JP7096760B2 - Filter design device, vibration suppression device, filter design method and program - Google Patents

Description

The present invention relates to a filter design device for giving a weighting coefficient to a filter for removing a vibration component of a vibration waveform, a filter design method and program, and a vibration suppression device for suppressing vibration of a controlled object.

The vibration generated during the operation of the servo control device is detected, the frequency with a large frequency component is extracted from the vibration, and if the frequency is lower than the predetermined value, a low-pass filter that cuts off the band above the frequency is applied as a vibration suppression filter, and the frequency. If is greater than or equal to a predetermined value, a notch filter that cuts off the band near the frequency is applied as a vibration suppression filter. A method for setting a vibration suppression filter that confirms the suppression effect and sets an appropriate Q value is known (see, for example, Patent Document 1).

Japanese Unexamined Patent Publication No. 2006-288113

When a notch filter that cuts off a band near a frequency having a large frequency component is applied as a vibration suppression filter, it may not be possible to completely remove the vibration component of the vibration waveform.

An object of the present invention is to increase the possibility that the vibration component of the vibration waveform can be completely removed as compared with the case where a notch filter that cuts off a band near a frequency having a large frequency component is applied as a vibration suppression filter.

For this purpose, the present invention is a filter for removing the vibration component of the vibration waveform, and N weighting coefficients are added to each value of the vibration waveform at an arbitrary N (N ≧ 2) time points. It is a filter design device that gives N weight coefficients to the filter that calculates the average by multiplying the corresponding weight coefficients, and each time series data is N pieces for each time series data from the vibration waveform. For each time-series data of the acquisition means for acquiring M (M ≧ 1) time-series data including the value of the vibration waveform at the time point and the time-series data of M pieces of time-series data acquired by the acquisition means. The N weight coefficients are determined so that the condition that the value obtained by multiplying each value of the vibration waveform values at N time points by the corresponding weight coefficient of the N weight coefficients and adding them is 0 is satisfied. Provided is a filter design device including a determination means for determining and an output means for outputting N weighting coefficients determined by the determination means.

Here, the acquisition means are the interval of N time points for the first time series data of M (M ≧ 2) time series data and N pieces for the second time series data of M time series data. It may be the one that acquires M time series data so that the intervals at the time points of are equal to each other.

The acquisition means has at least N time points for the first time series data of M (M ≧ 2) time series data and N time points for the second time series data of M time series data. It may be the one that acquires M time series data so as to partially overlap.

The acquisition means is the M time series data so that the interval between two adjacent time points out of the N time points with respect to any one of the M time series data is longer than the period of the vibration waveform. May be the one to get.

The acquisition means is M times so that the interval between two adjacent time points out of N time points with respect to any time series data of M time series data is 1/2 of the period of the vibration waveform. It may be one that acquires series data.

Further, the determining means may be one that determines N weighting coefficients so that the designated weighting coefficient among the N weighting coefficients becomes a designated value.

The determining means may be one that determines N weighting coefficients so that the sum of N weighting coefficients becomes a specified value. In that case, the specified value may be 1.

The determining means is a ₁ = a _N , a ₂ = a _N-1 , a ₃ = a _N-2 , ... When N weighting coefficients are a ₁ , a ₂ , ..., A _N. As such, it may be one that determines N weighting coefficients.

The determining means may be one that determines the N weighting coefficients so that the sum of the absolute values of the N weighting coefficients is minimized.

Further, the acquisition means has N pieces of each time-series data for each time-series data from L (L ≧ 2) vibration waveforms y _i (t) (i = 1, 2, ..., L) having different vibration cycles. Mi (Mi ≧ 2) time-series data including the value of the vibration waveform _{y i} (t) at the time of (N ≧ 2 × L + 1 ₎ is acquired, and the determination means is M ₁ acquired by the acquisition means. + M ₂ + ... + For each time series data of _ML time series data, N pieces in each value of the vibration waveform y _i (t) corresponding to each time series data at N time points for each time series data. The N weighting coefficients may be determined so that the condition that the value obtained by multiplying the corresponding weighting coefficients by the weighting coefficients of the above is 0 is satisfied.

Further, the present invention is a vibration suppression device that suppresses vibration of a controlled object, and uses a control means for controlling the controlled object and a filter to which N weight coefficients are given by any of the above filter design devices. Further, a vibration suppression device including a processing means for processing a signal input to the control means or a signal output from the control means is also provided.

Here, the processing means may be one that processes a signal for issuing a command to a control target input to the control means by using a filter.

The processing means may be one that uses a filter to process a signal that is fed back from the controlled object and input to the control means.

The processing means may be one that uses a filter to process a signal for issuing a command to the control target output from the control target.

Further, the present invention is a filter for removing the vibration component of the vibration waveform, and corresponds to each value of the vibration waveform at an arbitrary N (N ≧ 2) time points out of N weight coefficients. This is a filter design method in which the computer gives N weight coefficients to the filter that calculates the average by multiplying the weight coefficients to be performed. An acquisition step of acquiring M (M ≧ 1) time-series data including values of vibration waveforms at N time points with respect to the data, and a computer determining means of the M time-series data acquired in the acquisition step. For each time-series data, the condition that the value obtained by multiplying each value of the vibration waveform values at N time points for each time-series data by the corresponding weighting coefficient among the N weighting coefficients is 0 is satisfied. As such, a filter design method including a determination step for determining N weight coefficients and an output step in which a computer output means outputs N weight coefficients determined in the determination step is also provided.

