JP5656675B2 - Drive device - Google Patents

Description

  The present invention relates to a drive device.

Conventionally, a motor such as a stepping motor has been used as a drive source of a drive device that drives a robot arm, a transfer stage, and the like. The rotation angle θ _M of the rotor of the stepping motor is equal to the product of the number of pulses (number of steps) S of the pulse signal input to the stepping motor and a predetermined step angle θ _ST per one pulse (step). . Therefore, it is possible to control the rotation angle theta _M of the stepping motor by controlling the number of pulses S.

Further, since the rotation angle per one step of the driven body such as a robot arm in small than the step angle theta _ST of the stepping motor, it is also often provided a reduction gear between the stepping motor and the robot arm from the prior . Rotation angle theta _R of the robot arm for one step according to a predetermined reduction ratio R of the reduction gear is smaller than the step angle theta _ST of the stepping motor. Thus, the position of the robot arm can be controlled with high accuracy by using the speed reducer.

Here, the speed reducer is configured by a plurality of gears or a combination of rollers such as a sun gear (or sun roller) or a planetary gear (planetary roller), and slippage between gears or rollers may occur. As shown in FIG. 9, the actual rotation angle θ _ACT of the robot arm 100 is the product of the rotation angle θ _M of the stepping motor 102 and the reduction ratio R of the speed reducer 104, as shown in FIG. Deviation from _CAL .

  Therefore, in order to correct the deviation due to the slip, for example, in Patent Document 1, the actual moving distance of the transfer stage is detected by a detector such as a linear scale, and the difference between the detected actual moving distance and the theoretical moving distance is detected. The correction pulse corresponding to is obtained and input to the stepping motor. In Patent Document 2, the actual rotation angle of the driven body is detected by a detector such as an encoder, and a correction pulse corresponding to the difference between the detected actual rotation angle and the theoretical rotation angle is obtained and stepping is performed. Input to the motor.

  Here, in the conventional slip correction control, the position and angle at which the detector is disposed are used when the actual position and angle of the driven body are obtained. That is, the position or angle of the driven body at the time of passing through the detector (passing time) is equal to the position or angle at which the detector is disposed. It is calculated as the position of the driven body. The theoretical position and angle of the driven body are the theoretical position and angle at the time of acquisition when the control unit receives the detection signal. For example, the theoretical position and angle of the driven body are calculated based on the number of pulses of the drive signal sent from the control unit to the motor from the drive start time to the acquisition time of the driven body.

JP-A-5-337788 JP 2003-339191 A

In the conventional slip correction control, as shown in FIG. 10, the detector 106 starts moving from the time when the driven body 100 passes through the detector 106 (hereinafter, this time is referred to as the passing time t ₀ ). delay it takes to detect the passage (hereinafter, this delay is referred to as the detection delay Delta] t _d) is generated. Also, a sampling period for acquiring the detection signal the control unit 108 acquires a detection signal is predetermined from the detector 106, a delay due to the sampling cycle (hereinafter, referred to as the lag between acquisition delay Delta] t _r) is generated . That is, the passing time t _0, when the actual control unit acquires the data (hereinafter, referred to as the time between acquisition time t ₁₎ is not a simultaneous acquisition time t ₁ to the passage time t _{0 =} ( A time difference (delay) occurs in t ₀ + Δt _d + Δt _r ). Here, the theoretical rotation angle of the driven body at the acquisition time t ₁ is represented by θ _CAL (t ₀ + Δt _d + Δt _r ).

That is, in the conventional slip correction control, the actual rotation angle θ _ACT (t ₀ ) of the driven body at the passage time t ₀ and the theoretical rotation angle θ _CAL (t ₀ + Δt of the driven body at the acquisition time t ₁ . _d + Δt _r ) is calculated, and control is performed based on the difference. However, an error is included in the control based on this difference, and there is an increasing demand for slip correction control with higher accuracy that can correct this error.

  SUMMARY OF THE INVENTION An object of the present invention is to provide a driving device that can perform slip correction that reflects a delay that occurs in a detector or a control unit.

