Motor control device and crane device

Abstract

A motor control device (50) comprises: a speed command generation unit (4) that generates a speed command for a carriage (2); a vibration control speed command generation unit (7) that calculates a vibration control acceleration / deceleration time period on the basis of a suspended load position measurement value and a suspended load speed measurement value measured by a load swing measurement unit (6) and on the basis of a suspended load vibration frequency, which is the frequency of vibration generated by a suspended load (3), and generates a vibration control speed command resulting from the vibration control acceleration / deceleration time period such that an acceleration operation and a deceleration operation become reciprocating operations; and a control unit (5) that controls the torque of a motor (1) on the basis of the speed command and the vibration control speed command. The vibration control speed command generation unit (7) calculates, as the vibration control acceleration / deceleration time period, a time period obtained by adding a time period that is 1 / 2 of the time period difference with the time at which the suspended load position measurement value, as based on the time at which the vibration control speed command is generated, reaches 0, and a time period that is 0-times or an integer multiple of 1 / 4 of the vibration period generated by the suspended load.

Description

Motor control device and crane device

[0001] The present disclosure relates to a motor control device that controls a motor and a crane apparatus that is driven by the motor.

[0002] Examples of crane devices include overhead traveling cranes and slewing cranes, which move a load suspended from a rope suspended from a moving device such as a cart. In these overhead traveling cranes and slewing cranes, the load suspended from the rope can vibrate like a pendulum due to external disturbances such as acceleration and deceleration of the load during movement and wind that the load experiences during movement. If vibrations generated in the load remain after the moving device is stopped, the load cannot be lowered until the vibrations have subsided, resulting in an increased takt time. Furthermore, residual vibrations generated in the load can sometimes cause unintended contact with other objects. To address these issues, various vibration suppression control technologies have been proposed to suppress residual vibrations after the device is stopped.

[0003] For example, Patent Document 1 below discloses a crane apparatus that reduces braking distance while suppressing load sway that occurs when stopping a crane. The crane apparatus described in Patent Document 1 has a speed command generator that generates a movement speed command for a horizontal movement device, and a crane control unit that moves the horizontal movement device in accordance with the speed command. The speed command generator of the crane apparatus generates a speed pattern that performs acceleration and deceleration to cancel out load sway that occurs when the horizontal movement device is driven.

[0004] Japanese Patent Application Laid-Open No. 2020-90332

[0005] When accelerating and decelerating to suppress load sway, there is a problem that the stopping position of the moving device changes, causing the position of the suspended load to deviate from the target position. Furthermore, because the speed pattern for accelerating and decelerating to counteract load sway is determined by the period and amplitude of the load sway, there is also a problem that it is difficult to grasp the amount of change in the stopping position. Furthermore, if the stopping position of the moving device changes and moves to an unintended position, it may come into contact with another object. For this reason, it is desirable for a crane apparatus to minimize the deviation between the position of the suspended load and the target position while suppressing the vibration of the suspended load.

[0006] The present disclosure has been made in view of the above, and aims to provide a motor control device that can reduce the deviation between the position of a suspended load and a target position while suppressing vibration of the suspended load.

[0007] In order to solve the above-mentioned problems and achieve the object, a motor control device according to the present disclosure is applied to a crane apparatus including a cart that suspends a load and moves it horizontally, a motor that drives the cart, and a load sway measurement unit that measures the position of the load relative to the position of the cart and the speed of the load relative to the speed of the cart, and controls the motor. The motor control device includes a speed command generation unit, a vibration-damping speed command generation unit, and a control unit. The speed command generation unit generates a speed command for the cart. The vibration-damping speed command generation unit calculates a vibration-damping acceleration / deceleration time based on the measured load position and speed values ​​measured by the load sway measurement unit and a load vibration frequency, which is the frequency of vibrations generated by the load, and generates a vibration-damping speed command such that the acceleration and deceleration movements due to the vibration-damping acceleration / deceleration time become reciprocating movements. The control unit controls the torque of the motor based on the speed command and the vibration-damping speed command. In addition, the vibration damping speed command generation unit calculates the vibration damping acceleration / deceleration time as the sum of half the time difference between the time at which the measured value of the suspended load position becomes 0, based on the time at which the vibration damping speed command is generated, and the time obtained by multiplying 0 or an integer by 1 / 4 of the vibration period generated by the suspended load.

[0008] The motor control device according to the present disclosure has the effect of reducing the deviation between the position of the suspended load and the target position while suppressing vibration of the suspended load.

[0009] 1 is a diagram showing an example of the configuration of a crane apparatus equipped with a motor control device according to embodiment 1; FIG. 2 is an operation curve diagram used to explain a vibration phenomenon that can occur when acceleration / deceleration control is performed on the carriage of the crane apparatus shown in FIG. 1; FIG. 3 is an operation curve diagram used to explain the operation when vibration suppression control is further performed during the operation of FIG. 2; FIG. 4 is a phase plane trajectory corresponding to the vibration suppression control of FIG. 4; 12 is a diagram showing a configuration example of a crane apparatus equipped with a motor control device according to embodiment 4; 15 is a diagram showing a phase plane trajectory corresponding to the vibration damping control of FIG. 15; 16 is a diagram showing a configuration example of a crane apparatus equipped with a motor control device according to embodiment 4; 17 is a diagram showing a phase plane trajectory corresponding to the vibration damping control of FIG. 15; 18 is a diagram showing a configuration example of a crane apparatus equipped with a motor control device according to embodiment 4;

[0010] A motor control device and a crane apparatus according to an embodiment of the present disclosure will be described in detail below with reference to the accompanying drawings.

[0011] Embodiment 1. Fig. 1 is a diagram showing an example of the configuration of a crane apparatus 100 equipped with a motor control device 50 according to embodiment 1. Fig. 1 shows a motor 1, a carriage 2, a suspended load 3, a load swing measurement unit 6, and the motor control device 50. The motor control device 50 includes a speed command generation unit 4, a control unit 5, and a vibration-damping speed command generation unit 7.

[0012] A load 3 is suspended from the carriage 2. The carriage 2 is driven by a motor 1 to move in the horizontal direction. The motor 1 is attached to the carriage 2 so as to move the carriage 2, and moves the load 3 suspended from the carriage 2 to a target position. A motor control device 50 controls the motor 1. That is, the motor control device 50 controls the motor 1 that drives the carriage 2, which moves in the horizontal direction while suspending the load 3.