Furthermore, the present invention is a filter for removing the vibration component of the vibration waveform, and is out of N weight coefficients for each value of the vibration waveform at an arbitrary N (N ≧ 2) time points. It is a program that makes a computer function as a filter design device that gives N weight coefficients to a filter that calculates the average by multiplying the corresponding weight coefficients. Acquisition means for acquiring M (M ≧ 1) time-series data including values of vibration waveforms at N time points with respect to time-series data, and time-series data of M time-series data acquired by the acquisition means. The condition that the value obtained by multiplying each value of the vibration waveform values at N time points for each time series data by the corresponding weight coefficient among the N weight coefficients is 0 is satisfied. Also provided are a determination means for determining N weight coefficients and a program for functioning as an output means for outputting N weight coefficients determined by the determination means.

According to the present invention, there is an increased possibility that the vibration component of the vibration waveform can be completely removed as compared with the case where a notch filter that cuts off a band near a frequency having a large frequency component is applied as a vibration suppression filter.

It is a figure which showed the step input to the vibration control object. It is a figure which showed the method of inserting a notch filter. It is a graph which showed that the vibration of an output y (t) does not stop even if a notch filter is inserted. It is a figure which showed the method of inserting a half-period average filter. It is a graph which showed that the residual vibration of an output y (t) remains even if a half-period average filter is inserted. It is a block diagram which showed the functional structure example of the filter design apparatus in embodiment of this invention. It is a graph which showed about the collection of the time series data in Embodiment 1. It is a figure which showed the application of the moving average filter to the vibration waveform in Embodiment 1. FIG. It is a graph which showed the application result of the moving average filter to the vibration waveform in Embodiment 1. It is a flowchart which showed the operation example of the filter design apparatus in Embodiment 1. It is a figure which showed the case where the moving average filter of Embodiment 1 was inserted before the input of the control object. It is a graph which showed the step response when the gain is not adjusted at the time of inserting the moving average filter of Embodiment 1. FIG. It is a graph which showed the step response when the gain at the time of inserting the moving average filter of Embodiment 1 is set to 1. It is a graph which showed about the collection of the time series data in Embodiment 3. It is a graph which showed the step response at the time of inserting the moving average filter which set the gain of Embodiment 3 to 1. It is a graph which showed about the collection of the time series data in Embodiment 3'. It is a graph which showed the step response when the time series data of Embodiment 3 was used. It is a graph which showed about the collection of the time series data in Embodiment 4. It is a graph which showed the step response when the time series data of Embodiment 4 was used. It is a graph which showed about the collection of the time series data in Embodiment 5. It is a graph which showed the step response when the vibration waveform of one vibration mode was suppressed by using the time series data of Embodiment 5. It is a graph which showed the step response when the vibration waveform of the other vibration mode was suppressed by using the time series data of Embodiment 5. It is a flowchart which showed the operation example of the filter design apparatus in Embodiment 5. It is a graph which showed about the collection of the time series data in Embodiment 6. It is a graph which showed the step response when the time series data of Embodiment 6 was used. It is a graph which showed about the collection of the time series data in Embodiment 7. It is a graph which showed the step response when the time series data of Embodiment 7 was used. It is a figure which showed the configuration example of the robot system to which Embodiment 9 applies. It is a figure which showed the filter insertion position in the robot controller in Embodiment 9. It is a figure which showed the hardware configuration example of the computer which realizes the filter design apparatus of Embodiment 1-8 and the robot controller of Embodiment 9.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

[Background and outline of this embodiment]
FIG. 1 is a diagram showing a step input for a vibrationally controlled object. As shown in the figure, when the step input u (t) is given to the vibrationally controlled object, the vibrational output y (t) is output.

Therefore, as a general method, as shown in FIG. 2, a method of inserting a notch filter that completely sets the natural vibration frequency of the controlled object to 0 at the input (or feedback value or the like) to suppress the vibration can be considered.

However, as shown in FIG. 3, the vibration of the output y (t) cannot be eliminated by simply inserting the notch filter that eliminates the natural vibration frequency. In this way, the natural vibration frequency is known, and even if a notch filter that completely removes it is inserted, the vibration does not stop. It is necessary to design a vibration suppression filter by setting appropriate parameters for the vibration (vibration waveform) to be controlled, but it is necessary to adjust the parameters by trial and error in the notch filter as described above.

Further, as another general method, it is conceivable to use a filter that utilizes the information of the vibration period. Specifically, as shown in FIG. 4, a method of inserting a half-cycle average filter that takes the average of the value before the half-cycle and the current value and gives a counter to the vibration can be considered.

However, when the half-period average filter is inserted, as shown in FIG. 5, the vibration is suppressed to some extent as compared with the above-mentioned unadjusted notch filter, but the residual vibration of the output y (t) remains. .. This is because only the information of the vibration cycle is used, and it is necessary to consider the influence of damping etc. in order to completely eliminate the vibration. In addition, the design conditions of the half-cycle average filter are limited, such as the sample interval is limited to half-cycle, it is impossible to take measures such as shortening the delay time, and a free sample interval cannot be selected. Therefore, it is not possible to completely suppress vibration while ensuring the degree of freedom in filter design.

