JP5388956B2 - Vibration suppression method - Google Patents

Description

  The present invention relates to a vibration suppression method for suppressing vibration generated in a moving body in association with acceleration or deceleration movement, and in particular, when the posture of the moving body itself changes during the movement, at least generated in the moving body. The present invention relates to a vibration suppressing method that suppresses time-varying vibration with one degree of freedom.

  A robot arm that performs motion to perform various operations uses a speed reducer between the motor and the arm. Since the speed reducer behaves as a torsion spring, the vibration of the arm remains even after the motor stops. As a result, it is not possible to move to the next work until the vibration is settled, and work efficiency cannot be improved.

  The problem associated with such residual vibration is not limited to only the robot arm, but is common to moving bodies that perform motions including acceleration or deceleration, such as machine tools and cranes.

  In order to suppress vibration by feedback control, a detector is required. Therefore, a method for suppressing vibration by feedforward control that does not require a detector is required.

  An input shaping method is known as a vibration suppression method in feedforward control (see, for example, Non-Patent Document 1). This input shaping method is a vibration suppression method that is effective when the natural frequency does not change as in a machine tool, and various proposals have been made.

JP 2009-29617 A

Neil C. Singer and Warren P. Seering: Preshaping Command Inputs to Reduce System Vibration, Trans. ASME Journal of Dynamic Systems, Measurement, and Control, Vol.112, No.1, 76-82 (1990) Pyung Hun Chang and Hyung-Soon Park: Time-varying input shaping technique applied to vibration reduction of an industrial robot, Control Engineering Practice 13 (2005) 121-130

  The robot arm generally has multiple joints and multiple degrees of freedom in order to be able to handle various tasks. Therefore, in a robot arm, when another joint is driven while performing a motion operation in which one joint is driven, the posture of the arm itself performing the motion operation changes. Therefore, the natural frequency of the arm changes with time. In such a case, since it becomes a time-varying vibration system, simply applying the conventional input shaping method for a time-invariant vibration system cannot cope with vibration suppression.

  Several proposals have been made as methods for suppressing vibration in such a time-varying vibration system (for example, see Patent Document 1 and Non-Patent Document 2). However, there is a need for a vibration suppression method that can effectively apply the input shaping method to time-varying vibration suppression.

  Accordingly, an object of the present invention is to solve the above-mentioned problem, and to effectively apply at least one degree of freedom and time-varying vibration generated in a moving body in accordance with acceleration or deceleration movement by using an input shaping method. An object of the present invention is to provide a vibration suppression method that suppresses vibrations.

  In order to achieve the above object, the present invention is configured as follows.

  According to one aspect of the present invention, in a vibration body that performs acceleration or deceleration motion, in the vibration suppression method that suppresses vibration of at least one degree of freedom and time-varying generated in the motion body in association with acceleration or deceleration motion, The first impulse response generated in the moving body by the first impulse input added to the body is generated by adding the second impulse input to the moving body at the time when the displacement of the first impulse response becomes zero. When applying the input shaping method in which two impulse responses are overlaid and cancel each other out, the work with Coriolis force caused by the posture of the moving body itself changing during acceleration or deceleration is taken into account. And the vibration suppression method which determines the magnitude | size of the 2nd impulse input with respect to a 1st impulse input is provided.

  According to the present invention, when suppressing at least one degree of freedom and time-varying vibration generated in a moving body with acceleration or deceleration movement using the input shaping method, it occurs with a change in posture of the moving body itself. Since the magnitude of the second impulse input is determined in consideration of the work performed by the Coriolis force, the second impulse input is compared with the time-varying vibration system in which the amplitude of the first impulse response changes with time. Vibration can be effectively suppressed by superimposing impulse responses.

Schematic diagram of a robot arm to which the vibration suppressing method according to the first embodiment of the present invention is applied. Diagram showing changes in acceleration during robot arm movement Diagram showing speed change in robot arm movement Relationship between impulse response displacement and time in time invariant Relationship between time and displacement of impulse response and time Relationship between time and displacement of impulse response and time Relationship between time and displacement of impulse response and time Schematic diagram of a model to which the vibration suppression method of Embodiment 1 is applied Illustration of the operation pattern in the in-plane direction of the arm Diagram showing changes in moment of inertia Diagram showing the impulse response generated in the model The figure which shows the calculation result of ratio α of the size of impulse input The figure which shows the calculation result of the ratio γ of the magnitude of the impulse input in consideration of the correction due to the change of the natural period Diagram showing impulse response overlay result Diagram showing the relationship between the duration of forced excitation force and vibration level Diagram showing acceleration pattern for vibration suppression The figure which shows the forced excitation force pattern for performing vibration suppression Diagram showing the relationship between the duration of forced excitation force and vibration level Flow chart of a procedure for operating a moving body by a drive device by applying a vibration suppression method The figure which shows the calculation result of ratio (alpha) (t) of the magnitude | size of an impulse input in the vibration suppression method concerning Embodiment 2 of this invention. The figure which shows the calculation result of 1 / (beta) (t) about ratio (beta) (t) of the time width of an impulse input The figure which shows the calculation result of ratio (gamma) (t) of the magnitude | size of an impulse input It is a figure which shows the driving | running pattern in the whole duration of operation | movement of an arm, (a) is a figure which shows an external force pattern, (b) is a figure which shows an acceleration pattern, (c) is a figure which shows a speed pattern.

  Embodiments according to the present invention will be described below in detail with reference to the drawings.

(Embodiment 1)
A method for suppressing vibration of a moving body according to the first embodiment of the present invention will be described using a robot arm 10 which is an example of a moving body. A schematic diagram of this robot arm is shown in FIG.

  As shown in FIG. 1, the robot arm 10 includes a plurality of arms, a plurality of joints that connect the respective arms so as to allow rotational movement, and a hand tool attached to the arm at the tip. Specifically, the robot arm 10 includes joints 11a, 11b, and 11c, arms 12a and 12b, and a hand tool 13 attached to the tip of the arm 12b. Further, in each of the joints 11a to 11c, a driving device (for example, a motor, not shown) that rotationally drives the arms 12a and 12b, and a reduction gear that transmits the driving force from the driving device to each joint (see FIG. Not shown).

In the robot arm 10 of FIG. 1, the joint 11a can turn the arm 12a around the vertical rotation axis 14a (turning angle θ), and the joint 11b rotates the arm 12a around the horizontal rotation axis 14b. movement (rotation angle [psi ₁₎ is to be able, joints 11c can be rotated movement arm 12b around the horizontal rotation axis 14c (rotation angle [psi _2).

