JP2013089089A - Resonance suppression device and resonance suppression method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To draw an attention on the change of a resonance frequency.SOLUTION: The resonance suppression device includes: a notch filter installed in a control system for suppressing the resonance of the control system; and a filter coefficient adjustment part for updating the filter coefficient of the notch filter so that the center frequency of the notch filter is coincident with the resonance frequency of the control system. The update processing of the filter coefficient includes: determining whether or not the amount of change of the resonance frequency with the existing center frequency of the notch filter as a reference is within an allowable range; and outputting a warning when it is determined that the amount of change is beyond the allowable range.

Description

  The present invention relates to a resonance suppression device and a resonance suppression method using a notch filter.

  There is known a resonance suppression device that changes the center frequency of a notch filter in a machine control device that suppresses mechanical resonance using a notch filter (see, for example, Patent Document 1). The apparatus includes a signal generator that generates a minute signal corresponding to a center frequency manipulated variable that changes the center frequency of the notch filter, an amplitude detector that detects the amplitude of resonance of the machine, the minute signal, and the amplitude of the resonance. A multiplication unit that multiplies the output of the multiplication unit, a subtraction unit that takes a difference between the output of the multiplication unit, an integration unit that integrates the output of the subtraction unit, a coefficient unit that multiplies the output of the integration unit, and a coefficient unit Is added to the minute signal.

JP 2002-104859 A

  According to the above-described resonance suppression device, when the resonance frequency of the machine changes, the center frequency of the notch filter automatically tracks it. However, the change in resonance frequency may be caused by some modulation that has occurred in the machine during the previous operation. Such a modulation is easily overlooked because the automatic tracking of the notch filter appears to continue to operate normally on the surface. There is a risk that the abnormality will not be discovered until the state of the machine is further deteriorated. In practice, it may have been desirable to perform a maintenance check at a time when some change in the resonance frequency has occurred, rather than continuing machine operation.

  The present invention has been made in view of such circumstances, and one of exemplary purposes of an aspect thereof is to provide a resonance suppression device and a resonance suppression method capable of calling attention regarding a change in resonance frequency. .

  One embodiment of the present invention relates to a resonance suppression device. This device has a notch filter provided in the control system to suppress resonance of the control system and a filter coefficient of the notch filter so that the center frequency of the notch filter matches the resonance frequency of the control system. And a filter coefficient adjustment unit for updating. The update process of the filter coefficient is performed by determining whether or not the variation of the resonance frequency based on the existing center frequency of the notch filter is at an allowable level, and determining that the variation has deviated from the allowable level. Output a warning if it is.

  Another aspect of the present invention relates to a resonance suppression method for suppressing resonance of a control system using an adaptive notch filter. The method includes updating a filter coefficient of the notch filter so that a center frequency of the notch filter matches a resonance frequency of the control system. The updating is performed by determining whether or not the variation of the resonance frequency based on the existing center frequency of the notch filter is at an allowable level, and determining that the variation has deviated from the allowable level. Output a warning in some cases.

  In addition, what replaced the component and expression of this invention between methods, apparatuses, systems, etc. is also effective as an aspect of this invention.

  According to the present invention, it is possible to call attention regarding a change in the resonance frequency.

It is a block diagram which shows the structure of the adaptive notch filter which concerns on one Embodiment of this invention. It is a figure which shows an example of the timing of the filter coefficient update process of the some notch filter which concerns on one Embodiment of this invention. It is a flowchart for demonstrating the filter coefficient update process which concerns on one Embodiment of this invention. It is a flowchart for demonstrating the resonance frequency monitoring process shown in FIG. It is a figure which shows the example of the frequency characteristic of the notch filter which concerns on one Embodiment of this invention. It is a figure which shows the example of the frequency characteristic of the peak filter which concerns on one Embodiment of this invention. It is a figure which shows the relationship between center frequency (omega) ₀ and the coefficient k of the notch filter which concerns on one Embodiment of this invention. It is a figure which shows the principle of correction of center frequency (omega) ₀ of the notch filter which concerns on one Embodiment of this invention as a frequency characteristic. It is a figure which shows the average value of the center frequency correction amount of the Example which uses a peak filter for a phase difference filter. 1 is a block diagram illustrating an example of a system configuration including a resonance suppression device according to an embodiment of the present invention.

  The present invention will be described below based on preferred embodiments with reference to the drawings. The same or equivalent components, members, and processes shown in the drawings are denoted by the same reference numerals, and repeated descriptions are omitted as appropriate. The embodiments do not limit the invention but are exemplifications, and all features and combinations thereof described in the embodiments are not necessarily essential to the invention.

  The resonance suppression device according to an embodiment corrects the notch filter as usual when the change in the resonance frequency is small and within the allowable range, and outputs a warning when the change in the resonance frequency is out of the allowable range. It is expected that changes due to anomalies are greater than changes in resonance frequency that can occur during normal operation of the machine. By issuing a warning, it is possible to notify a user (for example, an operator or a manager of a machine) that an abnormality has occurred (or that an abnormality may have occurred). In this way, it is possible to provide the user with an opportunity to consider the necessity of early maintenance inspection.

  FIG. 1 is a block diagram showing a configuration of a resonance suppression device 10 according to an embodiment of the present invention. The resonance suppression apparatus 10 includes, for example, an adaptive notch filter that is incorporated in and used in a control system in order to suppress resonance in an arbitrary control system.

The resonance suppression device 10 includes a notch filter 12 for suppressing one or more resonance frequency components that may occur in the control system. The notch filter 12 is a known filter having a frequency characteristic shown in FIG. 5, for example. Notch filter 12, at the center frequency omega ₀ has a minimum value of the amplitude gain, and outputs to the output signal tau ₂ removes frequency components of the center frequency omega ₀ of the input signal tau _1.

