JP2011094695A - Method and apparatus for controlling active mass damper - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To improve a vibration damping effect while preventing unstable control by minimizing an influence of the compliance of a mounting part for an AMD (Active Mass Damper) 3 at the feedback control of diminishing the vibration of an object such as an apparatus D mounted with the AMD 3. <P>SOLUTION: A basic control part 8a of a controller 8 outputs a control signal to a linear motor 5 according to the vibration state of an apparatus D detected by a vibration sensor 7. This generates a control force diminishing the vibration of the apparatus D as a reaction to drive a plumb 4. A compensation filter (compensation control part 8b) is interposed in the feedback loop of the control for canceling an influence of resonance generated by the compliance of the mounting part of the AMD 3. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to the control of an active mass damper for adding a control force that is attached to an object and attenuates its vibration.

  Conventionally, as described in Patent Document 1, for example, it is known to attach an active mass damper (hereinafter abbreviated as AMD) to a region where vibration tends to be locally large in an object. In AMD, a mass member is supported on an object via a spring element and a damping element, and a reaction force when the mass member is driven by an actuator is added to the object as a control force that attenuates the vibration.

  In the above literature, when an actuator is controlled by feeding back a signal from a sensor that detects a vibration state of an object, an additional mass member (mass member) is supported by giving negative rigidity and negative damping. It is described that the spring characteristic of the spring element to be canceled can be canceled and the damping force of the damper element can be brought close to 0, thereby realizing an ideal skyhook damper.

  On the other hand, when the applicant of the present application feeds back a sensor signal to control AMD in the same manner as in the above document, a digital filter is inserted in the feedback loop, and the weight (mass member) of the AMD and the leaf spring are inserted. Proposed to eliminate the influence of resonance of the additional vibration system, and has already filed a patent application (see Patent Document 2).

JP 2007-285430 A JP 2008-303997 A

  However, as described above, AMD is often retrofitted to a site where vibration is likely to increase locally on the object, and if the mounting rigidity is insufficient, a sufficient damping effect cannot be obtained. That is, if AMD is attached later to a device or the like, a sufficient fastening space may not be secured in the first place, and a hole for passing a bolt may not necessarily be formed at a desired position.

  If sufficient rigidity cannot be obtained at the mounting portion of the AMD, not only the weight of the AMD but also the entire AMD including the spring element and case supporting the AMD or the integral vibration sensor becomes a movable mass. Since the device or the like is vibrated, and the AMD control is unstable due to the influence, the feedback gain cannot be set sufficiently large.

  Such knowledge has been found by the inventors of the present invention in the process of earnestly researching to enhance the vibration damping effect of AMD. That is, in the open loop transfer function of the AMD control as described above, an anti-resonance appears, for example, near 100 Hz as shown in FIG. 4, and the gain increases toward the high frequency side with this as a boundary. On the other hand, in the figure, there is a phase intersection near 300 Hz, and since the gain margin here is small, the feedback gain cannot be increased any more.

  In other words, in the example shown in the figure, the feedback gain cannot be set sufficiently large due to the influence of anti-resonance near 100 Hz. As a result of repeated experiments and considerations to find the cause of this anti-resonance, the inventors. As described above, it was estimated that the anti-resonance was caused by the fact that the entire AMD had a movable mass, and the device was vibrated by compliance of the site where it was attached to the device.

  Based on such new knowledge, the object of the present invention is to prevent AMD from being adversely affected by the compliance of the mounting portion even when the mounting rigidity of the AMD device or the like (object) is insufficient. The purpose is to increase the damping effect while preventing stabilization.

  In order to achieve the above object, in the present invention, the influence of compliance in the attachment portion of the AMD to the object is excluded from the feedback loop that controls the AMD based on the vibration state of the object.