  The present invention relates to a drive device. The driving device includes a motor that drives the driven body based on the driving signal, a detector that detects the passage of the driven body and outputs a detection signal, and sends the driving signal to the motor and receives the detection signal from the detector. And a control unit to acquire. The control unit is the position of the driven body at the passing time point when the driven body passes the detector and the moving distance of the driven body in the detection delay period from the passing time point to the output time point when the detector outputs the detection signal. Driven at the acquisition time using the first distance and at least one of the second distance that is the movement distance of the driven body in the acquisition delay period from the output time to the acquisition time when the control unit acquires the detection signal Find the actual position of the body. Further, the control unit obtains the theoretical position of the driven body at the acquisition time determined by the drive signal output to the motor from the drive start time to the acquisition time of the driven body, and calculates the difference between the actual position and the theoretical position. The drive signal after the acquisition time is determined based on the above.

  Moreover, in the said invention, it is suitable for a control part to obtain | require a 1st distance by the theoretical moving speed or acceleration of a to-be-driven body decided by a drive signal, and a detection delay period.

  Moreover, in the said invention, it is suitable for a control part to obtain | require a 2nd distance with the theoretical moving speed or acceleration of a to-be-driven body decided by a drive signal, and an acquisition delay period.

  In the above invention, the motor is preferably a stepping motor, and the drive signal is preferably a pulse signal for driving the stepping motor. In this case, the control unit obtains the theoretical position of the driven body at the acquisition time from the number of pulses of the pulse signal output to the stepping motor from the drive start time to the acquisition time, and the actual position and the theoretical position of the driven body. It is preferable to obtain the number of correction pulses according to the difference from the upper position and increase or decrease the number of pulses of the pulse signal after the acquisition time by the number of correction pulses.

  According to the present invention, it is possible to perform the slip correction reflecting the delay generated in the detector and the control unit.

It is a figure which illustrates the drive device concerning this embodiment. It is a figure which illustrates the reflective surface of a detection pin. It is the figure which illustrated the movement pattern of the motor. It is the figure which illustrated the control part and its peripheral device. It is a figure explaining the acquisition delay of a control part. It is a figure which shows a result when slip correction control which concerns on this embodiment is implemented. It is a figure which shows a result when slip correction control which concerns on this embodiment is implemented. It is a figure which shows a result when slip correction control which concerns on this embodiment is implemented. It is a figure which illustrates the conventional drive device. It is a figure explaining a detection delay and an acquisition delay.

  FIG. 1 illustrates a drive device 10 according to this embodiment. The driving device 10 includes a motor 14 that transmits a driving force to the driven body 12, a detector 16 that detects passage of the driven body 12, and a control unit 18 that is electrically connected to the motor 14 and the detector 16. It is comprised including.

The motor 14 is composed of a stepping motor, for example, and is driven according to a pulse signal sent from the control unit 18. When the number of pulses (step number) of the pulse signal is S and the rotation angle (step angle) of the motor 14 per pulse is θ _ST , the theoretical rotation angle θ _M of the motor 14 is θ _M = S · θ _ST It can ask for.

  Further, a reduction gear 20 is connected to the output shaft of the motor 14. The speed reducer 20 is a device that reduces the rotational speed and rotation angle of the output shaft of the motor 14 and outputs the reduced speed. Of these, it is preferable to use a planetary roller speed reducer in order to reduce rotational unevenness and gear noise caused by the meshing of the gears and obtain a smooth rotational motion.

The reduction gear 20 has a reduction gear ratio R in advance, and the theoretical rotation angle θ _R on the output shaft of the reduction gear 20 can be obtained from θ _R = θ _M · R. On the other hand, the reduction gear 20 slips when driving force is transmitted between gears or rollers. Affected by the slip, the rotation angle of the output shaft of the actual reduction gear 20 becomes a value different from the rotation angle theta _R on the theory.

  A driven body 12 is connected to the output shaft of the speed reducer 20. Although a robot arm is connected as the driven body 12 in FIG. 1, any end effector such as a transfer stage, a welding torch, a drill, or a spray nozzle may be used.

  The driving device 10 is provided with a detector 16 for detecting the position and angle of the driven body 12. The detector 16 may have any method and configuration as long as the position and angle of the driven body 12 can be detected. In the present embodiment, a case where an optical sensor is applied as the detector 16 will be described.

The detector 16 is fixed to, for example, a fixing member 26 and is disposed at a position along the movement path of the driven body 12. Specifically, the detector 16 is disposed on an installation angle θ _D between the first stop angle θ ₁ and the second stop angle θ ₂ that is the destination of the driven body 12. In FIG. 1, the first stop angle θ ₁ = 0 °, and the angles when rotating clockwise from the first stop angle θ ₁ are represented as a _second stop angle θ ₂ and an installation angle θ _D.