  Therefore, the movement of the robot arm 10 includes a turning motion around the vertical rotation axis 14a (hereinafter referred to as “movement in the turning direction”) and a rotation motion around the horizontal rotation shafts 14b and 14c (hereinafter “ In-plane (vertical plane) direction "). In the robot arm 10, when the movement in the turning direction and the movement in the in-plane direction are performed simultaneously and acceleration or deceleration movement is performed, free vibration is generated in the turning direction and the in-plane direction thereafter. In the first embodiment, in order to facilitate understanding of the description, as an example, vibration in the turning direction is handled.

  In describing the vibration suppressing method according to the first embodiment, the equation of motion of the arms (arms 12a and 12b) with respect to the turning direction will be described first using the robot arm 10 as a model.

この式（１）より、式（２）に示す運動方程式を導くことができる。

さらに、式（２）にて、相対角変位を式（３）のようにおいて整理すると、式（４）を導くことができる。

なお、式（４）における左辺の第２項はコリオリの力であり、詳細については後述する。 The time is t, the moment of inertia in the turning direction is J (where J is a function of time), the reduction spring constant of the reduction gear is k, the target angle of the reduction device is θ ₀ , and the rotation angle of the rotary shaft 14a is θ Then, since the change of the angular momentum in the turning direction is equal to the moment of the external force, it can be expressed as in Expression (1). Here, “·” in the formula (1) represents differentiation with respect to time.

From this equation (1), the equation of motion shown in equation (2) can be derived.

Furthermore, when the relative angular displacement is rearranged in the equation (2) as in the equation (3), the equation (4) can be derived.

Note that the second term on the left side in Equation (4) is the Coriolis force, which will be described in detail later.

In such a robot arm 10, when the acceleration motion, constant velocity motion, and subsequent deceleration motion of the arm are performed as shown in FIG. 2, the driving device (motor, etc.) follows the trapezoidal velocity law as shown in FIG. Drive along. 2 is a graph showing the relationship between acceleration (vertical axis) and time (horizontal axis), and FIG. 3 is a graph showing the relationship between speed (vertical axis) and time (horizontal axis).
If the forced excitation force (moment) F generated by the movement of the driving device is expressed by equation (5), the equation of motion represented by equation (4) is generated by the movement of the driving device as shown in equation (6). It can be seen that this corresponds to a vibration system to which a forced excitation force F is applied.

ここで、Ｈ（ｔ，τ）は、時変のインパルス応答関数であり、時刻τにインパルス入力を与えた特の時刻ｔにおける応答の値である。 Further, assuming the trapezoidal velocity law as described above, the forced excitation force F becomes a known function, and the relative angular displacement can be expressed as the following equation (7) by integration with the impulse response.

Here, H (t, τ) is a time-varying impulse response function, and is a response value at a particular time t when an impulse input is given at time τ.

  Next, the concept of the input shaping method will be described.

The input shaping method is a method of suppressing free vibration when a constant external force is applied for a finite time to a vibration system with one degree of freedom having a constant coefficient as in a machine tool. In the above equation (4), if the moment of inertia J in the turning direction is a constant, that is, it does not change with time, the following equation (8) can be derived.

  Here, the concept of superimposition of impulse responses in the input shaping method is shown in FIG. FIG. 4 shows the relationship between the displacement of the impulse response (vibration amount: vertical axis) and time (horizontal axis).

As shown in FIG. 4, the external force received moving body such as a robot arm in a certain time t ₁ the free vibration generated by the (forced excitation force, the first impulse input P ₁₎ (first impulse response Q _1: indicated by the solid line. the) half period (T / 2) later certain time t ₂ to external force to the moving body (forced vibration force of the first natural period T of the impulse response P _1, the second A second impulse response Q ₂ (indicated by a broken line) generated by applying the impulse input Q ₂ ) is superimposed. By this superposition, after time t ₂ , the first impulse response Q ₁ and the second impulse response Q ₂ cancel each other, and the impulse response can be made zero.

Further, it can be seen from Equation (8) that the excitation force, which is an external force that generates such vibrations, is generated when acceleration or deceleration of the moving body is performed by the driving device. Furthermore, in the case where a short time system is considered in this vibration system and there is no substantial attenuation, in order to cancel the first impulse response Q ₁ by the second impulse response Q ₂ , after the first half period of the impulse response Q _1, may be continues providing a first impulse input P ₁ second as large as the impulse input P _2. Therefore, when acceleration or deceleration of the moving body is performed by the driving device, a constant acceleration that adds the _second impulse input P2 is given to the moving body over the section of the natural period T. , Free vibration can be suppressed. Such a concept can be applied to an integer multiple of the natural period T.

  Next, the vibration suppression method of the first embodiment, that is, the control law for the time-varying vibration system will be described in detail.

When the movement of the robot arm in the turning direction is performed, the movement in the in-plane direction is also performed, and the moment of inertia J changes when the posture of the robot arm changes. That is, in the robot arm 10, when the arms 12a and 12b are moved in the turning direction, for example, when the arm 12a is moved in the in-plane direction, the relative posture of the arm 12a with respect to the arm 12b changes. Accordingly, the moment of inertia J of the robot arm 10 also changes. If an impulse input of magnitude A _i is given to the robot arm, that is, the moving body at time t _i , the equation of motion shown in Equation (6) is expressed by Equation (9) using the delta function δ (t). ).

FIG. 5 shows the impulse response calculated with the moment of inertia increasing with time. Note that FIG. 5 shows the relationship between the displacement of the impulse response (vibration amount: vertical axis) and time (horizontal axis). In FIG. 5, the first impulse response Q ₁ (solid line) generated by applying the _first impulse input P ₁ to the moving body at time t = 0, and the first impulse response Q ₁ is the displacement 0. the time to be _t j (j = 1,2 ...) Distant, time t = _{t 1} to the second second caused by applying an impulse input _{P 2} relative movement of the impulse response _Q 2 ( (Broken line). As shown in FIG. 5, the first impulse response Q ₁ second impulse response Q ₂ is the time at which the displacement becomes 0 are the same, the amplitude of the displacement is different.

ここで、式（１０）のエネルギの関係式における右辺の項は、時刻ｔ_ｉでのインパルス入力により運動体に与えられたエネルギであり、一定値となる。ただし、この値はインパルス入力を与える時刻ｔ_ｉによって異なるため、右辺の項を次の式（１１）のようにおく。

また、式（１０）のエネルギの関係式における左辺の３つの項の和は一定となり、左辺の第２項はコリオリの力がする仕事に相当し、時間によりその値が変化するため、次の式（１２）のようにおいて式（１０）を整理すると、式（１３）のようになる。

この式（１３）より、運動エネルギとポテンシャルエネルギの和は、時間によって変化することが分かる。 Next, by multiplying the equation of motion of Equation (9) by “differentiation of φ with respect to time” and integrating with time, the following energy relational equation of Equation (10) is obtained.

