Control method, positioning device, and program

Abstract

To provide a control method, a positioning device, and a program that are able to prevent residual vibration of a base.SOLUTION: A positioning device includes: a base; a moving portion capable of moving relative to the base; and a driving unit that changes a relative position between the base and the moving portion by applying a force to the base and the moving portion. In the positioning device, a control method positions the moving portion relative to the base by performing posicast control of a force applied to the base and the moving portion by the driving unit, based on a set of pulse patterns calculated assuming that no frictional force acts between the base and the moving portion and the base performs non-damped vibration.SELECTED DRAWING: Figure 7

Description

[Technical Field]

[0001] The present invention relates to a control method, a positioning device, and a program. [Background technology]

[0002] Conventionally, a positioning device has been known that includes a base (base platform), a moving part that is movable relative to the base, and a driving part (motor, etc.) that applies a force to the base and the moving part to change the relative position between the base and the moving part. In such a positioning device, the driving part applies an appropriate force to the base and the moving part, thereby guiding the moving part to a predetermined relative position with respect to the base. Hereinafter, guiding the moving part to a predetermined relative position with respect to the base may be referred to as "positioning the moving part (with respect to the base)." [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2000-56837 Summary of the Invention [Problem to be solved by the invention]

[0004] In such a positioning device, vibrations may remain in the base (i.e., residual vibrations may occur in the base) due to the force applied by the drive unit to the base and the moving unit. Such residual vibrations are likely to occur, for example, in positioning devices that employ a lightweight base for the purpose of reducing weight. The occurrence of such residual vibrations has been an obstacle to improving the accuracy and speed of positioning the moving unit.

[0005] As a technique for suppressing residual vibration of the base, for example, the technique described in Patent Document 1 is known. In this technique, real-time feedback control is performed based on the vibration of the base. However, performing real-time feedback control requires advanced control, which can be difficult to achieve.

[0006] The present invention has been made in consideration of the above circumstances, and an object of the present invention is to provide a control method, a positioning device, and a program that are capable of suppressing residual vibration of the base. [Means for solving the problem]

[0007] In order to solve the above problem, a control method according to one embodiment of the present invention provides a positioning device comprising a base, a moving part that can move relative to the base, and a drive part that changes the relative position between the base and the moving part by applying force to the base and the moving part, in which the drive part positions the moving part relative to the base by positive-cast controlling the force that the drive part applies to the base and the moving part based on a set of pulse patterns calculated assuming that no frictional force acts between the base and the moving part and that the base vibrates undamped.

[0008] Furthermore, a positioning device according to one aspect of the present invention comprises a base, a moving part that is movable relative to the base, a drive part that changes the relative position between the base and the moving part by applying force to the base and the moving part, and a control part that positions the moving part relative to the base by positive-cast controlling the force that the drive part applies to the base and the moving part based on a set of pulse patterns calculated assuming that no frictional force acts between the base and the moving part and that the base vibrates undamped.

[0009] Furthermore, one aspect of the present invention provides a program for causing a computer to execute the following in a positioning device comprising a base, a moving unit capable of moving relative to the base, and a drive unit that changes the relative position between the base and the moving unit by applying force to the base and the moving unit: positioning the moving unit relative to the base by positive-cast controlling the force that the drive unit applies to the base and the moving unit based on a set of pulse patterns calculated on the assumption that no frictional force acts between the base and the moving unit and that the base vibrates undamped. [Effects of the Invention]

[0010] According to the above aspects of the present invention, it is possible to provide a control method, a positioning device, and a program that are capable of positioning a moving part while suppressing residual vibration of a base. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a perspective view showing a positioning device according to a first embodiment. [Figure 2] FIG. 2 is a diagram showing a dynamic model of the positioning device according to the first embodiment. [Figure 3] (a) A graph showing the unit step function force exerted by the drive unit, (b) A graph showing the change in the position of the base over time, and (c) A graph showing the change in the velocity of the base over time. [Figure 4] 10A is a graph showing an example of the force exerted by the drive unit, FIG. 10B is a graph showing the change in the position of the base over time, and FIG. 10C is a graph showing the change in the speed of the base over time. [Figure 5] 10A is a graph showing an example of the force exerted by the drive unit, FIG. 10B is a graph showing the change in the position of the base over time, and FIG. 10C is a graph showing the change in the speed of the base over time. [Figure 6] FIG. 6 is a diagram illustrating the forces shown in FIG. 5(a). [Figure 7](a) A graph showing an example of the force exerted by the drive unit. (b) A graph showing the change in position of the moving unit over time. (c) A graph showing the change in speed of the moving unit over time. (d) A graph showing the change in position of the base over time. (e) A graph showing the change in speed of the base over time. (f) A graph showing the change in acceleration of the base over time. [Figure 8] FIG. 7 is a diagram showing a modification of FIG. 6. [Figure 9] 10 is a graph showing the change in the effective value of the magnitude of residual vibration of the base when the time width of the pulse pattern in positive cast control is changed. [Figure 10] FIG. 10 is a diagram showing an example of a pulse pattern according to the second embodiment. [Figure 11] 10 is a graph showing the change in the speed of the bass over time. [Figure 12] 10A and 10B are diagrams illustrating other examples of the force exerted by the drive unit according to the second embodiment. [Figure 13] FIG. 10 is a block diagram showing a base according to a third embodiment. [Figure 14] FIG. 10 is a block diagram showing a positioning device according to a third embodiment. [Figure 15] 1A is a graph showing the damping vibration of the base, FIG. 1B is a graph showing the external force applied to the base by the external force application unit, and FIG. 1C is a diagram showing the change in the position of the base over time when the external force shown in FIG. 1B is applied. DETAILED DESCRIPTION OF THE INVENTION

[0012] (First embodiment) A control method, a positioning device, and a program according to a first embodiment of the present invention will be described below with reference to the drawings.