[0013] The load sway measuring unit 6 is attached to the cart 2, and measures the suspended load position, which is the position of the suspended load 3, to obtain a suspended load position measurement value, which is a measurement value of the suspended load position based on the position of the cart 2. In addition, the load sway measuring unit 6 measures the suspended load speed, which is the speed of the suspended load 3, to obtain a suspended load speed measurement value, which is a measurement value of the suspended load speed based on the speed of the cart 2.

[0014] The speed command generation unit 4 generates a speed command for the bogie 2 and outputs it to the control unit 5. The vibration-damping speed command generation unit 7 calculates a vibration-damping acceleration / deceleration time based on the suspended load position measurement value, the suspended load speed measurement value, and the frequency of vibrations generated in the suspended load 3. Then, the vibration-damping speed command generation unit 7 generates a vibration-damping speed command, which is a speed command for suppressing vibrations generated in the suspended load 3, based on the calculated vibration-damping acceleration / deceleration time, and outputs this to the control unit 5. The vibration-damping acceleration / deceleration time and the vibration-damping speed command will be described in detail later. The control unit 5 controls the torque of the motor 1 based on the speed command generated by the speed command generation unit 4 and the vibration-damping speed command generated by the vibration-damping speed command generation unit 7.

[0015] Next, the operation of the crane apparatus 100 shown in Figure 1 will be described. In the crane apparatus 100, the motor 1 serves as a drive source for the carriage 2, and by moving the carriage 2, the load 3 suspended from the carriage 2 is moved to a desired position. The motor 1 operates in accordance with a control signal output from the control unit 5 and generates a desired torque. The control unit 5 controls the torque generated by the motor 1 so that the carriage 2 moves in accordance with a speed command generated by the speed command generation unit 4. The speed command generation unit 4 generates a speed command based on set acceleration, deceleration, and speed in response to an operator's operation.

[0016] The load sway measuring unit 6 attached to the carriage 2 outputs the measured load position and load speed measurements to the vibration damping speed command generating unit 7. As described above, the load position measurement is a measurement of the position of the load 3 based on the position of the carriage 2, and the load speed measurement is a measurement of the speed of the load 3 based on the speed of the carriage 2. The load speed measurement may be calculated by time differentiating the load position measurement. Therefore, the load sway measuring unit 6 may output only the load position measurement to the vibration damping speed command generating unit 7, and the load speed measurement may be determined by internal calculation processing of the vibration damping speed command generating unit 7. The vibration damping speed command generating unit 7 generates a vibration damping speed command based on the load sway state of the load 3 that is determined from the load position measurement and the load speed measurement. As described above, the vibration damping speed command is a speed command for suppressing vibrations occurring in the load 3.

[0017] Here, in the crane apparatus 100, when the carriage 2 is moved in accordance with the speed command output from the speed command generating unit 4, the load 3 may oscillate like a pendulum when the carriage 2 stops due to acceleration or deceleration of the carriage 2. The phenomenon of the load 3 oscillating like a pendulum can also occur when an external disturbance such as wind acts on the load 3.

[0018] FIG. 2 is an operating curve diagram illustrating a vibration phenomenon that can occur when acceleration / deceleration control is performed on the bogie 2 of the crane apparatus 100 shown in FIG. 1 . The upper part of FIG. 2 shows the time-varying waveform of the bogie speed command, which is a speed command for the bogie 2. The middle part of FIG. 2 shows the time-varying waveform of the bogie position with a dashed line, and the time-varying waveform of the suspended load position with a solid line. The lower part of FIG. 2 shows the time-varying waveform of the suspended load vibration amplitude, which is the amplitude value of the vibration of the suspended load 3. In the lower part of FIG. 2, the suspended load position when the load 3 is perpendicular to the bogie 2 is set to 0, with the stopped position of the bogie 2 as the reference, and the amplitude when the load 3 swings in the same direction as the movement direction before the bogie 2 stopped is shown as positive, and the amplitude when the load 3 swings in the opposite direction to the movement direction of the bogie 2 is shown as negative.

[0019] As shown in the waveforms in the middle and bottom sections of the graph in Figure 2, the suspended load 3 may continue to vibrate even after the cart 2 has stopped. If the suspended load 3 is vibrating, when performing work such as lowering the suspended load 3, it is necessary to wait until the vibrations have attenuated and the work can be carried out, which may have the effect of extending the work time. Similarly, if an external disturbance such as wind acts on the suspended load 3, vibrations may occur even after the cart 2 has stopped, affecting the work time.

[0020] FIG. 3 is a diagram showing an example of a phase plane trajectory when the load 3 experiences vibration as shown in FIG. 2 . In the phase plane trajectory of FIG. 3 , the horizontal axis represents the measured load position X, and the vertical axis represents V / ω, which is the measured load velocity V divided by the load vibration frequency ω. The load vibration frequency is the frequency of vibration when vibration occurs in the load 3. The measured load position X on the horizontal axis is set to 0 when the load 3 is perpendicular to the cart 2, with the cart 2 as the reference. Positions in the same direction as the movement of the cart 2 are positive, and positions in the opposite direction to the movement of the cart 2 are negative. V / ω on the vertical axis is set to 0 when the measured load velocity V is 0. The phase plane trajectory in FIG. 3 is drawn clockwise, starting from point ST at coordinates (0,0), which is the starting point. At point ST, the load position measurement value X and the load speed measurement value V are both 0, and therefore the example in Figure 3 indicates that point ST is the state where the load 3 is not vibrating.

[0021] The acceleration or deceleration of the carriage 2 is a [m / s ２ ], the phase plane trajectory is (-a / ω ２ , 0) is a clockwise circular orbit. The following explains this using the examples of Figures 2 and 3.

[0022] First, as shown in the upper part of FIG. 2, the carriage 2 moves at a speed of 0.7 [m / s ２ ], and after acceleration, it operates at a constant speed, and then ２2, the vibration frequency of the load 3 is set to 1 [rad / s]. Therefore, in the phase plane trajectory of FIG. 3, during acceleration, the carriage 2 describes a clockwise circular orbit centered on point C at coordinates (-0.7, 0) indicated by an x ​​on the left, and during deceleration, the carriage 2 describes a clockwise circular orbit centered on point D at coordinates (0.7, 0) indicated by an x ​​on the right. Furthermore, when the carriage 2 is moving at a constant speed without accelerating or decelerating, or when the carriage 2 is stopped, the carriage 2 describes a clockwise circular orbit centered on point ST at coordinates (0, 0).