On the other hand, a detection pin 22 is provided on the driven body 12 as a detection element for the detector 16. The detection pin 22 is provided at the distal end portion of the driven body 12 (in the vicinity of the arm portion in FIG. 1) away from the rotation axis C of the driving device 10, and a reflection surface 24 that faces the detector 16 is formed. The reflecting surface 24 is mirror-finished, for example, to enable reflection of an optical signal or the like. Detecting surface of the detector 16, the detection pin 22 is disposed so as to face the reflecting surface 24 of the detection pin 22 traverses the installation angle theta _D. The light output from the detection surface of the detector 16 is reflected by the reflection surface 24 of the detection pin 22 and enters the detector 16. Thus, detector 16 of the installation angle theta _D driven member 12 has crossed is detected.

Here, the detector 16 is preferably arranged in the vicinity of the first stop angle θ ₁ or the second stop angle θ ₂ of the driven body 12. As will be described later, although the slip due to the speed reducer 20 is corrected according to the detection result of the detector 16, the slip due to the slip is accumulated again thereafter, so that the slip is as small as possible after passing the detector 16. Is preferred. Therefore, in the present embodiment, the detector 16 is arranged in the vicinity of the stop angle of the driven body 12 to suppress slip that occurs after passing the detector 16. Specifically, the angle difference between the first stop angle θ ₁ or the second stop angle θ ₂ and the installation angle θ _D is preferably 0 ° to 10 °. For example, when the first stop angle θ ₁ is 0 ° and the second stop angle θ ₂ is 90 °, the installation angle θ _D is preferably 0 ° to 10 ° or 80 ° to 90 °.

  In the embodiment shown in FIG. 1, the reflection surface 24 of the detection pin 22 is a plane parallel to the detection surface of the detector 16, but this is not a limitation. For example, as shown in FIG. 2, the shape of the reflecting surface 24 may be configured to be a curved surface having a curvature 1 / r based on the distance r from the rotation axis C of the driving device 10 to the reflecting surface 24. If the reflecting surface 24 is a flat surface, the distance from the detector 16 changes between the center portion and the outer edge portion of the reflecting surface 24, and an error may occur in the detection timing depending on the reflecting position. By setting the curved surface to 1 / r, the distance to the detector 16 is equal regardless of the position on the reflecting surface 24, so that the detection timing error due to the reflecting position can be suppressed.

The control unit 18 includes a storage medium such as a ROM and a RAM, and an arithmetic circuit such as a CPU, and is electrically connected to the motor 14 and the detector 16. As will be described later, when the encoder 19 is used, it is also electrically connected to the encoder 19. The control unit 18 outputs a command signal of the number of pulses necessary for the driven body 12 to move between the first stop angle θ ₁ and the second stop angle θ ₂ to the motor 14 and will be described later. Thus, a correction signal is output to the motor 14 in accordance with the detection signal from the detector 16.

The control unit 18 controls the rotation speed of the motor 14 by changing the pulse frequency (number of pulses per unit time) in generating the command signal. For example, as shown in FIG. 3, the motor 14 is stopped from the predetermined speed at the time of acceleration in which the rotational speed of the motor 14 is increased from the start of driving the driven body 12 to a predetermined speed, at a steady time maintaining the predetermined speed. When divided into the time of deceleration, the control unit 18 sets a pulse frequency according to each operation condition. For example, the pulse frequency is set to gradually increase from 0 [kHz] during acceleration, is set to be a predetermined pulse frequency during steady state, and is set to 0 [kHz] from the predetermined pulse frequency during deceleration. Is set to decrease gradually. When the detector 16 is disposed in the vicinity of the first stop angle θ ₁ or the second stop angle θ ₂ , the detector 16 detects the driven body 12 when the driven body 12 is accelerated or decelerated. Will do.

FIG. 4 shows the main configuration of the control unit 18 and its peripheral devices. The control unit 18 includes a command signal generation unit 30 electrically connected to the motor 14 and a theoretical angle calculation unit 32 connected to the command signal generation unit 30. Further comprises a detector angle setting unit 34 setting angle theta _D of the detector 16 is stored, and a delay correction unit 36. Furthermore, a correction switching unit 38 electrically connected to the detector 16 is provided.