Here, the term on the right side in the energy relational expression of Expression (10) is the energy given to the moving body by the impulse input at time t _i , which is a constant value. However, since this value differs depending on the time t _{i at} which the impulse input is applied, the term on the right side is set as in the following equation (11).

In addition, the sum of the three terms on the left side in the energy relational expression of Equation (10) is constant, and the second term on the left side corresponds to the work of Coriolis force, and its value changes with time. When formula (10) is rearranged in formula (12), formula (13) is obtained.

From this equation (13), it can be seen that the sum of kinetic energy and potential energy varies with time.

Here, the first impulse response when the first impulse input having the magnitude A ₀ is given at time ₀ is φ ₀ (t), and the second impulse input having the magnitude A ₁ is given at time t ₁ . Let the second impulse response at the time be φ ₁ (t). In the first and second impulse responses, since the potential energy Keifai ^2/2 is zero at the time the displacement is 0, the formula (14) can be derived equation (15), equation (16).

Further, the second impulse input is equivalent to giving the initial velocity shown by the equation (17) to the moving body whose displacement is 0 at the time t ₁ , and the first impulse response is the time t _This is equivalent to giving an initial velocity represented by the equation (18) to a moving body having a displacement of ₁ and a displacement of 0. Therefore, when the relationship shown in Expression (19) is established, the first impulse response and the second impulse response can cancel each other.

式（１５）および式（２０）より、第１のインパルス入力の大きさＡ_０に対する第２のインパルス入力の大きさＡ_１の割合（比）αは、次の式（２１）のように表すことができる。

ここで、Ｅ（０）は、時刻ｔ＝０にて第１のインパルス入力により運動体に与えられるエネルギであり、Ｊ（０）は、時刻ｔ＝０にて運動体が有する運動エネルギであり、Ｊ（ｔ_１）は、時刻ｔ＝ｔ_１にて運動体が有する運動エネルギであり、Ｃ（ｔ_１）は、時刻ｔ＝ｔ_１にて運動体においてコリオリの力がする仕事である。 Therefore, the relationship between the first impulse input magnitude A ₀ and the second impulse input magnitude A ₁ is A ₁ = αA _0, and the ratio α of the inputs such that the two impulse responses cancel each other. Set. Specifically, the equation (16) can be expressed as the following equation (20) using α from the equation (14).

From Expression (15) and Expression (20), the ratio (ratio) α of the second impulse input magnitude A ₁ to the first impulse input magnitude A ₀ is expressed as the following Expression (21). be able to.

Here, E (0) is the energy given to the moving body by the first impulse input at time t = 0, and J (0) is the kinetic energy of the moving body at time t = 0. , J (t ₁ ) is the kinetic energy of the moving body at time t = t ₁ , and C (t ₁ ) is the work that Coriolis force is exerted on the moving body at time t = t ₁ .

Thus, by using the equation (21), the ratio α of the second impulse input magnitude A ₁ to the first impulse input magnitude A ₀ can be calculated. As a result, by using the ratio α calculated, to determine the magnitude of A ₁ of the second impulse input, at time t = t _1, the second impulse input magnitude A _1, which is previously determined motion By adding to the body, the first impulse response and the second impulse response can cancel each other. Therefore, even when the amplitude of the impulse response varies with time in a time-varying vibration system, vibration can be effectively suppressed by appropriately setting the magnitude of the second impulse input.

  Next, in the vibration suppressing method of the first embodiment, a method for correcting when the natural period changes will be described.

In FIG. 5, if the forced excitation force is applied to the moving body from time 0 to time t ₂ , the vibration generated in the moving body is expressed by the following expression (22) using Expression (7). be able to.

  So far, cancellation has been considered by superimposing impulse responses delayed by half a cycle, but the natural period may change in the impulse response of a time-varying vibration system. Therefore, as shown in FIG. 6, the superposition of impulse responses when a constant external force is continuously applied to the moving body for a predetermined time is considered.

このような考え方に基づくインパルス応答の打ち消しを時刻０から時刻ｔ_２までにわたって考えると、ｔ＞ｔ_１（すなわち、時刻ｔ_１以降の時間帯）で式（２２）の値を０にすることができる。なお、時間幅ΔＴは、インパルス応答の周期に比して十分に小さいものと仮定することができ、さらに、インパルス入力を発生させる駆動装置（モータ等）の駆動を制御するサンプリング時間は、インパルス応答の周期に比して十分に短い時間である。したがって、時間幅ΔＴを過大に長くとらない限り、上述のようなブロック同士を相殺するという考え方を適用することができる。 Specifically, as shown in FIG. 6, the first impulse input P ₁ having the magnitude A ₀ is continuously given to the moving body from time 0 to the time width ΔT, and is generated in the moving body. The first impulse response Q ₁ is applied to the moving body with the _second impulse input P ₂ having an appropriate magnitude (A ₀ · γ ₁ ) from the time t ₁ to the time width (β ₁ · ΔT). Let us consider canceling with the second impulse response Q ₂ generated in the moving body by giving continuously. Expressed in a simplified and easy-to-understand manner, in FIG. 6, energy received by the moving body by the first impulse input P ₁ having the magnitude A ₀ is continuously added between the time 0 and the time width ΔT. Here, it is the product of the magnitude of impulse input and time.) (A ₀ · ΔT) and the second (A ₀ · γ1) between the time t ₁ and the time width (β ₁ · ΔT). by impulse input P ₂ of are sequentially added, as energy moving body receives and _{{(a 0 · γ 1)} × (β 1 · ΔT)} is substantially same, the ratio of the time width ( The ratio is set to β ₁ and the ratio (ratio) γ ₁ of the magnitude of the impulse input. That is, the concept of canceling out the respective energy blocks is used. This concept can be expressed by the following equation (23).

Considering the cancellation of the impulse response based on this concept from time 0 to time t ₂ , the value of equation (22) can be set to 0 at t> t ₁ (ie, the time zone after time t ₁ ). it can. Note that the time width ΔT can be assumed to be sufficiently smaller than the period of the impulse response, and further, the sampling time for controlling the driving of the driving device (motor or the like) that generates the impulse input is the impulse response. The time is sufficiently shorter than the period. Therefore, as long as the time width ΔT is not excessively long, the concept of canceling out the blocks as described above can be applied.