  Specifically, the invention of claim 1 is for detecting a vibration state of an object when an AMD (active mass damper) is attached to the object and control is performed so as to add a control force that attenuates the vibration. The sensor is fed back, the signal from the sensor is fed back, the AMD is controlled by the controller based on the vibration state of the object, and the object of AMD is detected among the vibration states of the object detected by the sensor. It is characterized in that the control of AMD by the controller is corrected so as to ignore the influence of compliance in the attachment portion to the object.

  According to the above method, first, the vibration state of the object is detected by the sensor, and the reaction force that drives the mass member of the AMD is controlled by feeding back the signal from the sensor and controlling the AMD by the controller. It is added to the object as a control force that reduces the vibration.

  At this time, if the compliance of the mounting portion of the AMD is large, the AMD as a whole becomes a movable mass and vibrates the object, which may cause the control of the AMD to become unstable. In view of this, it is possible to prevent control anxiety by ignoring the adverse effects caused by the compliance of the mounting portion among the vibration states of the object detected by the sensor, that is, the influence caused by the vibration of the entire AMD as described above. it can.

  Specifically, in order to cancel the resonance characteristic due to compliance as described above, a filter whose transfer function G (s) is represented by the following expression (A) may be inserted in the feedback loop (claim 2). ).

In the above formula (A), m ₁ is the mass of the object, k ₁ and c ₁ are the spring constant and damping coefficient of the object, respectively, and k ₂ and c ₂ are the attachment parts of the active mass damper, respectively. Is a spring constant and a damping coefficient.

  In other words, the present invention provides a control device for adding a control force for reducing vibration of an object by an active mass damper, the sensor for detecting the vibration state of the object, and the sensor. The control means for controlling the active mass damper according to the vibration state of the object, and the mounting portion of the active mass damper to the object among the vibration states of the object detected by the sensor And correction means for correcting the control by the control means so as to ignore the influence of compliance in (Claim 3).

  If this control device is used, the control method according to the invention of claim 1 can be easily executed, and the effects thereof can be obtained. The correcting means can be realized by the filter according to claim 2 (claim 4).

  As described above, according to the AMD control according to the present invention, the above-described transfer function formula (in the feedback loop that generates the control force that operates the AMD according to the vibration state of the object and attenuates the vibration) By inserting a filter represented by A), it is possible to eliminate the influence of compliance at the attachment portion with the object. As a result, the feedback gain can be set sufficiently large without destabilizing the AMD control, and the vibration damping performance is improved.

It is a schematic diagram which shows the structure which applied AMD which concerns on this invention to the apparatus on a vibration isolator. It is a perspective view which shows an example of the internal structure of AMD. It is the simplified block diagram of AMD control. It is the graph which measured the open loop transfer function of AMD control. It is a model figure which paid its attention to the compliance of the attachment part to the apparatus of AMD. It is a graph of a compliance simulation (a) and an actual measurement result (b). FIG. 6 is a diagram corresponding to FIG. 6A when the compensation filter of the embodiment is used. FIG. 5 is a diagram corresponding to FIG. 4 when the compensation filter of the embodiment is used. It is a graph which shows the fall of the vibration transmissibility in embodiment. It is a figure which shows an example of the analog circuit which implement | achieves a compensation filter.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In addition, the following description of preferable embodiment is only an illustration essentially, and is not intending restrict | limiting this invention, its application thing, or its use.

  FIG. 1 schematically shows an embodiment in which an active mass damper according to the present invention is applied to a device D on a vibration isolation table. In the example shown in the figure, the device D is, for example, an electron microscope, and includes a housing d1 in which a stage or the like on which a sample is placed is accommodated, and a mirror tower d2 extending upward from the ceiling. In the example shown in the figure, the device D is placed on a surface plate 1 of a so-called passive vibration isolation table, and although only two are shown in the figure, they are supported on the floor by a plurality of vibration isolators 2, 2,. . The vibration isolator 2 preferably uses an air spring, but may be an anti-vibration rubber or a coil spring.

