Control apparatus, positioning apparatus, lithographic apparatus, and article manufacturing method

Abstract

Control apparatus, positioning apparatus, lithographic apparatus, and device manufacturing method are disclosed. A control apparatus for controlling a control object includes a measurement device configured to measure a state of the control object, and a controller configured to generate a manipulated variable corresponding to an output of the measurement device and a target value. The controller includes a compensator configured to output an index corresponding to the output of the measurement device and the target value, and a converter configured to convert the index into a manipulated variable such that a probability of generating a predetermined manipulated variable is a target probability.

Description

TECHNICAL FIELD

[0001] The present application relates to a control device, a positioning device, a lithographic apparatus, and an object manufacturing method. BACKGROUND

[0002] Japanese Patent Laid-Open No. 2019-71405 describes a control system for controlling a stage by using a neural network. This control system includes a first control unit that outputs a first manipulated variable based on control deviation information and a second control unit that outputs a second manipulated variable from a neural network based on the control deviation information, and an adder for adding the first manipulated variable and the second manipulated variable. The second control unit includes a limiter unit for limiting an upper limit and a lower limit of the second manipulated variable.

[0003] Unfortunately, when simply limiting the upper limit and the lower limit of the manipulated variable as described in Japanese Patent Laid-Open No. 2019-71405, the neural network generates an unnecessary manipulated variable, and this can hinder improvement of the control characteristics. SUMMARY

[0004] The present application provides a technique that is advantageous for improving control characteristics.

[0005] A first aspect of the present application provides a control device for controlling a controlled object, including: a measurement device configured to measure a state of the controlled object; and a controller configured to generate a manipulated variable corresponding to an output of the measurement device and a target value, wherein the controller includes a compensator configured to output an index corresponding to the output of the measurement device and the target value, and a converter configured to convert the index into a manipulated variable such that a probability of generating a predetermined manipulated variable is a target probability.

[0006] A control device for controlling a control object according to a second aspect of the present application includes a measurement device configured to measure a state of the control object, a first controller configured to generate a first manipulated variable corresponding to an output of the measurement device and a target value, a second controller configured to generate a second manipulated variable corresponding to the output and the target value, and a calculator configured to generate a manipulated variable for manipulating the control object based on the first manipulated variable and the second manipulated variable, wherein the second controller includes a compensator configured to output an index corresponding to the output and the target value, and a converter configured to convert the index into the second manipulated variable according to a conversion rule, and the conversion rule is a conversion rule corresponding to a probability distribution of the first manipulated variable when the control object is controlled in a mode in which the calculator generates the manipulated variable based on the first manipulated variable, not the second manipulated variable.

[0007] A control device for controlling a control object according to a third aspect of the present application includes a measurement device configured to measure a state of the control object, a first controller configured to generate a first manipulated variable corresponding to an output of the measurement device and a target value, a second controller configured to generate a second manipulated variable corresponding to the output and the target value, a calculator configured to generate a manipulated variable for manipulating the control object based on the first manipulated variable and the second manipulated variable, and a setting device, wherein the second controller includes a compensator configured to output an index corresponding to the output and the target value, and a converter configured to convert the index into the second manipulated variable according to a conversion rule, and the setting device sets the conversion rule according to a probability distribution of the first manipulated variable when the control object is controlled in a mode in which the calculator generates the manipulated variable based on the first manipulated variable, not the second manipulated variable.

[0008] A positioning device according to a fourth aspect of the present application includes a gantry mechanism including a gantry, a driver configured to drive the gantry mechanism, a measurement device configured to measure a state of the gantry, and a control device as defined in the first, second, or third aspect of the present application, wherein the control device is configured to control the gantry as a control object.

[0009] A lithography device for transferring a pattern of a master onto a substrate according to a fifth aspect of the present application includes a positioning device as defined in the fourth aspect of the present application, wherein the gantry of the positioning device holds the substrate.

[0010] A sixth aspect of the present application provides a product manufacturing method including: forming a pattern on a substrate by using a lithography apparatus defined as the fifth aspect of the present application; and obtaining an article by processing the substrate on which the pattern is formed.