Therefore, the time width ratio β ₁ and the impulse are set by first setting the time width ΔT using the concept of superimposing impulse responses in consideration of the predetermined time width as shown in the equation (23) and FIG. The ratio γ ₁ of the input magnitude can be set, and the magnitude of the second impulse input P ₂ and the time width to be added to the moving body using the set ratios β ₁ and γ _1. Is determined and the impulse responses are overlapped, so that vibration can be reliably suppressed even when the natural period changes in the impulse response of the time-varying vibration system.

インパルス応答の周期だけが変化する場合には、式（２４）において、β_１＝１と置けば良く、また、インパルス応答の振幅だけが変化する場合には、式（２４）において、α（ｔ_１）＝１と置けば良い。なお、β_１およびγ_１は、式（２３）および式（２４）を満たす範囲で適切に設定すれば良い。このようにして、α（ｔ_１）、β_１、γ_１を設定することができる。 In addition, in the impulse response of the time-varying vibration system as described above, when the amplitude is changed in addition to the change of the natural period, the ratio shown by the equation (21) is added to the idea shown by the equation (23). It is desirable to use α together. Specifically, as shown in FIG. 6, the first impulse response Q ₁ when the _first impulse input P ₁ is given to the moving body at time 0 has a displacement of 0 at time t ₁ . On the other hand, the first impulse response Q ₁ ′ when the _first impulse input P ₁ ′ is given to the moving body at the time ΔT (that is, 0 + ΔT) is the time (t ₁ + β ₁・ The displacement becomes zero at ΔT). Accordingly, the ratio α (t ₁ ) at the time t ₁ and the ratios β ₁ and γ ₁ have a relationship as shown in the following equation (24).

When only the period of the impulse response changes, β ₁ = 1 may be set in the equation (24), and when only the amplitude of the impulse response changes, α (t ₁ ) = 1. Note that β ₁ and γ ₁ may be set appropriately within a range that satisfies the expressions (23) and (24). In this way, α (t ₁ ), β ₁ , γ ₁ can be set.

  In the above description, as mainly shown in FIGS. 5 and 6, the case where the amplitude of the impulse response decreases and the natural period becomes longer as time passes has been described as an example. The vibration suppressing method of the first embodiment is not limited only to such a case. Instead of such a case, for example, as shown in FIG. 7, even when the amplitude of the impulse response increases and the natural period becomes shorter as time passes, The vibration suppressing method of the first form can be applied.

Specifically, in FIG. 7, the amplitude of the first impulse response Q ₁ generated by applying the _first impulse input P ₁ to the moving body at time t = 0 is increased with time. Even when the natural period decreases, the second impulse response Q generated by applying the _second impulse input P ₂ to the moving body at time t = t ₁ . By superimposing the _two , impulse responses can be canceled out. Further, when superimposing the impulse responses, Expression (21), Expression (23), and Expression (24) can be applied.

Example 1
Next, an example in which the time-varying vibration suppression method using the input shaping method of the first embodiment is applied will be described.

In the first embodiment, a model 20 having a conveyance object 22 having a weight m ₁ at the tip of an arm 21 having a length L and a weight m simulating a robot arm as shown in FIG. 8 is used. In the model 20, when the arm 21 and the conveyed product 22 are integrally operated in the turning direction (turning angle θ) around the vertical rotation shaft 23 a by the drive device 24, the horizontal rotation shaft is driven by the drive device 25. Consider a case where the arm 21 and the conveyed product 22 are integrally operated in the in-plane direction (rotation angle ψ) around 23b. The operation of the model 20 according to the first embodiment is performed when only the rotation angle ψ ₁ changes in the robot arm 10 shown in FIG. 1 without changing the rotation angle ψ ₂ of the in-plane movement. Equivalent to. Moreover, in the model 20, the arm 21 and the conveyed product 22 are examples of a moving body.

Specifically, in the model 20 of FIG. 8, assuming that the moment of inertia generated by the movement of the arm 21 in the turning direction changes greatly, the rotation angle ψ ₁ in the in-plane direction of the arm 21 is 10 ° to 90 °. Consider an operating pattern that changes to 0.2 ° in 0.2 seconds. However, the time for performing the acceleration motion and the deceleration motion is 0.05 seconds, and the time for performing the constant speed motion is 0.1 seconds. Here, FIG. 9 shows the operation pattern in the in-plane direction of the arm 21, and FIG. 10 shows the change of the moment of inertia. Table 1 shows various parameters used in the calculation when applying the vibration suppression method.

In this model 20, the impulse response (first impulse response) generated in the arm 21 when the movement in the turning direction and the movement in the in-plane direction are performed according to the operation pattern shown in FIGS. 9 and 10 is shown in FIG. 11. Show. In FIG. 11, the time when the displacement in the impulse response becomes 0 is set to t _j (j = 1, 2, 3,...). Since the operation in the in-plane direction of the arm 21 is finished in 0.2 seconds, the operation in the turning direction is also finished in about 0.2 seconds accordingly. Driving in the turning direction is classified into three sections of acceleration, constant speed, and deceleration, and free vibration occurs in each section. However, in the first embodiment, only the deceleration section that is the most problematic in actual motion is targeted. Consider free vibration. Specifically, the deceleration time is set to t ₄ ≦ t ≦ t _6, and the free vibration after the end of deceleration is treated as an initial condition that no vibration is generated at the time t = t ₄ .

First, let us consider a correction based on a change in amplitude in a one-degree-of-freedom and time-varying impulse response. The ratio α (t) of the magnitude of the input that generates the impulse response to be superimposed on the impulse response shown in FIG. 11 (however, for the deceleration time t ₄ ≦ t ≦ t ₆ ) was obtained using the equation (21). The results are shown in FIG. Here, since the section that must be considered to cancel each other by superimposing the impulse responses is the section of t ₅ ≦ t ≦ t ₆ , α (t) = 1 for the section of t ₄ ≦ t ≦ t _5. It is said.

Next, a correction based on a change in natural period in a one-degree-of-freedom time-varying impulse response will be considered. Since ΔT is a finite value, the ratio γ (t) of the magnitude of the impulse input is approximate. The time width ratio β _i is calculated by ΔT = 0.005 seconds, and γ (t) is calculated from γ _i = α (t _i ) / β _i represented by the equation (24). Shown in

Using the ratios α and γ (t) obtained in FIG. 12 and FIG. 13, the forced excitation force of F (t) = Aγ (t) with the deceleration time t ₄ ≦ t ≦ t ₆ in the turning direction FIG. 14 shows a result of superimposing the second impulse response on the first impulse response so as to suppress the residual vibration, that is, the response when applying to the arm 21. In FIG. 14, the vertical axis represents relative angular displacement (φ [rad]: amplitude), and the horizontal axis represents time (s).