[0023] The phase plane trajectory in FIG. 3 will be explained below, starting from point ST (0,0). First, during acceleration, starting from point ST (0,0), the robot traces a clockwise circular trajectory centered on point C (-0.7,0) and moves to point P1. During constant speed operation, the robot traces a clockwise circular trajectory centered on point ST (0,0) from point P1 to point P2 and moves to point P2. During deceleration, the robot traces a clockwise circular trajectory centered on point D (0.7,0) from point P2 to point P3 and moves to point P3. After the carriage 2 stops, it traces a clockwise circular trajectory centered on point ST (0,0) from point P3. All trajectories are continuous, and the outermost circular trajectory represents the vibration after stopping. Each circular trajectory is traced so as to complete one clockwise revolution with a vibration period T (= 2π / ω) [sec] of the suspended load 3.

[0024] Here, to suppress vibration of the suspended load 3, the phase plane trajectory should be (0,0) when the load is stopped. In other words, a vibration suppression operation involving acceleration and deceleration of the bogie 2 is performed from point P3 where the bogie 2 has decelerated and stopped, and the bogie 2 is stopped so that the phase plane trajectory becomes (0,0). This control is called "vibration suppression control." The operation when vibration suppression control is performed will be described below with reference to FIGS. 4 and 5. FIG. 4 is an operating curve diagram used to explain the operation when vibration suppression control is further performed during the operation of FIG. 2. FIG. 5 is a diagram showing the phase plane trajectory corresponding to the vibration suppression control of FIG. 4.

[0025] The types of waveforms and the coordinate axes of each diagram shown in Fig. 4 are basically the same as those in Fig. 2, and therefore redundant explanations will be omitted. In the upper part of Fig. 4, the vibration damping speed command generated during vibration damping control is shown by a broken line. In the example of Fig. 4, immediately after the bogie 2 stops, the acceleration +A [m / s ２] and accelerates for the set vibration damping acceleration time Ta [sec]. After the acceleration is completed, the carriage 2 is decelerated at the set deceleration rate -A [m / s ２ ], and the carriage 2 is decelerated for the set vibration damping deceleration time Ta [sec], and then stopped.

[0026] Basically, the vibration damping acceleration time Ta [sec] and the vibration damping deceleration time Ta [sec] are equal in time. In this paper, these are sometimes collectively referred to as "vibration damping acceleration / deceleration time Ta", and the vibration damping acceleration time and the vibration damping deceleration time are sometimes collectively referred to as "vibration damping acceleration / deceleration time". Also, basically, acceleration + A [m / s ２ ] and deceleration - A [m / s ２ In this document, these may be collectively referred to as "acceleration / deceleration A," and acceleration and deceleration may be collectively referred to as "acceleration / deceleration."

[0027] The operation at this time will be described using the phase plane trajectory in Fig. 5. In Fig. 5, the point (-A / ω ２ , 0), and the point (A / ω ２ , 0) are omitted from the illustration.

[0028] First, during the acceleration operation of the vibration suppression control, starting from point P3, ２ During the deceleration operation of the vibration suppression control, the rotational speed of the rotor 1 starts from the point P4 and moves to the point (A / ω ２ The point PE moves in a clockwise circular orbit around the center PE(0,0) and moves to the point PE(0,0).

[0029] Next, acceleration / deceleration A [m / s ２ ] and the vibration damping acceleration / deceleration time Ta [sec] are calculated as follows. ２ ] is the acceleration + A [m / s ２ ] with the sign reversed.

[0030] The coordinates of point P3 on the phase plane orbit are (X ｐ３ , Y ｐ３ ), the coordinates of point P4 on the phase plane orbit are (X ｐ４ , Yｐ４ ) At this time, the point PE (0,0) and the point P4 (X ｐ４ , Y ｐ４ ) is expressed by the following equation (1): ２ , 0) as the center, the coordinates of the point P4 (X ｐ４ , Y ｐ４ ) In the phase plane of FIG. 5, the positive direction of rotation is defined as counterclockwise.

[0031]

[0032] Next, point P3 (X ｐ３ , Y ｐ３ ) to the point (-A / ω ２ , 0) and draw a circular orbit around point P4 (X ｐ４ , Y ｐ４ ) is moved to point P4 (X ｐ４ , Y ｐ４ ) to the point (-A / ω ２ , 0) and rotated counterclockwise by φ [rad] is P3 (X ｐ３ , Y ｐ３ ) can be expressed as

[0033]

[0034] Here, the rotation angle of the phase plane orbit in FIG. 5, taken from the positive part of the vertical axis to the positive side of the horizontal axis, is represented by "ρ". The rotation angle ρ is defined as being positive in the counterclockwise direction, just like the rotation angle φ. Also, the point P3 (X ｐ３ , Y ｐ３ ) and rotate the point ST(0,0) by ρ[rad] from the origin to the point (0,Y ０ ) the relational expression shown in the following equation (3) is obtained.

[0035]

[0036] Then, the following equation (4) is obtained from the above equations (2) and (3).

[0037]

[0038] Since the phase plane orbit describes a clockwise circular orbit, the rotation angle φ [rad] that satisfies the above formula (4) is a positive value. Therefore, the rotation angle φ [rad] that satisfies the above formula (4) can be expressed as the following formula (5) using an integer N (N = 0, 1, 2, 3, ...) that is equal to or greater than 0.

[0039]

[0040] The first term on the right side of the above equation (5), "φ=N·2π", can be found from the condition that "1-cosφ" in the above equation (4) becomes "1-cosφ=0". Also, the second term on the right side of the above equation (5), "φ=(2N+1)π / 2-ρ", can be found from the condition that "cos(φ+ρ)" in the above equation (4) becomes "cos(φ+ρ)=0".

[0041] Here, if you select "φ=π / 2-ρ" with N=0 in the conditional expression "φ=(2N+1)π / 2-ρ", the acceleration +A [m / s ２ ] can be expressed by the following equation (6).

[0042]

[0043] Point P3(X ｐ３ , Y ｐ３ ) is obtained from the measurement value of the suspended load position and the measurement value of the suspended load speed acquired by the load swing measurement unit 6. Also, from the above formula (6), acceleration + A [m / s ２ ] and deceleration - A [m / s ２ ] can be calculated. In addition, the vibration damping acceleration time Ta and the deceleration −A [m / s ２ ] can be calculated by Ta [sec] = φ / ω. If these measured and calculated values ​​are used to control the motor 1, the operations shown in Figures 4 and 5 can be realized, and vibration of the suspended load 3 can be suppressed. Note that, since the vibration-suppression acceleration / deceleration time Ta is determined by the rotation angle φ, φ must be greater than 0.