The input signal τ ₁ to the notch filter 12 is, for example, a control command in a control system to which the notch filter 12 is applied. The input signal τ ₁ is generated based on, for example, an error between an output detection value obtained as a result of the control command and a desired target command value. The input signal τ ₁ may be a target command value. The input signal τ ₁ may be an observation amount (for example, position, velocity, acceleration, etc.) in the control system. The output signal τ ₂ of the notch filter 12 is used as a control command instead of the input signal τ ₁ .

The filter coefficient of the notch filter 12 is set in advance, for example, when the apparatus 10 is shipped so as to remove the resonance frequency component of the control system from the input signal τ ₁ . Alternatively, the filter coefficient is set by initial setting work when the resonance suppression apparatus 10 is installed in the control system and starts to be used. Through the setting operation, the center frequency ω ₀ of the notch filter 12 is adjusted to coincide with any one of the resonance frequency components of the control system. Further, during use of the resonance suppression device 10 after the initial setting, the filter coefficient of the notch filter 12 is adjusted at any time by a filter coefficient update process described later.

  The notch filter 12 may be configured to remove a plurality of frequency components. For example, the notch filter 12 may be configured of a plurality of notch filters connected in series. Each of the plurality of notch filters can set a center frequency to an arbitrary frequency component. The operating band of each notch filter is not divided in advance. Therefore, the notch filter can be flexibly assigned according to the distribution of the resonance frequency. For example, even when two resonance frequency components are relatively close to each other, a notch filter can be assigned to each. However, the operation band of each notch filter may be divided in advance. In that case, it is desirable that the division is performed in advance so that the resonance frequency component becomes one for each division handled by each notch filter.

The resonance suppression apparatus 10 includes a filter coefficient adjustment unit 13 for updating the filter coefficient of the notch filter 12. The filter coefficient update process is a process for making the center frequency ω ₀ of the notch filter 12 coincide with the resonance frequency of the control system to which the notch filter 12 is applied. In the filter coefficient updating process, not only the center frequency ω ₀ but also the coefficients (for example, notch width and notch depth) of the notch filter 12 other than the center frequency ω ₀ may be adjusted.

The filter coefficient adjustment unit 13 corrects the filter coefficient of the notch filter 12 based on the reference signal r. Similarly to the input signal τ ₁ , the reference signal r may be a control command to a control target to which the notch filter 12 is applied, or may be an observation amount from the control target. The filter coefficient adjustment unit 13 may use a reference signal r generated from noise generated by the vibration of the control target. For this purpose, a reference signal generation unit that analyzes a sound generated by the control target and generates a reference signal r may be provided. A sound collector such as a microphone may be provided for collecting the sound generated by the control target and supplying the collected sound to the reference signal generation unit. As described above, the filter coefficient adjustment unit 13 may use any signal that can extract the vibration component to be controlled as the reference signal r.

The filter coefficient adjustment unit 13 includes a center frequency calculation unit 17 for adjusting the center frequency ω ₀ of the notch filter 12. In this case, the center frequency calculation unit 17 may include a phase difference filter 16 and a correction calculation unit 18, and details thereof will be described later. In one embodiment, the center frequency calculator 17 includes a peak filter having a peak at the current value of the center frequency ω ₀ , and the product of the output signal and the input signal obtained by applying the peak filter to the input signal. Based on this, a correction amount Δω ₀ of the center frequency is calculated. Given the correction amount Δω _{0, the} center frequency ω ₀ tracks the resonance frequency of the control system. As an alternative, the center frequency calculation unit 17 may calculate the center frequency from the input signal by a method using an all-pass filter instead of the peak filter or by any other method.

It is not always easy to grasp the true value of the resonance frequency of the control system. Instead, the center frequency ω ₀ obtained in the filter coefficient update process can be used as an estimated value of the resonance frequency. In this way, the resonance suppression device 10 can monitor the resonance frequency during operation using the filter coefficient adjustment unit 13. That is, the resonance suppression apparatus 10 monitors the resonance frequency of the control system using frequency tracking for the adaptive notch filter. Therefore, it can be said that the filter coefficient adjustment unit 13 is a frequency monitoring unit for monitoring the resonance frequency of the control system.

  The filter coefficient adjustment unit 13 repeatedly executes the filter coefficient update process. In many cases, the variation of the resonance frequency is moderate, and the change appears when monitored over the long term. Therefore, the filter coefficient update process may be repeatedly executed repeatedly. That is, there may be an update suspension period between the previous filter coefficient update process and the current filter coefficient update process. Compared with the case where the update process is always executed, the calculation load can be reduced. However, when importance is attached to the followability of the center frequency (when it is predicted that the resonance frequency of the control system is likely to change), the filter coefficient update process may be executed repeatedly at all times.

The filter coefficient adjustment unit 13 includes a prefilter 14 for limiting the band of the input signal to the center frequency calculation unit 17. The prefilter 14 is provided to remove a frequency component unnecessary for correcting the center frequency ω ₀ of the notch filter 12 from the reference signal r. The pre-filter 14 receives the reference signal r and outputs a signal u including a band including a frequency component to be removed by the notch filter 12. The signal u preferably contains only frequency components to be removed by the notch filter 12. That is, the prefilter 14 extracts the frequency component to be removed by the notch filter 12 from the reference signal r.