As shown in FIG. 14, with respect to the maximum value of the amplitude (that is, the maximum angular displacement of vibration) R ₁ generated in the section of the deceleration time t ₄ ≦ t ≦ t ₆ , the time t ₆ ≦ t after the end of the deceleration motion It can be seen that the amplitude R _{2 of the} residual vibration generated in the section is suppressed to be quite low. In FIG. 14, the maximum displacement increases until time t = t ₅ , starts to decrease after time t = t ₅ , and is ideally decreased at time t = t ₆ .

Next, in the deceleration time t ₄ ≦ t ≦ t ₆ , further data analysis shows that residual vibration can be suppressed when such a forced excitation force of F (t) = Aγ (t) is applied to the arm 21. Confirm by doing.

FIG. 15 shows a comparison of the amplitudes of residual vibration when the excitation force duration is Ti and the forced excitation force is applied to the arm 21 at t ₄ ≦ t ≦ T _i . However, F (t) = Aγ (t) in the section of t ₄ ≦ t ≦ T _i , F (t) = A in the section of t6 <t, and F (t) = 0 in the section of Ti <t. Further, the horizontal axis of FIG. 15 represents the duration Ti of the forced excitation force, and the vertical axis represents the maximum value of the relative angular displacement φ (t) after the input of the forced excitation force and the relative angular displacement after the input ends. It is a value (vibration level) expressed in decibels based on the value when the maximum value of φ (t) is the largest (when T _i = t ₅ ). As is apparent from FIG. 15, it can be seen that vibration is well suppressed in the vicinity of T _i = t ₆ .

As shown in the above equation (5), such a forced excitation force can be expressed as the following equation (25).

Therefore, based on the impulse input magnitude ratio γ shown in FIG. 13, the forced excitation force capable of suppressing the vibration is obtained, and the acceleration by the driving device (motor) so that the obtained forced excitation force can be generated. FIG. 16 shows the calculated pattern. In FIG. 16, the vertical axis represents acceleration (rad / s ² ) and the horizontal axis represents time (s). FIG. 17 shows the forced excitation force applied to the arm 21 when the drive device is driven based on the acceleration pattern shown in FIG. In FIG. 17, the vertical axis represents the forced excitation force F (t) and the horizontal axis represents time (s). Further, FIG. 15 as well as the relative angular displacement of the finish entering by varying the duration T _i of the external force compares the magnitude of the (residual vibration) (vibration level: decibel) is shown in Figure 18.

As shown in FIGS. 16, 17, and 18, by applying acceleration along the acceleration pattern shown in FIG. 16 to the section of deceleration time t ₄ ≦ t ≦ t ₆ , the turning direction after the end of the deceleration motion It can be seen that the residual vibration can be effectively suppressed.

  Here, the vibration suppression method described in the first embodiment and the first embodiment is applied so as to suppress one-degree-of-freedom and time-varying vibration generated in a moving body that performs acceleration or deceleration. The procedure for operating the moving body using the apparatus will be described with reference to the flowchart shown in FIG.

  First, in step S1 of the flowchart of FIG. 19, the operating condition of the moving body that is operated using the driving device is set. Examples of such driving conditions include spatial coordinates of the driving start position and target position of the moving body, time constraint conditions required for the operation, and the presence / absence of a transported object. Furthermore, the specification (rotation spring constant) of the speed reducer for transmitting the weight of the moving body or the driving force of the driving device to the moving body is also set as the operating condition.

  Next, in step S2, the driving pattern of the moving body is set. The operation pattern is set based on the operation condition set in step S1. Specifically, it sets the driving section and time for acceleration, constant speed, and deceleration of the moving body based on the driving conditions such as the driving start position, target position, operating time, and weight of the moving body, and two different moving bodies. , For example, each driving pattern of the movement in the turning direction and the movement in the in-plane direction is set.

Next, in step S3, based on the set driving pattern of the moving body, the acceleration pattern of the moving body by the driving device that suppresses the residual vibration is calculated. This acceleration pattern is calculated using the above-described equations (21), (23), and (24) in consideration of the work performed by the Coriolis force accompanying the change in the moment of inertia in the moving body. This is done by calculating α (t _i ), β _i , γ _{i and the} like. In addition, it is desirable to calculate the acceleration pattern in a deceleration zone where free vibration is likely to be a problem.

  Thereafter, in step S4, based on the calculated acceleration pattern information, the driving device is driven to perform acceleration, constant speed, and deceleration operations of the moving body. In the moving body, it is possible to perform an operation in which residual vibration is suppressed.

  It should be noted that the condition setting and calculation processing from step S1 to S4 can be performed, for example, in a control device that controls the driving operation of the driving device. Further, instead of such a case, using the computer device in which the program for performing the above-described calculation processing is installed, the condition setting and calculation processing in steps S1 to S3 are performed, and the calculated acceleration pattern information is driven. The drive operation of the drive device may be controlled by the control device by inputting to the control device of the device.

  In addition, when the moving body has a plurality of driving patterns, an acceleration pattern by the driving device that suppresses the residual vibration is calculated for each driving pattern and input to the control device. The driving operation of the driving device can also be controlled by an acceleration pattern corresponding to the selected driving pattern. In selecting the operation pattern, means for selecting an appropriate operation pattern (for example, means using a sensor or the like) can be used.

(Embodiment 2)
In the first embodiment, the vibration suppression method in the case where the time-varying vibration system is considered to have no substantial attenuation considering a short time system is described. However, in the time-varying vibration system in consideration of the attenuation, A vibration suppression method will be described in the second embodiment. For example, when a speed reducer is used in the robot arm, thermal energy generated by friction or the like in the speed reducer is such attenuation.

When damping is considered in the time-varying vibration system, the second impulse with respect to α in the equation (21), that is, the magnitude A ₀ of the first impulse input, is compared with the case where substantial damping is not taken into consideration. The ratio (ratio) α of the input size A ₁ is different. However, a method for correcting the change of the natural period (formula (22), formula (23), formula (24), etc.) can be considered in the same manner as when substantial attenuation is not considered. Therefore, in the second embodiment, only α when attenuation is considered will be described.

When damping is considered in a time-varying vibration system, a motion equation in which the term of the damping coefficient c is added to the motion equation of Equation (6) is considered, and an impulse input of magnitude A _i is given at time t _i in this motion equation. Then, it can be expressed as in Expression (26).

ここで、式（２８）のエネルギ関係式における左辺第２項は、減衰により損失するエネルギに相当し、時間により値が変化するため、同第２項を次の式（２９）のようにおく。

さらに、式（２９）を式（２８）に代入して整理すると、次の式（３０）のようになる。

Next, by multiplying the equation of motion of the equation (26) by “differentiation over time of φ” and integrating with time, it can be expressed as the following equation (27), and the energy relational expression of the equation (28) is can get.