[0044] Looking at the operation curve in the middle section of Figure 4, it becomes clear that the stopping position of the bogie 2 changes due to the vibration suppression operation, which in turn causes a change in the stopping position of the suspended load 3. To address this issue, if the vibration suppression operation of the bogie 2 is changed to a reciprocating operation, vibration can be suppressed without changing the stopping position. This operation will be explained with reference to Figures 6 and 7. Figure 6 is an operation curve diagram used to explain the operation when the vibration suppression control of Figure 4 is changed to vibration suppression control using a reciprocating operation. Figure 7 is a diagram showing a phase plane trajectory corresponding to the vibration suppression control of Figure 6.

[0045] The types of waveforms and the coordinate axes of each diagram shown in Fig. 6 are the same as those in Fig. 4. In the example of Fig. 6, immediately after the carriage 2 stops, the set acceleration of the carriage 2 +A [m / s ２ ] and accelerates for the set vibration damping acceleration time Ta [sec]. Immediately after the acceleration is completed, the carriage 2 is decelerated at the set deceleration rate -A [m / s ２ ] and decelerates for the set vibration damping deceleration time Ta [sec]. After that, the carriage 2 is decelerated in the reverse direction at the set acceleration -A [m / s ２ ] and accelerates for the set vibration damping acceleration time Ta [sec]. Immediately after the acceleration is completed, the carriage 2 is decelerated to the set deceleration + A [m / s ２ ], and the carriage 2 is decelerated for the set vibration damping deceleration time Ta [sec], and then stopped.

[0046] The operation at this time will be described using the phase plane trajectory in Fig. 7. In Fig. 7, the point (-A / ω ２ , 0) and the point (A / ω) which is the center of the circular orbit during acceleration or deceleration of the vibration suppression control ２ , 0), and the rotation angle φ are omitted from the illustration. In the following explanation, the coordinates of the point P5 on the phase plane orbit are expressed as (X ｐ５ , Y ｐ５ ) far away.

[0047] First, point P3 (X ｐ３ , Y ｐ３ ) and the point (-A / ω ２ , 0) and draw a circular orbit that rotates by -φ [rad] around point P4 (X ｐ４ , Y ｐ４ Next, move to point P4 (X ｐ４ , Yｐ４ ) and the point (A / ω ２ , 0) and draw a circular orbit that rotates by -2φ [rad] to point P5 (X ｐ５ , Y ｐ５ ) and then start from point P5 and move to point (-A / ω ２ The phase plane orbit in FIG. 7 is rotated counterclockwise to form a circular orbit that rotates by −φ [rad] around point PE(0,0).

[0048] Point P3(X ｐ３ , Y ｐ３ ) to point P4 (X ｐ４ , Y ｐ４ ), the acceleration operation continues until point P4 (X ｐ４ , Y ｐ４ ) to point P5 (X ｐ５ , Y ｐ５ ), the first -φ [rad] rotation of the -2φ [rad] rotation is a deceleration operation, and the next -φ [rad] rotation is an acceleration operation. ｐ５ , Y ｐ５ ) to point PE(0,0), the deceleration operation is performed. ｐ３ , Y ｐ３ ) to point PE(0,0), the phase plane trajectory in FIG. 7 is a reciprocating motion in which acceleration and deceleration operations are alternately performed twice each during the vibration suppression acceleration / deceleration time Ta.

[0049] Point P5(X ｐ５ , Y ｐ５ ) to the point (-A / ω ２ The operation of rotating by -φ [rad] around the point PE(0,0) and moving to the point PE(0,0) is performed by rotating from the point PE(0,0) to the point (-A / ω ２ , 0) as the center, the coordinates rotated by φ [rad] are P5 (X ｐ５ , Y ｐ５ ) can be expressed as

[0050]

[0051] Also, point P4 (X ｐ４ , Y ｐ４ ) to (A / ω ２, 0) and rotate by -2φ [rad] to point P5 (X ｐ５ , Y ｐ５ ) is moved to point P5 (X ｐ５ , Y ｐ５ ) to (A / ω ２ , 0) is rotated by 2φ [rad] and the coordinates of point P4 (X ｐ４ , Y ｐ４ ) can be expressed as

[0052]

[0053] Also, point P3 (X ｐ３ , Y ｐ３ ) to (-A / ω ２ , 0) and rotate by -φ [rad] to get point P4 (X ｐ４ , Y ｐ４ ) is moved to point P4 (X ｐ４ , Y ｐ４ ) to (-A / ω ２ , 0) is rotated by φ [rad] around point P3 (X ｐ３ , Y ｐ３ ) can be expressed as

[0054]

[0055] Here, as in FIG. 5, point P3 (X ｐ３ , Y ｐ３ ) and rotate the point on the positive part of the vertical axis by ρ [rad] around the origin point ST (0, 0). ０ ) is set, the relational expression shown in the above formula (3) is obtained. Then, the following formula (10) is obtained from the above formula (3) and the above formula (9).

[0056]

[0057] Since the phase plane orbit describes a clockwise circular orbit, the rotation angle φ [rad] that satisfies the above formula (4) is a positive value. Therefore, the rotation angle φ [rad] that satisfies the above formula (4) can be expressed as the following formula (11) using an integer N (N = 0, 1, 2, 3, ...) that is equal to or greater than 0.

[0058]

[0059] Although detailed calculation procedures will be omitted, the first term on the right-hand side of the above equation (11), "φ=N·π", and the second term on the right-hand side of the above equation (11), "φ=(N·π−ρ) / 2", can each be derived from the condition that the X coordinate written on the right-hand side of the above equation (10), "cos(4φ+ρ)−2cos(3φ+ρ)+2cos(φ+ρ)−cosρ", is 0.

[0060] Here, if "φ = (N·π - ρ) / 2" is selected from the conditional expression (11) above, the vibration damping acceleration / deceleration time Ta [sec] and acceleration / deceleration A [m / s ２ ] can be expressed by the following equation (12).

