached drawings, identical or similar configurations are given the same reference numerals, and redundant descriptions are omitted.

[0011] Figure 1 is a schematic diagram showing the configuration of an exposure apparatus EXP according to one embodiment. The exposure apparatus EXP is a lithography apparatus that transfers the pattern of the master plate 103 onto the substrate 106. In this example, the exposure apparatus EXP is a step-and-scan type exposure apparatus (scanning type exposure apparatus). However, the exposure apparatus EXP may be a step-and-repeat type or other type exposure apparatus. The exposure apparatus EXP may include, for example, an illumination light source 101, an illumination optical system 102, a master plate stage mechanism 140, a projection optical system 105, a substrate stage mechanism 150, detectors 131, 132, and a control unit 133.

[0012] The illumination light source 101 may include, for example, a mercury lamp, a laser light source, an EUV light source, or an LED light source. The type and number of light sources constituting the illumination light source 101 are arbitrary. The illumination optical system 102 is an optical system that illuminates the illumination area of ​​the master plate 103 using exposure light 108 from the illumination light source 101. The illumination area may have an elongated shape in the X-axis direction perpendicular to the Y-axis direction, which is the scanning direction. Depending on the type of projection optical system 105, it may be preferable for the illumination area to have an arc shape. The illumination optical system 102 may include, for example, a beam shaping optical system that shapes the cross-sectional shape of the light from the illumination light source 101, and an optical integrator that forms a number of secondary light sources for illuminating the master plate 103 with a uniform illuminance distribution.

[0013] The master plate stage mechanism 140 may include a master plate stage 141 having a master plate chuck for holding the master plate 103, and a master plate stage drive mechanism 142 for driving the master plate stage 141 in the X-axis direction, Y-axis direction, Z-axis direction, and rotation around each axis. The surface of the master plate 103 or the substrate 106 is arranged parallel to the XY plane, and the scanning direction of the master plate 103 and the substrate 106 is the Y-axis direction, and the direction perpendicular to the XY plane is the Z-axis direction. The master plate 103 has a pattern to be transferred to the substrate 106. Exposure light 108 illuminating the master plate 103 is diffracted by the master plate 103 (and its pattern) and projected onto the substrate 106 by the projection optical system 105. The master plate 103 and the substrate 106 are arranged in an optically conjugate relationship. In this embodiment, the exposure apparatus EXP is a step-and-scan type exposure apparatus, and the pattern of the master plate 103 is transferred to the substrate 106 by synchronously scanning the master plate 103 and the substrate 106. The master plate 103 may also be called a reticle or mask.

[0014] The projection optical system 105 is an optical system that projects the pattern of the master plate 103 onto the substrate 106. The projection optical system 105 can be a refractive system, a reflective refractive system, or a reflective system. The pattern of the master plate 103 is projected and transferred onto the substrate 106. The substrate 106 is coated with a photoresist (photosensitive material). The substrate 106 may be, for example, a semiconductor wafer or a glass plate. The substrate stage mechanism 150 may include a substrate stage 151 having a substrate chuck for holding the substrate 106, and a substrate stage drive mechanism 152 for driving the substrate stage 151 in the X-axis direction, Y-axis direction, Z-axis direction, and rotation around each axis.

[0015] Detector 131 detects the position of the master plate stage 141 and provides the detected position value of the master plate stage 141 to the control unit 133. Detector 131 may include, for example, a laser interferometer, a laser scale, or an encoder. Detector 132 detects the position of the substrate stage 151 and provides the detected position value of the substrate stage 151 to the control unit 133. Detector 132 may include, for example, a laser interferometer, a laser scale, or an encoder. The master plate stage mechanism 140, detector 131, and control unit 133 can constitute a master plate positioning device for positioning the master plate 103. The substrate stage mechanism 150, detector 132, and control unit 133 can constitute a substrate positioning device for positioning the substrate 106. The control unit 133 may be composed of, for example, a PLD (Programmable Logic Device) such as an FPGA (Field Programmable Gate Array), an ASIC (Application Specific Integrated Circuit), a general-purpose or dedicated computer with a program installed, or a combination of all or part of these.

[0016] Figure 2(a) shows a first configuration example of a control device 200 that controls a controlled object 220 based on a feedforward manipulated variable. The control device 200 in the first configuration example includes a feedforward control system. The control device 200 in the first configuration example may comprise, for example, a processor 210 and a controlled object 220 controlled by the processor 210. The processor 210 may consist of, for example, a PLD such as an FPGA, or an ASIC, or a general-purpose or dedicated computer with a program installed, or a combination of all or part thereof. The processor 210 may be incorporated into the control unit 133. In one example, the controlled object 220 may be a master plate stage mechanism 140 and a detector 131, and the detected value of the position of the master plate stage 141 in the master plate stage mechanism 140 is given by the detector 131. In another example, the controlled object 220 may be a substrate stage mechanism 150 and a detector 132, and the detected value of the position of the substrate stage 151 in the substrate stage mechanism 150 is given by the detector 132.

[0017] The processor 210 may include, for example, a feedforward controller 211, a subtractor 214 that calculates the difference between a target value and a detected value, i.e., the control deviation, and a determination unit 213 that determines the gain (feedforward table) of the feedforward controller 211. The control device 200 controls the controlled object 220 by providing the controlled object 220 with a feedforward manipulated variable generated by the feedforward controller 211 according to the target value. The gain of the feedforward controller 211 is determined by the determination unit 213 so as to cause the controlled object 220 to track the target value. The feedforward controller 211 can generate a feedforward manipulated variable by multiplying the target value by the gain of the feedforward controller 211. The determination unit 213 can acquire a control deviation data sequence showing the change in the control deviation (output of the subtractor 214) of the controlled object 220 while a predetermined target value is provided to the subtractor 214. The predetermined target value may be given as a time-series data sequence. The determination unit 213 can acquire a data sequence of detected values ​​output from the controlled object 220, i.e., a response data sequence showing the response characteristics of the controlled object 220, while a specific manipulated variable for identifying the characteristics of the controlled object 220 is applied to the controlled object 220. Based on the control deviation data sequence and the response data sequence, the determination unit 213 can determine the gain of the feedforward controller 211.