  In the illustrated example, an active mass damper 3 (hereinafter referred to as AMD) is attached to the top of the mirror tower d2 of the device D. This is to cope with the problem that the horizontal vibration tends to be structurally large at the top of the mirror tower d2 that is long in the vertical direction as shown in the figure, thereby causing the position of the optical system to shift slightly. Thus, if AMD3 is attached to a site where vibration is likely to increase locally, the effect of reducing vibration is high.

-Example structure of AMD-
As an example, AMD3 drives the weight 4 accommodated in it by the linear motor 5, and the reaction force of the driving force is added with respect to the apparatus D as control force which attenuates the vibration. In the illustrated example, the weight 4 and the housing of the linear motor 5 are integrated, and the integrated mass member is supported by the leaf springs 6 and 6 at two locations separated in the axis X direction. Further, in the example shown in the figure, the vibration sensor 7 is also integrated with the AMD 3, and a signal indicating the vibration state of the device D detected by this, that is, acceleration, speed, or displacement is output to the controller 8.

  Referring to FIG. 2 in more detail, the AMD3 case 30 has a rectangular cylindrical shape as shown by a virtual line in the figure, and vibrates on one end side (the left front side in the figure) in the direction of the cylindrical axis (axis X). A sensor 7 is provided. The weight 4 has a cylindrical shape as a whole, and has a concave section 4 a having a circular cross section that opens so as to surround an end portion of the adjacent vibration sensor 7. A fastening ring 41 is screwed to the tip of the peripheral wall surrounding the recess 4a so as to sandwich the inner peripheral portion of the leaf spring 6.

  On the other hand, a yoke that also serves as a housing for the linear motor 5 is attached to the opposite side of the weight 4. The yoke has a bottomed cylindrical shape that opens to the right rear side in the figure, and is combined in a non-contact state so as to surround a bobbin (not shown), and electromagnetic force acts between them. A fastening ring 51 is screwed to the front end (right rear end in the figure) of the cylindrical wall portion of the yoke, and the inner peripheral portion of the leaf spring 6 is sandwiched in the same manner as the fastening ring 41 described above.

  That is, in the illustrated AMD, the integrated weight 4 and the yoke of the linear motor 5 are supported on the peripheral wall of the case 30 by the two leaf springs 6 and 6, and can move in the cylinder axis direction of the case 30. (The two fastening rings 41 and 51 are also included precisely). On the other hand, the bobbin of the linear motor 5 is fixed to the other end wall of the case 30, and the reaction force for driving the mass member, that is, the weight 4, the yoke, and the like is transmitted through the case 30 to the lens tower d 2 of the device D. And becomes a control force for reducing the vibration of the mirror tower d2.

-Control of AMD-
Next, control of AMD3 by the controller 8 will be described. The controller 8 of this embodiment basically feeds back a signal from the vibration sensor 7 to control the linear motor 5 of the AMD 3 and thereby obtains a control force as a reaction force for driving the weight 4 as described above. The basic control unit 8a (control means) for performing such basic control is provided in the form of a software program (see FIG. 1).

  As shown in FIG. 3 as an example, the basic control unit 8a feeds back a signal from the vibration sensor 7, that is, a signal representing the vibration state of the object, and performs a filtering process for removing noise as necessary. After performing various arithmetic processes, the feedback gain is multiplied and inverted, and then input to the plant as a control signal. The plant includes the characteristics of the linear motor 5 and the vibration sensor 7 in addition to the device D.

  Thus, by feeding back the signal from the vibration sensor 7 and controlling the linear motor 5, an appropriate control force corresponding to the actual vibration state can be added to the device D, and the resonance magnification of the plant Decreases. FIG. 4 shows a graph of the results of actually measuring the open-loop transfer function of AMD control, that is, the phase curve at the upper stage and the gain curve at the lower stage, and the peak of wrinkles appearing near 20 Hz of the gain curve due to the resonance of device D It can be seen that is suppressed.

  Further, there is a notch (antiresonance point) in the vicinity of 100 Hz of the gain curve, and the gain increases toward the high frequency side with this as a boundary. On the other hand, looking at the phase curve, the phase delay is larger on the higher frequency side than 100 Hz, and in the example shown in the figure, a phase intersection appears in the vicinity of 300 Hz. This is an effect of an anti-aliasing filter for performing digital signal processing.