[0011] Further features of the present application will become clear from the following description of exemplary embodiments with reference to the attached drawings. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 is a diagram showing a configuration of a system of a first embodiment;

[0013] Figure 2 is a diagram showing an example in which a control device in the system of the first embodiment is applied to a positioning device;

[0014] Figure 3 is a diagram showing Figure 2 is a diagram showing a more detailed configuration of the control device (positioning device) shown in

[0015] Figure 4 is a flowchart showing an example of a neural network learning sequence using reinforcement learning according to the first embodiment;

[0016] Figure 5 is a diagram showing an example of a configuration for determining a manipulation amount of a driver by inputting a control bias to a controller;

[0017] Figure 6 is a diagram showing a conversion rule in a comparative example;

[0018] Figure 7 is a diagram showing a frequency of use of each manipulation amount at the time of obtaining a maximum reward by learning in the comparative example;

[0019] Figure 8 is a diagram showing an example of determining a plurality of manipulation amounts based on a target probability distribution in an embodiment;

[0020] Figure 9 is a diagram showing an example of a conversion rule in the embodiment;

[0021] Figure 10 is a diagram showing an example of a control bias in the comparative example and the embodiment;

[0022] Figure 11 is a diagram showing another example of a configuration for determining a manipulation amount of a driver by inputting a control bias to a controller;

[0023] Figure 12is a diagram showing an example in which the control device in the system of the second embodiment is applied to the positioning device;

[0024] Figure 13 is a flowchart showing an example of a neural network learning sequence using reinforcement learning according to the second embodiment;

[0025] Figure 14 is a diagram showing a configuration example of an exposure apparatus as a lithography apparatus; and

[0026] Figure 15 is a diagram showing a configuration example of an imprint apparatus as a lithography apparatus. DETAILED DESCRIPTION

[0027] Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. Note that the following embodiments are not intended to limit the scope of the claimed invention. A plurality of features are described in the embodiments, but the invention is not limited to inventions requiring all such features, and a plurality of such features can be appropriately combined. Furthermore, in the drawings, the same reference signs are given to the same or similar configurations, and redundant descriptions thereof are omitted.

[0028] Figure 1 A configuration of a system SYS of an embodiment is shown. The system SYS can include, for example, a control device 1 including a control object, a control server 2 for controlling the control device 1, and a learning server 3 for performing learning of the control device 1 via the control server 2. The control device 1 includes a compensator including a neural network. The learning server 3 can transmit a parameter value of the neural network to the control device 1 via the control server 2, and transmit a drive command to the control device 1 via the control server 2. The control device 1 can perform an operation of driving the control object according to the drive command, and transmit a drive result (for example, a control deviation) to the learning server 3 via the control server 2. The learning server 3 can calculate a reward based on the drive result, and update the parameter value of the neural network based on the reward.

[0029] The functions of the control server 2 can be incorporated in the control device 1 in whole or in part. Alternatively, the functions of the control server 2 can be incorporated in the learning server 3 in whole or in part. Alternatively, the functions of the control server 2 and the learning server 3 can be partially incorporated in the control device 1. Alternatively, the control device 1, the control server 2, and the learning server 3 can be integrated. The control server 2 can be a host device of the control device 1. For example, the control device 1 can be one constituent element of a lithography apparatus, and the control server 2 can be a main control device of the lithography apparatus, or a comprehensive control device for controlling a plurality of lithography apparatuses including the lithography apparatus.

[0030] Figure 2 A configuration in which Figure 1The control device 1 in the system SYS shown in FIG. 1 is applied to an example of a positioning device. The control device 1 configured as a positioning device can be configured so as to control a stage ST as a control object. Figure 2 The control device 1 shown in FIG. 1 can include a stage mechanism 5, a measurement device 6, a driver 7, and a control board (control unit) 8. The stage mechanism 5 can include a stage ST and an actuator (not shown) for driving the stage ST. The stage ST can hold a positioning target such as a substrate. The actuator can include at least one of a linear motor, an electromagnetic actuator, a voice coil motor, and a rack and pinion mechanism. The control object can be the stage ST, or a member (e.g., a substrate) held on the stage ST. More macroscopically, the control object can be understood as the stage mechanism 5. The measurement device 6 can measure a state (e.g., a position) of the control object. The control board 8 can send a command (manipulation amount) to the driver 7, and output a current to the actuator of the stage mechanism 5. The state (driving result) of the stage mechanism 5 or the stage ST can be measured or detected by the measurement device 6, and provided to the control board 8.