[0018] Figure 2(b) shows a second configuration example of a control device 200 that controls a controlled object based on a feedforward manipulated variable. The control device 200 in the second configuration example includes a feedforward control system and a two-degree-of-freedom control system that combines the feedforward control systems. The control device 200 in the second configuration example may comprise, for example, a processor 210 and a controlled object 220 controlled by the processor 210. The processor 210 may be composed of, for example, a PLD such as an FPGA, or an ASIC, or a general-purpose or dedicated computer with a program installed, or a combination of all or part thereof. The processor 210 may be incorporated into the control unit 133. In one example, the controlled object 220 may be a master plate stage mechanism 140 and a detector 131, and the detected value of the position of the master plate stage 141 in the master plate stage mechanism 140 is given by the detector 131. In another example, the controlled object 220 may be a substrate stage mechanism 150 and a detector 132, and the detected value of the position of the substrate stage 151 in the substrate stage mechanism 150 is given by the detector 132.

[0019] The processor 210 may include, for example, a feedforward controller 211 that generates a feedforward control variable according to a target value and provides it to the controlled object 220. The processor 210 may also include a subtractor 214 that calculates the difference between the target value and the detected value, i.e., the control deviation of the controlled object 220, and a feedback controller 215 that generates a feedback control variable according to the control deviation and provides it to the controlled object 220. The processor 210 may also include an adder 216 that generates the sum of the feedforward control variable and the feedback control variable as a control variable for controlling the controlled object 220. The processor 210 may also include a determination unit 213 that determines the gain of the feedforward controller 211. The gain of the feedforward controller 211 is determined by the determination unit 213 so as to cause the controlled object 220 to track the target value. The feedforward controller 211 can generate a feedforward control variable by multiplying the target value by the gain of the feedforward controller 211. The determination unit 213 can acquire a control deviation data sequence showing the change in the control deviation (output of the subtractor 214) of the controlled object 220 while a predetermined target value is given to the subtractor 214. The predetermined target value may be given as a time-series data sequence. The determination unit 213 can acquire a data sequence of detected values ​​output from the controlled object 220, i.e., a response data sequence showing the response characteristics of the controlled object 220, while a specific manipulated variable for identifying the characteristics of the controlled object 220 is given to the controlled object 220. Based on the control deviation data sequence and the response data sequence, the determination unit 213 can determine the gain of the feedforward controller 211.

[0020] The following describes the operation of determining the gain of the feedforward controller 211 in the control device 200 of the second configuration example illustrated in Figure 2(b). This explanation is also applicable to the operation of determining the gain of the feedforward controller 211 in the control device 200 of the first configuration example illustrated in Figure 2(a).

[0021] The gain determination process for determining the gain of the feedforward controller 211 will be explained below with reference to Figures 3A, 3B, and 3C. First, in the process shown in Figure 3A, the determination unit 213 does not provide a feedforward operation amount to the controlled object 220, but provides a predetermined target value to the subtractor 214, and obtains the control deviation e(t) of the controlled object 220 output from the subtractor 214. Then, the determination unit 213 determines the time interval for performing a predetermined process (in this example, substrate exposure processing), and obtains the control deviation data sequence e for the exposure processing time interval from the control deviation e(t). exp Extract the following. If the exposure processing time interval is from time 1 to time m, the extracted control deviation data sequence e exp This can be expressed as shown in equation (1) below.

[0022]

number

[0023] Next, in the process shown in Figure 3B, the feedforward controller 211 provides the controlled object 220 with a specific manipulated variable Δf(t) as a feedforward manipulated variable at a certain time, and acquires a data sequence of detected values ​​which is the response Δy(t) of the controlled object 220 to it. Then, the determination unit 213 extracts the response data sequence y0 for the exposure processing time interval from the response Δy(t) of the controlled object 220. The response data sequence y0 is expressed as shown in equation (2) below. The waveform of the specific manipulated variable Δf(t) may, for example, have an impulse shape.

[0024]

number

[0025] Response data sequence y0 is the detected value output from the controlled device 220. On the other hand, the other response data sequences y2, y3, ..., y nThe decision unit 213 defines a virtual data sequence. Specifically, the decision unit 213 assumes that if a similar feedforward control variable Δf(t) is applied to the controlled object 220 after a 1-sample period in which the feedforward control variable Δf(t) is applied, a similar response will be obtained, and this response is denoted as y1. Similarly, the responses after 2 sample periods, 3 sample periods, ..., n sample periods are denoted as y2, y3, ..., y n Then, y0, y1, ..., y n This can be expressed as shown in equation (3) below.

[0026]

number

[0027] Here, assuming that the response of the controlled object 220 to the input is linear, the response to the feedforward manipulated variable gΔf(t) is expressed as gΔy(t), where g is the gain. Therefore, the gain after n sample periods is g n Therefore, the following equation (4) holds true.

[0028]

number

[0029] Next, we estimate the response of the controlled object 220 when all of the feedforward manipulation amounts Δf(t) from 0 to n samples after the controlled object 220 are applied. If we let Y be the response data for the time interval of the exposure process extracted from this response, then Y is the sum of n responses, and the following equation (5) holds.

[0030]

number

[0031] By providing a feedforward control amount to the controlled object 220, the control deviation (control deviation data sequence e) is determined during the exposure processing time interval. expTo eliminate (), the response data Y should be equal to the control deviation e exp That is, the gains g0 to g of the feed-forward controller 211 can be determined using the inverse matrix or the pseudo-inverse matrix as shown in the following equation (6). n g0 to g n is a parameter set indicating the characteristics of the feed-forward controller 211 and can be called a feed-forward table.