[0013] FIG. 1 is a perspective view showing a positioning device 1 according to the first embodiment. As shown in FIG. 1, the positioning device 1 according to this embodiment includes a base (base stand) 10, a moving unit (table) 20, a driving unit 30, and a control unit 40.

[0014] The base 10 according to this embodiment is attached to an attachment object 50 via a plurality of spring members 51. In the illustrated example, the attachment object 50 is a plate-shaped fixed member. The fixed member is fixed to a fixed surface of a desk, floor, or the like (not shown). However, the type of attachment object 50 is not particularly limited, and can be changed as appropriate as long as the base 10 can be attached to it. For example, the attachment object 50 may be a desk, floor, or the like.

[0015] The base 10 according to this embodiment includes a main body 11, a pair of standing portions 12, and a pair of rails 13. However, the configuration of the base 10 can be modified as appropriate. The base 10 may include a stopper to prevent the moving portion 20 from falling off.

[0016] The main body 11 is a plate-shaped member that is attached to the attachment object 50 via a plurality of spring members 51. The pair of standing portions 12 are erected on both side edges of the main body 11. Rails 13 that extend in one direction are provided on the upper ends of the pair of standing portions 12.

[0017] The rail 13 guides the direction of relative movement of the moving unit 20 with respect to the base 10 in the direction in which the rail 13 extends. Hereinafter, the direction of relative movement of the moving unit 20 guided by the rail 13 will be referred to as the moving direction A. Furthermore, one direction in the moving direction A will be referred to as the positive direction, and the direction opposite to the positive direction will be referred to as the negative direction. In this embodiment, the moving direction A coincides with the direction in which the rail 13 extends. The rail 13 functions as a linear guide that guides the direction of relative movement of the moving unit 20 in the moving direction A. The positioning device 1 may be provided with a rolling mechanism or the like to reduce friction between the base 10 (rail 13) and the moving unit 20.

[0018] The moving unit 20 is configured to be movable relative to the base 10. More specifically, the moving unit 20 according to this embodiment moves relative to the base 10 in the direction in which the rail 13 extends (moving direction A). The moving unit 20 according to this embodiment has a plate-like shape. However, the shape of the moving unit 20 can be changed as appropriate.

[0019] The driving unit 30 applies a force to the driven object in accordance with the control of the control unit 40, thereby changing the relative position between the base 10 and the moving unit 20. Here, the "driven object" refers to the object to which the driving unit 30 applies a force. The driven object is the base 10 and the moving unit 20.

[0020] In this embodiment, the driving unit 30 is a linear motor. The driving unit 30, which is a linear motor, applies a force in a positive or negative direction in the moving direction A to the base 10 and the moving unit 20 in accordance with control by the control unit 40. Although detailed illustration is omitted, the linear motor (driving unit 30) according to this embodiment includes a permanent magnet functioning as a mover, a ferromagnetic yoke, and an electric winding wound around the yoke. The permanent magnet functions as the mover, and the yoke and the electric winding function as a stator. When a current (DC current) flows through the electric winding, a corresponding magnetic force is generated. The generated magnetic force repels or attracts the magnetic force generated by the permanent magnet, generating a relative force (thrust) between the mover and the stator. Here, one of the mover and the stator is fixed to the base 10, and the other of the mover and the stator is fixed to the moving unit 20. Therefore, the driving unit 30 generates a relative force (thrust) between the base 10 and the moving unit 20 through the action of the mover and the stator described above. According to the law of action and reaction, the force that the driving unit 30 applies to the moving unit 20 and the force that the driving unit 30 applies to the base 10 are equal in magnitude but opposite in direction to each other.

[0021] The control unit 40 controls the force applied to the driven object by the driving unit 30 based on pulse patterns calculated under the following first and second assumptions, thereby performing positive cast control of the force applied to the driven object by the driving unit 30. The first assumption is that no frictional force acts between the base 10 and the moving unit 20. The second assumption is that the base 10 vibrates without damping (i.e., the damping constant D is zero).

[0022] The control (positioning control) performed by the control unit 40 will be described in detail below.

[0023] FIG. 2 is a diagram showing a dynamic model of the positioning device 1 according to the first embodiment. The definitions of the parameters in Figure 2 are as follows: f [N]: force exerted by the driving unit 30 x [m]: position of the moving part 20 in the moving direction A m [kg]: Mass of moving part 20 X [m]: Position of base 10 in movement direction A M [kg]: Mass of base 10 K [N / m]: Spring constant of spring 61 D [N / (m / s)]: damping constant of damping 62 Specifically, the force f is the force that the driving unit 30 applies to the moving unit 20. According to the law of action and reaction, the force that the driving unit 30 applies to the base 10 is expressed as −f.