Here, the unnecessary frequency components in the correction of the center frequency omega _0, includes a frequency component of a frequency region lower than the center frequency omega _0. In general, in the reference signal r, a frequency component in a lower frequency range than the center frequency ω ₀ such as a DC component (in other words, a frequency component of 0 Hz) or a main frequency component of the target command has a large amplitude. Many. The frequency tracking method according to an embodiment attempts to make the center frequency coincide with a frequency component having a large amplitude in the vicinity of the current center frequency. In this case, the center frequency ω ₀ tends to be corrected slightly lower than the resonance frequency component to be controlled due to the influence of the low-frequency component having a large amplitude in the reference signal r. Therefore, it is preferable that the pre-filter 14 includes, for example, a high-pass filter whose pass band is a frequency region higher than the control frequency band.

Further, the prefilter 14 may be configured to remove frequency components (for example, noise unrelated to resonance) included in a frequency region higher than the center frequency ω ₀ . In this case, the pre-filter 14 may include a band-pass filter whose pass band is a frequency region including the center frequency ω ₀ and frequency components in the vicinity thereof.

  The filter coefficient adjustment unit 13 includes a vibration evaluation unit 19. The vibration evaluation unit 19 evaluates the vibration level of the reference signal r or other input signal. The input signal to the vibration evaluation unit 19 may be the output signal u of the prefilter 14. For example, the vibration evaluation unit 19 calculates a vibration level from the input signal, and determines whether or not the obtained vibration level exceeds a reference. Whether or not the vibration level exceeds the reference is determined by, for example, whether or not the output signal u of the prefilter 14 has a sufficient amplitude. In order to evaluate whether or not the output signal u of the prefilter 14 has a sufficient amplitude, for example, a signal obtained by applying a low-pass filter to the square of the output signal u and the square of the resolution of the reference signal r It is determined whether the ratio is greater than a reference value. The vibration evaluation unit 19 may evaluate the vibration level by other known appropriate methods.

  When the resonance suppression apparatus 10 includes a plurality of notch filters 12, the filter coefficient adjustment unit 13 is shared by the plurality of notch filters 12. The filter coefficient adjustment unit 13 sequentially executes filter coefficient update processing for the plurality of notch filters 12. By shifting the timing of the update process between one notch filter and another notch filter, the concentration of calculation load can be reduced.

  Preferably, the filter coefficient adjustment unit 13 individually executes the filter coefficient update process of the plurality of notch filters 12 one after another. That is, the filter coefficient adjustment unit 13 switches and executes notch filter update processing one by one, and circulates each notch filter. Thus, the calculation load of the filter coefficient adjustment unit 13 can be made constant over time. Further, the amount of calculation can be reduced as compared with the case where the filter coefficient update processing of the plurality of notch filters 12 is performed simultaneously.

  Note that there may be a pause period between two notch filter update processes, or they may partially overlap. The update process of each notch filter may not be executed in a fixed order, and the order may be changed as necessary. The update frequency of each notch filter may not necessarily be uniform, and a specific notch filter may be updated more frequently than other notch filters.

  FIG. 2 is a diagram illustrating an example of the timing of the filter coefficient update process of the plurality of notch filters 12. FIG. 2 shows an application example of the resonance suppression apparatus 10 to the XY stage. The resonance suppression apparatus 10 includes three-stage notch filters NX1, NX2, and NX3 for suppressing resonance of the control axis in the X direction, and three-stage notch filters NY1, NY2 for suppressing resonance of the control axis in the Y direction. , NY3 and a total of six notch filters.

  As shown in the figure, the filter coefficient update processing is switched and executed for the six notch filters in the order of NX1, NX2, NX3, NY1, NY2, NY3. The processing time is set equally for the update processing of each notch filter. In this example, it is 2 seconds. In the figure, the processing time is indicated by an arrow.

  When the update process for a certain notch filter is completed, the update process for the next notch filter is started. At this time, the band setting of the pre-filter 14 is switched according to the notch filter to be updated. In this example, the band setting of the prefilter 14 is switched every 2 seconds.

  The pre-filter 14 passes a resonance frequency component assigned to a notch filter for which filter coefficient update processing is executed among a plurality of notch filters, and a pass band is set so as to exclude resonance frequency components other than the resonance frequency component. It has been done. In this way, during the update process of a certain notch filter, it is possible to reduce or prevent the influence of vibration components other than the resonance frequency assigned to the notch filter on the update process.

Specifically, the prefilter 14 is set to a narrow passband in the filter coefficient update process. The pass band of the pre-filter 14 in the filter coefficient update process is set, for example, in the vicinity of the previously set center frequency ω ₀ (for example, a band of ± 5% of the center frequency ω ₀ ). In the initial setting operation of the resonance suppression device 10, the prefilter 14 is set so as to have a sufficiently wide pass band than the filter coefficient updating process in order to transmit the frequency component to be suppressed to the center frequency calculation unit 17. Or disabled.

  In addition, after the update process of the three-stage notch filters NX1, NX2, and NX3 for the X-direction control axis is completed, the update process of the three-stage notch filters NY1, NY2, and NY3 for the Y-direction control axis is completed. Is started. The update process in the X direction is performed based on the reference signal r in the X direction, and the update process in the Y direction is performed based on the reference signal r in the Y direction. Therefore, when the update process in the X direction ends and the update process in the Y direction starts, the input signal to the filter coefficient adjustment unit 13 is switched from the X direction signal to the Y direction signal. Similarly, when switching from the update process in the Y direction to the update process in the X direction, the input signal to the filter coefficient adjustment unit 13 is switched from the signal in the Y direction to the signal in the X direction. In this example, the input signal to the filter coefficient adjustment unit 13 is switched every 6 seconds. In FIG. 2, switching of the input signal is indicated by a bold line.

  Following the update process of the last notch filter NY3, the update process of the first notch filter NX1 is performed again. In this way, the update process of each notch filter is repeated (in this example, every 12 seconds).

  FIG. 3 is a flowchart for explaining filter coefficient update processing according to an embodiment of the present invention. The filter coefficient update process includes a resonance frequency monitoring process (S10), a verification process (S12), and a switching process (S14), and the filter coefficient adjustment unit 13 sequentially executes these for each notch filter.