[0032]

Equation

[0033] The feed-forward operation amount determined according to this gain (that is, the determined gain g n multiplied by the feed-forward operation amount Δf(t + t n ) is the feed-forward operation amount g n Δf(t + t n ) that is applied to the control object 220 during operation as shown in Fig. 3C. When the feed-forward operation amount is applied to the control object 220, it is expected that the control deviation in the time interval of the exposure process will be smaller and the control accuracy will be improved compared to the case where the feed-forward operation amount is not applied to the control object 220.

[0034] Here, the control accuracy of the scanning exposure apparatus may be evaluated by the maximum value of the moving standard deviation or the moving average of the control deviation in the time interval of the exposure process with the length in the scanning direction of the exposure light as the window width. Since the exposure apparatus EXP is a scanning exposure apparatus that scans in the Y-axis direction, the control accuracy can be evaluated by the maximum value of the moving standard deviation of the control deviation in the time interval of the exposure process with the length of the exposure light 108 in the Y-axis direction as the window width. Here, it can be evaluated that the higher the control accuracy, the smaller the maximum value of the moving standard deviation of the control deviation in the time interval of the exposure process. The feed-forward operation amount g n Δf(t + t nFigure 4 shows an example of the moving standard deviation of the control deviation of the master plate stage mechanism 140 when a certain value is applied to the master plate stage mechanism 140 of the exposure apparatus EXP. Figure 4(a) is a graph showing the moving standard deviation of the control deviation of the master plate stage mechanism 140 in time series from time 0 to time 1000 during the exposure processing time interval. Figure 4(b) is a graph showing the maximum value of the moving standard deviation of the control deviation from time 0 to time 1000 in Figure 4(a).

[0035] In Figure 4(a), the vertical axis represents the moving standard deviation of the control deviation of the master plate stage mechanism 140, and the horizontal axis represents time. In Figure 4(a), the dashed line shows the moving standard deviation of the control deviation when the feedforward control amount described above is not applied to the master plate stage mechanism 140. In Figure 4(a), the solid line shows the moving standard deviation of the control deviation when the feedforward control amount described above is applied to the master plate stage mechanism 140. In Figure 4(b), the vertical axis is the maximum value of the moving standard deviation of the control deviation of the master plate stage mechanism 140 from time 0 to time 1000. In Figure 4(b), the left vertical bar shows the maximum value of the moving standard deviation of the control deviation when the feedforward control amount described above is not applied to the master plate stage mechanism 140. In Figure 4(b), the right vertical bar shows the maximum value of the moving standard deviation of the control deviation when the feedforward control amount described above is applied to the master plate stage mechanism 140.

[0036] In Figures 4(a) and 4(b), when a feedforward control amount is applied to the master plate stage mechanism 140, the maximum value of the moving standard deviation of the control deviation of the master plate stage 104 is larger compared to when no feedforward control amount is applied to the master plate stage mechanism 140. In other words, what should have been improved has not improved but has actually worsened. The above phenomenon is caused by the low reproducibility of disturbances in the exposure apparatus EXP. In other words, when the reproducibility of disturbances is low, the feedforward control amount g n Δf(t+t n The control deviation data sequence e used in the decision process of ) exp The reproducibility is low, therefore, the optimal feedforward manipulation amount g n Δf(t+t n) will not be determined.

[0037] The reproducibility of the control deviation of the master plate stage mechanism 140 in the exposure apparatus EXP will be examined with reference to Figure 5. Figure 5 is a graph showing the reproducibility of the control deviation of the master plate stage mechanism 140 over time, from time 0 to time 1000, during the exposure processing time interval. In Figure 5, the vertical axis represents the control deviation of the master plate stage mechanism 140, and the horizontal axis represents time. In Figure 5, the dashed line represents the control deviation of the master plate stage mechanism 140 obtained in the first of multiple acquisitions, and the solid line represents the control deviation of the master plate stage mechanism 140 obtained in the second acquisition.

[0038] As is clear from Figure 5, there is a significant difference between the control deviation of the master plate stage mechanism 140 acquired the first time and the control deviation of the master plate stage mechanism 140 acquired the second time. The feedforward control amount g mentioned above n Δf(t+t n The method for determining the feedforward control variable g assumes that the control deviation of the master plate stage mechanism 140 has high reproducibility (the difference in control deviations obtained over multiple attempts is small enough to be ignored). Therefore, in situations where the reproducibility of the control deviation is low, as illustrated in Figure 5, the effect of improving control accuracy will not be observed. In order to obtain the effect of improving control accuracy even in situations like those illustrated in Figure 5, the feedforward control variable g must be determined considering the disturbance environment with low reproducibility. n Δf(t+t n A method for determining this is required. The solution to the above problem will be explained below.

[0039] Consider the control error e(t) of a controlled object 220 under a disturbance environment with low reproducibility. The control error e1 at time 1 is given by the component e with high reproducibility. 1_steady and component e1 with low reproducibility ’ Assuming that it can be separated into two parts, the control error e1 can be expressed as shown in equation (7) below.

[0040]

number

[0041] Similarly, the control deviation at time 2, the control deviation at time 3, ..., the control deviation at time m are e2, e3, ..., e m Therefore, the control deviation data sequence e in equation (1) exp This can be expressed as shown in equation (8) below.

[0042]

number

[0043] Control deviation data sequence e exp Let's consider the case where the data is obtained multiple times. The control deviation data column obtained the first time, the control deviation data column obtained the second time, ..., the control deviation data column obtained the kth time are e exp1 , e exp2 , , , e expk Let's assume that the average value of the control deviation data series obtained from the 1st to the kth time is e exp_ave Therefore, the mean value e of the control deviation data column exp_ave This can be expressed as shown in equation (9) below.

[0044]

number

[0045] Here, we assume that the disturbance component with low reproducibility is completely random, and that if k is sufficiently large, the sum of the values ​​in the control deviation data column obtained from the 1st to the kth time converges to zero. Under this assumption, the mean value e of the control deviation data column exp_ave This can be expressed as shown in equation (10) below.