[0031] Figure 3 A more detailed configuration example of the control device 1 shown in FIG. 1 is shown. Figure 2 A more detailed configuration example of the control device 1 shown in FIG. 1 is shown.

[0032] Figure 4A neural network learning sequence S100 using reinforcement learning is shown. First, in step S101, the learning server 3 communicates with the control device 1 via the control server 2 and initializes the parameter values of the neural network of the controller 10. Then, in step S102, the learning server 3 sends a predetermined operation command to the control device 1 via the control server 2 so as to drive the gantry mechanism 5 (gantry ST). In the example, upon receiving the operation command, the control server 2 can supply a drive command (target value string) to the control device 1 so as to drive the gantry ST of the gantry mechanism 5 along a drive track corresponding to the operation command. The control device 1 can be configured to accumulate the drive results of the gantry mechanism 5, for example, the difference value (control deviation) calculated by the calculator 9, and provide the drive results to the control server 2 or the learning server 3 according to a request from the control server 2 or the learning server 3.

[0033] In step S103, the learning server 3 acquires the drive results accumulated by the operation in step S102 from the control device 1 via the control server 2. In step S104, the learning server 3 calculates a reward based on the drive results acquired in step S103. The formula for calculating the reward can be determined to obtain a high reward when the control deviation is small, for example. In step S105, the learning server 3 determines whether the reward calculated in step S104 satisfies a learning termination condition. If the reward satisfies the learning termination condition, the learning server 3 advances the process to step S106; if not, the learning server 3 advances the process to step S107. In step S107, the learning server 3 changes the parameter values of the neural network of the controller 10, and thereafter executes steps S102 to S105 again. In step S106, the learning server 3 saves the latest parameter values of the neural network as a learning result.

[0034] Figure 5An example of a configuration for determining a manipulated variable for the driver 7 by inputting a control deviation to the controller 10 is shown. The controller 10 can include a compensator 510 for outputting an index 503 corresponding to a control deviation (a difference between an output from the measurement device 6 and a target value), and a converter 520 for converting the index 503 to a manipulated variable 504 according to a conversion rule 521. The conversion rule 521 can be given by, for example, a conversion table for defining a plurality of manipulated variables 504 corresponding to a plurality of indices 503, respectively. The compensator 510 is formed of a neural network, and the neural network can include an input layer 500, a hidden layer 501, and an output layer 502. The output layer 502 can be formed of a plurality of neurons corresponding to a plurality of indices 503 that can be taken by an input to the conversion rule 521, respectively. An operation of the neural network forming the compensator 510 is defined by preset parameter values, and the neural network calculates an activity of each neuron in the hidden layer 501 and the output layer 502 based on a control deviation input to the input layer 500. Then, the neural network forming the compensator 510 selects an index 503 corresponding to a most active neuron among the plurality of neurons in the output layer 502, and outputs the index 503 as a calculation result of the neural network. The most active neuron among the plurality of neurons is a neuron whose activity has a largest numerical value. The converter 520 outputs a manipulated variable 504 corresponding to the input index 503 according to the conversion rule 521. In other words, the converter 520 converts the input index 503 to a manipulated variable 504 according to the conversion rule 521, and outputs the manipulated variable 504.

[0035] One feature of this embodiment is the conversion rule 521. In order to understand the conversion rule 521 of this embodiment in depth, a comparative example and a problem of the comparative example will be explained first.

[0036] Figure 6 The conversion rule in the comparative example is shown. Referring to Figure 6 , the abscissa indicates an index, and the ordinate indicates a conversion rule as a manipulated variable Fn. In this comparative example, the conversion rule is defined so that when a minimum value of the manipulated variable Fn is F0, a maximum value of the manipulated variable Fn is FN, and an index is n, the index n and the manipulated variable Fn have a linear relationship as indicated by the following formula (1):

[0037] Fn = n x (FN - F0) / N + F0 (n = 0 ~ N)... (1)

[0039] The learning was executed in a state where the conversion rule as described above was set. As the configuration of the control board 8, each of the number of neurons in the output layer 502, the number of indexes 503, and the number of manipulated variables 504 was set to 9, and F0 was determined so that F4 = 0. Under this condition, the learning was executed so that the control deviation is reduced when the drive command (target value) of the control device 1 has a predetermined value.