  The resonance frequency monitoring process (S10) is a process including estimating the resonance frequency of the control system using, for example, frequency tracking described later in order to update the filter coefficient of the notch filter 12. Details of the resonance frequency monitoring process (S10) will be described later with reference to FIG.

The verification process (S12) includes determining whether or not the fluctuation amount of the resonance frequency obtained by the monitoring process (S10) is within an allowable range (S16). This allowable range is set based on the reference frequency, and for example, an upper limit and a lower limit are set including the reference frequency as a center. The reference frequency is, for example, the center frequency already acquired before the start of the current update process. That is, the reference frequency is the existing center frequency of the notch filter 12. Therefore, the reference frequency may be, for example, the notch filter center frequency acquired by the initial setting of the resonance suppression device 10, or the center frequency at the start of the update process (that is, the center frequency acquired by the previous update process). It may be. For example, the allowable range is set in the vicinity of the previously set center frequency ω ₀ (for example, a band of ± 5% of the center frequency ω ₀ ), similarly to the pass band of the pre-filter 14.

  In the verification process (S12), when it is determined that the resonance frequency is included in the set allowable range (Y in S12), the filter coefficient adjustment unit 13 updates the filter coefficient of the notch filter (S18). ). The filter coefficient adjustment unit 13 corrects the filter coefficient so that the center frequency of the notch filter matches the resonance frequency newly acquired by the monitoring process (S10). That is, when the fluctuation of the resonance frequency is at an allowable level, the filter coefficient is updated as usual, and the frequency characteristic of the resonance suppression device 10 is corrected.

  On the other hand, when it is determined that the resonance frequency has deviated from the set allowable range (N in S12), the filter coefficient adjustment unit 13 outputs a warning (S20). By outputting the warning, it is possible to notify the user that an abnormality has occurred (or that an abnormality may have occurred). The warning output method may be any known method. The filter coefficient adjustment unit 13 may generate and output a command to stop the operation of the machine (operation of the apparatus) together with the warning output or instead of the warning output.

  The update of the filter coefficient of the notch filter is completed by the monitoring process (S10) and the verification process (S12). In preparation for the next notch filter update process, the filter coefficient adjustment unit 13 executes the switching process (S14) following the monitoring process (S10) and the verification process (S12). The switching process (S14) includes switching the band setting of the pre-filter 14 for the next notch filter. Further, the switching process (S14) includes switching of an input signal to the filter coefficient adjustment unit 13 as necessary.

FIG. 4 is a flowchart for explaining the resonance frequency monitoring process shown in FIG. The resonance frequency monitoring process (S10) mainly includes a frequency tracking process (S24) described later. The frequency tracking process (S24) includes obtaining an updated value ω ₀ [n + 1] by adding the correction amount Δω ₀ to the current value ω ₀ [n] of the center frequency ω ₀ according to Equation 1 described later. Note that the filter coefficient adjustment unit 13 may calculate the center frequency by any method other than the frequency tracking process.

  In order to determine whether it is appropriate to execute the frequency tracking process (S24), the resonance frequency monitoring process determines whether a start condition for the frequency tracking process is satisfied (S22). The start condition includes that the vibration level of the output signal u of the prefilter 14 exceeds a reference. In order to determine whether or not the vibration level of the output signal u of the prefilter 14 exceeds the reference, the filter coefficient adjustment unit 13 determines whether the output signal u of the prefilter 14 has a sufficient amplitude, for example, as described above. Determine whether or not.

When it is determined that the vibration level has reached the reference (Y in S22), the filter coefficient adjustment unit 13 performs frequency tracking processing (S24). On the other hand, when it is determined that the vibration level does not satisfy the standard (N in S22), the filter coefficient adjustment unit 13 does not execute the frequency tracking process. This is to prevent the center frequency ω ₀ of the notch filter from converging to an abnormal value due to the influence of noise, other resonance components, command components, and the like.

  After the frequency tracking process (S24) or when it is determined that the vibration level does not satisfy the standard (N in S22), the filter coefficient adjustment unit 13 determines whether the monitoring time has elapsed. (S26). The monitoring time is a processing time allowed for the filter coefficient updating process, and is, for example, 2 seconds in the example shown in FIG.

  When it is determined that the monitoring time has elapsed (Y in S26), the filter coefficient adjustment unit 13 proceeds from the resonance frequency monitoring process (S10) to the verification process (S12) (see FIG. 3). When it is determined that the monitoring time has not elapsed (N in S26), the filter coefficient adjustment unit 13 repeats the resonance frequency monitoring process (S10).

  As an alternative, the monitoring time elapse determination (S26) may be performed after the verification process (S12). In this case, the verification process (S12) is executed every time a new calculation result is obtained in the frequency tracking process (S24). The frequency tracking process (S24) and the verification process (S12) are repeated until the monitoring time elapses.

In many cases, in the actual update process, the center frequency ω ₀ converges to the resonance frequency by the frequency tracking process at the beginning of the monitoring time (for example, about 0.1 second). If it converges, the frequency tracking process is terminated. The vibration level is suppressed below the reference by the updated notch filter. For this reason, the frequency tracking process is often not activated in the latter half of the monitoring time.

  Next, frequency tracking processing according to an embodiment of the present invention will be described.

As shown in FIG. 1, the phase difference filter 16 receives the output signal u of the pre-filter 14 and outputs a phase difference filter output signal p. Here, the phase difference filter 16 refers to a filter that gives a phase shift according to a frequency component. The phase characteristic of the phase difference filter 16 is that the phase shift of the output signal p is changed from the first phase shift to the second as the frequency of the input signal u increases from the lower limit frequency to the upper limit frequency of the local frequency region including the center frequency ω ₀ . Change monotonically to phase shift. In the lower frequency region than the lower limit frequency, the phase shift is substantially equal to the first phase shift, and in the higher frequency region than the upper limit frequency, the phase shift is substantially equal to the second phase shift.