[0046]

number

[0047] As is clear from equation (10), the mean value of the control deviation data column obtained multiple times is e exp_ave By calculating the control deviation data sequence e exp This method can remove the less reproducible disturbance components included in the data. In the example above, we used a method to calculate the mean, but we may also use a method to calculate the median. Assuming that the median converges to zero when k is sufficiently large, we can similarly derive equation (10). Alternatively, we may use a method to calculate a measure of central tendency instead of the mean or median. A measure of central tendency is a value that indicates the central trend of a group.

[0048] Based on the above, by calculating the mean or median of the control deviation data column, the control deviation data column e exp Only the highly reproducible disturbance components are extracted, and the feedforward manipulation amount g is used. n Δf(t+t n It is useful to determine the following. With this method, even in environments containing disturbances with low reproducibility, control accuracy can be improved by feedforward control. Several embodiments are described below.

[0049] Figure 6 shows an example configuration of the control device 200 of the first embodiment. Matters not mentioned regarding the control device 200 of the first embodiment can be described in the explanations of the control device 200 of the first and second configuration examples. The processor 210 may include, for example, a feedforward controller 211 that generates a feedforward manipulated variable according to a target value and provides it to the controlled object 220. The processor 210 may also include a subtractor 214 that calculates the difference between the target value and the detected value, i.e., the control deviation of the controlled object 220, and a feedback controller 215 that generates a feedback manipulated variable according to the control deviation and provides it to the controlled object 220. The processor 210 may also include an adder 216 that generates the sum of the feedforward manipulated variable and the feedback manipulated variable as an manipulated variable for controlling the controlled object 220. The processor 210 may also include a determination unit 213 that determines the gain of the feedforward controller 211.

[0050] The determination unit 213 generates a representative value data sequence consisting of representative values ​​of the control deviation at each time based on a plurality of control deviation data sequences acquired multiple times, and can determine the gain of the feedforward controller 211 based on the representative value data sequence and the response data sequence. The determination unit 213 may include, for example, a storage unit 601, a processing unit 602, and an arithmetic unit 603. The processor 210 acquires a control deviation sequence showing the change in the control deviation of the controlled object 220 multiple times, and the storage unit 601 can store the plurality of control deviation data sequences acquired multiple times. The processing unit 602 generates a representative value data sequence consisting of representative values ​​of the control deviation at each time based on the plurality of control deviation data sequences stored in the storage unit 601 and provides it to the arithmetic unit 603. The arithmetic unit 603 can determine the gain of the feedforward controller 211 based on the representative value data sequence provided by the processing unit 602 and the response data sequence provided by the controlled object 220. Here, the response data sequence is a data sequence of detected values ​​output from the controlled object 220 when a specific manipulated variable for identifying the characteristics of the controlled object 220 is provided to the controlled object 220, as described above.

[0051] Figure 7 is a flowchart illustrating the procedure for determining the gain of the feedforward controller 211. This procedure is performed by the processor 210. In step S701, the processor 210 acquires multiple control deviation data sequences and stores them in the storage unit 601. The processing unit 602 generates a representative value data sequence from the multiple control deviation data sequences and provides it to the calculation unit 603. In step S702, the processor 210 acquires a response data sequence. In step S703, the processor 210 (calculation unit 603) determines the gain of the feedforward controller 211 based on the representative value data sequence and the response data sequence. Note that step S702 may be performed before step S701.

[0052] Figure 8 is a flowchart illustrating the details of the process (process S701) for acquiring a representative value data sequence of the control deviation in the first embodiment. In process S801, the processor 210 acquires a control deviation data sequence showing the change in the control deviation (output of the subtractor 214) of the controlled object 220 while a predetermined target value is provided to the subtractor 214. In process S802, the processor 210 stores the control deviation data sequence acquired in process S801 in the storage unit 601. In process S803, the processor 210 determines whether the sequence consisting of processes S801 and S802 has been performed a predetermined number of times. If the processor 210 determines that the sequence has been performed a predetermined number of times, it proceeds to process S804; otherwise, it executes the sequence consisting of processes S801 and S802.

[0053] In step S804, the processor 210 generates a representative value data sequence consisting of representative values ​​of the control deviation of the controlled object 220 at each time, based on multiple control deviation data sequences acquired multiple times by the processing unit 602 and stored in the storage unit 601. In step S805, the processor 210 provides the representative value data sequence generated in step S804 to the calculation unit 603.

[0054] The operation of step S701 shown in Figure 8 will be explained in more detail below. First, the processor 210, in accordance with (1), for example, acquires a control deviation data sequence for the time interval of the exposure process and repeats the process in the storage unit 601 a specified number of times. The processor 210 then stores, for example, the control deviation data sequence acquired the first time, the control deviation data sequence acquired the second time, ..., the control deviation data sequence acquired the kth time in e exp1 , e exp2 , , , e expkThe data is stored in the storage unit 601. The processing unit 602 generates a representative value data sequence consisting of representative values ​​of the control deviation of the controlled object 220 at each time point, based on the multiple control deviation data sequences stored in the storage unit 601. The processing unit 602 may generate a representative value data sequence based on all the control deviation data sequences stored in the storage unit 601, or it may generate a representative value data sequence based on at least two control deviation data sequences selected from all the control deviation data sequences stored in the storage unit 601. However, the following describes an example in which a representative value data sequence is generated based on all the control deviation data sequences stored in the storage unit 601. Furthermore, the following describes an example in which the mean value is used as the representative value. By generating a representative value data sequence based on multiple control deviation data sequences, it is possible to remove disturbance components with low reproducibility that may be included in the multiple control deviation data sequences.

[0055] If the number of control deviation data sequences used is k, then according to equation (10), the representative value data sequence e obtained from the k control deviation data sequences is obtained. exp_ave This can be expressed as shown in equation (11) below.