[0061]

[0062] In the above formula (12), "-(ρ / 2π)·T" included in the vibration damping acceleration / deceleration time Ta [sec] is the time T when the lifted load position measurement value X becomes X=0, as shown in the following formula (13). Ｘ０ The suspended load 3 is at point P3 (X ｐ３ , Y ｐ３ ) at time T ｐ３ The time shown in the figure is the time after subtracting the above.

[0063]

[0064] From the above equation (13) and the second equation of the above equation (12), the vibration damping acceleration / deceleration time Ta [sec] is calculated by adding together half the time difference between the time when the suspended load position measurement value X, based on the time when the vibration damping speed command is generated, and the time when X = 0, and the time when 1 / 4 of the vibration period T generated in the suspended load 3 is multiplied by 0 or N. The vibration damping speed command generating unit 7 calculates this added time as the vibration damping acceleration / deceleration time Ta [sec].

[0065] The range of the rotation angle ρ is −π / 2<ρ<π / 2, and therefore −T / 8<(ρ / 2π)·(T / 2)<T / 8.

[0066] Point P3(X ｐ３ , Y ｐ３ ) and the rotation angle ρ can be calculated using the following equation (14) based on the suspended load position measurement value X and the suspended load speed measurement value V acquired by the load swing measurement unit 6.

[0067]

[0068] Using the value of the rotation angle ρ obtained by the above formula (14), the acceleration / deceleration A [m / s ２ 6 and 7 can be realized by accelerating or decelerating the carriage 2 at a speed of [s] [s] and setting the time for the acceleration and deceleration to the vibration-damping acceleration / deceleration time Ta [sec]. This makes it possible to reduce the deviation between the position of the load 3 and the target position while suppressing the vibration of the load 3.

[0069] As described above, the motor control device 50 according to the first embodiment includes a speed command generating unit 4 that generates a speed command for the bogie 2, a vibration suppression speed command generating unit 7 that generates a vibration suppression speed command that is a speed command for suppressing vibrations occurring in the suspended load 3, and a control unit 5 that controls the torque of the motor 1 based on the speed command and the vibration suppression speed command. The vibration suppression speed command generating unit 7 calculates the vibration suppression acceleration / deceleration time Ta based on the suspended load position measurement value X and the suspended load speed measurement value V measured by the load swing measuring unit 6 and the suspended load vibration frequency ω that is the frequency of vibrations occurring in the suspended load 3, and generates a vibration suppression speed command such that the acceleration and deceleration movements during the vibration suppression acceleration / deceleration time Ta result in reciprocating movements. According to the motor control device 50 according to the first embodiment, the vibration suppression speed command generating unit 7 generates a vibration suppression speed command such that the acceleration and deceleration movements during the vibration suppression acceleration / deceleration time Ta result in reciprocating movements, and therefore, at the end of vibration suppression control, the bogie 2 operates to return to the position of the bogie 2 at the start of vibration suppression control. As a result, the position of the suspended load 3 is also controlled in the same way as the carriage 2, so that it is possible to reduce the deviation between the position of the suspended load 3 and the target position while suppressing vibration of the suspended load 3.

[0070] In the motor control device 50 configured as described above, the vibration damping acceleration / deceleration time Ta is calculated using the suspended load speed measurement value V measured by the load swing measurement unit 6, but this configuration is not limiting. The suspended load speed measurement value V may also be obtained inside the vibration damping speed command generation unit 7, for example, by performing a time differentiation operation on the suspended load position measurement value X.

[0071] In the motor control device 50 according to the first embodiment, the vibration damping speed command generating unit 7 can calculate the vibration damping acceleration / deceleration time Ta by adding together half the time difference between the time when the suspended load position measurement value X becomes 0, based on the time when the vibration damping speed command is generated, and the time obtained by multiplying 0 or an integer by 1 / 4 of the vibration period generated by the suspended load 3. Specifically, the vibration damping speed command generating unit 7 uses N, an integer greater than or equal to 0, and the constant π to calculate half the time difference between the time when the suspended load position measurement value X becomes 0 using the formula -(ρ / 2) / ω, and calculates the time obtained by multiplying 0 or an integer by 1 / 4 of the vibration period using the formula N π / 2, and adds these together to calculate the vibration damping acceleration / deceleration time Ta using the formula Ta = (N π / 2 - ρ / 2) / ω. As mentioned above, ρ is the angle of rotation of a phase plane trajectory, which is represented by the horizontal axis representing the measured value X of the suspended load position and the vertical axis representing the value obtained by dividing the measured value V of the suspended load velocity by the vibration frequency ω of the suspended load, with the positive part of the vertical axis being the starting line in the positive direction of the horizontal axis.

[0072] In motor control device 50 according to the first embodiment, vibration damping speed command generating unit 7 uses N, an integer equal to or greater than 0, and the circular constant π to calculate acceleration / deceleration A of the vibration damping speed command as follows: A=(ω ２ This can be calculated using the formula: (-2 sin ρ + 4 cos(N π / 2 + ρ / 2)) / (-2 sin ρ + 4 cos(N π / 2 + ρ / 2)). This formula can be expressed by modifying the third formula of the above formula (12).

[0073] In the above calculation method, acceleration / deceleration A [m / s ２ ] and vibration damping acceleration / deceleration time Ta [sec], four patterns can be obtained. ２ ] does not exceed the limit value. It goes without saying that if a pattern with a short vibration suppression acceleration / deceleration time Ta is selected, the time until vibration is suppressed can be shortened.

[0074] Furthermore, in the motor control device 50 according to the first embodiment, the vibration damping speed command generator 7 generates the vibration damping speed command immediately after the bogie 2 stops, but this does not have to be immediately after the bogie 2 stops, and it is sufficient if the bogie 2 is not accelerating or decelerating. Even in such a case, it is possible to suppress vibrations occurring in the suspended load 3. In this case, the vibration damping speed command may be calculated based on the suspended load position measurement value X and the suspended load speed measurement value V at the start of generation.

[0075] Embodiment 2. Figure 8 is a diagram showing an example of the configuration of a crane apparatus 100a equipped with a motor control device 50a according to embodiment 2. Compared to the motor control device 50 according to embodiment 1 shown in Figure 1, in motor control device 50a according to embodiment 2, vibration suppression speed command generator 7 is replaced with a vibration suppression speed command generator 7a. Other components with the same reference numerals are the same as those in Figure 1, and redundant description will be omitted.