When the correction of the center frequency ω ₀ is performed using the center frequency correction amount Δω ₀ described in detail below, the phase characteristic of the phase difference filter 16 is substantially lower in the lower frequency region than the lower limit frequency of the local frequency region. It is preferable that a phase delay of 0 degree is given to (i.e., the phase is not substantially delayed), and a phase delay of 180 degrees is given in a frequency region higher than the upper limit frequency. The phase characteristics of the phase difference filter 16 are such that the phase delay of the output signal p increases from 0 degrees to 180 degrees as the frequency of the input signal u increases from the lower limit frequency to the upper limit frequency in the local frequency region. When the frequency component of the input signal u is equal to the center frequency ω ₀ , the phase delay of the output signal p is set to be equal to 90 degrees.

In a preferred embodiment, the phase difference filter 16 may be a peak filter having a frequency amplitude characteristic having a gain peak having a bandwidth in the local frequency region at the center frequency ω ₀ in addition to the above phase characteristic. This bandwidth (that is, peak width) is a frequency range in which the gain is attenuated from the peak by a predetermined amount (for example, 1 / √2). An example of the frequency amplitude characteristic and frequency phase characteristic of the peak filter is shown in FIG. As shown in frequency-phase characteristic of FIG. 6, the phase contrast filter 16, the center frequency omega ₀ takes a reference phase delay (e.g. 90 degrees) at the center frequency omega ₀ sufficiently small phase lag than the reference phase delay in the neighborhood of It has a phase characteristic that changes from (for example, 0 degrees) to a sufficiently large phase delay (for example, 180 degrees).

In another embodiment, the phase difference filter 16 may be an all-pass filter having the above phase characteristics. The all-pass filter has a frequency amplitude characteristic with a gain value of 1 in the entire frequency region. The phase difference filter 16 may be a phase shifter or FIR filter that causes a phase delay in proportion to the difference between the frequency ω of the input signal u and the center frequency ω ₀ .

The correction calculation unit 18 corrects the filter coefficients of the notch filter 12 and the phase difference filter 16 based on the phase difference filter input signal u and the phase difference filter output signal p. That is, the correction calculation unit 18 updates the filter coefficient at the time point n of the notch filter 12 and the phase difference filter 16 to the filter coefficient at the time point n + 1 based on the input signal u and the output signal p. For example, the correction calculation unit 18 updates the center frequency ω ₀ to the value ω ₀ [n] at the time point n with the value ω ₀ [n + 1] at the time point n + 1 by the following equation. That is, the correction calculation unit 18 obtains the updated value ω ₀ [n + 1] by adding the correction amount Δω ₀ to the current value ω ₀ [n] of the center frequency ω ₀ .

The second term on the right side of Equation 1 is the correction amount Δω ₀ of the center frequency ω ₀ . Here, u [n] and p [n] denote the input signal u and the output signal p of the phase difference filter at time n, respectively. Φ _p [n] is a correction coefficient at time n. Although this correction coefficient will be described later, it is a correction coefficient for reducing the influence of the amplitude α of the input signal u. The correction coefficient Φ _p [n] is, for example, a smoothed square of the phase difference filter output signal p [n]. Since the output signal p [n] is a signal including a vibration component, it may take 0 or a value close to 0. Therefore, in order to avoid that the correction coefficient Φ _p [n] is 0 or a value close to 0 and the center frequency correction amount Δω ₀ is excessive, it is preferable to perform a smoothing process. The smoothing process may be performed by, for example, a low-pass filter. μ is a correction gain for adjusting the correction amount Δω.

  The correction coefficient may be obtained by smoothing the square of the phase difference filter input signal u. Alternatively, the correction coefficient may be the square root of the square of the product pu of the input signal u and the output signal p. In this case, the square root of the square of the product pu may or may not be smoothed. When the smoothing process is performed, the square root of the square of the product pu may be smoothed, or the square of the product pu may be smoothed to obtain the square root. Each of the square of the output signal p and the square of the input signal u may be used. May be the square root of the product of the smoothed signals, or the product of the smoothed absolute values of the output signal p and the input signal u.

The correction calculation unit 18 may increase the update frequency of the filter coefficient of the phase difference filter 16 more than the update frequency of the filter coefficient of the notch filter 12. For example, the correction calculation unit 18 may sequentially update the filter coefficient of the phase difference filter 16 at each control cycle, and may update the filter coefficient of the notch filter 12 at a low frequency (for example, every several control cycles). . Alternatively, the correction calculation unit 18 may correct the filter coefficient of the notch filter 12 after confirming that the center frequency ω ₀ matches the natural frequency to be controlled. In this case, the notch filter 12 may determine whether or not the center frequency ω ₀ matches the natural frequency of the controlled object by observing the control output from the controlled object.

Specific examples of the notch filter 12 and the phase difference filter 16 will be described. A specific example of the phase difference filter 16 is a peak filter. FIG. 5 is a diagram illustrating an example of frequency characteristics of the notch filter. FIG. 6 is a diagram illustrating an example of frequency characteristics of the peak filter. If the notch filter 12 and peak filter is a digital filter, the transfer function G _N and the transfer function G _P of the peak filter of the notch filter 12 is represented by the respective formulas 2 and Formula 3.

The filter coefficient of the notch filter 12 is expressed by Expression 4, and the filter coefficient of the peak filter is expressed by Expression 5. Here, ω ₀ is the center frequency of the notch filter 12. ζ ₁ and ζ ₂ are parameters for determining a gain peak and a notch width at the center frequency ω _0, respectively. Ts is a sampling time. ζ ₃ is a parameter for determining the peak width of the peak filter.