Therefore, the present embodiment first proposes a method of deriving the conditions for the filter for completely suppressing the vibration from the vibration waveform itself including the influence of the vibration cycle and the damping. Second, we propose a method that can derive conditions without imposing restrictions on sample spacing. Thirdly, we propose a method that can give not only the conditions for vibration suppression but also the conditions for various performances together.

[Configuration of filter design device]
FIG. 6 is a block diagram showing a functional configuration example of the filter design device 10 according to the present embodiment. As shown in the figure, the filter design device 10 includes a vibration waveform acquisition unit 11, a time series data acquisition unit 12, a weighting coefficient determining unit 13, and a weighting coefficient output unit 14.

The vibration waveform acquisition unit 11 acquires the vibration waveform to be controlled.

The time-series data acquisition unit 12 has M (M ≧ 1) time-series data including vibration waveform values at N (N ≧ 2) sample points from the vibration waveform acquired by the vibration waveform acquisition unit 11. To get. Here, the N sample points may be set for each of the M time series data. In this embodiment, N sample points are used as an example of N time points, and a time series data acquisition unit 12 is provided as an example of acquisition means for acquiring M time series data.

For each of the M time-series data acquired by the time-series data acquisition unit 12, the weighting coefficient determination unit 13 corresponds to each of the vibration waveform values at the N sample points among the N weighting coefficients. N weighting coefficients are determined so that the condition that the value obtained by multiplying the coefficients and adding them is 0 is satisfied. In the present embodiment, the weighting coefficient determining unit 13 is provided as an example of the determining means for determining N weighting coefficients.

The weighting coefficient output unit 14 outputs N weighting coefficients determined by the weighting coefficient determining unit 13 to the outside. In the present embodiment, the weighting coefficient output unit 14 is provided as an example of the output means for outputting N weighting coefficients.

Here, the filter design device 10 is used as a device that performs a process of outputting a weighting coefficient. This is based on the assumption that, for example, the user sets the output weighting coefficient in a filter already incorporated in the robot controller described later. In this case, the filter design device 10 can be regarded as a filter design support device that assists the user in designing the filter. Alternatively, the filter design device 10 may be a device that performs not only the process of outputting the weighting coefficient but also the process of generating the filter in which the weighting coefficient is set. This is intended to incorporate this generated filter into, for example, a robot controller described later. In this case, the filter design device 10 can be regarded as a filter generation device that generates a filter.

[Embodiment 1]
In the first embodiment, the time-series data acquisition unit 12 sets N = 6 and M = 2 with respect to the vibration waveform y (t) to be controlled acquired by the vibration waveform acquisition unit 11. For example, 6 points and 2 sets of time series data are collected in a fixed sample cycle. Here, the time series data 1 {y (t ₁ + δ ₁ ), y (t ₁ + δ ₂ ), ..., y (t ₁ + δ ₆ )} and the time series data 2 {y (t ₂ + δ ₁ ), y (T ₂ + δ ₂ ), ..., y (t ₂ + δ ₆ )} and so on shall be collected.

In addition, collecting time-series data at a fixed sample cycle means that the interval between N time points for the first time-series data of M time-series data and the second time-series of M time-series data. This is an example of acquiring M time series data so that the intervals at N time points with respect to the data are equal to each other.

The weighting coefficient determining unit 13 satisfies the following two conditions in which the sum of the products of the time series data and the weighting coefficient {a ₁ , a ₂ , ..., A ₆ } of the filter is 0, so as to satisfy the following two conditions. Determine a ₁ , a ₂ , ..., a ₆ }.

At this time, the condition that the weighting coefficient {a ₁ , a ₂ , ..., A ₆ } should be satisfied is that the null space of the following matrix A having each time series data as an element and the vector a = [a] having the weighting coefficient as an element. ₁ , a ₂ , ..., a ₆ ] Equivalent to the inclusion of ^T ∈ R ⁶ .

Now, the null space of the matrix A is N-rank (A), that is, four vectors {e ₁ , e ₂ , e ₃ , e ₄ } (e _j ∈ R ⁶ , j = 1, 2, 3, 4). Assuming that the basis is stretched, the vector a is given by the following linear sum of _ej .

The above four basis vectors can be easily calculated given the matrix A.

The weighting coefficient output unit 14 outputs the weighting coefficient calculated by the weighting coefficient determining unit 13. The figure shows the result of applying the moving average filter using the output weighting coefficient (in the present specification, the "moving average filter" is a weighted moving average filter) to the vibration waveform to be suppressed as shown in FIG. Shown in 9.

FIG. 9 shows four results when c _i = 1 (i = j), c _i = 0 (i ≠ j), and a = ej ( _j = 1, 2, 3, 4). There is. In all four results, the output x (t) fluctuates in the transient response from 0 to 1 [2π / ω sec], but the output x (t) after the transient response is completely 0. .. From this, it can be seen that the vibration component of the vibration waveform y (t) is completely suppressed by the moving average filter.

In FIG. 9, four results are shown when a = ej ( _j = 1, 2, 3, 4), but a given by Eq. (3) is given to an arbitrary coefficient c _i . The same applies when used. That is, the moving average filter having {a ₁ , a ₂ , ..., A ₆ } determined by the vector a as the weighting factor also completely removes the vibration component of the vibration waveform y (t) to be suppressed. be able to.