[0024] As shown in Fig. 2, in this embodiment, the moving part 20 is assumed to be a simple mass system, and the base 10 is assumed to be a second-order vibration system. In Fig. 2, a spring 61 is an element that applies a force to the base 10 proportional to the relative position between the base 10 and the attachment object 50. Furthermore, a damping 62 is an element that applies a force to the base 10 proportional to the relative velocity between the base 10 and the attachment object 50. In the positioning device 1 shown in Fig. 1, the spring member 51 corresponds to the spring 61. From the second assumption, it is assumed that the damping constant D is zero (in other words, damping 62 does not exist).

[0025] The above-mentioned parameters satisfy the differential equations (equations of motion) expressed by the following formulas (1) and (2). Based on the first assumption, formulas (1) and (2) do not include a term for the friction force acting between the base 10 and the moving part 20.

[0026]

number

[0027] In this embodiment, "positioning the moving part 20 relative to the base 10" is formulated as follows: That is, changing the states of the base 10 and the moving part 20 from the initial state shown in the following equation (3) to the final state shown in equation (4) is defined as "positioning the moving part 20 relative to the base 10." Note that the parameters in equations (3) and (4) are defined as follows: t[s]: Time t p [s]: Positioning time (time required for positioning) r [m]: Positioning position (position to which the moving part 20 is guided by positioning (constant))

[0028]

number

[0029] As shown in equation (4), in the final state according to this embodiment (i.e., the state where positioning is completed), the position and velocity of the base 10 are both constant at zero, and the base 10 does not vibrate. That is, in this embodiment, a condition is imposed that no residual vibration occurs in the base 10 in the final state.

[0030] The control unit 40 according to this embodiment controls the drive unit 30 so that the drive unit 30 exerts a force f that satisfies the conditions of formulas (3) and (4). Specifically, the force f expressed by the following formula (5) (so-called Bang-Bang) is considered as the force f that satisfies the conditions of formulas (3) and (4). The parameters in formula (5) are defined as follows: F[N]: Positioning force (constant)

[0031]

number

[0032] As shown in equation (5), the force f exerted by the driving unit 30 in this embodiment in response to the control by the control unit 40 is expressed as follows: pThe first pulse pattern is applied between t p / 2 to time t p and a second pulse pattern applied between the first pulse and the second pulse pattern, the second pulse pattern having the same amplitude and opposite direction as the first pulse pattern.

[0033] This control of applying two pulse patterns (a set of pulse patterns) of the same magnitude but opposite directions at different times is called positive cast control. In this embodiment, the force f applied in the first pulse pattern is constant at F throughout the entire application of the first pulse pattern. Similarly, the force f applied in the second pulse pattern is constant at -F throughout the entire application of the second pulse pattern. Note that the constant value F can be changed as appropriate depending on the positioning conditions, etc. (details will be described later). The value of F may be, for example, the maximum value (maximum force) of the force that the drive unit 30 can exert.

[0034] Hereinafter, it will be explained that the force f shown in formula (5) satisfies the conditions of formulas (3) and (4) under the first and second assumptions described above. In other words, it will be explained that the force f shown in formula (5) enables the positioning of the moving part 20 while suppressing the residual vibration of the base 10 under the first and second assumptions described above.

[0035] FIG. 3(a) is a diagram showing an example of the force f exerted by the driving unit 30. In this example, a unit step function force is used as the force f. FIG. 3(b) is a graph showing the change in the position of the base 10 over time when the force f shown in FIG. 3(a) is applied. FIG. 3(c) is a graph showing the change in the velocity of the base 10 over time when the force f shown in FIG. 3(a) is applied.

[0036] In FIG. 3(a), the magnitude of the force f is normalized using the positioning force F described above. Similarly, in FIG. 3(b), the position of the base 10 is normalized by the amplitude of the undamped vibration performed by the base 10. In FIG. 3(c), the speed of the base 10 is normalized by a predetermined value. Also, in FIGS. 3(a) to 3(c), the time is normalized by the normalized time τ defined by the following equations (6) to (8). In equations (6) to (8), ω n is the natural angular frequency of the undamped vibration of the base 10, and T n is the natural time of the undamped oscillation of the base 10.

[0037]

number

[0038] Figures 3(b) and 3(c) are graphs showing the results of simulations based on the first and second assumptions, respectively. That is, Figures 3(b) and 3(c) show the results of simulations of position (X) and velocity (the first derivative of X) when 0 is substituted for D in equation (2) and f is expressed by equation (5).

[0039] The simulations in FIGS. 3(b) and 3(c) are based on a different positioning device 1' that does not have a moving unit 20, different from the positioning device 1. Specifically, the simulations are based on the response of the base 10, which is attached to a stationary object via a spring 61 (i.e., a one-degree-of-freedom vibration system composed of a mass and a spring) when a force -f (see Equation (2)) is applied to the base 10 by a motor that is fixed to the object and does not move. This simulation (the graphs in FIGS. 3(b) and 3(c)) corresponds to determining the response of the base 10 to the force -f, which is a reaction to the force f (action) when the force f shown in FIG. 3(a) is applied to the moving unit 20 of the positioning device 1. This also applies to the simulations in FIGS. 4(b), 4(c), 5(b), and 5(d), which will be described later.