  In the example shown in the figure, the gain margin at the phase intersection is only about 5 dB, and the feedback gain cannot be increased beyond this. However, the feedback gain of AMD control at the time of actual measurement is about 10, which is sufficient. Absent. That is, in the example shown in the figure, the gain of the feedback control by the basic control unit 8a of the controller 8 cannot be set sufficiently large due to the anti-resonance effect near 100 Hz, and the damping effect becomes insufficient. ing.

  Therefore, in this embodiment, the correction control unit 8b for correcting the control of the AMD 3 by the basic control unit 8a of the controller 8 so as to eliminate the anti-resonance near 100 Hz from the open loop transfer function (correction means: see FIG. 1). Is provided. Specifically, as shown in FIG. 3 described above, the correction control unit 8b is obtained by inserting a digital filter (compensation filter) that cancels the influence of anti-resonance in the feedback loop of AMD control.

-Compensation filter-
Specifically, first, the inventors of the present invention assumed a vibration system model as shown in FIG. 5 in order to investigate the cause of anti-resonance near 100 Hz in the open loop transfer function. In the illustrated model, attention is paid to the compliance of a bracket or the like (attachment portion) for attaching the AMD 30 case 30 to the top of the device D. Note that the mounting portion is not limited to a bracket or the like, and the case 30 may be fastened directly to the top of the device D, and when fastening is difficult, it may be possible to bond the case 30.

In the figure, m ₁ is the mass of the device D, the surface plate 1 or the like that is the object of vibration control, and the spring constant and damping coefficient of the vibration isolator 2 that supports it are k ₁ and c ₁ , respectively. The spring constant and the damping coefficient can be determined in consideration of the elastic deformation of the device D and taking into account its rigidity and internal loss. In the figure, m ₂ represents the mass of the entire AMD 3 including not only the weight 4 but also the linear motor 5, the leaf spring 6, and the vibration sensor 7. The influence of compliance at the mounting portion of the AMD 3 is expressed by the spring constant k ₂ and it represents an attenuation coefficient c _2.

Further, in the figure, f ₂ is an inertial force generated as a reaction force when the weight 4 is driven by the linear motor 5 of the AMD 3, and the displacements x ₀ , x ₁ , x ₂ are the floor (foundation) and the equipment, respectively. It represents the displacement of D and AMD3. In the figure, for the sake of convenience, the displacements x ₀ , x ₁ , and x ₂ are shown in the vertical direction.

The equations of motion of the two-degree-of-freedom system as shown in FIG. 5 are as shown in the following equations (1) and (2). In both formulas, the black dot “·” is added to the displacement x, as is well known, that is, it represents the differentiation with respect to time, that is, the speed and acceleration. It is replaced and described. Then, when the Laplace operator s is introduced into each of the equations of motion (1) and (2) and the variable X ₁ is eliminated and rearranged, the following equation (3) is obtained.

Therefore, until the transfer function of the compliance X ₂ / F ₂ of the attachment portion of the AMD 3 to the device D, that is, the inertia force f ₂ generated by the operation of the AMD 3 vibrates the AMD 3 itself and is detected by the vibration sensor 7. Is expressed as the following equation (4).

  The result of simulating the compliance frequency response according to the equation (4) is as shown in FIG. 6 (a), which is in good agreement with the actual measurement result shown in FIG. 6 (b). In both cases, a resonance point appears in the vicinity of 20 Hz, which coincides with the natural frequency of the main vibration system including the device D and the vibration isolation table. Further, an anti-resonance point appears in the vicinity of 100 Hz, and it is assumed that this is the cause of the anti-resonance in the vicinity of 100 Hz of the above-described open loop transfer function.