FIG. 10 is a flowchart showing an operation example of the filter design device 10 in the first embodiment.

In the filter design device 10, first, the vibration waveform acquisition unit 11 acquires the vibration waveform y (t) to be controlled (step 101).

Next, the time-series data acquisition unit 12 acquires time-series data of N points and M sets from the vibration waveform y (t) acquired by the vibration waveform acquisition unit 11 (step 102).

Next, the weighting coefficient determination unit 13 satisfies the condition of M that the sum of the products of the N points of the time series data of the M set acquired by the time series data acquisition unit 12 and the weighting coefficient is 0. The coefficient is determined (step 103).

After that, the weighting coefficient output unit 14 outputs the weighting coefficient determined by the weighting coefficient determining unit 13 (step 104).

[Embodiment 1']
In the first embodiment, the time-series data acquisition unit 12 sets N = 6 and M = 2 for the vibration waveform y (t) to be controlled, and collects 6 points and 2 sets of time-series data. > 2, and more than two sets of time series data may be collected. In the first embodiment, the time-series data acquisition unit 12 sets N = 6 and M = 7, and collects 6 points and 7 sets of time-series data.

In this case, the weighting coefficient determining unit 13 determines the weighting coefficient {a ₁ , a ₂ , ..., A ₆ } so as to satisfy the following seven conditions.

At this time, the condition that the weighting coefficient {a ₁ , a ₂ , ..., A ₆ } should be satisfied is that the null space of the following matrix A having each time series data as an element and the vector a = [a] having the weighting coefficient as an element. ₁ , a ₂ , ..., a ₆ ] Equivalent to the inclusion of ^T ∈ R ⁶ .

However, when the vibration waveform is a second-order damped vibration, the rank (A) remains 2 even if M> 2, and N-rank (A) = 4. After that, it is exactly the same as the first embodiment, and the null space of the matrix A is four vectors {e ₁ , e ₂ , e ₃ , e ₄ } (e _j ∈ R ⁶ , j = 1, 2, 3, 4). Assuming that the basis is stretched, the vector a is given by the following linear sum of _ej .

The result of applying the moving average filter using the weighting coefficient calculated by the weighting coefficient determining unit 13 in the first embodiment to the vibration waveform to be suppressed as shown in FIG. 8 is also the same as that of FIG.

Note that the operation example of the first embodiment only limits the number of time-series data acquired in step 102 in FIG. 10, and the processing is the same, so the description thereof will be omitted.

[Embodiment 2]
Consider the case of FIG. 11 in which the filter is inserted before the input of the controlled object as shown in FIGS. 2 and 4. In this case, the step response y (t) when the moving average filter of the first embodiment is inserted deviates from 1 as shown in FIG. In general, the basis vector ej of the null space is set to satisfy _∥ej ∥ = 1 ( _∥X∥ indicates the Euclidean norm of X). In order to set the step response y (t) to 1, it is necessary to set the gain of the filter to 1, that is, the weighting coefficient of the moving average filter satisfies the following conditions.

When the basis vector _ej of the first embodiment is used, the weighting coefficient determining unit 13 determines a that satisfies the equation (4) by calculating the following equation.

As a result, a filter having a step response output y (t) of 1 can be obtained while completely suppressing vibration as shown in FIG.

In the operation example of the second embodiment, in FIG. 10, only the condition that the sum of the weighting coefficients is 1 is added to the condition used in step 103, and the processing flow is the same, so the description thereof will be omitted.

[Embodiment 3]
In the first embodiment, a large value is given as N and M, but the time series data acquisition unit 12 sets N = 3 (N = 2 depending on the condition) and M = 2 (M = 1 depending on the condition) and 3 It is sufficient to collect time series data of points (2 points depending on the conditions) and 2 sets (1 set depending on the conditions). Further, in the first embodiment, different sample points are used for each time-series data, but for example, overlapping sample points may be used between the time-series data.

Therefore, in the third embodiment, for the vibration waveform y (t) acquired by the vibration waveform acquisition unit 11, the time-series data acquisition unit 12 has, for example, four time-series data {y (t) with a constant sample period δ. ), Y (t + δ), y (t + 2δ), y (t + 3δ)}. At that time, as shown in FIG. 14, the first three points {y (t), y (t + δ), y (t + 2δ)} are set as time series data 1, and the three points {y (t + δ) starting from y (t + δ) are shifted by one. Let y (t + δ), y (t + 2δ), y (t + 3δ)} be the time series data 2.

It should be noted that the use of overlapping sample points between the time-series data means that the N time-series data for the first time-series data of the M time-series data and the second time-series data of the M time-series data. This is an example of acquiring M time series data so that the N time points with respect to the data overlap at least partially.

The weighting coefficient determining unit 13 satisfies the following two conditions in which the sum of the products of each time series data and the weighting coefficient {a1 _{, a2} , a3 _} of the filter is ₀ , and the weighting coefficient {a1 is satisfied. , A ₂ , a ₃ }.

Further, in the first and second embodiments, the weighting coefficient determining unit 13 derives the null space of the matrix A to determine the weighting coefficient, but the weighting coefficient determining unit 13 determines the weighting coefficient {a ₁ , a ₂ , a ₃ } May be calculated by explicitly giving a condition that makes it non-zero.