[0056]

number

[0057] The number of times a control deviation data sequence is accumulated (specified number of times) may be determined by the following method. Figure 9 is a flowchart illustrating the details of the process for determining the number of times a control deviation data sequence is accumulated (specified number of times) in the first embodiment. Process S901 is performed before process S801, and process S902 is performed between process S801 and process S802. Also, processes S903 and S904 are performed between process S804 and process S805, and processes S905 to S908 are performed after process S703. In process S901, the processor 210 initializes the number of data acquisitions to 0. In process S902, the processor 210 increases the number of data acquisitions by 1. In process S903, the processor 210 performs a calculation for termination determination. Specifically, the processor 210 calculates the sum of the absolute values ​​of the differences between the control deviations at each time point of the two most recent control deviation data sequences output from the machining unit 602. In step S904, the processor 210 determines whether the sum calculated in step S903 is less than a threshold. The threshold may be determined, for example, based on the amplitude of the control deviation data sequence, based on experience, or by other means. If the determination result is true, the processor 210 proceeds to step S805; otherwise, it returns to step S801.

[0058] In step S905, the processor 210 acquires a control deviation data column of the controlled object 220 while a feedforward manipulated variable is applied to the controlled object 220. In step S906, the processor 210 calculates the maximum value of the moving standard deviation of the control deviation data column acquired in step S905. In this example, the explanation describes the case where the maximum value of the moving standard deviation of the control deviation data column is obtained, but it does not necessarily have to be a moving standard deviation; for example, it could be a moving average with the length of the Y-axis direction of the exposure light 108 as the window width. In step S907, the processor 210 determines whether the result calculated in step S906 is less than a threshold. The threshold may be determined, for example, based on the required control accuracy, based on experience, or according to other methods. If the determination result is true, the processor 210 proceeds to step S908; if the determination result is false, it returns to step S801. In step S908, the processor 210 determines the current number of data acquisitions as the accumulated number. Based on the above, the number of accumulated control deviation data sequences can be determined according to the sequence.

[0059] Figure 10 is a flowchart illustrating the details of the process for acquiring a response data sequence (process S702) in the first embodiment. In process S1001, the processor 210 provides a specific manipulated variable to the controlled object 220. In process S1002, the processor 210 acquires a first response data sequence output from the controlled object 220 in response to the provision of the specific manipulated variable. In process S1003, the processor 210 provides the first response data sequence acquired in process S1002 to the arithmetic unit 603.

[0060] As described above, the mean value e of the control deviation data sequence is obtained according to equation (11). exp_ave A first response data sequence y0, expressed by equation (2), is prepared. Based on these, the arithmetic unit 603 calculates the gain g of the feedforward controller 211 according to equation (6). n The arithmetic unit 603 determines the gain g of the feedforward controller 211 using the inverse matrix or pseudo-inverse matrix as shown in equation (12) below. n To decide.

[0061]

number

[0062] The feedforward control variable (i.e., the determined gain g) is determined according to the gain determined in this way. n The feedforward manipulated variable Δf(t+t) n The feedforward control variable g multiplied by ) n Δf(t+t n This can be applied to the controlled object 220 during operation. In this case, compared to when no feedforward operation is applied to the controlled object 220, the control deviation in the time interval of the exposure process is reduced, and the control accuracy is improved.

[0063] Figure 11 shows the feedforward control variable g. n Δf(t+t nThe moving standard deviation of the control deviation of the master plate stage mechanism 140 when a feedforward operation amount determined by the first embodiment is applied to the master plate stage mechanism 140 is illustrated. Figure 11(a) is a graph showing the moving standard deviation of the control deviation of the master plate stage mechanism 140 in time series from time 0 to time 1000 in the time interval of the exposure process. Figure 11(b) is a graph showing the maximum value of the moving standard deviation of the control deviation from time 0 to time 1000 in Figure 11(a). In Figure 11(a), the vertical axis is the moving standard deviation of the control deviation of the master plate stage mechanism 140, and the horizontal axis is time. In Figure 11(a), the dashed line shows the moving standard deviation of the control deviation when the feedforward operation amount determined by the first embodiment is not applied to the master plate stage mechanism 140. In Figure 11(a), the solid line shows the moving standard deviation of the control deviation when the feedforward operation amount determined by the first embodiment is applied to the master plate stage mechanism 140. In Figure 11(b), the vertical axis represents the maximum value of the moving standard deviation of the control deviation of the master plate stage mechanism 140 from time 0 to time 1000. In Figure 11(b), the left vertical bar shows the maximum value of the moving standard deviation of the control deviation when the feedforward operation amount determined by the first embodiment is not applied to the master plate stage mechanism 140. In Figure 11(b), the right vertical bar shows the maximum value of the moving standard deviation of the control deviation when the feedforward operation amount determined by the first embodiment is applied to the master plate stage mechanism 140. From Figures 11(a) and (b), it can be seen that when the feedforward operation amount determined by the first embodiment is applied to the master plate stage mechanism 140, the maximum value of the moving standard deviation of the control deviation of the master plate stage mechanism 140 is smaller compared to when it is not applied.

[0064] As described above, according to the first embodiment, control accuracy can be improved by feedforward control even in environments containing disturbances with low reproducibility.

[0065] The control device 200 of the second embodiment will be described below. Matters not mentioned with respect to the control device 200 of the second embodiment may be described in accordance with the description of the control device 200 of the first embodiment. In the second embodiment, the processor 210 generates a first representative value data sequence consisting of representative values ​​of the control deviation of the controlled object 220 at each time based on a plurality of control deviation data sequences acquired multiple times. The processor 210 also determines a second representative value data sequence consisting of representative values ​​of the response characteristics of the controlled object 220 at each time based on a plurality of response data sequences acquired multiple times. The processor 210 then determines the gain (feedforward table) of the feedforward controller 211 based on the first representative value data sequence generated from the plurality of control deviation data sequences and the second representative value data sequence generated from the plurality of response data sequences.

[0066] Figure 12 shows an example configuration of the control device 200 of the second embodiment. The processor 210 of the control device 200 of the second embodiment differs from the configuration of the determination unit 213 of the first embodiment in the configuration of the determination unit 213. In the control device 200 of the second embodiment, the determination unit 213 may include a first storage unit 601, a first processing unit 602, a second storage unit 1201, a second processing unit 1202, and an arithmetic unit 603. The processor 210 acquires a control deviation sequence showing the change in the control deviation of the controlled object 220 multiple times, and the first storage unit 601 can store multiple control deviation data sequences acquired multiple times. The first processing unit 602 generates a representative value data sequence consisting of representative values ​​of the control deviation for each time period based on the multiple control deviation data sequences stored in the first storage unit 601 and provides it to the arithmetic unit 603.