[0040] As shown in FIG. 3(b) and FIG. 3(c), when a unit step function force is used as the force f, under the first assumption and the second assumption, the position and velocity of the base 10 change over a natural time (vibration period) T n It was confirmed that the vibration continues to be undamped.

[0041] 4(a) is a diagram showing an example of the force f exerted by the driving unit 30. The force f in this example is T after the force f is applied, compared to the force f shown in FIG. n 4(a) is applied to the base 10. FIG. 4(b) is a graph showing the change in the position of the base 10 over time when the force f shown in FIG. 4(a) is applied. FIG. 4(c) is a graph showing the change in the velocity of the base 10 over time when the force f shown in FIG. 4(a) is applied.

[0042] In Figures 4(a) to 4(c), the parameters are normalized in the same way as in Figures 3(a) to 3(c). Also, Figures 4(b) and 4(c), like Figures 3(a) and 3(b), are graphs showing the results of simulations based on the first and second assumptions.

[0043] As shown in Figures 4(b) and 4(c), when a force f as shown in Figure 4(a) is used, it has been confirmed that the position and velocity of the base 10 respond non-oscillatory under the first and second assumptions. More specifically, from the start of applying the force f to T n It was confirmed that after 1 / 2 has elapsed, the position of the base 10 remains constant at a position twice the amplitude from the initial position, and the speed of the base 10 remains constant at zero. Hereinafter, the pattern of force f shown in Figure 4(a) may be referred to as the positive cast step pattern S.

[0044] Fig. 5(a) is a diagram showing an example of the force f exerted by the driving unit 30. Fig. 5(b) is a graph showing the change in the position of the base 10 over time when the force f shown in Fig. 5(a) is applied. Fig. 5(c) is a graph showing the change in the speed of the base 10 over time when the force f shown in Fig. 5(a) is applied.

[0045] In Figures 5(a) to 5(c), the parameters are normalized in the same way as in Figures 3(a) to 3(c). Figures 5(b) and 5(c), like Figures 3(a) and 3(b), are graphs showing the results of simulations based on the first and second assumptions.

[0046] Here, the force f shown in Fig. 5(a) is equivalent to two consecutive positive cast step patterns S and S' that are in opposite directions. Fig. 6 is a diagram for explaining this.

[0047] As shown on the left side of Figure 6, a force based on a certain positive cast step pattern S is applied, and then T n Consider applying a force based on the opposite positive cast step pattern S' after a time period of 1 / 2 has elapsed. When the two positive cast step patterns S and S' are combined, as shown on the right side of Figure 6, the influence of the positive cast step pattern S and the influence of the positive cast step pattern S' partially cancel each other out, and the magnitude is constant at F and the time duration T is T. n In other words, the two positive cast step patterns S and S' are equivalent to one pulse pattern P.

[0048] As shown in Figures 5(b) and 5(c), when such a pulse pattern P is used as the force f, it was confirmed that the position and velocity of the base 10 respond non-oscillatory under the first and second assumptions, similar to the examples of Figures 4(b) and 4(c). Furthermore, in the examples of Figures 5(b) and 5(c), the force f starts to be applied and then T nIt was confirmed that after a certain time had passed (that is, after the application of the pulse pattern P was completed), both the position and the velocity of the base 10 became constant at zero.

[0049] This result shows that by using pulse pattern P as force f, the position and velocity of the base 10 are kept constant at zero before and after pulse pattern P, and the force f is generated from time t=0 to time t=T n This means that it is possible to simultaneously apply a constant force F to the moving part 20 for a period of time. That is, under the first and second assumptions, by using the above-described pulse pattern P as the force f, it is possible to accelerate or decelerate the moving part 20 without causing residual vibration in the base 10. More specifically, by using a pulse pattern P with a magnitude of F, it is possible to accelerate the moving part 20 (an operation to move the moving part 20 in a positive direction; also referred to as "posicast acceleration"), and by using a pulse pattern P' with a magnitude of -F, it is possible to decelerate the moving part 20 (an operation to move the moving part 20 in a negative direction; also referred to as "posicast deceleration").

[0050] FIG. 7(a) is a diagram showing an example of the force f exerted by the driving unit 30. FIG. 7(b) is a graph showing the change in position of the moving unit 20 over time when the force f shown in FIG. 7(a) is applied. FIG. 7(c) is a graph showing the change in speed of the moving unit 20 over time when the force f shown in FIG. 7(a) is applied. FIG. 7(d) is a graph showing the change in position of the base 10 over time when the force f shown in FIG. 7(a) is applied. FIG. 7(e) is a graph showing the change in speed of the base 10 over time when the force f shown in FIG. 7(a) is applied. FIG. 7(f) is a graph showing the change in acceleration of the base 10 over time when the force f shown in FIG. 7(a) is applied.

[0051] 7(a) to 7(f), each parameter is normalized in the same way as in FIGS. 3(a) to 3(c). The position and velocity of the moving part 20 are normalized by a predetermined value. Similarly to FIGS. 3(a) and 3(b), FIGS. 7(b) to 7(f) are graphs showing the results of simulations based on the first assumption and the second assumption.