For example, a non-zero condition may be given by directly specifying a value of an appropriate weighting coefficient _aj . When such a value is set to 1, for example, and a condition of a ₁ = 1 is given, the following simultaneous equations may be solved.

It should be noted that this is an example of determining N weighting coefficients so that the designated weighting coefficients among the N weighting coefficients become the designated values.

Alternatively, when equation (4) is given as a non-zero condition, the following simultaneous equations may be solved.

This is an example of determining the N weighting coefficients so that the sum of the N weighting coefficients becomes a specified value.

Here, the weighting coefficients {a ₁ , a ₂ , a ₃ } obtained from the equation (7) satisfy the equation (4). Therefore, by using this weighting coefficient {a ₁ , a ₂ , a ₃ }, a moving average filter having a step response of 1 while suppressing vibration is directly derived. FIG. 15 shows the step response when the moving average filter satisfying the equation (7) is inserted. From FIG. 15, it can be seen that the transient time is as short as 0.4 [2π / ω sec] because the gain is 1 and N = 3 while suppressing the vibration.

In the operation example of the third embodiment, in FIG. 10, the time series data acquired in step 102 is limited to those having overlapping sample points, and the conditions used in step 103 include the conditions of the formula (7) or the formula (8). Is just added, and the processing flow is the same, so the explanation is omitted.

[Embodiment 3']
In the third embodiment, the time-series data acquisition unit 12 collects overlapping time-series data with respect to the vibration waveform y (t) acquired by the vibration waveform acquisition unit 11, but in the third embodiment, FIG. 16 shows. As shown, collect non-overlapping time series data. In FIG. 16, N = 3 and M = 2.

Also in this case, if the gain is 1, as shown in FIG. 17, the step response is the same as that in FIG.

In addition, in FIG. 10, the operation example of the third embodiment is limited to the time-series data acquired in step 102 so that the sample points do not overlap, and the processing is the same, so the description thereof will be omitted.

[Embodiment 4]
In the fourth embodiment, the time-series data acquisition unit 12 samples the vibration waveform y (t) acquired by the vibration waveform acquisition unit 11 at a sampling frequency lower than the aliasing frequency of the vibration cycle, as shown in FIG. I do. In FIG. 18, N = 3 and M = 2.

When sampling at a sampling frequency lower than the aliasing frequency of the vibration cycle, the interval between two adjacent time points out of N time points with respect to any time series data of the M time series data is the vibration waveform. This is an example of acquiring M time-series data so as to be longer than the period of.

Also in this case, by installing the filter in front of the controlled object as shown in FIG. 11, the vibration component can be removed as shown in FIG. In FIG. 19, the gain is 1.

In addition, in FIG. 10, the operation example of the fourth embodiment is limited to the time-series data acquired in step 102 whose sampling frequency is lower than the aliasing frequency, and the processing is the same. Therefore, the description thereof will be omitted. ..

[Embodiment 5]
In the fifth embodiment, the vibration of a plurality of vibration modes is suppressed by one filter. When suppressing L vibration waveforms at the same time, N ≧ 1 + 2 × L and M ≧ 2 × L, and a point and a set of time-series data satisfying these are required.

The vibration waveform acquisition unit 11 acquires a plurality of vibration waveforms. Here, L = 2 and two vibration waveforms are acquired.

As shown in FIG. 20, the time-series data acquisition unit 12 sets N = 5 and M = 4 for the two vibration waveforms acquired by the vibration waveform acquisition unit 11, for example, 5 points and 4 points in a constant sample cycle. Collect a set of time-series data. Here, for one vibration waveform y ₁ (t), time series data 1 {y ₁ (t ₁ + δ ₁ ), y ₁ (t ₁ + δ ₂ ), ..., y ₁ (t ₁ + δ ₅ )} And time series data 2 {y ₁ (t ₂ + δ ₁ ), y ₁ (t ₂ + δ ₂ ), ..., y ₁ (t ₂ + δ ₅ )} are collected. Further, for the other vibration waveform y ₂ (t), time series data 3 {y ₂ (t ₁ + δ ₁ ), y ₂ (t ₁ + δ ₂ ), ..., y ₂ (t ₁ + δ ₅ )} , Time series data 4 {y ₂ (t ₂ + δ ₁ ), y ₂ (t ₂ + δ ₂ ), ..., y ₂ (t ₂ + δ ₅ )}.

21 and 22 show the results when the weighting coefficient determining unit 13 suppresses the vibration of the two vibration modes with one moving average filter using the weighting coefficient determined from these time series data.

So far, we have dealt with the second-order damped vibration in which the vibration is linear, but in many non-linear vibrations, the vibration frequency and damping coefficient change non-linearly depending on the situation. Such non-linear vibration can be dealt with by treating this as a set of linear second-order damped vibrations and designing a filter that suppresses vibrations in a plurality of vibration modes as in the fifth embodiment. ..

FIG. 23 is a flowchart showing an operation example of the filter design device 10 in the fifth embodiment.

In the filter design device 10, first, the vibration waveform acquisition unit 11 acquires the vibration waveform y _i (t) (i = 1, 2, ..., L) to be controlled (step 151).

Next, the time-series data acquisition unit 12 obtains N points (N ≧ 1 + 2 × L), M from the vibration waveform y _i (t) (i = 1, 2, ..., L) acquired by the vibration waveform acquisition unit 11. Acquire time-series data of set _i (Mi ≧ 2 ₎ (step 152).