Here, the second term on the left side in the energy relational expression of Equation (28) corresponds to energy lost due to attenuation, and the value changes with time. Therefore, the second term is set as in the following Equation (29). .

Further, when formula (29) is substituted into formula (28) and rearranged, the following formula (30) is obtained.

また、インパルス入力を与えた時刻では、コリオリの力がする仕事Ｃ（ｔ）および減衰による損失エネルギＤ（ｔ）も０となるため、次の式（３２）、式（３３）、式（３４）、式（３５）を導くことができる。

Here, at the time when the displacement becomes 0, the potential energy (the second term on the left side in the equation (30)) is 0, so the equation (30) can be expressed as the following equation (31).

At the time when the impulse input is given, the work C (t) generated by the Coriolis force and the loss energy D (t) due to the attenuation are also zero, so the following equations (32), (33), and (34) ), Equation (35) can be derived.

ここで、次の式（３７）の関係を満たせば、第１のインパルス応答と第２のインパルス応答とは互いに打ち消し合うことが可能となる。したがって、減衰を考慮した場合における第１のインパルス入力の大きさＡ_０に対する第２のインパルス入力の大きさＡ_１の割合αは、次の式（３８）のように表すことができる。

Here, when the relationship between the first impulse input magnitude A ₀ and the second impulse input magnitude A ₁ is represented by A ₁ = αA ₀ , the first impulse response and the second impulse response are The ratio α that cancels each other out can be expressed by the following equation (36) from the equations (33) and (34).

Here, if the relationship of the following equation (37) is satisfied, the first impulse response and the second impulse response can cancel each other. Accordingly, the ratio α of the second impulse input magnitude A ₁ to the first impulse input magnitude A ₀ when attenuation is considered can be expressed as the following equation (38).

  Therefore, when damping is considered in a time-varying vibration system, vibration can be effectively suppressed by superimposing impulse responses by using the ratio α represented by the equation (38).

  Further, such consideration of attenuation is preferably carried out, for example, when a reduction gear or the like is used in the moving body drive device. On the other hand, in a case where a direct-coupled motor or the like is used in the drive device and a reduction gear is not used, and when it can be determined that the attenuation is relatively small, no substantial attenuation occurs. Judgment may be made and equation (21) of the first embodiment may be applied.

(Embodiment 3)
Next, the third embodiment of the present invention employs the vibration suppression method in the time-varying vibration system of the first or second embodiment described above to suppress vibration, and further moves the moving body to the target position. This is a vibration suppressing method that can be moved with high accuracy.

  In the vibration suppression method of the time-varying vibration system using the input shaping method in each of the first and second embodiments described above, for example, when canceling out by superimposing impulse responses delayed by a half cycle, the Coriolis force is In consideration of the work to be performed, the magnitude of the impulse input corresponding to the change in the amplitude of the impulse response and the change in the natural period and the continuous addition time are determined to suppress the vibration. However, in the case of a time-varying system, in addition to the change in the amplitude and natural period of the impulse response, the magnitude of the external force (impulse input) is not constant, so most impulse responses can be canceled, It is difficult to completely cancel each other. On the other hand, it is necessary to control the operation of such a moving body, for example, a hand tool attached to the tip of a robot arm so that it can be accurately moved to a target position.

From such a viewpoint, in the third embodiment, the moving body can be accurately moved to the target position while suppressing the vibration generated in the moving body using the input shaping method in the time-varying vibration system. A vibration suppression method will be described. In the third embodiment, in the robot arm model 20 of FIG. 8 used in the first embodiment described above, the arm 21 and the transported object 22 are integrally operated in the turning direction, and the arm 21 and the transport are performed. An operation pattern (see FIGS. 9, 10, and 11) in which the rotation angle ψ _{1 in the in-} plane direction of the object 22 changes from 10 ° to 90 ° in 0.2 seconds will be described as an example.

The duration of the movement of the arm 21 in the turning direction is set by the even-numbered time when the impulse response becomes 0 (zero) such as t = 0 to t = t ₂ , t ₄ , t ₆ (see FIG. 11). In the example of the model 20 in FIG. 8, the duration of the movement of the arm 21 in the turning direction is 0 ≦ t ≦ t ₆ .

Next, in the time-varying impulse response shown in FIG. 11, a pair of adjacent sections for each half cycle, that is, the section 0 ≦ t ≦ t ₁ and the section t ₁ ≦ t ≦ t ₂ are divided into the sections t ₂ ≦ t _2. t ≦ t ₃ and interval t ₃ ≦ t ≦ t _4, and interval t ₄ ≦ t ≦ t ₅ and interval t ₅ ≦ t ≦ t ₆ cancel each other. Although it is possible to cancel the sections that are not adjacent to each other, the adjacent sections can cancel each other more effectively because the amount of expansion of the error of the impulse response to cancel is small.

  Further, in either the first half or the second half of a pair of adjacent sections, the arm 21 gives the arm 21 the acceleration necessary for carrying out the above-described driving pattern, and the acceleration given in the other section is , Based on the input magnitude ratio γ that produces the impulse response to be superimposed. Usually, in a pair of adjacent sections, it is preferable to give an acceleration for driving pattern execution to the first half section and determine the acceleration of the second half section by calculation in consideration of the impulse response to be overlapped.

Specifically, first, a correction by a change in amplitude in a time-varying impulse response is considered. The ratio α (t) of the magnitude of the input that generates the impulse response to be superimposed on the impulse response shown in FIG. 11 in three pairs of sections in the duration time 0 ≦ t ≦ t ₆ of the arm 21 in the turning direction, FIG. 20 and FIG. 21 show the input time width ratio β (t). FIG. 21 shows 1 / β (t).

  As shown in FIGS. 20 and 21, α (t) = 1 and 1 / β (t) = 1 are set in the first half section of each pair of sections, and cancellation of impulse responses is considered in the second half section. α (t) and 1 / β (t) are calculated. Note that α (t) and 1 / β (t) in consideration of cancellation of the impulse responses can be calculated by the method described in the first embodiment.

  Next, let us consider the correction by the change of the natural period in the time-varying impulse response. When α (t) and 1 / β (t) calculated in FIGS. 20 and 21 are used to calculate the ratio γ (t) of the magnitude of impulse input, γ (t) in each pair of sections is As shown in FIG. Note that γ (t) can be calculated using Expression (24).