[0052] The force shown in FIG. 7(a) includes a pulse pattern P (first pulse pattern P1) corresponding to positive cast acceleration and a pulse pattern P (second pulse pattern P2) corresponding to positive cast deceleration. That is, after the moving part 20 is accelerated by the first pulse pattern P1, the moving part 20 is decelerated by the second pulse pattern P2. More specifically, the application of the second pulse pattern P2 starts at the same time as the application of the first pulse pattern P1 ends. This force f is calculated by the above-mentioned formula (5) as follows: p =2T n This matches the above.

[0053] As shown in Figures 7(d) and 7(e), when the force f based on Equation (5) is used, under the first and second assumptions, the force f is applied within 2T n (t p ) has elapsed (i.e., positioning time t p It was confirmed that no residual vibration occurred in the base 10 after the elapse of time.

[0054] 7(b) and 7(c), the moving part 20 is moved a predetermined distance from the initial position by the force f and stops at that position. The moving distance of the moving part 20 can be changed by changing the magnitude F of the pulse pattern P. Therefore, by appropriately adjusting the magnitude F of the pulse pattern P, the moving part 20 can be stopped at any position (positioning position r in equation (4)) (i.e., the moving part 20 can be positioned).

[0055] As described above, the position of the moving unit 20 is 0 at the time when the application of force f begins (positioning start time t = τ), and the position of the moving unit 20 is 1 at the time when the application of force f ends (positioning end time t = 3τ). On the other hand, no residual vibration occurs in the base 10 after the positioning end time. The position response of the moving unit 20 obtained in this manner, when focusing on the time periods before the positioning start time and after the positioning end time, is consistent with the response when the same operating force (force f) is applied to a rigid body with absolutely no vibration characteristics (i.e., bang-bang control of a rigid body, which provides the shortest time response) (detailed proof omitted). In other words, according to the control shown in FIG. 7, regardless of the presence of vibration characteristics, the same response as that obtained when controlling a rigid body with absolutely no vibration characteristics can be obtained at the time of positioning completion (after the positioning end time).

[0056] Thus, in equation (5), the positioning time t p =2T n By using the force f (in other words, the time span T is T n (By using the pulse pattern P where P is the same as above), it is possible to position the moving part 20 without generating residual vibration of the base 10 under the first and second assumptions. In other words, the positioning formulated by the equations (3) and (4) can be realized. More specifically, the natural time T of the undamped vibration of the base 10 n is calculated or measured in advance, and the control unit 40 calculates the characteristic time T n The force f is calculated based on the formula (5), and the driving unit 30 is controlled so as to apply the calculated force f to the driving unit 30. According to this method using the force f shown in formula (5), the acceleration and deceleration of the moving unit 20 can be performed with energy efficiency as if the base 10 did not exist (i.e., rigidly).

[0057] As shown in FIG. 7(c), the speed of the moving part 20 changes from the time when the force f starts to be applied to the moving part 20 to the time when the force f starts to be applied. n (t pThis means that this method can eliminate the influence of interference (inertial force) that the acceleration of the moving part 20 has on the motion of the base 10. Furthermore, this method can eliminate the influence of interference (inertial force) that the acceleration of the moving part 20 has on the motion of the base 10 at the positioning time t p is 2T n Therefore, high-speed positioning is possible.

[0058] In the above description, the second pulse pattern P2 is applied immediately after the first pulse pattern P1, but a force-free section where f=0 may be provided between the first pulse pattern P1 and the second pulse pattern P2. As shown in Figures 7(d) and 7(e), the force f is applied from the start of application to T n (t p Even after a force-free interval (r / 2) has elapsed, the position and velocity of the base 10 are zero. Therefore, even if such a force-free interval is provided, the movable unit 20 can be operated without causing residual vibration in the base 10. Furthermore, during the force-free interval, the movable unit 20 continues to move due to inertia. Therefore, by adjusting the length of the force-free interval, it is also possible to adjust the positioning position r described above.

[0059] Furthermore, although a detailed explanation of the principle will be omitted, when the base 10 undergoes damped vibration (in other words, when the damping constant D is not zero), it is possible to position the moving part 20 without residual vibration by modifying the positive cast step patterns S and S'. More specifically, by setting the values of parameters p1 and p2 shown in FIG. 6 as in the following equations (9) to (11) according to the value of the damping constant D, it is possible to position the moving part 20 while suppressing residual vibration. In equations (9) to (11), ζ is the damping ratio (0≦ζ<1).

[0060]

number

[0061] The above-described pre-correction podcast step pattern S (i.e., the podcast step pattern S when it is assumed that the base 10 performs undamped vibration) corresponds to the case where ζ = 0 in equations (9) to (11) (p1 = T n / 2, p2 = F). When ζ ≠ 0 (i.e., when the base 10 performs damped vibration), the value of the parameter p1 becomes smaller than T n / 2, and the value of the parameter p2 becomes smaller than F. When p1 < T n / 2 and p2 < F, if two podcast step patterns S and S' in opposite directions are combined as shown in FIG. 6, a pulse pattern as shown on the right side of FIG. 8 is obtained. This pulse pattern is not constant with a magnitude of F, and the magnitude changes to F' (<F) at time p1. Conversely, the fact that the magnitude of the pulse pattern P is constant with a magnitude of F as shown in FIGS. 5(a) and 6 can also be regarded as corresponding to the second assumption that the base 10 performs undamped vibration.