In the case of this specific example, the correction calculation unit 18 first obtains an update value ω ₀ [n + 1] of the center frequency using Equation 1, and updates each filter coefficient of Equation 4 and Equation 5 using this update value. It should be noted that the coefficient l _p expressed in Equation 5 may be fixed at the initial value and not updated, or may be updated at an update frequency lower than the update frequency of the center frequency. When the coefficient l _p is not updated, the peak width of the peak filter changes due to the change of the center frequency ω ₀ . By reducing (or not performing) the update frequency of the coefficient l _p , the calculation amount in the correction calculation unit 18 can be reduced.

Another example of the notch filter 12 and the peak filter will be described. Notch filter 12 and peak filter is a digital filter, and when the gain at the center frequency omega ₀ is -∞dB, the transfer function G _N and the transfer function G _P of the peak filter notch filter 12 and a respective formulas 6 It is represented by Formula 7. Equation 7 is the same as Equation 3. Each filter coefficient is expressed by Equation 8.

Also in this example, the correction calculation unit 18 first obtains an update value ω ₀ [n + 1] of the center frequency using Equation 1, and updates each filter coefficient of Equation 8 using this update value. Note that the coefficients l _N and l _p expressed in Expression 8 may be fixed at their initial values and not updated, or may be updated at an update frequency lower than the update frequency of the center frequency. Good. When the coefficients l _N and l _p are not updated, the notch width of the notch filter and the peak width of the peak filter change due to the change of the center frequency ω ₀ . By reducing (or not performing) the update frequency of the coefficients l _N and l _p , the calculation amount in the correction calculation unit 18 can be considerably reduced.

The coefficient l _N, in the case of sequential updating the same frequency as the center frequency omega ₀ a l _p, the coefficients l _N corresponding to the center frequency omega _{0 (or} coefficient _k), calculated in advance a table of l _p By preparing, the amount of calculation in the correction calculation unit 18 can be reduced. The correction calculation unit 18 can obtain the coefficients l _N and l _p corresponding to the updated value of the center frequency (or coefficient k) by referring to the table stored in the storage unit (not shown).

FIG. 7 is a diagram showing the relationship between the center frequency ω ₀ and the coefficient k. Here, the sampling time Ts is 4 ms. As shown, the coefficient k decreases monotonously as the center frequency ω ₀ increases. Therefore, instead of updating the center frequency ω ₀ using Equation 1, the correction calculation unit 18 may directly update the coefficient k using the following equation. Expression 9 is the same as Expression 1, but the correction gain is replaced with a correction gain μ _k for adjusting the coefficient k.

  Therefore, the correction calculation unit 18 directly corrects the coefficient k based on the phase difference filter input signal u and the phase difference filter output signal p. That is, the correction calculation unit 18 updates the coefficient k [n] at the time point n to the coefficient k [n + 1] at the time point n + 1 based on the input signal u and the output signal p.

Next, the principle of correcting the center frequency ω ₀ in one embodiment of the present invention will be described. For simplicity, it is assumed that the input signal u to the phase difference filter 16 is a sine wave having a single frequency component having an amplitude α and a frequency ω. At this time, the input signal u and the output signal p of the phase difference filter 16 are expressed by Expression 10. Here, the amplitude gain and the phase shift of the phase difference filter 16 are expressed as | _GP (jω) | and φ _p (ω), respectively.

In one embodiment, the center frequency correction amount Δω ₀ is determined to depend on the product pu of the input signal u and the output signal p of the phase difference filter 16. The average value E [pu] of the product pu is expressed by Equation 11.

As described above, the phase characteristic of the phase difference filter 16 indicates that the phase shift of the output signal p is first as the frequency of the input signal u increases from the lower limit frequency to the upper limit frequency in the local frequency region including the center frequency ω ₀ . The phase shift is monotonously changed from the phase shift to the second phase shift. At the center frequency ω ₀ , a reference phase shift is taken between the first phase shift and the second phase shift. In the example shown in FIG. 6, the phase contrast filter 16, the center frequency omega given reference phase delay (e.g. 90 degrees) at _0, the center frequency omega ₀ reference phase delay smaller phase lag than in the low frequency region near the And has a phase characteristic that gives a phase lag greater than the reference phase lag in the high frequency region near the center frequency ω ₀ .

Therefore, the center frequency omega ₀ in sign determining factor cos _{(φ p} (ω)) is zero, sign determining factor when the frequency omega is less than the center frequency omega ₀ of the input signal u is a positive value, the input signal u When the frequency ω is greater than the center frequency ω ₀ , the sign determination coefficient is a negative value. This can be summarized by Expression 12.

Therefore, it can be said that the average value E [pu] of the product pu has cos (φ _p (ω)) as a sign determination coefficient. The sign determination coefficient cos (φ _p (ω)) determines the sign of the average value of the center frequency correction amount Δω ₀ according to the phase shift φ _p (ω) of the output signal p of the phase difference filter 16. As can be seen from Equation 11, the portion of the average value E [pu] other than the sign determination coefficient cos (φ _p (ω)) is clearly a positive value, and the code constant portion where the code is constant regardless of the frequency component. It is. The average value E [pu] is represented by the product of the constant code portion and the code determination coefficient.

That is, the sign of the average value E [pu] of the product pu is determined by the magnitude relationship between the frequency ω of the input signal u to the phase difference filter 16 and the center frequency ω ₀ . If the frequency ω of the input signal u is smaller than the center frequency ω ₀ , the product pu has a positive value, and if the frequency ω of the input signal u is greater than the center frequency ω ₀ , the product pu has a negative value. Thus, as represented in Equation 13, by updating the center frequency omega ₀ using a recurrence formula whose center frequency correction amount a product pu, to the input frequency omega of the center frequency omega ₀ of the notch filter 12 It is possible to match.