[0040] Figure 7 The frequency of use of each manipulated variable when the maximum return is obtained by the learning in the comparative example is shown. This result shows that the manipulated variables F0, F2, F5, and F7 are not used at all. That is, as a result of the learning, it is determined that these manipulated variables are unnecessary. Figure 3 The configuration shown in the comparative example has a limitation that the controller 10 must generate the output (i.e., the manipulated variable) at a predetermined cycle, and thus the amount of calculation of the controller 10 is expected to be wasted. However, in the comparative example, there are unnecessary manipulated variables among the calculated manipulated variables, and thus it is necessary to delete these manipulated variables or replace them with other manipulated variables.

[0041] The conversion rule 521 of the converter 520 according to this embodiment will be explained below in comparison with the comparative example mentioned above. In this embodiment, the conversion rule 521 is set so that the probability distribution of the manipulated variable output from the converter 520 or the controller 10 follows a target probability distribution. The manipulated variable probability distribution is a distribution of the probability that each value of the manipulated variable can occur within the range of the minimum value and the maximum value of the manipulated variable. When the learning is started by defining or setting the conversion rule 521 as described above, the wasted calculation of the controller 10 can be omitted by reducing the generation of unnecessary manipulated variables. This is advantageous in improving the control characteristics of the control device 1.

[0042] The manipulated variable must be output so as to reduce the control deviation of the stand ST. Therefore, when the manipulated variable is plotted on the horizontal axis and the probability is plotted on the vertical axis, the conversion rule 521 preferably has a shape (probability distribution) that is convex upward in the entire region between the minimum value and the maximum value of the manipulated variable. Also, this shape preferably has a peak in the position where the manipulated variable is 0 when the offset value is 0, and has a peak in the position where the manipulated variable is the offset value when the offset value is not 0. Note that the offset value can be used to eliminate individual differences caused by tolerances and the like. The shape that is convex upward can be, for example, a normal distribution.

[0043] In the example, as shown in Figure 8 The plurality of manipulated variables F0 to F8 can be determined based on the target probability distribution 900 so that the frequency of use (probability) of the plurality of manipulated variables F0 to F8 is constant (the area in Figure 8 Figure 9 The relationship between the index and the manipulated variable (i.e., the conversion rule) is shown, which is the same as​Figure 8 The target probability distribution 900 and the plurality of manipulated variables F0 to F8 correspond to each other as shown in FIG. 9. The maximum value F8 and the minimum value F0 of the manipulated variable can be determined based on, for example, the weight of the stage ST as the control object and the maximum driving acceleration and the size of the assumed maximum control deviation. Further, when the target probability distribution 900 having the shape convex upward is a normal distribution, its variance value is related to the resolution of the manipulated variable and thus can be determined in accordance with the assumed maximum control deviation.

[0044] Figure 10 The control deviation in the state where the parameter value obtaining the maximum reward is set in the neural network is shown in relation to the comparative example (dotted line) and this embodiment (solid line). When compared with the comparative example, in this embodiment, the manipulated variable close to zero (F4) can be used, and thus the output resolution of the driver 7 is improved, and as a result, the control deviation is more suppressed. This means that the control characteristics of this embodiment are superior to those of the comparative example. Also, the time required for learning of this embodiment is shorter than that of the comparative example. Further, the number of neurons in the neural network forming the compensator 510 of this embodiment is the same as that of the comparative example, and thus the amount of computation of the controller 10 of this embodiment is also the same as that of the comparative example. However, the position accuracy of the stage ST of this embodiment is higher than that of the comparative example. Further, even when the compensator 510 is not formed by the neural network, the effect of this embodiment can be obtained.