[0067] The processor 210 applies a specific operation variable to the controlled object 220 to identify its characteristics and acquires a series of response data outputs from the controlled object 220 multiple times. The second storage unit 1201 stores the multiple response data series acquired multiple times. The second processing unit 1202 generates a second representative value data series, consisting of representative values ​​of the response characteristics of the controlled object 220 at each time, based on the multiple response data series acquired multiple times, and provides it to the calculation unit 603. The calculation unit 603 can determine the gain (feedforward table) of the feedforward controller 211 based on the first representative value data series provided by the processing unit 602 and the second representative value data series provided by the controlled object 220.

[0068] Figure 13 is a flowchart illustrating the details of the process (step S702) for acquiring a representative value data sequence of response characteristics in the second embodiment. In the second embodiment, steps S1301 to S1306 are performed after step S1002. In step S1301, the processor 210 stores the response data sequence acquired in step S1002 in the second storage unit 1201. In step S1302, the processor 210 determines whether the sequence consisting of steps S1001, S1002, and S1301 has been performed over a predetermined number of storage intervals. If the processor 210 determines that the sequence has been performed over the number of storage intervals, it proceeds to step S1303; otherwise, it executes the sequence consisting of steps S1001, S1002, and S1301. The number of stored data points may be determined, for example, by applying the control deviation data point determination flow shown in Figure 9 to the response data point determination flow, or by the memory capacity allocated to the storage unit 601. Alternatively, the number of stored data points may be determined empirically or by other methods.

[0069] In step S1303, the processor 210 determines whether all response data sequences contained in the second storage unit 1201 were obtained by controlling the controlled object 220 under the same target value (same position in this example). If the determination result is true, the processor 210 proceeds to step S1304; if the determination result is false, it performs step S1305 and then returns to step S1001. In step S1304, the processor 210 generates a second representative value data sequence, which consists of representative values ​​for each time period of the response characteristics of the controlled object 220, based on multiple response data sequences obtained multiple times and stored in the second storage unit 1201 by the second processing unit 1202. The second processing unit 1202 may generate the second representative value data sequence based on all response data sequences stored in the second storage unit 1201. Alternatively, the second processing unit 1202 may generate a second representative value data sequence based on at least two response data sequences selected from all response data sequences stored in the second storage unit 1201.

[0070] In step S1305, the processor 210 deletes all response data sequences stored in the second storage unit 1201. However, although this example describes deleting all response data sequences, it is not necessary to delete all response data sequences; response data sequences obtained with the same target value (same position) may be retained, while response data sequences obtained with other target values ​​may be deleted. In step S1306, the processor 210 provides the second representative value data sequence generated in step S1304 to the arithmetic unit 603.

[0071] In the second embodiment, the processor 210 determines the gain of the feedforward controller 211 based on a first representative value data sequence generated from multiple control deviation data sequences acquired multiple times, and a second representative value data sequence generated from multiple response data sequences. Therefore, even in environments containing disturbances with low reproducibility, control accuracy can be improved by feedforward control.

[0072] The control device 200 of the third embodiment will be described below. Matters not mentioned with respect to the control device 200 of the third embodiment may be described in accordance with the description of the control device 200 of the first or second embodiment. In the first and second embodiments, the processor 210 stores the control deviation data sequence in the storage unit 601 without determining whether the control deviation data sequence of the controlled object 220 contains disturbance components with low reproducibility. However, in a disturbance environment with high reproducibility, the control deviation data sequence does not contain disturbance components with low reproducibility that should be removed. That is, the control deviations in individual control deviation data sequences acquired multiple times and their representative values ​​will be equivalent, so it is not necessary to acquire control deviation data sequences multiple times and generate a representative value data sequence based on them.

[0073] Figure 14 shows an example configuration of the control device 200 according to the third embodiment. In the third embodiment, the determination unit 213 includes a reproducibility evaluation unit 1401. The reproducibility evaluation unit 1401 compares the control deviation data sequence stored in the storage unit 601 with the newly acquired control deviation data sequence of the controlled object 220 and evaluates the reproducibility of the control deviation data sequence. If the reproducibility evaluation unit 1401 evaluates that the reproducibility meets the criteria, it provides the newly acquired control deviation data sequence to the calculation unit 603. If the reproducibility evaluation unit 1401 evaluates that the reproducibility does not meet the criteria, it stores the control deviation data sequence in the storage unit 601 until the same number of control deviation data sequences as a predetermined number of stored sequences are stored in the storage unit 601. The processing unit 602 generates a representative value data sequence based on the multiple control deviation data sequences stored in the storage unit 601 and provides it to the calculation unit 603.

[0074] Figure 15 is a flowchart illustrating the details of the process for acquiring a representative value data sequence of control deviations in the third embodiment. After process S801, process S1501 is performed. In process S1501, the processor 210 determines whether one or more control deviation data sequences have been stored in the storage unit 601. If the determination result is true, the processor 210 proceeds to process S1502; if the determination result is false, it performs process S802 and then returns to process S801. In process S1502, the processor 210 determines whether process S1504 has been performed once or more. If the determination result is true, the processor 210 proceeds to process S1506; if the determination result is false, it proceeds to process S1503. In step S1503, the processor 210 calculates an evaluation value as the sum of the absolute values ​​of the differences between control deviations at each time point between the control deviation data sequence stored in the memory unit 601 and the control deviation data sequence newly acquired in step S801. In step S1504, it is determined whether the sum calculated as the evaluation value in step S1503 is less than a predetermined threshold, that is, whether the reproducibility of the control deviation data sequence meets the criteria. The threshold may be determined, for example, based on the amplitude of the control deviation data sequence, based on experience, or according to other methods. If the determination result is true, the processor 210 proceeds to step S1505; if the determination result is false, it proceeds to step S1506. In step S1505, the processor 210 provides the control deviation data sequence acquired in step S801 to the arithmetic unit 603. In step S1506, the processor 210 determines whether the number of times the control deviation data sequence has been stored in the memory unit 601 (i.e., the number of stored control deviation data sequences) satisfies a predetermined number of storage cycles. If the determination result is true, the processor 210 proceeds to step S804; if the determination result is false, it performs step S802 and then returns to step S801.