The theoretical angle calculation unit 32 obtains the theoretical angle θ _CAL (t) of the driven body at an arbitrary time t based on the command signal and the reduction ratio R of the speed reducer 20. Instead of obtaining the theoretical angle θ _CAL (t) based on the command signal and the reduction ratio R, the rotation angle θ _M of the output shaft of the motor 14 is obtained from the encoder 19 shown in FIG. And the theoretical angle θ _CAL (t) may be obtained based on the reduction ratio R.

  The delay correction unit 36 calculates the detection delay of the detector 16 and the acquisition delay of the control unit 18. In addition, the correction switching unit 38 performs disconnection / connection switching of a feedback loop that feeds back a correction pulse signal to the motor.

Next, the slip correction control performed by the control unit 18 will be described. The slip angle Θ (t ₁ ) of the driven body 12 at the time point (acquisition time) t ₁ when the control unit 18 acquires the detection signal from the detector 16 is the theoretical angle θ of the driven body 12 at the acquisition time point t ₁ . It can be obtained from the difference between _CAL (t ₁ ) and the actual rotation angle θ _ACT (t ₁ ) of the driven body 12 at the acquisition time t ₁ .

The actual rotation angle θ _ACT (t ₁ ) of the driven body 12 is obtained as follows. An acquisition time t ₁ is the time when the driven member 12 passes through the detector 16 (passing time) t _0, a detection delay period Delta] t _d of the detector 16, be represented by the sum of the acquisition delay period Delta] t _r of the control unit 18 Can do. From this, the actual rotation angle θ _ACT (t ₁ ) of the driven body 12 at time t ₁ is equal to the rotation angle θ _ACT (t ₀ ) of the driven body at the passage timing t ₀ and the detection delay of the detector 16. Can be obtained from the advance angle Δθ _d of the driven body 12 and the advance angle Δθ _r of the driven body 12 due to the acquisition delay of the control unit 18. In addition, the angle θ _ACT (t ₀ ) of the driven body 12 at the passage time t ₀ is equal to the installation angle θ _D of the detector 16. From the above, the slip angle Θ (t ₁ ) of the driven body 12 at time t ₁ can be expressed as the following Equation 1.

Here, the detection delay of the detector 16 refers to a delay time taken from when the detection pin 22 passes the detector 16 to when the detector 16 detects the passage of the detection pin 22. When the reflected light from the detection pin 22 is received, it indicates a delay time required for photoelectric conversion and charge transfer in the optical element of the detector 16. In the present embodiment, a delay period measured in advance is used as the detection delay period Δt _d of the detector 16. Further, as shown in FIG. 5, the control unit 18 is set to acquire a detection signal (position signal) from the detector 16 for each predetermined sampling period, and the detector 16 is configured to detect the detection pin 22. The period from the detection of the passage to the latest sampling timing is the acquisition delay period. For acquisition delay period in the present embodiment uses an average value Delta] t _Rave acquisition delay period Delta] t _r at the time of pre-performed a plurality of times sampling.

The advance angle Δθ _d based on the detection delay of the detector 16 can be expressed by the following equation 2 using the acceleration α of the motor 14, the detection delay period Δt _d of the detector 16, and the reduction ratio R of the speed reducer 20.

  Further, it can be expressed as the following Equation 3 using the speed V of the motor 14.

Here, the acceleration α and the speed V of the motor 14 are calculated based on the drive signal output to the motor 14. For example, when the motor rotational speed defining a driving signal so as to vary as shown in FIG. 3, the frequency of the drive signal in the acquisition point t _1, the step angle of the motor 14, the acceleration of theoretical from the deceleration ratio R and the like of the speed reducer 20 Alternatively, the speed is obtained, and the theoretical acceleration or speed is substituted into Equations 2 and 3.

Further, the advance angle Δθ _r based on the acquisition delay of the control unit 18 can be expressed as the following Equation 4.

  Moreover, it can also represent like the following Numerical formula 5 using the speed V of the motor 14. FIG.

  Therefore, the advance angle Δθ based on the detection delay and the acquisition delay can be expressed as Equation 6 below.