[0045] Figure 11Another example of a configuration for determining a manipulation amount of the driver 7 by inputting a control deviation to the controller 10 is shown. The controller 10 can include a compensator 610 for outputting an index 603 corresponding to the control deviation (a difference between the output value of the measurement device 6 and the target value) and a converter 620 for converting the index 603 to a manipulation amount according to a conversion rule 621. The compensator 610 is formed of a neural network, and the neural network can include an input layer 600, a hidden layer 601, and an output layer 602. The output layer 602 is formed of a single neuron. The operation of the neural network forming the compensator 610 is defined by preset parameter values. The neural network calculates the activity of each neuron in the hidden layer 601 and the output layer 602 based on the control deviation input to the input layer 600. Then, the neural network forming the compensator 610 outputs the index 603 in which the numerical value of the neuron activity in the output layer 602 is normalized to a numerical value from 0 to 1 as a result of the calculation of the neural network. The conversion rule 621 of the converter 620 gives the manipulation amount 604 when matching the area (integral value) from F0 to the index 603 in a target probability distribution (for example, a normal distribution) having an upwardly convex shape. In other words, the conversion rule 621 is set so that the probability distribution of the manipulation amount 604 follows the target probability distribution. The converter 620 calculates the manipulation amount 604 according to such a conversion rule 621, and outputs the manipulation amount 604 as the output of the controller 10. When the target probability distribution defining the conversion rule 621 is a normal distribution, the mean value and the variance value of this normal distribution are arbitrary values.

[0046] When a plurality of drive profiles are prepared to control the drive of the gantry mechanism 5 or the stand ST, the controller 10 can be installed for each drive profile, and a controller 10 corresponding to the drive profile is selected from the plurality of controllers 10. In this case, the conversion rule of the converters 520 and 620 can be determined for each controller 10.

[0047] In the controller 10 having an index-manipulation amount relationship (conversion rule) determined based on a given target probability distribution, in order to achieve higher positioning accuracy after executing a series of learning sequences, the learning sequences can be executed again by changing the target probability distribution. For example, in the controller 10 having an index-manipulation amount relationship determined based on a given target probability distribution, in order to achieve higher positioning accuracy after executing a series of learning sequences, the learning sequences can be executed again by changing the target probability distribution. This change of the target probability distribution can include, for example, a change of at least one of the mean value and the variance value.

[0048] The adjustment of the controller 10 as described above will be explained below. Figure 3In this case, after the parameter values 20 of the neural network are obtained by executing the learning sequence S100 in the first gantry control device, the learned parameter values 20 can be applied to the second gantry control device. Therefore, the second gantry control device can achieve positioning accuracy equivalent to that of the first gantry control device without the need to perform any learning. The learning sequence S100 can also be executed by applying the learned parameter values 20 as initial values to the second gantry control device. In this case, the learning can also be performed by changing the shift amount in the direction of the manipulated variable of the target probability distribution that provides the conversion rule of the controller 10 of the second gantry control device and the spread amount.

[0049] A second embodiment will be explained below. Items not mentioned in the second embodiment follow those of the first embodiment. Figure 12 The configuration of the control device 1 of the second embodiment is shown. The control device 1 of the second embodiment is configured as a positioning device in this example, but the control device 1 can also be configured as another form of control device. The control board 8 can include a calculator 9 for calculating the difference (control deviation) between the state (e.g., position) of the control object measured by the measurement device 6 and the drive command (target value) for controlling the control object, and first and second controllers 30 and 40 for generating first and second manipulated variables corresponding to the output of the calculator 9. The controllers 30 and 40 can also be understood as constituent elements for generating a manipulated variable based on the state of the control object and the drive command. The first controller 30 can be, for example, a PID controller. The second controller 40 operates as a compensator defined by the parameter values of the neural network provided from the learning server 3. Like the controller 10 of the first embodiment, the second controller 40 includes a compensator 510 (610) and a converter 520 (620). The control board 8 can also include a calculator (adder) 60 for generating a manipulated variable for manipulating the control object based on the first and second manipulated variables, and a switch 50 for opening / closing the path connecting the second controller 40 and the calculator 60. The driver 7 can convert the manipulated variable provided by the control board 8 or the controller 10 into a current.

[0050] Figure 13 An example of the learning sequence 200 of the control device 1 of the second embodiment is shown. Figure 13 An example of the learning sequence 200 of the control device 1 of the second embodiment is shown. Figure 12The configuration shown in FIG. 6 corresponds to a neural network learning sequence using reinforcement learning. First, in step S201, the learning server 3 turns off the switch 50. As a result, the control board 8 or the control device 1 is set to a mode in which the calculator 60 generates the manipulation amount on the basis of the first manipulation amount, not the second manipulation amount. Then, in step S202, the learning server 3 sends a predetermined operation command to the control device 1 via the control server 2 so as to operate the gantry mechanism 5. In this example, upon receipt of the operation command, the control server 2 can supply a drive command (target value string) to the control device 1 so as to drive the gantry ST along a drive track corresponding to the operation command. The control device 1 can be configured to accumulate the manipulation amount generated by the control board 8 (the first controller 30) and provide the drive result to the control server 2 or the learning server 3 upon request from the control server 2 or the learning server 3. In step S203, the learning server 3 obtains the manipulation amount accumulated by the operation in step S202 from the control device 1 via the control server 2. In step S204, the learning server 3 determines whether the number of times of execution of steps S202 and S203 is equal to or greater than a predetermined value. If the number of times of execution is equal to or greater than the predetermined value, the learning server 3 advances the process to step S205; if not, the learning server 3 executes steps S202 and S203 again.