[0062] As described above, the positioning device 1 according to the present embodiment includes a base 10, a moving part 20 that is relatively movable with respect to the base 10, and a driving part 30 that changes the relative position between the base 10 and the moving part 20 by applying a force to the base 10 and the moving part 20. Then, assuming that no frictional force acts between the base 10 and the moving part 20 (the first assumption) and that the base 10 performs undamped vibration (the second assumption), the driving part 30 performs positive-cast control on the forces applied to the base 10 and the moving part 20 based on the set of pulse patterns P (the first pulse pattern P1 and the second pulse pattern P2) calculated, thereby positioning the moving part 20 with respect to the base 10. Further, the positioning device 1 may include a control part 40, and the control part 40 may perform the above-described positioning control.

[0063] According to this configuration, in the positioning device 1 in which the first assumption and the second assumption are established or can be regarded as substantially established, the moving part 20 can be positioned while suppressing residual vibration.

[0064] (Second Embodiment) Next, a second embodiment will be described, but the basic configuration is similar to that of the first embodiment. Therefore, the same components are given the same reference numerals, and the description thereof will be omitted, and only the differences will be described.

[0065] In an actual positioning device 1, the frictional force acting between the base 10 and the movable part 20 cannot be ignored in many cases. In other words, there are cases where the first assumption described above cannot be considered valid. The purpose of the second embodiment is to make it possible to perform positioning control with suppressed residual vibration even when the frictional force between the base 10 and the movable part 20 cannot be ignored by making appropriate modifications to the force f (pulse pattern P) in the first embodiment.

[0066] FIG. 9 is a graph showing the change in the root mean square (RMS) value of the residual vibration magnitude of the base 10 when the time width T of the pulse pattern P in positive cast control (see also the right side of FIG. 6) is changed.

[0067] The graph in FIG. 9 is based on the results of an actual experiment performed on the positioning device 1, in which the position of the base 10 was acquired by a sensor or the like. In addition, based on prior measurements, the natural time T n was found to be 19 ms.

[0068] As shown in FIG. 9, it was confirmed that the magnitude of the residual vibration of the base 10 changes depending on the time width T of the pulse pattern P. In particular, when the time width T of the pulse pattern P is set to the characteristic time T n By setting the time span T to a specific value greater than 19 ms (for example, 22 ms), the time span T becomes the specific time T n It was confirmed that residual vibration could be suppressed compared to when the delay time was set to 19 ms.

[0069] As a result, as shown in FIG. 10, the time width T of the pulse pattern P (first pulse pattern P1 and second pulse pattern P2) in the first embodiment is set to the characteristic time T nThis means that by correcting this to an appropriate value greater than the above, it is possible to position the moving part 20 while suppressing residual vibration of the base 10, even when the frictional force between the base 10 and the moving part 20 cannot be ignored.

[0070] Specifically, the dependency of the effective value of the magnitude of the residual vibration of the base 10 on the time width T (see FIG. 9 ) may be measured in advance, and the value of the corrected time width T may be set based on the measurement results. For example, a time width T that minimizes the time width T of the effective value of the magnitude of the residual vibration of the base 10 may be selected. Information about such time width T may be set in the control unit 40. The control unit 40 may control the drive unit 30 so that the drive unit 30 exerts a force f based on the pulse pattern P having the set time width T.

[0071] Fig. 11 is a diagram showing the change in the speed of the base 10 over time when various forces f that decelerate the moving part 20 are applied to the base 10, which moves at a constant speed. The graph in Fig. 11 is based on the results of an actual experiment conducted using the positioning device 1, in which the position of the base 10 was acquired by a sensor or the like.

[0072] In FIG. 11, lines L1 and L2 show the response when a pulse pattern P with a positive F is applied to the base 10. When F is positive, a negative force is applied to the base 10 (see equation (2)), and therefore, by using a pulse pattern P with a positive F, it is possible to decelerate the base 10. Line L1 corresponds to the case where the time width T of the pulse pattern P is 15 ms, and line L2 corresponds to the case where the time width T of the pulse pattern P is 22 ms. As shown in FIG. 11, when the time width T of the pulse pattern P is set to 22 ms (line L2), the residual vibration of the base 10 is suppressed.

[0073] In FIG. 11, lines L3 and L4 show the response when a pulse pattern P with a positive F is applied to the base 10 multiple times. Here, the magnitude F" of the pulse pattern P in the cases of lines L3 and L4 is set smaller than the magnitude F in the case of line L2. FIG. 12 is a diagram showing this schematically. Line L3 shows the case when a pulse pattern P with a magnitude F" = F / 2 is used twice, and line L4 shows the case when a pulse pattern P with a magnitude F" = F / 4 is used four times. In this way, when decelerating the base 10 using multiple pulse patterns P, the magnitude F" of each pulse pattern P may be determined so as to be inversely proportional to the number of times the pulse pattern P is applied. Note that in both lines L3 and L4, the time width T of the pulse pattern P is 22 ms, the same as in the case of line L2.

[0074] 11, in lines L3 and L4 where the base 10 is decelerated over multiple pulse patterns P, the residual vibration of the base 10 is smaller than in the case (line L2) where the base 10 is decelerated using only one pulse pattern P. In other words, the control unit 40 performs control to decelerate the base 10 based on multiple pulse patterns P (to bring the absolute value of the speed of the base 10 closer to zero), thereby making it possible to further suppress the residual vibration of the base 10.