[0075] As described above, in the third embodiment, the control device 200 determines whether the system is in a disturbance environment with low reproducibility. If the control device 200 determines that the system is in a disturbance environment with low reproducibility, it uses a representative value data sequence generated based on multiple control deviation data sequences to determine the gain of the feedforward controller 211. On the other hand, if the control device 200 determines that the system is in a disturbance environment with high reproducibility, it uses the most recent control deviation data sequence to determine the gain of the feedforward controller 211. Therefore, according to the third embodiment, control accuracy can be improved by feedforward control regardless of whether or not the system contains disturbances with low reproducibility.

[0076] The control device 200 of the fourth embodiment will be described below. Matters not mentioned with respect to the control device 200 of the fourth embodiment may be described in accordance with the description of the control device 200 of any of the first to third embodiments. In the first embodiment, a representative value data sequence is generated using a predetermined number of accumulated control data sequences. However, in an environment containing disturbances with low reproducibility, the number of accumulated control deviation data sequences required to remove the disturbance components with low reproducibility from the control deviation data sequence may change.

[0077] Figure 16 shows an example of the configuration of the control device 200 according to the fourth embodiment. In the fourth embodiment, the determination unit 213 includes a count determination unit 1601. The count determination unit 1601 counts the number of passes in which the sum of the absolute values ​​of the differences between the two most recent representative value data sequences output by the processing unit 602 at each time point is less than a predetermined threshold, and stores the control deviation data sequence in the storage unit 601 until the number of passes reaches a predetermined number.

[0078] Figure 17 is a flowchart illustrating the details of the process for acquiring a representative value data sequence of control deviations in the fourth embodiment. Process S1701 is performed before process S801. Processes S1702 to S1705 are performed between processes S804 and S805. In process S1701, the processor 210 initializes the number of successful attempts held by the count determination unit 1601 to 0. In process S1702, the count determination unit 1601 calculates the sum of the absolute values ​​of the differences between the representative values ​​at each time point in the two most recent representative value data sequences generated by the processing unit 602 as the evaluation value. In process S1703, the count determination unit 1601 determines whether the evaluation value calculated in process S1702 is less than a predetermined threshold, i.e., whether the evaluation value meets the acceptance criteria. The threshold may be determined, for example, based on the amplitude of the control deviation data sequence, based on experience, or according to other methods. If the judgment result is true, the processor 210 proceeds to process S1704; otherwise, it proceeds to process S1705. In process S1704, the number of successful attempts held by the count determination unit 1601 is increased by 1. In process S1705, the processor 210 determines whether the number of successful attempts held by the count determination unit 1601 is equal to or greater than a predetermined number (threshold number). The threshold number can be predetermined, for example, based on experience. If the judgment result is true, the processor 210 proceeds to process S805; otherwise, it returns to process S801.

[0079] As described above, in the fourth embodiment, the number of control deviation data sequences needed to remove the less reproducible disturbance components included in the control deviation data sequence used to determine the gain of the feedforward controller 211 in an environment containing disturbances with low reproducibility is dynamically determined. This makes it possible to determine the gain of the feedforward controller 211 based on a representative value data sequence corresponding to the reproducibility of the disturbance. Therefore, even in an environment containing disturbances with low reproducibility, the controlled object 220 can be controlled based on a sufficient number of control deviation data sequences.

[0080] When the control device 200 is applied to the exposure apparatus EXP, the controlled object 220 may be the master plate stage mechanism 140 or the substrate stage mechanism 150, but the controlled object 220 may be other components to be feedforward controlled. The master plate stage mechanism 140 and / or the substrate stage mechanism 150 are examples of stage mechanisms for aligning the master plate 103 and the substrate 106.

[0081] The following describes a method for manufacturing articles using lithography, such as an EPX exposure apparatus. The article manufacturing method may include a transfer step of transferring a pattern from a master plate onto a substrate using a lithography apparatus, and a processing step of processing the substrate after the transfer step to obtain an article. The article may be, for example, a microdevice such as a semiconductor device or a display, or an element such as a MEMS having a fine structure. The lithography apparatus is not limited to an exposure apparatus, but may be, for example, an imprint apparatus. The processing steps may include, for example, development, etching, oxidation, film formation, vapor deposition, doping, planarization, resist stripping, dicing, bonding, packaging, etc.