Further, the following expression 7 may be used using the speed V of the motor 14. By substituting Equation 6 or Equation 7 into Equation 1, the slip angle Θ (t ₁ ) of the driven body 12 can be obtained.

With reference to FIG. 4 again, the operation of each component of the control unit 18 during the slip correction control will be described. When the correction switching unit 38 of the control unit 18 receives the detection signal (position signal) from the detector 16, the correction switching unit 38 changes the feedback loop to the motor 14 from the disconnected state to the connected state in order to perform the slip correction control. Switch. In response to the fact that the control unit 18 has acquired the detection signal from the detector 16, the theoretical angle calculation unit 32 calculates the theoretical angle θ _CAL (t ₁ ) of the driven body 12 at the acquisition time t ₁ . That is, the number of pulses S (t ₁ ) of the drive signal output from the control unit 18 to the motor 14 during the period from the drive start time of the driven body 12 to the acquisition time t ₁ , the step angle θ _{ST of the} motor 14, and the speed reducer The theoretical angle θ _CAL (t ₁ ) of the driven body 12 is obtained from the product of the reduction ratio R of 20.

Further, the delay correction unit 36 performs the calculation according to Expression 6 or 7, and outputs the advance angle Δθ based on the detection delay and the acquisition delay. The theoretical angle θ _CAL (t ₁ ) output from the theoretical angle calculation unit 32, the installation angle θ _D output from the detector angle setting unit 34, and the advance angle Δθ output from the delay correction unit 36. Each is calculated based on Equation 1, and the slip angle Θ (t ₁ ) at the acquisition time t ₁ is calculated.

Further, the control unit 18 generates a correction signal based on the slip angle Θ (t ₁ ). The number of pulses ΔS in the correction signal is calculated based on the following formula 8.

The correction signal is added to the command signal output from the motor command signal generator 30 and sent to the motor 14. When the motor 14 is driven based on the command signal on which the correction signal is superimposed, the slip caused by the speed reducer 20 is corrected. For example, when the correction pulse number ΔS based on the slip is 10, the number of pulses of the acquisition time t ₁ after the command signal is 10 increased from a preset with the number of pulses was driving amount of that amount motor increases.

FIG. 6 shows the result when the slip correction control in this embodiment is performed. Figure 6 upper part and the angle value of the theoretical of the driven body 12 multiplied by the reduction ratio R of the step angle theta _ST and reduction gear 20 of the motor 14 to the pulse number of the command signal sent to the motor 14, the output of the speed reducer 20 A time change of the rotation angle value of the shaft, that is, the actual rotation angle value of the driven body 12 is shown. Further, the middle part of FIG. 6 shows a change in rotational speed of the driven body 12. The lower part of FIG. 6 shows the slip correction amount. Note that the 5 ° the installation angle theta _D of the detector 16 in the correction control of FIG. That is, the detector 16 is disposed at a position of 5 ° clockwise from the first stop angle θ ₁ (= 0 °). Furthermore, the operation of the driven member 12, and to rotate in a first stop angle theta ₁ again after being rotated from the first stop angle theta ₁ to the second stop angle theta _2, the first stop angle theta ₁ Slip correction control is performed when returning to step 1.

FIG. 7 shows an enlarged view when the driven body 12 returns from the _second stop angle θ ₂ to the first stop angle θ ₁ . In the lower part of FIG. 7, slip correction is performed in accordance with detection of the detection pin 22, and the slip angle Θ is calculated. A correction signal is superimposed on the command signal based on the slip angle Θ. Thus the driven member 12 increasing the number of pulses of the command signal can return to theta _1. Note that the rotational speed increases when slip correction is performed in the middle stage of FIG. 7 because the number of pulses per unit time increases and the pulse frequency increases as a result of the correction signal being superimposed on the command signal.

  Next, FIG. 8 shows the position of the driven body 12 when the slip correction control is performed in this embodiment (shown by a solid diamond plot) and the position of the driven body 12 when the slip correction control is not performed ( Comparison with (shown by open diamond plot). In the figure, the horizontal axis represents the load torque of the driven body 12, and the vertical axis represents the deviation from the position of the stop angle. A 0.0 point is plotted on the upper left in the figure, and this point is set as a target stop angle. As shown in FIG. 8, the driven body 12 when the slip correction control according to the present embodiment is performed is generally stopped at the stop angle, and up to the stop angle as compared with the case where the slip correction control is not performed. Can be moved with high accuracy.