[0051] In step S205, the learning server 3 generates a manipulation amount frequency distribution on the basis of the manipulation amounts obtained by the predetermined number of times and determines a target probability distribution corresponding to the frequency distribution. This target probability distribution corresponding to the frequency distribution can be a probability distribution having the same or similar shape as that of the frequency distribution, or a probability distribution having the same features as those extracted from the frequency distribution. However, the target probability distribution can also have another correlation with respect to the frequency distribution.

[0052] In step S206, the learning server 3 generates a conversion rule corresponding to the target probability distribution determined in step S205 and sets this conversion rule in the converter of the second controller 40. This process is the same as that of the first embodiment. In step S207, the learning server 3 turns on the switch 50. As a result, the control board 8 or the control device 1 is set to a mode in which the calculator 60 generates the manipulation amount to be supplied to the driver 7 on the basis of the first and second manipulation amounts. Then, in step S208, the learning server 3 executes steps S101 to S107 shown in FIG. 6. Note that the neural network parameter values are set in the neural network of the second controller 40. Figure 4

[0053] ​In the second embodiment, the conversion rule to be set in the converter of the second controller 40 is a conversion rule corresponding to a probability distribution of the first manipulation amount when the control target is controlled in a mode in which the calculator 60 generates the manipulation amount not based on the second manipulation amount but based on the first manipulation amount. The learning server 3 functions as a setting device for setting such a conversion rule in the converter of the second controller 40. Such a setting device can also be incorporated into the control apparatus 1.

[0054] The above-mentioned positioning device can be incorporated into a lithography apparatus for transferring a pattern of a master onto a substrate, and the stage ST of this positioning device can be configured to hold and position the substrate. Figure 14 An example of a configuration of an exposure apparatus EXP as an example of a lithography apparatus incorporating the above-mentioned stage mechanism is shown. The exposure apparatus EXP can include a projection optical system PO for projecting a pattern of a master R onto a substrate W. The exposure apparatus EXP can also include a substrate positioning device PA for positioning the substrate W, a master positioning device RSM for positioning the master R, and an illumination optical system IO for illuminating the master R. The above-mentioned positioning device can be applied to the substrate positioning device PA. The substrate positioning mechanism PA can include a stage WS as a movable part for holding the substrate W, and an actuator WSA for driving the stage WS. Alternatively, the above-mentioned positioning device can be applied to the master positioning device RSM.

[0055] Figure 15 An example of a configuration of an imprint apparatus IMP as an example of a lithography apparatus incorporating the above-mentioned stage mechanism is shown. The imprint apparatus IMP transfers a pattern of a master M onto an imprint material IM on a substrate W. The imprint apparatus IMP can include a substrate positioning device PA for positioning the substrate W, an imprint head IH for driving the master M, and a curing unit CU for curing the imprint material. The imprint head IH can bring a pattern region of the master M into contact with the imprint material IM on the substrate W, and can separate the master M from the cured imprint material IM. The curing unit CU can irradiate the imprint material IM with a curing energy (e.g., light energy) while the pattern region of the master M is in contact with the imprint material IM on the substrate W, thereby curing the imprint material IM. The above-mentioned positioning device can be applied to the substrate positioning device PA.

[0056] The above-mentioned lithography apparatus can be applied to an article manufacturing method for manufacturing an article. This article manufacturing method can include a pattern forming step of forming a pattern on a substrate by using the above-mentioned lithography apparatus, and a processing step of obtaining an article by processing the substrate on which the pattern is formed. The processing step can include a step of etching the substrate by using the pattern as an etching mask. The processing step can include a step of forming a film on the substrate, a step of sealing the substrate, and the like. The article manufacturing method can also perform a multiple pattern forming method.