[0082] This specification and accompanying drawings include the following disclosures: (Item 1) A control device that controls a controlled object based on a feedforward manipulated variable generated by a feedforward controller, The system includes a determination unit that determines the gain of the feedforward controller based on a control deviation data sequence showing the change in the control deviation of the controlled object and a response data sequence showing the response characteristics of the controlled object when a specific manipulated variable is applied to the controlled object. The determination unit generates a representative value data sequence consisting of representative values ​​of the control deviation of the controlled object at each time based on a plurality of control deviation data sequences acquired multiple times, and determines the gain based on the representative value data sequence and the response data sequence. A control device characterized by the following features. (Item 2) A feedback controller that generates a feedback manipulated variable based on the control deviation of the controlled object, An adder that generates the sum of the feedforward manipulated variable and the feedback manipulated variable as an manipulated variable to be applied to the controlled object, The control device according to item 1, further comprising the following: (Item 3) The determination unit acquires the control deviation data sequence when the feedback operation amount among the feedforward operation amount and the feedback operation amount is provided to the controlled object through the adder. The control device according to item 2, characterized in that (Item 4) The determination unit acquires a response data sequence showing the response characteristics when the specific operation amount, as the feedforward operation amount, is provided to the adder, and the sum of the specific operation amount and the feedback operation amount is provided to the controlled object through the adder. The control device according to item 2, characterized in that (Item 5) The aforementioned representative value is either the mean or the median. A control device according to any one of items 1 to 4, characterized in that it is a control device. (Item 6) The determination unit generates a second representative value data sequence, which consists of representative values ​​for each time step of the response characteristics of the controlled object, based on a plurality of response data sequences acquired multiple times, and determines the gain of the feedforward controller based on the representative value data sequence and the second representative value data sequence. A control device according to any one of items 1 to 5, characterized in that it is a control device. (Item 7) The determination unit determines the second representative value data column based on a plurality of response data columns acquired multiple times. The control device according to item 6, characterized in that (Item 8) The determination unit evaluates the reproducibility of the plurality of control deviation data sequences, and if the reproducibility does not meet the criteria, it generates the representative value data sequence and determines the gain of the feedforward controller based on the representative value data sequence and the response data sequence. A control device according to any one of items 1 to 7, characterized in that it is a control device. (Item 9) The determination unit evaluates the reproducibility based on at least two of the control deviation data sequences among the plurality of control deviation data sequences. The control device according to item 8, characterized in that it is a control device. (Item 10) The determination unit evaluates the reproducibility based on the sum of the absolute values ​​of the time-dependent differences of the at least two control deviation data sequences. The control device according to item 9, characterized in that (Item 11) If the number of times the sum satisfies the passing criteria exceeds a predetermined number, it is determined that the reproducibility satisfies the criteria. The control device according to item 10, characterized in that (Item 12) The waveform of the aforementioned specific manipulated variable has an impulse shape. A control device according to any one of items 1 to 11, characterized in that it is a control device. (Item 13) The controlled object is a stage mechanism. A control device according to any one of items 1 to 12, characterized in that it is a control device. (Item 14) Stage mechanism, A control device according to any one of items 1 to 12, configured to perform control with the aforementioned stage mechanism as the control target, A positioning device characterized by comprising: (Item 15) A lithography apparatus for transferring the pattern of an original plate onto a substrate, A stage mechanism for aligning the original plate and the substrate, A control device according to any one of items 1 to 12, configured to perform control with the aforementioned stage mechanism as the control target, A lithography apparatus characterized by comprising the following: (Item 16) A transfer process in which the pattern of the original plate is transferred to the substrate using the lithography apparatus described in item 15, A processing step to obtain an article by processing the substrate that has undergone the transfer step, A method for manufacturing articles, characterized by including the following: (others) The invention is not limited to the embodiments described above, and various modifications and variations are possible without departing from the spirit and scope of the invention. Accordingly, claims are attached to disclose the scope of the invention.

Claims

1. A control device that controls a controlled object based on a feedforward manipulated variable generated by a feedforward controller, The system includes a determination unit that determines the gain of the feedforward controller based on a control deviation data sequence showing the change in the control deviation of the controlled object and a response data sequence showing the response characteristics of the controlled object when a specific manipulated variable is applied to the controlled object. The determination unit generates a representative value data sequence consisting of representative values ​​of the control deviation of the controlled object at each time based on a plurality of control deviation data sequences acquired multiple times, and determines the gain based on the representative value data sequence and the response data sequence. A control device characterized by the following features.

2. A feedback controller that generates a feedback manipulated variable based on the control deviation of the controlled object, An adder that generates the sum of the feedforward manipulated variable and the feedback manipulated variable as an manipulated variable to be applied to the controlled object, The control device according to claim 1, further comprising the following:

3. The determination unit acquires the control deviation data sequence when the feedback operation amount among the feedforward operation amount and the feedback operation amount is provided to the controlled object through the adder. The control device according to claim 2.

4. The determination unit acquires a response data sequence showing the response characteristics when the specific operation amount, as the feedforward operation amount, is provided to the adder, and the sum of the specific operation amount and the feedback operation amount is provided to the controlled object through the adder. The control device according to claim 2.

5. The aforementioned representative value is either the mean or the median. The control device according to feature 1.

6. The determination unit generates a second representative value data sequence, which consists of representative values ​​for each time step of the response characteristics of the controlled object, based on a plurality of response data sequences acquired multiple times, and determines the gain of the feedforward controller based on the representative value data sequence and the second representative value data sequence. The control device according to feature 1.

7. The determination unit determines the second representative value data sequence based on a plurality of response data sequences acquired multiple times. The control device according to claim 6.

8. The determination unit evaluates the reproducibility of the plurality of control deviation data sequences, and if the reproducibility does not meet the criteria, it generates the representative value data sequence and determines the gain of the feedforward controller based on the representative value data sequence and the response data sequence. The control device according to feature 1.

9. The determination unit evaluates the reproducibility based on at least two of the control deviation data sequences among the plurality of control deviation data sequences. The control device according to claim 8.

10. The determination unit evaluates the reproducibility based on the sum of the absolute values ​​of the time-dependent differences of the at least two control deviation data sequences. The control device according to feature 9.

11. If the number of times the sum satisfies the passing criteria exceeds a predetermined number, it is determined that the reproducibility satisfies the criteria. The control device according to claim 10.

12. The waveform of the aforementioned specific manipulated variable has an impulse shape. The control device according to feature 1.

13. The controlled object is a stage mechanism. The control device according to any one of claims 1 to 12.

14. Stage mechanism, A control device according to any one of claims 1 to 12, configured to perform control with the stage mechanism as the control target, A positioning device characterized by comprising:

15. A lithography apparatus for transferring the pattern of an original plate onto a substrate, A stage mechanism for aligning the original plate and the substrate, A control device according to any one of claims 1 to 12, configured to perform control with the stage mechanism as the control target, A lithography apparatus characterized by comprising the following:

16. A transfer step of transferring the pattern of the master plate onto a substrate using the lithography apparatus described in claim 15, A processing step to obtain an article by processing the substrate that has undergone the transfer step, A method for manufacturing articles, characterized by including the following:

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