Next, the weighting coefficient determination unit 13 says that the sum of the products of the N points of the time-series data of the M ₁ + M ₂ + ... + _ML set acquired by the time-series data acquisition unit 12 and the weighting coefficient is ₀ . The weighting coefficient is determined so as to satisfy the conditions of ₂ + ... + _ML (step 153).

After that, the weighting coefficient output unit 14 outputs the weighting coefficient determined by the weighting coefficient determining unit 13 (step 154).

[Embodiment 6]
In the sixth embodiment, the time-series data acquisition unit 12 samples the vibration waveform y (t) acquired by the vibration waveform acquisition unit 11 at different sample intervals. Specifically, as shown in FIG. 24, the time-series data acquisition unit 12 sets N = 3 and M = 2, and collects three points and two sets of time-series data at different sample intervals, for example. Here, the time series data 1 {y (t ₁ + δ ₁ ), y (t ₁ + δ ₂ ), y (t ₁ + δ ₃ )} and the time series data 2 {y (t ₂ + δ ₁ ), y (t). ₂ + δ ₂ ), y (t ₂ + δ ₃ )} and are collected. Here, the different sample intervals mean that δ ₂ -δ ₁ ≠ δ ₃ -δ ₂ .

FIG. 25 shows the result when the weighting coefficient determining unit 13 suppresses the vibration with the moving average filter using the weighting coefficient determined from these time series data. In FIG. 25, the gain is 1.

In addition, in FIG. 10, the operation example of the sixth embodiment is limited to the time-series data acquired in step 102 having different sample intervals, and the processing is the same, so the description thereof will be omitted.

[Embodiment 7]
Normally, in order to determine the weighting coefficient of the moving average filter that suppresses one vibration waveform, N ≧ 3 and M ≧ 2, and two or more sets of time series data having three or more sample points are required. rice field. Here, if the sample interval is set to a half cycle of the vibration cycle (constraints are given to the sample interval), N ≧ 2 and M ≧ 1, and only one set or more of time series data having two or more sample points is obtained. It can be used to design a moving average filter.

Now, consider a second-order damped vibration system given by the following transfer function.

The vibration period T of this second-order damped vibration system is given by the following equation.

Therefore, in the seventh embodiment, the time-series data acquisition unit 12 sets the sample interval _Tn to T / 2 with respect to the vibration waveform y (t) acquired by the vibration waveform acquisition unit 11, and as shown in FIG. 26, Time series data 1 {y (t ₁ ), y (t ₁ + T _n )} is collected. In FIG. 26, N = 2 and M = 1.

In addition, when the sample interval is set to a half cycle of the vibration cycle, the interval between two adjacent time points out of N time points with respect to any time series data of the M time series data is 1 of the period of the vibration waveform. This is an example of acquiring M time-series data so as to be / 2.

The weighting coefficient determining unit 13 sets the condition that the sum of the products of the time series data 1 {y (t ₁ ), y (t ₁ + T _n )} and the weighting coefficient {a ₁ , a ₂ } is 0, and (4). ), The weighting coefficients {a ₁ , a ₂ } are determined from the following simultaneous equations.

The following moving average filter using the weighting coefficient determined in this way has a vibration suppressing effect as shown in FIG. 27.

In addition, in FIG. 10, the operation example of the seventh embodiment is limited to the time-series data acquired in step 102 whose sampling is a half cycle of the vibration cycle, and the processing is the same, so the description thereof is omitted. do.

[Embodiment 8]
In the above, the case where the condition that the gain is 1 is used in addition to the vibration suppression has been shown, but this is not the case. In the eighth embodiment, other conditions are added. However, in this case, it is necessary to increase the minimum value of N.

For example, when group delay identification (characteristic that the delay time is constant at all frequencies) is given to the moving average filter, the weighting coefficient determining unit 13 sets the weighting coefficients {a ₁ , a ₂ , ..., a _N }. It may be derived by adding the following conditions indicating that is symmetrical.

In this case, when N weighting coefficients are a ₁ , a ₂ , ..., a _N , a ₁ = a _N , a ₂ = a _N-1 , a ₃ = a _N-2 , ... This is an example of determining N weighting coefficients so as to be.

Alternatively, when it is desired to suppress the fluctuation of the filter output x (t) as small as possible, the weighting coefficient determining unit 13 may add the following conditions.

This is an example of determining the N weight coefficients so that the sum of the absolute values of the N weight coefficients is minimized.

Further, this is a constrained conditional optimization with a constraint that the sum of the products of the time series data and the weighting coefficient is 0 and a constraint that any of the weighting coefficients is non-zero.

The weighting coefficient determination unit 13 may determine the weighting coefficient {a ₁ , a ₂ , ..., A _N } by this constrained optimization.

In the operation example of the eighth embodiment, in FIG. 10, only the condition of the formula (13) or the condition of the formula (14) is added to the condition used in the step 103, and the processing flow is the same, so the description thereof will be omitted. ..

[Embodiment 9]
The ninth embodiment is an embodiment relating to a specific application target of the vibration suppression described so far. FIG. 28 is a diagram showing a configuration example of a robot system 20 which is an example of a specific application target. In this robot system 20, the robot 21 is mounted on a slider 22 which is an example of an auxiliary shaft, and the work 23 is positioned by the positioner 24. In the figure, the robot 21 is shown with axes S1 to S6 as rotation axes. Further, a robot controller 30 that controls the robot 21 is also shown as one of the components of the robot system 20.