  Here, the magnitude of the impulse input (forced excitation force (external force)) F (t) for canceling the impulse responses in each pair of sections is the ratio γ (shown in FIG. 22 in the first half section and the second half section). It is only necessary to satisfy the ratio of t), and it is not always necessary to set the external force pattern in the form of γ (t) shown in FIG.

  FIG. 23A shows a pattern of the external force F (t) applied to the arm 21 calculated based on the impulse input magnitude ratio γ (t) in each pair of sections shown in FIG.

また、算出された加速度パターンから、次の式（４０）を用いて、その時刻における速度（駆動装置におけるモータの速度）を算出する。ただし、速度は１データ前、すなわち時間間隔Δｔ前のデータを用いる。速度の算出においては、時刻ｔ_２、ｔ_４において連続するように算出する。また、アーム２１の運動の開始時（ｔ＝０）は静止状態となるため速度ゼロとなり、アーム２１の動作の継続時間の最終時刻（ｔ＝ｔ_６）は停止状態となるため速度ゼロとなる。算出された速度パターンを図２３（ｃ）に示す。

Further, based on the external force F (t) in FIG. 23A, the acceleration in each pair of sections is calculated using the following equation (39). The calculated acceleration pattern is shown in FIG.

Further, from the calculated acceleration pattern, the speed at that time (the speed of the motor in the driving device) is calculated using the following equation (40). However, the speed is one data before, that is, data before the time interval Δt. In calculating the speed, it is calculated so as to be continuous at times t ₂ and t ₄ . Further, when the motion of the arm 21 starts (t = 0), the speed is zero because the arm 21 is in a stationary state, and the final time (t = t ₆ ) of the duration time of the operation of the arm 21 is stopped, so the speed is zero. . The calculated speed pattern is shown in FIG.

  In this manner, when the speed pattern is calculated as shown in FIG. 23C during the entire duration of the movement of the arm 21 in the turning direction, the time-speed relationship (that is, the graph of FIG. 23C). The movement distance of the arm 21 is calculated from The acceleration pattern given in each pair of sections is adjusted so that the calculated movement distance matches the movement distance (that is, the control command value) from the stationary position of the arm 21 to the target position. Specifically, the ratio between the calculated movement distance and the movement distance that is the control command value is calculated, and this ratio is used as the similarity ratio, so that the acceleration pattern and graph for the entire duration shown in FIG. The external force pattern for the entire duration shown in FIG. 23 (a) is similarly deformed (that is, multiplied by the similarity ratio) to adjust the acceleration pattern and the external force pattern.

  By performing the operation of the arm 21 using the acceleration pattern and the external force pattern adjusted as described above, it is possible to suppress time-varying vibration and to move the arm 21 to a target position with high accuracy. it can.

  Note that the magnitude of acceleration that can be selected is limited by the capability of the drive device (motor capability, etc.), and therefore the limit for similar deformation of the acceleration pattern must be within the range of the capability of the drive device. For this reason, when the capacity of the driving device is exceeded, the number of the pair of sections is increased, that is, the duration of the operation is increased, and the speed pattern and the acceleration pattern are calculated again.

  In addition, in a time-varying system, even when the moving body is moving at a constant speed, an excitation force is generated. Therefore, acceleration is set to zero in the first half of a pair of adjacent sections, and vibration in the first half is canceled in the second half. The acceleration / deceleration value may be determined as described above.

  The condition setting and calculation processing described in the third embodiment can be performed, for example, in a control device that controls the driving operation of the driving device. Further, instead of such a case, using a computer device in which a program for performing these calculation processes is installed, condition setting and calculation processing are performed, and the information of the calculated acceleration pattern is transmitted to the control device of the driving device. The driving operation of the driving device may be input and controlled by the control device.

  In the description of the above-described embodiment, when performing acceleration or deceleration movement, vibration of one degree of freedom and time variation generated in a moving body accompanied by a change in posture of the moving body itself (for example, change in moment of inertia) The method of suppressing using the input shaping method was demonstrated. In a robot arm which is a typical example of such a moving body, a multi-joint structure having a high degree of freedom is employed in order to increase the degree of freedom of movement. Therefore, in reality, when the robot arm is driven, a plurality of degrees of freedom and time-varying vibrations are generated. On the other hand, in such a moving body, the most serious problem is low-frequency vibration. Therefore, in the case where time-varying vibration with respect to a plurality of degrees of freedom occurs in this way, the vibration suppressing method of the present embodiment with respect to the vibration with the lowest frequency among the vibrations with a plurality of degrees of freedom. Should be applied.

  In addition, the vibration suppression method of the present embodiment can be applied to vibrations generated when the moving body performs acceleration motion or deceleration motion. However, when the posture of the moving body changes during constant speed motion. When the Coriolis force performs work, the present invention can also be applied to vibration generated by performing such a constant speed motion.

  Further, in the present embodiment and examples, the case where the rotational motion is mainly performed has been described as an example in which the movement in the turning direction and the movement in the in-plane direction are performed simultaneously. Can also be applied.

  According to the present invention, when at least one degree of freedom and time-varying vibration generated in a moving body with acceleration or deceleration movement is suppressed using the input shaping method, Coriolis generated with a change in posture of the moving body. Since the magnitude of the second impulse input is determined in consideration of the work performed by the force, the second impulse input is compared with the time-varying vibration system in which the amplitude or period of the first impulse response changes with time. Can be effectively suppressed by superimposing the impulse responses. Therefore, it is possible to effectively suppress vibration generated in a moving body that performs an operation that involves a posture change during the operation, such as a robot arm, a machine tool, and a crane, by feedforward control.

  It is to be noted that, by appropriately combining arbitrary embodiments of the various embodiments described above, the effects possessed by them can be produced.