[0076] Next, the operation of the vibration damping speed command generating unit 7a according to embodiment 2 will be described. When the load position measurement value X and the load speed measurement value V output by the load swing measuring unit 6 satisfy a set first condition, the vibration damping speed command generating unit 7a uses the load position measurement value X and the load speed measurement value V at that time to generate a vibration damping speed command, which is a speed command for suppressing vibrations occurring in the load 3. The timing at which the load position measurement value X and the load speed measurement value V satisfy the first condition will be described below with reference to a specific example.

[0077] In the crane apparatus 100a, the movable range of the carriage 2 may be limited. In such cases, a vibration suppression speed command that would cause the carriage 2 and the load 3 to move outside the movable range during vibration suppression operation is not permitted. For example, in the vibration suppression operation described in the first embodiment, as shown by the dashed line in the middle part of Figure 6, the carriage 2 moves approximately 2.7 m from the stop position of 1.9 m, so there is a possibility that the carriage 2 and the load 3 will move outside the movable range. To deal with this event, the vibration suppression speed command generator 7a according to the second embodiment generates a vibration suppression speed command that causes the vibration suppression operation to be a reciprocating operation in the opposite direction. This corresponds to the value of A in the above equation (12) becoming negative. To realize this processing,ｐ３ａ , Y ｐ３ａ ) to the load position measurement value X and the load speed measurement value V, and then start vibration suppression operation. ｐ３ａ , Y ｐ３ａ ) wait until the load speed measurement value V satisfies V<0.

[0078] Figure 9 is an operation curve diagram used to explain the operation when vibration suppression control according to embodiment 2 is performed. The types of waveforms and coordinate axes of each diagram shown in Figure 9 are the same as those in Figure 6. Figure 9 shows how vibration suppression control is performed such that a waiting time Tb is provided so that the carriage 2 and the load 3 do not move outside the allowable range of movement during vibration suppression operation, and the vibration suppression operation is a reciprocating operation in the opposite direction. Note that in Figure 9, at time t1 when vibration suppression control is started, the vibration of the load position has passed its peak, and the measured load speed value V satisfies the condition V<0.

[0079] 10 is a diagram showing a phase plane trajectory corresponding to the vibration suppression control of FIG. 9. In FIG. 10, a point P3a is added to the phase plane trajectory of FIG. 7. In FIG. 7, the center of the circular trajectory from point P3 to point P4 is the point (-A / ω ２ 7 and 10, the center of the circular orbit from point P3 to point P3a is point ST(0,0), whereas in Fig. 10, the center of the circular orbit from point P3 to point P3a is point ST(0,0). For this reason, the shapes of the circular orbits in Fig. 7 and 10 are different.

[0080] Comparing Figure 9 with Figure 6, it can be seen that in Figure 9, the time it takes for the vibration to converge is longer and the amplitude value of the suspended load vibration amplitude is larger, but the position of the cart 2 does not become longer than 1.9 m, and the purpose of preventing the cart 2 from moving outside the allowable range of movement during the vibration control operation is achieved.

[0081] As described above, with the motor control device 50a according to the second embodiment, the vibration-damping speed command generator 7a determines the movement direction of the load 3 based on the load speed measurement value V, and waits until the movement direction of the load 3 becomes the desired direction before outputting a vibration-damping speed command. This enables the motor control device 50a to perform control so that the carriage 2 and the load 3 do not go outside the allowable range of movement during vibration-damping operation.

[0082] Embodiment 3. Figure 11 is a diagram showing an example configuration of a crane apparatus 100b equipped with a motor control device 50b according to embodiment 3. Compared to the motor control device 50 according to embodiment 1 shown in Figure 1, in motor control device 50b according to embodiment 3, vibration suppression speed command generator 7 is replaced with a vibration suppression speed command generator 7b. Other components with the same reference numerals are the same as those in Figure 1, and redundant description will be omitted.

[0083] Next, the operation of the motor control device 50b according to Embodiment 3 will be described. When the load position measurement value X and the load speed measurement value V output by the load swing measurement unit 6 satisfy a set second condition, the vibration damping speed command generation unit 7b uses the load position measurement value X and the load speed measurement value V at that time to generate a vibration damping speed command, which is a speed command for stopping vibrations occurring in the load 3. The timing at which the load position measurement value X and the load speed measurement value V satisfy the second condition will be described below with reference to a specific example.

[0084] In the crane device 100b, it is desirable to stop the vibration of the load 3 as quickly as possible. Here, the time for vibration suppression control is determined by four times Ta shown in the second equation of the above equation (12), that is, 4Ta. Also, if the angle on the phase plane orbit that rotates during the standby time is set to λ [rad], this angle λ is determined by the angle λ between the point P3 (X ｐ３ , Y ｐ３ ) and point P3b (X ｐ３ｂ , Y ｐ３ｂ In the third embodiment, the angle formed by the point P3 (X ｐ３ , Y ｐ３ ) is defined as the rotation angle ρ in the phase plane orbit of １ " and point P3b (X ｐ３ｂ, Y ｐ３ｂ ) is defined as the rotation angle ρ in the phase plane orbit of ２ ” is expressed as ρ ２ = ρ １ +λ. Therefore, point P3b (X ｐ３ｂ , Y ｐ３ｂ ) to ρ ２ [rad] The rotated point is the point (0,Y ０ ) and the relational expression shown in the following equation (15) is obtained.

[0085]

[0086] Furthermore, if the time required for vibration suppression control including the waiting time is defined as Tall, the time Tall is expressed by the following equation (16).

[0087]

[0088] Fig. 12 is an operation curve diagram used to explain the operation when vibration suppression control according to the third embodiment is carried out. The types of waveforms and coordinate axes of each diagram shown in Fig. 12 are the same as those in Fig. 6. Fig. 13 is a diagram showing a phase plane trajectory corresponding to the vibration suppression control of Fig. 12. Fig. 13 shows the relationship between the angle λ and the rotation angle ρ described above. １ , ρ ２ It is shown that:

[0089] Comparing FIG. 12 with FIG. 6, it can be seen that although the amplitude value of the suspended load vibration amplitude is slightly larger in FIG. 12, the stop time in FIG. 6 is 10.6 [sec] while the stop time in FIG. 12 is 9.2 [sec], and therefore the time required for vibration suppression control has been shortened.

[0090] As shown in the third equation of the above equation (16), the larger the angle λ, the shorter the movement time. ２ (=ρ １ +λ), -π / 2<ρ １ +λ<π / 2. Therefore, the point P3b (X ｐ３ｂ , Y ｐ３ｂ ) is calculated as ２ = ρ １ +λ becomes π / 2, that is, point P3b (X ｐ３ｂ , Yｐ３ｂ ) rotation angle ρ ２ It can be seen that if we wait until the time becomes π / 2, the time required for vibration suppression control, including the waiting time, becomes the shortest.