By the way, in such a robot system 20, in addition to the elastic deformation of the robot 21, the tip of the robot 21 and the work 23 vibrate due to the elastic deformation of the slider 22, the positioner 24, and the like. In particular, vibration due to elastic deformation of the slider 22 and the positioner 24 has a short vibration cycle, and there is a high need for vibration suppression during operation of the robot 21. On the other hand, the slider 22 and the positioner 24 are often non-general-purpose products ordered by one product. Therefore, the details of the actual vibration mode by the slider 22 and the positioner 24 are unknown until the system is completed. Especially for such non-general-purpose products, there is a strong need to configure a control system that quickly suppresses the actual vibration mode after the system is completed.

Therefore, in the ninth embodiment, after the non-general-purpose product such as the robot system 20 is completed, the acceleration pickup 25 is installed at the tip of the robot 21, the work 23, or the like, as shown in FIG. 28, during a trial run or the like. This enables the filter design device 10 to acquire a vibration waveform and quickly design a filter that suppresses vibration.

Further, the filter designed in this way may be inserted at any of the filter insertion positions in the robot controller 30. FIG. 29 is a diagram showing a filter insertion position in the robot controller 30. As shown in the figure, the robot controller 30 includes a command unit 31 and a control unit 32, and the filter insertion positions 33 to 35 are defined in relation to these. Here, the robot controller 30 is an example of a vibration suppressing device that suppresses the vibration of the controlled object, the control unit 32 is an example of the control means for controlling the controlled object, and the circuits at the filter insertion positions 33 to 35 are. , Is an example of a processing means for processing a signal. Further, in the figure, the motor 26, which is an example of the actuator for the controlled object, is also shown at the position of the controlled object.

In such a robot controller 30, the following can be considered as a specific insertion form of the filter. That is, first, as a pre-filter for the command value to the controlled object, the command value is inserted into the filter insertion position 33 before being output from the command unit 31 and input to the control unit 32. Secondly, as a notch filter for the feedback value from the controlled object, the feedback value is inserted into the filter insertion position 34 before being input to the control unit 32. Thirdly, as a notch filter for the output of the control unit 32 that controls the control target, it is inserted into the filter insertion position 35 after the command value is output from the control unit 32. This makes it possible to easily and quickly configure a control system capable of completely suppressing the vibration of the actual machine.

It should be noted that the collection of the vibration waveform is only necessary at the time of filter design such as the above-mentioned test run, and the vibration measurement by the acceleration pickup 25 or the like is not necessary at the time of normal operation. Therefore, it is possible to easily and quickly configure a control system that suppresses vibration without causing an extra increase in sensor cost.

[Hardware configuration of filter design device and robot controller]
The filter design device 10 of FIG. 6 and the robot controller 30 of FIG. 29 may be realized by, for example, a general-purpose computer. Therefore, assuming that the filter design device 10 and the robot controller 30 are realized by the computer 90, the hardware configuration of the computer 90 will be described.

FIG. 30 is a diagram showing a hardware configuration example of the computer 90. As shown in the figure, the computer 90 is realized by, for example, a general-purpose PC (Personal Computer) or the like, and includes a CPU 91 as a calculation means, a main memory 92 as a storage means, and a magnetic disk device (HDD: Hard Disk Drive) 93. Be prepared. Here, the CPU 91 executes various programs such as an OS (Operating System) and application software, and realizes each function of the filter design device 10 and the robot controller 30. Further, the main memory 92 is a storage area for storing various programs and data used for executing the various programs, and the HDD 93 is an example of a storage medium and stores input data for various programs and output data from various programs. It is a storage area to be used.

Further, the computer 90 reads / writes data to / from a communication I / F 94 for communicating with the outside, a display mechanism 95 including a video memory and a display, an input device 96 such as a keyboard and a mouse, and a storage medium. It is provided with a driver 97 for performing the above. Note that FIG. 30 merely illustrates the hardware configuration of the computer that realizes the filter design device 10 and the robot controller 30, and the computer 90 is not limited to the illustrated configuration.

[Effect of this embodiment]
As described above, in the present embodiment, in the moving average filter that outputs the average by multiplying the N sample points where the sample interval is arbitrarily given by the weighting coefficient, the N points of the vibration waveform to be removed by the moving average filter. Prepare M time-series data of, give M conditions that the sum of each sample point of M time-series data multiplied by a weighting coefficient is equal to 0, satisfy the M conditions, and The weighting coefficient is given so that at least one of the weighting coefficients is non-zero. This has increased the possibility that the vibration component of the vibration waveform can be completely removed.