Here, the anti-resonance frequency f _n in the frequency response of the compliance is obtained as the following equation (5) as the characteristic root of the numerator equation of the equation (4), but the rigidity of the mounting portion of the AMD 3 is since much higher than the elastic member 2 (k1«k2), anti-resonance frequency f _n is will be almost determined by the stiffness of the mass m ₁ and the attachment portion of the device D (the spring constant k _2), the mass of AMD3 It does not depend on m _2.

  In other words, if the anti-resonance appears in the open-loop transfer function of the feedback control of the AMD3 due to the influence of the compliance of the mounting portion of the AMD3 as described above, the mass of the AMD3 also changes at the frequency of this anti-resonance. But it should not change.

  Therefore, the present inventors removed the weight 4, linear motor 5, and vibration sensor 7 of the AMD 3, and again measured the open loop transfer function in a state where the weight was greatly reduced, and the anti-resonance frequency (100 Hz) was measured. It was confirmed that there was no change in the vicinity. Thereby, it can be estimated that the compliance of the attachment part of AMD3 is the cause of the anti-resonance in an open loop transfer function as said assumption.

Based on such novel knowledge, the inventors expressed the following formula (6) that makes the numerator of compliance X ₂ / F ₂ represented by the formula (4) 1: We decided to use a digital filter. In this case, it is necessary to compensate for the offset of the low-frequency, considering that the denominator is omega _n ² When s = 0 in the denominator of equation (6), multiplied by the omega _n ² in the molecule, the filter The transfer function anti_comp is expressed by the following equation (7).

  In this embodiment, as described above, the basic control unit 8a for performing feedback control of AMD3 is realized by a software program. Similarly, a digital filter (compensation filter) serving as the correction control unit 8b is also implemented by software software. It can be realized by a program. Various methods for deriving an equivalent digital filter program from the transfer function equation of the equation (7) are known (for example, Z conversion).

  In short, in this embodiment, in this embodiment, the controller 8 is provided with a compensation filter represented by the equation (7), and is inserted into an AMD control feedback loop that feeds back a signal from the vibration sensor 7, to the device D of the AMD 3. The effect of anti-resonance due to the compliance of the mounting part is canceled. In other words, the influence of the compliance is ignored in the feedback control of AMD3.

  FIG. 7 is a simulation result of compliance when the compensation filter is used. When compared with the case where the compensation filter is not used (indicated by a dotted line), a notch (antiresonance) near 100 Hz is eliminated by the compensation filter. It can be seen that the gain also decreases on the high frequency side. Similarly, in the open-loop transfer function shown in FIG. 8, the anti-resonance near 100 Hz disappears, the gain gradually decreases on the high frequency side, and it can be seen that there is a sufficient gain margin at the phase intersection.

  That is, even when the compensation filter is used as shown in FIG. 8, the influence of the anti-aliasing filter remains, so that the phase delay increases at 100 Hz or more in the phase curve. In this embodiment, a fourth-order Butterworth filter is used as an example, and a phase delay of 360 ° occurs in the vicinity of 300 Hz, which is the cut-off frequency. Therefore, a phase intersection appears in the vicinity of 130 Hz. However, in the example shown in the figure, the gain margin at the phase intersection is about 15 dB, and it can be seen that the feedback gain can still be increased.

  Therefore, according to this embodiment, first, the vibration state of the device D placed on the surface plate 1 is detected by the vibration sensor 7 of the AMD 3, and the basic control unit 8 a of the controller 8 that receives the signal from the vibration sensor 7. In, a control signal to the linear motor 5 is calculated. Then, the linear motor 5 that operates in response to the control signal drives the weight 4, and the reaction force of this driving force is added to the device D as a control force that attenuates the vibration.

  At this time, of the vibration state of the device D detected by the vibration sensor 7 as described above by the compensation filter (correction control unit 8b) inserted in the feedback loop, the attachment portion between the device D and AMD3. Since the influence of the resonance due to the compliance is canceled, the AMD control is not destabilized by the influence of the resonance, and the damping performance can be improved by sufficiently increasing the feedback gain.