[0091] The vibration suppression control according to the third embodiment can be used in combination with the vibration suppression control according to the first embodiment, that is, the vibration suppression control that generates a vibration suppression speed command such that the acceleration and deceleration operations due to the vibration suppression acceleration / deceleration time Ta become reciprocating operations. When used in combination with the vibration suppression control according to the first embodiment, the acceleration of the suspended load position is negative and the point P3b (X ｐ３ｂ , Y ｐ３ｂ ) The rotation angle ρ calculated by ２ becomes π / 2, and then a vibration suppression speed command is output to start vibration suppression control.

[0092] As described above, according to the motor control device 50b according to the third embodiment, the vibration-damping speed command generator 7b calculates the rotation angle ρ ２ The vibration damping speed command is output after waiting until the time t reaches π / 2 [rad]. This makes it possible to minimize the time required for vibration damping control.

[0093] Embodiment 4 Figure 14 is a diagram showing an example configuration of a crane apparatus 100c equipped with a motor control device 50c according to embodiment 4. Compared to motor control device 50 according to embodiment 1 shown in Figure 1, motor control device 50c according to embodiment 4 has vibration suppression speed command generator 7 replaced with vibration suppression speed command generator 7c. Other components with the same reference numerals are the same as those in Figure 1, and redundant description will be omitted.

[0094] Next, the operation of the motor control device 50c according to embodiment 4 will be described. When the load position measurement value X and the load speed measurement value V output by the load swing measurement unit 6 satisfy a set third condition, the vibration damping speed command generation unit 7c uses the load position measurement value X and the load speed measurement value V at that time to generate a vibration damping speed command, which is a speed command for stopping vibrations occurring in the load 3. The timing at which the load position measurement value X and the load speed measurement value V satisfy the third condition will be described below with reference to a specific example.

[0095] In the crane device 100c, it is desirable to stop the vibration of the suspended load 3 as quickly as possible, but the acceleration that the carriage 2 can output is often restricted. As explained in the third embodiment, point P3b (X ｐ３ｂ , Y ｐ３ｂ ) is calculated as ２ The closer this value is to π / 2, the shorter the time required for vibration suppression control becomes. However, there is a trade-off between the acceleration that the bogie 2 can output and the time required for vibration suppression control, and shortening the time required for vibration suppression control increases the acceleration of the bogie 2. Therefore, in the vibration suppression control according to the fourth embodiment, the acceleration / deceleration A during vibration suppression operation is reduced to the maximum acceleration that the bogie 2 can output at point P3c (X ｐ３ｃ , Y ｐ３ｃ ) and then starts vibration suppression control. In this way, it is possible to shorten the time required for vibration suppression control as much as possible while observing the constraint of the maximum acceleration.

[0096] Fig. 15 is an operation curve diagram illustrating the operation when vibration suppression control according to embodiment 4 is performed. The types of waveforms and coordinate axes of each diagram shown in Fig. 15 are the same as those in Fig. 6. Fig. 16 is a diagram showing a phase plane trajectory corresponding to the vibration suppression control of Fig. 15. Point P3c is added to the phase plane trajectory of Fig. 7 in Fig. 16. The center of the circular trajectory from point P3 to point P3c is point ST(0,0), which is the same as point P3a shown in Fig. 10 and point P3b shown in Fig. 13.

[0097] As explained in the third embodiment, the rotation angle ρ ２ 12 and 15, the time until the vibration is suppressed can be minimized by outputting the vibration suppression speed command after waiting until the rotation angle ρ reaches π / 2 [rad]. ２ When the acceleration / deceleration speed A [m / s ２ ] may become large and exceed the maximum acceleration. ２15. As shown in the upper part of FIG. 15, the acceleration / deceleration A [m / s ２ At time t2 when the acceleration .gtoreq.(a) reaches upper limit B, the generated vibration damping speed command is output to control unit 5 to start vibration damping control. Upper limit B is a set value that is set as the maximum acceleration.

[0098] Comparing Fig. 15 with Fig. 6, it can be seen that the stop time in Fig. 6 is 10.6 [sec] while the stop time in Fig. 15 is 9.8 [sec], which shows that the time required for vibration suppression control has been shortened. Also, comparing Fig. 15 with Fig. 12, the stop time in Fig. 12 is 9.2 [sec], which shows that the time required for vibration suppression control is slightly longer, but it is possible to shorten the time required for vibration suppression control while observing the constraint of not exceeding the maximum acceleration.

[0099] The vibration suppression control according to the fourth embodiment can be used in combination with the vibration suppression control according to the second embodiment, that is, the vibration suppression control that generates a vibration suppression speed command such that the acceleration and deceleration operations due to the vibration suppression acceleration / deceleration time Ta become reciprocating operations. When used in combination with the vibration suppression control according to the second embodiment, the acceleration of the suspended load position is negative, and the acceleration / deceleration A [m / s ２ ] reaches the upper limit value B, and then a vibration damping speed command is output to start vibration damping control.

[0100] As described above, according to motor control device 50c according to the fourth embodiment, vibration damping speed command generator 7c sequentially calculates acceleration / deceleration A of the vibration damping speed command, and calculates acceleration / deceleration A [m / s ２ ] reaches its upper limit before outputting the vibration suppression speed command. This makes it possible to shorten the time required for vibration suppression control while observing the constraint that the maximum acceleration is not exceeded.

[0101] Finally, the hardware configuration for realizing the functions of the motor control devices 50, 50a, 50b, and 50c described above will be described with reference to Fig. 17. Fig. 17 is a block diagram showing an example of a hardware configuration for realizing the functions of the motor control devices 50, 50a, 50b, and 50c according to the first to fourth embodiments.

[0102] 17, when realizing some or all of the functions of the motor control devices 50, 50a, 50b, and 50c according to embodiments 1 to 4, the configuration may include a processing circuit 90 that performs calculations and control processing, and an interface 91 that inputs and outputs signals and data. The processing circuit 90 may also include a processor 92 and a storage unit 93 that stores programs read by the processor 92 and data input and output by the interface 91.