10 ... Filter design device, 11 ... Vibration waveform acquisition unit, 12 ... Time series data acquisition unit, 13 ... Weight coefficient determination unit, 14 ... Weight coefficient output unit, 20 ... Robot system, 21 ... Robot, 22 ... Slider, 23 ... Work, 24 ... Positioner, 25 ... Accelerometer pickup, 26 ... Motor, 30 ... Robot controller, 31 ... Command unit, 32 ... Control unit, 33, 34, 35 ... Filter insertion position

Claims (17)

It is a filter for removing the vibration component of the input vibration waveform accompanied by attenuation, and is averaged by multiplying the value of the input vibration waveform at the time point of N (N ≧ 2) at an arbitrary interval by N weight coefficients. It is a filter design device that gives the N weight coefficients to the filter that calculates
An acquisition means for acquiring M (M ≧ 1) time-series data including the values of the vibration waveforms at N time points for each time-series data from the collected vibration waveforms .
The said is given by the linear sum of the basis vectors of the null space of the matrix having the values of the vibration waveforms at the N time points as elements for each time series data of the M time series data acquired by the acquisition means. Determining means for determining N weight coefficients,
A filter design device including an output means for outputting the N weighting coefficients determined by the determination means. The acquisition means has N time intervals for the first time series data of the M time series data (M ≧ 2) and N time points for the second time series data of the M time series data. The filter design apparatus according to claim 1, wherein the M time-series data are acquired so that the intervals at the time points of the above are equal to each other. The acquisition means has N time points for the first time series data of the M (M ≧ 2) time series data and N time points for the second time series data of the M time series data. The filter design apparatus according to claim 1, wherein the M time-series data are acquired so that the two are at least partially overlapped with each other. The acquisition means has the M pieces so that the interval between two adjacent time points out of the N time points with respect to any time series data of the M time series data is longer than the period of the vibration waveform. The filter design apparatus according to claim 1, wherein the time-series data of the above is acquired. The acquisition means said that the interval between two adjacent time points out of N time points with respect to any time series data of the M time series data is 1/2 of the period of the vibration waveform. The filter design apparatus according to claim 1, wherein M time-series data are acquired. The filter according to claim 1, wherein the determination means determines the N weight coefficients so that the specified weight coefficient among the N weight coefficients becomes a specified value. Design equipment. The filter design device according to claim 1, wherein the determination means determines the N weight coefficients so that the sum of the N weight coefficients becomes a designated value. The filter design apparatus according to claim 7, wherein the specified value is 1. The determining means has a ₁ = a _N , a ₂ = a _N-1 , a ₃ = a _N-2 , ... When the N weighting coefficients are a ₁ , a ₂ , ..., A _N. The filter design apparatus according to claim 1, wherein the N weighting coefficients are determined so as to be. The filter design apparatus according to claim 1, wherein the determination means determines the N weight coefficients so that the sum of the absolute values of the N weight coefficients is minimized. The acquisition means has N pieces of each time-series data for each time-series data from L (L ≧ 2) vibration waveforms y _i (t) (i = 1, 2, ..., L) having different vibration cycles. Acquire Mi (Mi _≧ 2) time series data including the value of the vibration waveform _{y i} (t) at the time of (N ≧ 2 × L + 1).
The determination means corresponds to each time-series data at N time points with respect to each time-series data for each time-series data of M ₁ + M ₂ + ... + _ML acquired by the acquisition means. The condition that the value obtained by multiplying each value of the vibration waveform y _i (t) by the corresponding weighting coefficient among the N weighting coefficients is 0 is satisfied. The filter design apparatus according to claim 1, wherein the weighting coefficient is determined. A vibration suppression device that suppresses vibration of a controlled object that accompanies damping.
A control means for controlling the control target and
A signal input to the control means or a signal output from the control means by using the filter to which the N weight coefficients are given by the filter design device according to any one of claims 1 to 11. A vibration suppression device characterized by being provided with a processing means for processing. The vibration suppression device according to claim 12, wherein the processing means uses the filter to process the signal for issuing a command to the control target input to the control means. The vibration suppression device according to claim 12, wherein the processing means uses the filter to process the signal that is fed back from the control target and input to the control means. The vibration suppression device according to claim 12, wherein the processing means uses the filter to process the signal for issuing a command to the control target output from the control target. It is a filter for removing the vibration component of the input vibration waveform accompanied by attenuation, and is averaged by multiplying the value of the input vibration waveform at the time point of N (N ≧ 2) at an arbitrary interval by N weight coefficients. This is a filter design method in which the computer gives the N weight coefficients to the filter that calculates.
The acquisition means of the computer acquires M (M ≧ 1) time-series data including the values of the vibration waveforms at N time points with respect to the time-series data for each time-series data from the collected vibration waveforms. To get the steps and
The determination means of the computer is a null space basis vector of a matrix having the values of the vibration waveforms at the N time points as elements for each time series data of the M time series data acquired in the acquisition step. A determination step for determining the N weight coefficients given by the linear sum of
A filter design method, wherein the output means of the computer includes an output step for outputting the N weighting coefficients determined in the determination step. It is a filter for removing the vibration component of the input vibration waveform accompanied by attenuation, and is averaged by multiplying the value of the input vibration waveform at the time point of N (N ≧ 2) at an arbitrary interval by N weight coefficients. A program that causes a computer to function as a filter design device that gives the N weight coefficients to the filter that calculates.
The computer
An acquisition means for acquiring M (M ≧ 1) time-series data including the values of the vibration waveforms at N time points for each time-series data from the collected vibration waveforms .
The said is given by the linear sum of the basis vectors of the null space of the matrix having the values of the vibration waveforms at the N time points as elements for each time series data of the M time series data acquired by the acquisition means. Determining means for determining N weight coefficients,
A program for functioning as an output means for outputting the N weight coefficients determined by the determination means.

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