DESCRIPTION OF SYMBOLS 10 Robot arm (moving body), 11a-11c joint, 12a-12b arm, 13 Hand tool, 14a-14c Axis of rotation, 20 model, 21 arm, 22 Carrying object, 24 Drive device, P1 _1st impulse input, P ₂ second impulse input, Q ₁ first impulse response, Q ₂ second impulse response

Claims (9)

In a vibration suppression method for suppressing at least one degree of freedom and time-varying vibration generated in a moving body in association with acceleration or deceleration movement in a moving body that performs acceleration or deceleration movement,
The first impulse response generated in the moving body by the first impulse input added to the moving body is generated by adding the second impulse input to the moving body at the time when the displacement of the first impulse response becomes zero. When applying the input shaping method that cancels each other by superimposing the second impulse response, the work with Coriolis force generated by the change of the posture of the moving body itself during acceleration or deceleration movement In consideration of the vibration suppression method, the magnitude of the second impulse input with respect to the first impulse input is determined. A vibration suppressing method that suppresses at least one degree of freedom and time-varying vibration generated in a moving body that accompanies acceleration or deceleration movement in a moving body that is accelerated or decelerated by an external force applied by a driving device. ,
At time 0, the first impulse response generated in the moving body by the first impulse input of magnitude A ₀ added to the moving body is changed to the first impulse response at time t ₁ when the displacement of the first impulse response becomes 0. In the case where the second impulse response generated by adding the second impulse input having the magnitude A ₁ different from the magnitude A ₀ of the impulse input to the moving body cancels each other,
The energy given to the moving body by the first impulse input at time 0 is E (0), the kinetic energy of the moving body at time 0 is J (0), and the movement the moving body has at time t ₁ The magnitude of the second impulse input with respect to the magnitude A ₀ of the first impulse input, where J (t ₁ ) is the energy and C (t ₁ ) is the work that the Coriolis force is exerted on the moving body at time t ₁ . The ratio α of A ₁ is calculated by Equation 1,
Using the calculated ratio alpha, to determine the size A ₁ of the second impulse input, such that the second impulse input is added to the movement body at time t _1, added to the movement body by a drive device Vibration control method for controlling the external force applied.

A vibration suppressing method that suppresses at least one degree of freedom and time-varying vibration generated in a moving body that accompanies acceleration or deceleration movement in a moving body that is accelerated or decelerated by an external force applied by a driving device. ,
The first impulse response generated in the moving body by the first impulse input of the magnitude A ₀ continuously added between time 0 and time width ΔT is expressed as time width (β ₁ · ΔT) from time t _1. In the case of canceling each other by the second impulse response generated by continuously adding the second impulse input of the magnitude (A ₀ · γ ₁ ) during
The energy given to the moving body by the first impulse input at time 0 is E (0), the kinetic energy of the moving body at time 0 is J (0), and the movement the moving body has at time t ₁ Assume that the energy is J (t ₁ ), and the work performed by the Coriolis force in the moving body at time t ₁ is C (t ₁ ). The total input (A ₀ · ΔT) of the first impulse input during the time width ΔT and calculates the time width (β ₁ · ΔT) second total input impulse input in _{(a 0 · γ 1 · β} 1 · ΔT) number 2 the ratio α of for), the ratio beta ₁ time width, The impulse input magnitude ratio γ ₁ is set so as to satisfy Equation (3),
Using the set time width ratio β ₁ and magnitude ratio γ ₁ , the addition time width and magnitude of the second impulse input are determined, and the second impulse input is continuously added to the moving body. A vibration suppressing method for controlling an external force applied to a moving body by a driving device.

A vibration suppressing method that suppresses at least one degree of freedom and time-varying vibration generated in a moving body that accompanies acceleration or deceleration movement in a moving body that is accelerated or decelerated by an external force applied by a driving device. ,
At time 0, the first impulse response generated in the moving body by the first impulse input of magnitude A ₀ added to the moving body is changed to the first impulse response at time t ₁ when the displacement of the first impulse response becomes 0. In the case where the second impulse response generated by adding the second impulse input having the magnitude A ₁ different from the magnitude A ₀ of the impulse input to the moving body cancels each other,
The energy given to the moving body by the first impulse input at time 0 is E (0), the kinetic energy of the moving body at time 0 is J (0), and the movement the moving body has at time t ₁ The energy is J (t ₁ ), the work performed by Coriolis force in the moving body at time t ₁ is C (t ₁ ), and the loss energy due to attenuation is D (t ₁ ) at time t ₁ . The ratio α of the second impulse input magnitude A ₁ to the impulse input magnitude A ₀ of
Using the calculated ratio alpha, to determine the size A ₁ of the second impulse input, such that the second impulse input is added to the movement body at time t _1, added to the movement body by a drive device Vibration control method for controlling the external force applied.

A vibration suppressing method that suppresses at least one degree of freedom and time-varying vibration generated in a moving body that accompanies acceleration or deceleration movement in a moving body that is accelerated or decelerated by an external force applied by a driving device. ,
The first impulse response generated in the moving body by the first impulse input of the magnitude A ₀ continuously added between time 0 and time width ΔT is expressed as time width (β ₁ · ΔT) from time t _1. In the case of canceling each other by the second impulse response generated by continuously adding the second impulse input of the magnitude (A ₀ · γ ₁ ) during
The energy given to the moving body by the first impulse input at time 0 is E (0), the kinetic energy of the moving body at time 0 is J (0), and the movement the moving body has at time t ₁ energy and J _{(t 1),} the task of Coriolis force in the moving body at time _{t 1} and C _{(t 1),} the energy loss due to attenuation at time _{t 1} as D _{(t 1),} the time width ratio of the total input of the first impulse input between ΔT _{(a 0} · ΔT) total input of the second impulse input in the time width (β ₁ · ΔT) for _{(a 0 · γ 1 · β} 1 · ΔT) α is calculated by Equation 5, and the time width ratio β ₁ and the impulse input magnitude ratio γ ₁ are set to satisfy Equation 6,
Using the set time width ratio β ₁ and magnitude ratio γ ₁ , the addition time width and magnitude of the second impulse input are determined, and the second impulse input is continuously added to the moving body. A vibration suppressing method for controlling an external force applied to a moving body by a driving device.

  Based on the magnitudes of the first and second impulse inputs, the movement distance by the acceleration or deceleration movement of the moving body is calculated, and the ratio of the target movement distance by the acceleration or deceleration movement of the movement body to the calculated movement distance is calculated. The ratio is determined by adjusting the magnitude of the first and second impulse inputs by multiplying the first and second impulse input values by using the ratio as a similarity ratio. Vibration suppression method.   2. In addition to acceleration and deceleration movements, even when the moving body moves at a constant speed, a second impulse input is added to suppress at least one degree of freedom and time-varying vibration generated in the moving body. The vibration suppressing method according to any one of items 1 to 6.   When the time-varying vibration system generated in the moving body has a plurality of degrees of freedom, the second impulse input is added to the moving body to suppress the vibration with respect to the vibration system having the lowest frequency of freedom. The vibration suppressing method according to any one of claims 1 to 7. The first impulse input and the first impulse response added to the moving body during driving are calculated and calculated based on the driving condition and driving pattern information of the moving body in the preset acceleration or deceleration movement. Calculating a second impulse input that cancels the first impulse response,
Creating information on the acceleration pattern of the driving device that generates the calculated first impulse input and second impulse input;
9. The external force applied to the moving body by the driving device when the driving device accelerates or decelerates the moving body based on the generated acceleration pattern information. The vibration suppression method according to 1.

Images