[0103] The processor 92 is an example of a computing means. The processor 92 may be a computing means called a microprocessor, a microcomputer, a central processing unit (CPU), or a digital signal processor (DSP). Examples of the storage unit 93 include non-volatile or volatile semiconductor memory such as random access memory (RAM), read-only memory (ROM), flash memory, erasable programmable read-only memory (EPROM), and electrically programmable read-only memory (EEPROM), as well as a magnetic disk, a flexible disk, an optical disk, a compact disk, a minidisk, and a digital versatile disk (DVD).

[0104] The storage unit 93 stores programs that execute the functions of the motor control devices 50, 50a, 50b, and 50c according to embodiments 1 to 4. The processor 92 exchanges necessary information via the interface 91, executes the programs stored in the storage unit 93, and references the data stored in the storage unit 93, thereby performing the above-mentioned processing. The results of calculations by the processor 92 can be stored in the storage unit 93.

[0105] Furthermore, instead of a configuration including the processor 92 and the storage unit 93, the processing circuit 90 may be configured as a single circuit, a composite circuit, an ASIC (Application Specific Integrated Circuit), an FPGA (Field-Programmable Gate Array), or a circuit combining these. Information input to and output from the processing circuit 90 can be exchanged via an interface 91. Furthermore, the motor control devices 50, 50a, 50b, and 50c may be configured with the processing circuit 90 configured as a single circuit, a composite circuit, an ASIC, or an FPGA, as well as the processor 92 and the storage unit 93.

[0106] The configurations shown in the above embodiments are merely examples, and may be combined with other known technologies, or different embodiments may be combined with each other. It is also possible to omit or modify parts of the configurations as long as they do not deviate from the gist of the invention.

[0107] REFERENCE SIGNS LIST 1 Motor, 2 Cart, 3 Suspended load, 4 Speed ​​command generation unit, 5 Control unit, 6 Load swing measurement unit, 7, 7a, 7b, 7c Vibration damping speed command generation unit, 50, 50a, 50b, 50c Motor control device, 90 Processing circuit, 91 Interface, 92 Processor, 93 Memory unit, 100, 100a, 100b, 100c Crane device.

Claims

1. A motor control device applied to a crane apparatus including a carriage that suspends a load and moves it horizontally, a motor that drives the carriage, and a load sway measurement unit that measures the position of the load relative to the position of the carriage and the speed of the load relative to the speed of the carriage, and controls the motor, comprising: a speed command generation unit that generates a speed command for the carriage; a vibration control speed command generation unit that calculates a vibration damping acceleration / deceleration time based on the load position measurement value and the load speed measurement value measured by the load sway measurement unit and the load vibration frequency, which is the frequency of vibration generated in the load, and generates a vibration control speed command that causes acceleration and deceleration operations due to the vibration control acceleration / deceleration time to be reciprocating movements; and a control unit that controls the torque of the motor based on the speed command and the vibration control speed command, the vibration damping speed command generating unit calculates, as the vibration damping acceleration / deceleration time, a time obtained by adding together half the time difference between the time at which the vibration damping speed command is generated and the time at which the measured value of the position of the suspended load becomes 0, and a time obtained by multiplying 0 or an integer by 1 / 4 of the vibration period generated by the suspended load.

2. The motor control device according to claim 1, wherein, when the measured value of the position of the suspended load is X, the measured value of the speed of the suspended load is V, the vibration frequency of the suspended load is ω, and, with respect to a phase plane trajectory represented with X on the horizontal axis and a value obtained by dividing V by ω on the vertical axis, ρ is the rotation angle taken in the positive direction of the horizontal axis from the positive part of the vertical axis as the starting line, the vibration damping speed command generating unit calculates the vibration damping acceleration / deceleration time Ta by the formula Ta = (N π / 2 - ρ / 2) / ω using N, an integer equal to or greater than 0, and π, the circular constant.

3. When the measured value of the position of the suspended load is X, the measured value of the speed of the suspended load is V, the vibration frequency of the suspended load is ω, and with respect to a phase plane trajectory represented with X on the horizontal axis and a value obtained by dividing V by ω on the vertical axis, the rotation angle taken in the positive direction of the horizontal axis from the positive part of the vertical axis as the starting line is ρ, the vibration damping speed command generating unit calculates the acceleration / deceleration A of the vibration damping speed command as follows: A=(ω ２ 2. The motor control device according to claim 1, wherein the calculation is performed using the formula: X sin ρ + ω V cos ρ) / (−2 sin ρ + 4 cos(N π / 2 + ρ / 2)).

4. The motor control device according to claim 1, characterized in that the vibration damping speed command generation unit sequentially calculates the acceleration / deceleration of the vibration damping speed command, waits until the acceleration / deceleration reaches an upper limit value, and then outputs the vibration damping speed command.

5. The motor control device described in claim 1, characterized in that the vibration damping speed command generation unit determines the movement direction of the load based on the load speed measurement value, waits until the movement direction of the load becomes the desired direction, and then outputs the vibration damping speed command.

6. The motor control device according to claim 1, wherein, when the measured value of the position of the suspended load is X, the measured value of the speed of the suspended load is V, the vibration frequency of the suspended load is ω, and the phase plane trajectory is represented with X on the horizontal axis and the value obtained by dividing V by ω on the vertical axis, the rotation angle taken in the positive direction of the horizontal axis from the positive part of the vertical axis as the starting line is ρ, the vibration damping speed command generation unit waits until ρ reaches π / 2 [rad] before outputting the vibration damping speed command.

7. A vehicle that moves horizontally while suspending a load; a motor that drives the vehicle; a load swing measurement unit that measures the position of the load relative to the position of the vehicle and the speed of the load relative to the speed of the vehicle; a speed command generation unit that generates a speed command for the vehicle; a vibration suppression speed command generation unit that calculates a vibration suppression acceleration / deceleration time based on the load position measurement value and the load speed measurement value measured by the load swing measurement unit and a load vibration frequency that is the frequency of vibrations generated in the load, and generates a vibration suppression speed command that causes acceleration and deceleration operations due to the vibration suppression acceleration / deceleration time to be reciprocating movements; and a control unit that controls the torque of the motor based on the speed command and the vibration suppression speed command, the vibration damping speed command generating unit calculates, as the vibration damping acceleration / deceleration time, a time obtained by adding together half the time difference between the time at which the vibration damping speed command is generated and the time at which the measured value of the position of the suspended load becomes 0, and a time obtained by multiplying 0 or an integer by 1 / 4 of the vibration period generated in the suspended load.

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