  FIG. 9 is an actual measurement result of the vibration transmissibility shown by comparing the damping effect by the AMD control of this embodiment with the case without the compensation filter. As shown by the dotted line graph in FIG. It can be seen that even if no compensation filter is provided, the resonance magnification of the device D is reduced as compared with a so-called passive filter (virtual line graph).

  However, when the compensation filter is not used, as described above, the feedback gain is restricted to about 10, for example, and cannot be increased beyond that. On the other hand, if the compensation filter is used, the feedback gain can be increased to about 30 in the example of the figure, and the vibration transmissibility at this time is as shown by the solid line graph in the figure, and there is no compensation filter ( It is much lower than the dotted line graph).

  As described above, the configurations of the AMD 3 and the vibration isolation table of the embodiment described above are merely examples, and these do not limit the configuration of the present invention. For example, it is not necessary to integrate the vibration sensor 7 with the AMD 3. Further, an actuator such as a piezoelectric element can be used instead of the linear motor 5.

  Further, the correction control unit 8b of the controller 8 can be configured by an analog circuit instead of a software program. That is, the compensation filter of the equation (7) is a general second-order low-pass filter, which is realized by an analog circuit as shown in FIG. The transfer function of this low-pass filter is expressed as the following equation (8).

In equation (8), ω ₀ , ω ₀ ² , and ω ₀ / Q are each expressed as the following equation (9).

Furthermore, in the above-described embodiment, the example in which the device D is mounted on the vibration isolation table is described. However, the device D is not only installed using the vibration isolation table, but also installed by a simpler method. The present invention can also be applied to the case where the AMD 3 is attached to another device. In this case, both the spring constant k ₁ and the damping coefficient c ₂ of the object correspond to the rigidity and damping characteristics of the device D itself.

  The basic feedback control of AMD3 is not limited to the so-called classical control method exemplified in the above embodiment, and may be based on a modern control method such as LQ control or H∞ control.

  As described above, according to the control of the active mass damper according to the present invention, the control gain can be sufficiently increased without causing instability, and the vibration damping effect can be enhanced. It is suitable for the target.

D Equipment (object)
3 Active Mass Damper (AMD)
7 Acceleration sensor (sensor)
8 Controller 8a Basic control unit (control means)
8b Correction control unit (filter, correction means)

Claims (4)

An active mass damper is attached to an object, and control is performed so as to add a control force that attenuates the vibration,
Preparing a sensor for detecting a vibration state of the object;
The signal from the sensor is fed back, and the active mass damper is controlled by the controller based on the vibration state of the object,
The control of the active mass damper by the controller is corrected so as to ignore the influence of the compliance in the attachment portion of the active mass damper to the target object among the vibration states of the target object detected by the sensor, Control method of active mass damper. A filter whose transfer function G (s) is represented by the following equation (A) is inserted in a feedback loop so as to cancel the resonance characteristic due to the compliance:

Where m ₁ is the mass of the object, k ₁ and c ₁ are the spring constant and damping coefficient of the object, respectively, and k ₂ and c ₂ are the spring constant and damping coefficient at the mounting portion of the active mass damper, respectively. The method of controlling an active mass damper according to claim 1. A control device for adding a control force for reducing vibration of an object by an active mass damper attached to the object,
A sensor for detecting a vibration state of the object;
Control means for feeding back a signal from the sensor and controlling an active mass damper according to a vibration state of the object;
Correction means for correcting the control of the active mass damper by the control means so as to ignore the influence of compliance in the attachment portion of the active mass damper to the object among the vibration states of the object detected by the sensor; ,
An active mass damper control device comprising: The correction means is a filter inserted in a feedback loop to cancel the resonance characteristic due to the compliance, and its transfer function G (s) is represented by the following equation (A).

Where m ₁ is the mass of the object, k ₁ and c ₁ are the spring constant and damping coefficient of the object, respectively, and k ₂ and c ₂ are the spring constant and damping coefficient at the mounting portion of the active mass damper, respectively. The control apparatus for an active mass damper according to claim 3.

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