When the input frequency ω is a natural frequency component to be controlled, the center frequency ω ₀ of the notch filter 12 can be matched with the natural frequency component. In this way, the center frequency ω ₀ of the notch filter 12 can be automatically adjusted to the natural frequency component to be controlled.

More preferably, the influence of the amplitude α of the input signal u can be reduced or eliminated by introducing a correction coefficient into the center frequency correction amount Δω ₀ . As can be seen from Equation 12, the product pu depends on the amplitude α of the input signal u. Formula 14 is a recurrence formula for updating the center frequency ω ₀ when the correction coefficient Φ [n] is introduced into the center frequency correction amount Δω ₀ .

Here, if the correction coefficient Φ [n] is rewritten as μ / Φ _p [n], Expression 14 corresponds to Expression 1. As an example, a case where Φ _p [n] is obtained by smoothing the square of the phase difference filter output signal p [n] as described above will be described. Smoothing is performed, for example, by processing the square of the output signal p [n] with a low-pass filter having a cutoff frequency ωcp. Then, the average value of Φ _p [n] is given by Equation 15.

Therefore, the average value E [Δω ₀ ] per correction operation of the center frequency correction amount corrected by the correction coefficient is given by Expression 16. As can be seen from Equation 16, the average value E [Δω ₀ ] is expressed in a format that does not depend on the amplitude α of the input signal u. Therefore, the influence of the amplitude α of the input signal u can be eliminated by introducing a correction coefficient into the center frequency correction amount Δω ₀ .

FIG. 8 is a diagram showing the principle of correcting the center frequency ω _{0 according} to one embodiment of the present invention as frequency characteristics. FIG. 8 is a Bode diagram created for the average value E [Δω ₀ ] shown in Equation 16 with a gain of 1 / | _GP (jω) | and a phase of φ _p (ω). The Bode diagram shown in FIG. 8 is an example when the phase difference filter 16 is a peak filter shown in FIG. The coefficient μ is set to μ = 1 for simplicity. As shown in FIG. 8, with respect to the amplitude characteristic, a notch corresponding to the gain peak of the peak filter appears. As for the phase characteristics, the phase characteristics corresponding to the phase characteristics of the peak filter are also shown.

FIG. 9 is a diagram showing an average value E [Δω ₀ ] of the center frequency correction amount when a peak filter is used as the phase difference filter 16. The average value E [Δω ₀ ] shown in FIG. 9 is the corrected correction amount shown in Expression 16. As shown in FIG. 9, the correction amount average value E [Δω ₀ ] is not only in the vicinity of the center frequency ω ₀ but also in a wide range of frequencies from the vicinity of zero to the vicinity of the Nyquist frequency ω _nyq (1/2 of the sampling frequency). In the region, it can be seen that there is a linear change with respect to the deviation between the center frequency ω ₀ and the input frequency ω. That is, in the band below the Nyquist frequency ω _nyq, the average value E [Δω ₀ ] of the center frequency correction amount is substantially proportional to the deviation between the center frequency ω ₀ and the input frequency ω.

Therefore, the correction amount Δω ₀ corresponding to the deviation between the center frequency ω ₀ and the input frequency ω can be obtained. That is, the correction amount Δω ₀ at the time of updating increases as the center frequency ω ₀ is farther from the frequency ω to be suppressed. Therefore, the center frequency ω ₀ can be brought close to the frequency ω of the input signal u with a small number of update processing iterations. Further, the correction amount Δω ₀ decreases as the center frequency ω ₀ approaches the frequency ω to be suppressed. Therefore, it is possible to prevent the center frequency omega ₀ varies vibrationally every update the center frequency omega ₀ in the vicinity of the frequency omega of the input signal u. The center frequency ω ₀ can be quickly matched with the frequency ω of the input signal u.

The filter coefficient adjustment unit 13 ends the frequency tracking process when the correction amount Δω ₀ becomes smaller than a certain threshold value. This threshold value is set to ensure that the deviation between the center frequency ω ₀ and the resonance frequency is sufficiently small, and can be set as appropriate empirically or experimentally.

FIG. 10 is a block diagram illustrating an example of a system configuration including the resonance suppression device 10 according to an embodiment of the present invention. The electric motor 20 drives the load 22. The electric motor 20 is, for example, an electric motor incorporated in a device whose control characteristics may be restricted by resonance of an industrial robot, an injection molding machine, a construction machine, a precision positioning stage, a precision machine tool, a galvano scanner, or the like. The detector 24 measures the output of the electric motor 20. The detector 24 is, for example, a speed detector that measures the detection speed ω ^* of the electric motor 20.

A speed command generator (not shown) of this system determines a speed command ω _dir . The speed control unit 26 generates a torque command signal to the motor 20 based on an error of the detected speed ω ^* with respect to the speed command ω _dir to the motor 20. The speed control unit 26 outputs a torque command τ ₁ so that the difference between the speed command ω _dir and the detected speed ω ^* of the electric motor 20 is zero and the detected speed ω ^* follows the speed command value ω _dir . For example, the speed control unit 26 outputs the result of proportional integration of the difference ω _dir −ω ^* between the speed command ω _dir and the detected speed ω ^* of the electric motor 20 as the torque command τ ₁ .