  In the above-described embodiment, the slip angle Θ is calculated based on both the detection delay of the detector 16 and the acquisition delay of the control unit 18 at the time of slip correction control. Either one of the delays may be reflected in the calculation of the slip angle Θ. By doing in this way, the precision of position control can be improved rather than the conventional slip correction control which did not reflect any delay. In addition, there is an advantage that arithmetic processing can be reduced by reducing delay elements to be considered.

In the embodiment described above, the speed reducer 20 is provided between the driven body 12 and the motor 14, but the present invention is not limited thereto. For example, the motor 14 and the driven body 12 may be directly connected. In this case, the theoretical angle θ _CAL (t ₁ ) of the driven body 12 is the pulse of the driving signal output from the control unit 18 to the motor 14 during the period from the driving start time of the driven body 12 to the acquisition time t _1. It is obtained from the product of the number S (t ₁ ) and the step angle θ _ST of the motor 14. In addition, Formula 8 for obtaining the number of pulses ΔS in the correction signal is calculated with the reduction ratio R omitted.

DESCRIPTION OF SYMBOLS 10 Drive apparatus, 12 Driven body, 14 Motor, 16 Detector, 18 Control part, 19 Encoder, 20 Reduction gear, 22 Detection pin, 24 Reflecting surface, 26 Fixed member, 30 Command signal generation part, 32 Theoretical angle calculation part , 34 Detector angle setting unit, 36 Delay correction unit, 38 Correction switching unit.

Claims (4)

A motor for rotating the driven body based on the drive signal;
A detector that detects the passage of the driven body and outputs a detection signal;
A controller that sends the drive signal to the motor and obtains the detection signal from the detector;
With
The control unit includes the position of the driven body at a passing time point when the driven body passes through the detector, and the detection delay period from the passing time point to an output time point when the detector outputs the detection signal. At least one of a first distance that is a movement distance of the driven body and a second distance that is the movement distance of the driven body in an acquisition delay period from the output time point to an acquisition time point when the control unit acquires the detection signal. And obtaining the actual position of the driven body at the acquisition time using the distance, and the acquisition time determined by the drive signal output to the motor from the drive start time of the driven body to the acquisition time Determining the theoretical position of the driven body in the above, and determining the drive signal after the acquisition time based on the difference between the actual position and the theoretical position ,
The detector is an optical sensor, and detects the passage of the driven body according to light reflection from a reflection surface of a detection pin provided on the driven body,
The drive device according to claim 1, wherein the reflection surface of the detection pin of the driven body is formed of a curved surface having a curvature of 1 / r based on a distance r from a rotation axis of the driven body to the reflection surface . A motor for driving the driven body based on the drive signal;
A detector that detects the passage of the driven body and outputs a detection signal;
A controller that sends the drive signal to the motor and obtains the detection signal from the detector;
With
The control unit includes the position of the driven body at a passing time point when the driven body passes through the detector, and the detection delay period from the passing time point to an output time point when the detector outputs the detection signal. At least one of a first distance that is a movement distance of the driven body and a second distance that is the movement distance of the driven body in an acquisition delay period from the output time point to an acquisition time point when the control unit acquires the detection signal. And obtaining the actual position of the driven body at the acquisition time using the distance, and the acquisition time determined by the drive signal output to the motor from the drive start time of the driven body to the acquisition time Determining the theoretical position of the driven body in the above, and determining the drive signal after the acquisition time based on the difference between the actual position and the theoretical position,
The motor is a stepping motor,
The drive signal is a pulse signal for driving the stepping motor,
The control unit obtains a theoretical position of the driven body at the acquisition time from the number of pulses of the pulse signal output to the stepping motor from the drive start time to the acquisition time, and A correction pulse number corresponding to a difference between the actual position and the theoretical position is obtained, and the number of pulses per unit time of the pulse signal after the acquisition time is increased or decreased by the correction pulse number. Drive device. The drive device according to claim 1 or 2 ,
The drive unit is characterized in that the control unit obtains the first distance based on a theoretical moving speed or acceleration of the driven body determined by the drive signal and the detection delay period . The drive device according to claim 1 or 2 ,
The drive unit is characterized in that the control unit obtains the second distance based on a theoretical moving speed or acceleration of the driven body determined by the drive signal and the acquisition delay period .

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