[0057] Other Embodiments

[0058] Embodiments of the present application can also be realized by a computer- readable storage medium having recorded thereon a program (e.g., one or more programs) of instructions to execute functions of one or more of the above-described embodiments and / or one or more circuits (e.g., application specific integrated circuit (ASIC)) for executing functions of one or more of the above-described embodiments, by a computer of a system or apparatus of the present application reading and executing the one or more programs recorded on the storage medium and by a method of the present application performed by the computer of the system or apparatus of the present application by, for example, reading and executing the one or more programs recorded on the storage medium to execute functions of one or more of the above-described embodiments and / or controlling the one or more circuits to execute functions of one or more of the above-described embodiments. The computer can include one or more processors (e.g., central processing unit (CPU), micro processing unit (MPU)) and can include a single computer or a network of separate computers to read and execute the computer-executable instructions. The computer-executable instructions can be provided from one or more computer program products of the present application to the computer, for example. The computer program product can be provided to the computer on a storage medium, through an application store or download interface, using a wired (e.g., digital subscriber line (DSL), cable modem) or wireless (e.g., Wi-Fi, WiMAX) communications channel, or any combination thereof. The storage medium can include one or more of a hard disk, a random access memory (RAM), a read only memory (ROM), a storage device of a distributed computing system, a compact disc read only memory (CD-ROM), digital versatile disc (DVD), Blu-ray Disc® or the like. TM

[0059] Embodiments of the present application can also be realized by a method of the present application, by providing a software (program) to a system or apparatus of the present application through a network or various storage media, and by a computer of the system or apparatus or a central processing unit (CPU), a micro processing unit (MPU) reading and executing the program.

[0060] While the present application has been described with reference to exemplary embodiments, it is to be understood that the application is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all the modifications and equivalent structures and functions.​

Claims

1. A control device for controlling a control object, comprising: a measurement device configured to measure a state of the control object; and a controller configured to generate a manipulated variable corresponding to an output of the measurement device and a target value, wherein the controller includes a compensator configured to output an index corresponding to the output of the measurement device and the target value, and a converter configured to convert the index into a manipulated variable such that a probability of generating a predetermined manipulated variable is a target probability, and wherein a distribution of the target probability has a shape that is convex upward in an entire region between minimum and maximum values of the manipulated variable when the manipulated variable is plotted on an abscissa and the probability is plotted on an ordinate. The distribution of the target probability is a normal distribution when the manipulated variable is plotted on an abscissa and the probability is plotted on an ordinate.

2. The apparatus of claim 1, wherein, The compensator determines the index in accordance with a difference between the output of the measurement device and the target value.

3. The apparatus of claim 1, wherein, 4. The device according to claim 1, wherein the compensator includes a neural network having an input layer, a hidden layer, and an output layer, and a parameter value of the neural network is determined by performing learning in a state where a conversion rule for converting the index into a manipulated variable is set.

5. The device according to claim 4, wherein the converter includes a conversion table for defining a plurality of manipulated variables corresponding to a plurality of indexes respectively, the output layer of the neural network is formed of a plurality of neurons corresponding to the plurality of indexes respectively, and the index to be output from the compensator corresponds to a most active neuron among the plurality of neurons. the output layer is formed of a single neuron, and the neural network determines the index in accordance with an activity of the neuron in the output layer.

6. The apparatus of claim 4, wherein, the index to be output from the compensator is obtained by normalizing the activity of the neuron in the output layer.

7. The apparatus of claim 6, wherein, 8. A positioning device comprising: a stage mechanism including a stage; a driver configured to drive the stage mechanism; a measurement device configured to measure a state of the stage; and a control device defined in any one of claims 1 to 7, wherein the control device is configured to control the stage as a control object.

9. A lithography device for transferring a pattern of a master onto a substrate, comprising the positioning device defined in claim 8, the stage of the positioning device holding the substrate.

10. The device according to claim 9, configured as an exposure device by further comprising a projection optical system configured to project the pattern of the master onto the substrate. wherein 11. The device according to claim 9, configured as an imprint device for transferring the pattern of the master onto an imprint material on the substrate.

12. An article manufacturing method comprising: forming a pattern on a substrate by using the lithography device defined in claim 9; and obtaining an article by processing the substrate on which the pattern is formed. ​ ​ ​

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