The notch filter 12 removes the frequency component of the center frequency ω ₀ from the torque command τ ₁ and outputs a new torque command τ ₂ . Since the center frequency ω ₀ matches the frequency component of the natural frequency ω _n of the system including the electric motor 20 and the load 22, the notch filter 12 torques the new torque command τ _{2 from} which the natural frequency component has been removed. Output to the control unit 28. The torque control unit 28 controls the electric motor 20 based on the output signal of the notch filter 12. The torque control unit 28 controls the supply current to the electric motor 20 so that the electric motor 20 outputs the torque τ ^* that matches the torque command τ ₂ . In this way, speed control of the electric motor 20 is performed.

As described with reference to FIG. 1, the filter coefficient adjustment unit 13 includes a pre-filter 14, a phase difference filter 16, and a correction calculation unit 18. The filter coefficient adjustment unit 13 uses the detection speed ω ^* as the reference signal r. The filter coefficient adjustment unit 13 corrects the coefficients of the notch filter 12 and the phase difference filter 16 so that the center frequency ω ₀ of the notch filter 12 matches the vibration frequency included in the speed ω ^* .

If the natural frequency ω _n of the system is included in the torque τ ^* output by the electric motor 20, the natural vibration of the system is excited by the driving of the electric motor and resonance occurs. The notch filter 12 is inserted between the speed control unit 26 and the torque control unit 28, the component of the natural frequency ω _n is removed from the output τ ₁ of the speed control unit 26, and the input torque command τ to the torque control unit 28 is removed. Resonance can be suppressed by generating ₂ . If the center frequency ω ₀ of the notch filter 12 deviates from the natural frequency ω _{n of the} system, resonance occurs and a component of the natural frequency ω _n of the system is included in the detection signal ω ^* . In this case, since the filter coefficient adjustment unit 13 uses the detection signal ω ^* as the reference signal r, it can automatically adjust the center frequency ω ₀ to coincide with ω _n .

  In this embodiment, the notch filter 12 is provided between the speed control unit 26 and the torque control unit 28, and the torque command from the speed control unit 26 is described as an input to the notch filter 12. However, in other embodiments, a speed command, a detected speed, or an error signal may be used as an input to the notch filter. That is, the notch filter may receive any of an input signal to the speed control unit, a signal for generating the input signal, and a torque command signal from the speed control unit. For example, in the configuration shown in FIG. 10, the notch filter 12 may be provided after the detector 24, that is, between the detector 24 and the speed control unit 26. Alternatively, the notch filter 12 may be provided after the speed command generation unit, that is, before the speed control unit 26. Even in this case, vibration can be similarly suppressed.

  The resonance suppression apparatus 10 according to the present embodiment determines whether or not the fluctuation of the resonance frequency is at an allowable level, and outputs a warning when it is determined that the fluctuation has deviated from the allowable level. Thereby, it is possible to notify the user that an abnormality (or a suspicion thereof) has occurred in the application target of the resonance suppression device 10. It is possible to provide the user with an opportunity to consider performing an early maintenance inspection of the machine. It is possible to detect and deal with abnormalities such as mechanical damage and loose screws early.

  On the other hand, the resonance suppression apparatus 10 corrects the notch filter according to the latest calculation result by the frequency tracking process when it is determined that the fluctuation of the resonance frequency is at an allowable level. Thus, compensation for changes in mechanical properties over time, which is the original usefulness of the adaptive notch filter, is also provided. In this way, it is possible to achieve both maintenance of control performance over time and informing the user of a suspected abnormality.

  Further, since the resonance suppression device 10 is an adaptive notch filter, the resonance frequency of the control system can be automatically acquired. An allowable level of resonance frequency fluctuation is set in conjunction with the acquired resonance frequency. Therefore, there is an advantage that a new work load is hardly required for setting the allowable level. It is not necessary to provide a new dedicated sensor for setting the allowable level.

  The resonance suppression apparatus 10 switches and executes update processing of the plurality of notch filters 12 one by one. Such individual execution can avoid the concentration of calculation load and reduce the calculation amount.

  In the above, this invention was demonstrated based on the Example. It will be understood by those skilled in the art that the present invention is not limited to the above-described embodiment, and various design changes are possible, various modifications are possible, and such modifications are within the scope of the present invention. By the way.

  DESCRIPTION OF SYMBOLS 10 Resonance suppression apparatus, 12 Notch filter, 13 Filter coefficient adjustment part, 14 Pre filter, 16 Phase difference filter, 17 Center frequency calculating part, 18 Correction calculating part, 20 Electric motor, 22 Load, 24 Detector, 26 Speed control part, 28 Torque control unit.

Claims (4)

A notch filter provided in the control system to suppress resonance of the control system;
A filter coefficient adjustment unit for updating a filter coefficient of the notch filter so as to match a center frequency of the notch filter with a resonance frequency of the control system,
The update process of the filter coefficient is performed by determining whether or not the variation of the resonance frequency based on the existing center frequency of the notch filter is at an allowable level, and determining that the variation has deviated from the allowable level. A resonance suppression device, comprising: outputting a warning when it is performed. The resonance suppression device includes a plurality of notch filters,
The resonance suppression apparatus according to claim 1, wherein the filter coefficient adjustment unit sequentially executes filter coefficient update processing of the plurality of notch filters.   The filter coefficient adjustment unit passes a resonance frequency component assigned to a notch filter in which the filter coefficient update process is executed among the plurality of notch filters, and excludes a resonance frequency component other than the resonance frequency component. The resonance suppression device according to claim 2, further comprising a pre-filter in which a pass band is set. A resonance suppression method for suppressing resonance of a control system using an adaptive notch filter,
Updating a filter coefficient of the notch filter so that a center frequency of the notch filter matches a resonance frequency of the control system,
The updating is performed by determining whether or not the variation of the resonance frequency based on the existing center frequency of the notch filter is at an allowable level, and determining that the variation has deviated from the allowable level. Outputting a warning in some cases, and a method for suppressing resonance.

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