[0075] As described above, in this embodiment, for example, the control unit 40 determines the natural time T n The driving unit 30 controls the force applied to the base 10 and the moving unit 20 based on a pulse pattern P having a time width T longer than the pulse width T. With this configuration, even when the frictional force between the base 10 and the moving unit 20 cannot be ignored, it is possible to position the moving unit 20 while suppressing residual vibration of the base 10.

[0076] Furthermore, for example, the control unit 40 may perform control to decelerate the base 10 based on a plurality of pulse patterns P. According to this configuration, residual vibration of the base 10 can be further suppressed.

[0077] (Third embodiment) Next, a third embodiment will be described, but the basic configuration is similar to that of the first embodiment. Therefore, the same components are given the same reference numerals, and the description thereof will be omitted, and only the differences will be described.

[0078] In an actual positioning device 1, the damping constant D in equation (2) is often not negligible. That is, there are cases where the second assumption described above cannot be considered to be valid (in other words, cases where the base 10 undergoes damped vibration). The purpose of the third embodiment is to make it possible to apply the positioning control of the first embodiment even when the base 10 undergoes damped vibration by introducing an appropriate external force.

[0079] FIG. 13 is a block diagram showing the base 10 according to this embodiment. As shown in Fig. 13, in this embodiment, a force due to damping 62 is applied to the base 10. Note that "s" in the figure is a variable in the Laplace transform. Also, "freal" is the resultant force of the force f of the driving unit 30 described above and external forces f1 and f2 described below.

[0080] FIG. 14 is a block diagram showing the positioning device 1 according to this embodiment. As shown in FIG. 14, the positioning device 1 according to this embodiment further includes a first external force application unit 71 that applies an external force f1 to the base 10, and an external force application unit 72 that applies an external force f2 to the base 10.

[0081] That is, in the present embodiment, a resultant force freal of the force f by the drive unit 30, the external force f1 by the first external force application unit 71, and the external force f2 by the second external force application unit 72 is applied to the base 10. The external forces f1 and f2 by the external force application units 71 and 72 both act to bring the damped vibration of the base 10 closer to undamped vibration. The application of the external forces f1 and f2 by the first external force application unit 71 and the second external force application unit 72 may be controlled by, for example, the control unit 40.

[0082] Specifically, the external force f1 is a force proportional to the following (A) and (B) (see FIG. 14). (A) Response Vr of the velocity of the normal vibration R when a force f of the driving unit 30 is applied to the normal vibration R (B) Value 2ζω n Here, the normal vibration R is a virtual oscillator corresponding to the base 10 when ζ = 0. ζ and ω n The value of may be calculated based on a previous measurement.

[0083] Furthermore, the external force f2 is a force based on the difference between the response of the reference vibration R when the force f of the driving unit 30 is applied to the reference vibration R and the actual response of the base 10 to which the resultant force freal is applied (see FIG. 14).

[0084] More specifically, the external force f2 is a force expressed as the sum of the following forces fa and fb. The force fa is proportional to the following (C) and (D) (see Figure 14). (C) The difference between the position response Xr of the reference vibration R when the force f of the driving unit 30 is applied to the reference vibration R and the position response X(t) of the base 10 to which the resultant force freal is applied. (D) Predetermined gain Kp (constant) The force fb is proportional to the following (E) and (F) (see FIG. 14). (E) The difference between the response Vr of the velocity of the reference vibration R when the force f of the driving unit 30 is applied to the reference vibration R and the response V(t) of the velocity of the base 10 to which the resultant force freal is applied. (F) Predetermined gain Kv (constant) The values of the gains Kp and Kv may be set appropriately depending on the response characteristics.

[0085] Fig. 15(a) is a graph showing the damped vibration of the base 10 when external forces f1 and f2 are not present. Fig. 15(b) is a graph showing the external forces (resultant force of external forces f1 and f2) applied to the base 10 by the external force application units 71 and 72. Fig. 15(c) is a diagram showing the change in the position of the base 10 over time when the external forces shown in Fig. 15(b) are applied. Note that Figs. 15(a) to 15(c) are graphs showing the results of a simulation based on the block diagrams shown in Figs. 13 and 14.

[0086] It was confirmed that the base 10 (see FIG. 15(a)), which undergoes damped vibration when there are no external forces f1, f2, also undergoes undamped vibration as shown in FIG. 15(c) when external forces f1, f2 as shown in FIG. 15(b) are applied. That is, it was confirmed that the damped vibration of the base 10 can be converted to undamped vibration by the external forces f1, f2 applied by the external force application units 71, 72. Therefore, by applying such external forces f1, f2, it is possible to position the moving unit 20 while suppressing residual vibration using a method similar to that of the first embodiment.

[0087] It is also possible to convert the damped vibration of the base 10 into undamped vibration by removing the second external force application portion 72 and using only the first external force application portion 71. However, when ζ and ω n If the accuracy of the pre-calculation of the values of ζ and ω is insufficient or if the values of ζ and ω are degraded due to aging, etc. n When the value of f1 changes, the conversion may not be performed with sufficient accuracy using only the external force f1 of the first external force application unit 71. Therefore, by introducing the second external force application unit 72 as described above, sufficient conversion accuracy can be ensured even in such cases. In other words, the second external force application unit 72 has the effect of improving the robustness of the control.

[0088] When the second external force application unit 72 is used, the positioning device 1 may include a sensor (not shown) that acquires at least one of the position, velocity, and acceleration of the base 10. The sensor may output the acquired information to the control unit 40. The control unit 40 may calculate responses X(t) and V(t) based on the information output from the sensor. The control unit 40 may control the application of the external force f2 by the second external force application unit 72 based on the calculated responses X(t) and V(t).

[0089] Furthermore, if it is possible to bring the damped vibration of the base 10 closer to undamped vibration, an external force may be applied to the moving part 20 instead of the base 10. Alternatively, an external force may be applied to both the base 10 and the moving part 20. In other words, the external force for bringing the damped vibration of the base 10 closer to undamped vibration may be applied to at least one of the base 10 and the moving part 20.

[0090] As described above, in this embodiment, external forces f1 and f2 that cause the damped vibration of the base 10 to approach undamped vibration are applied to at least one of the base 10 and the moving unit 20. Furthermore, the positioning device 1 may further include external force application units 71 and 72 that apply such external forces f1 and f2. With this configuration, even when the base 10 undergoes damped vibration, it is possible to position the moving unit 20 while suppressing residual vibration of the base 10.

[0091] The technical scope of the present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the spirit of the present invention.

[0092] For example, in the above embodiment, the driving unit 30 is described as a linear motor, but the type of driving unit 30 is not limited to this. The type of driving unit 30 can be changed as appropriate as long as the relative position between the base 10 and the moving unit 20 can be changed by applying a force to the base 10 and the moving unit 20. Furthermore, the base 10 and the moving unit 20 are not limited to the above example and can be changed as appropriate as long as the relative position changes depending on the force exerted by the driving unit 30. In other words, the method of the above embodiment is applicable to general positioning systems.

[0093] In addition, it is possible to replace the components in the above-described embodiments with well-known components as appropriate, and the above-described embodiments and variations may be combined as appropriate, without departing from the spirit of the present invention. For example, the second embodiment may be combined with the third embodiment. According to this configuration, even when the friction between the base 10 and the moving part 20 cannot be ignored and the base 10 undergoes damped vibration, the moving part 20 can be positioned while suppressing the residual vibration of the base 10.

[0094] The control unit 40 described above is configured using a processor such as a CPU (Central Processing Unit) and a memory (main storage device). The control unit 40 functions when the processor executes a program. Note that all or part of the functions of the control unit 40 may be realized using hardware such as an ASIC (Application Specific Integrated Circuit), a PLD (Programmable Logic Device), or an FPGA (Field Programmable Gate Array).

[0095] The above program may be recorded on a computer-readable recording medium. Examples of the computer-readable recording medium include portable media such as a flexible disk, a magneto-optical disk, a ROM, a CD-ROM, and a semiconductor storage device (e.g., an SSD (Solid State Drive)), and storage devices such as a hard disk or semiconductor storage device built into a computer system. The above program may be transmitted via a telecommunications line. [Explanation of symbols]

[0096] 1... Positioning device 10... Base 20... Moving unit 30... Driving unit 40... Control unit 71... First external force application unit (external force application unit) 72... Second external force application unit (external force application unit) P... Pulse pattern

Claims

1. A positioning device including a base, a moving part that is movable relative to the base, and a driving part that applies a force to the base and the moving part to change the relative position between the base and the moving part, The driving unit performs positive cast control of the force applied to the base and the movable unit based on a set of pulse patterns calculated on the assumption that no frictional force acts between the base and the movable unit and that the base vibrates without damping, thereby positioning the movable unit relative to the base. Control method.

2. the driving unit controls the force applied to the base and the moving unit based on a pulse pattern having a time width longer than a natural time of the undamped vibration. The control method according to claim 1 .

3. Controlling the base to decelerate based on a plurality of pulse patterns. The control method according to claim 1 or 2.

4. applying an external force to at least one of the base and the moving part so as to bring the damped vibration of the base closer to undamped vibration; The control method according to claim 1 or 2.

5. With the base, a moving part that is movable relative to the base; a driving unit that applies a force to the base and the moving unit to change the relative position between the base and the moving unit; and a control unit that performs positive cast control of the force that the drive unit applies to the base and the moving unit based on a set of pulse patterns calculated on the assumption that no frictional force acts between the base and the moving unit and that the base vibrates without damping, thereby positioning the moving unit relative to the base. Positioning device.

6. the control unit controls the force applied by the drive unit to the base and the moving unit based on a pulse pattern having a time width longer than a natural time of the undamped vibration. The positioning device according to claim 5 .

7. The control unit performs control to decelerate the base based on a plurality of pulse patterns.

7. The positioning device according to claim 5 or 6.

8. an external force applying unit that applies an external force to at least one of the base and the moving unit so as to cause the damped vibration of the base to approach undamped vibration; 7. The positioning device according to claim 5 or 6.

9. A positioning device including a base, a moving part that is movable relative to the base, and a driving part that applies a force to the base and the moving part to change the relative position between the base and the moving part, On the computer, The driving unit performs positive cast control of the force applied to the base and the movable unit based on a set of pulse patterns calculated on the assumption that no frictional force acts between the base and the movable unit and that the base vibrates without damping, thereby positioning the movable unit relative to the base. A program to make it happen.

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