Relative Vibration Suppression in a Positioning Machine

IEEJ Journal of Industry ApplicationsVol.7 No.1 pp.15–21 DOI: 10.1541/ieejjia.7.15

Paper

Relative Vibration Suppression in a Positioning MachineUsing Acceleration Feedback Control

Takashi Kai∗a)Member, Hiroyuki Sekiguchi∗ Member

Hidetoshi Ikeda∗ Member

(Manuscript received Nov. 8, 2016, revised Aug. 8, 2017)

A method to suppress the residual vibration of relative displacement is proposed. In factory automation, the posi-tioning machines are precisely controlled by servo motors; however, their reaction force will unavoidably vibrate themachine stand on which the motors are mounted. A common problem is that the resulting residual vibrations causedisturbances that prevent high speed and accurate positioning, due to the inherent flexible structures in the machinestand, thereby unexpectedly extending the settling time in some industrial applications. This paper presents machinestand acceleration feedback (MSAFB) control, which detects the acceleration signal of the machine stand using an ac-celerometer to improve the robustness against disturbances from the environment and uncertainty in the system. Thisfeedback strategy is superior to input shaping strategy, which is based on feedforward control. Simulations and ex-periments show the effectiveness of the proposed MSAFB controller, which was designed specifically for mechanicalplants with rocking mode vibration.

Keywords: servo motor, acceleration feedback, vibration control, rocking mode, machine stand, disturbance localization

1. Introduction

Servo motors are widely used in machines that must per-form accurate and repeated movements, such as semicon-ductor manufacturing equipment, chip shooters, industrialrobots, and food processing machines (1). We now standpoised at the next generation of machine development, sohigh demand exists for positioning to speed-up and to im-prove the positioning accuracy in order to reduce the cycletime of the manufacturing process, which is called takt time.The settling time of the machines has to be shortened duringthe positioning without degrading the accuracy.

In general system configurations, servo amplifiers provideelectrical current to the servo motors, which must be con-trolled to follow positioning commands. Command profilesare programmed by programmable logic controllers (PLCs),motion controllers, or pulse drivers. Installed rotary encodersor linear scales detect angular or linear positions to constituteposition and velocity feedback loops to improve disturbancesuppression ability.

In general machine configurations, a mover of the mo-tor is connected to positioning objects, while a stator isrigidly fixed on a machine stand that is used as a base plat-form. However, when the action force is generated betweenthe mover and the stator, its reaction force causes vibra-tions of the machine stand at low frequency, e.g., a rockingmode vibration (2) (3). This phenomenon mostly stems from the

a) Correspondence to: Takashi Kai. E-mail: [email protected]∗ Mitsubishi Electric Corporation

8-1-1, Tsukaguchihonmachi, Amagasaki, Hyogo 661-8661,Japan

inherent flexibility and low stiffness of the columns or level-ing bolts that support the machine in keeping it standing flatagainst the floor.

One well-established strategy to suppress the resultingresidual vibrations of the relative position between the ma-chine stand and the mover is input shaping control (ISC) (4)–(6).This useful strategy is effective when applied in suppressingvibrations at the tip of a connected mechanism. The ISC canreduce residual vibration in an entire machine and can mostlyshorten the takt time. However, two issues remain with theISC:

[1] The settling time is sometimes extended, especiallyin short stroke positioning because the delay in thecommands becomes relatively large.

[2] Robustness against disturbances from the environ-ment and uncertainty in the system is not guaranteedbecause the ISC is designed with a feedforward-basedapproach.

In this paper, we propose machine stand acceleration feed-back (MSAFB) to overcome the aforementioned issues. Asis discussed in previous studies (7)–(9), MSAFB can suppressthe residual vibration of relative displacement between themover and the stator, which is usually measured by positionencoders. Nevertheless, in practical industrial applications,because the positioning objects come equipped with adsorp-tion mechanisms, e.g., robot hands and adsorption nozzles,the vibrations of relative displacement between the tip of thepositioning objects and the machine stand need to be sup-pressed. The latter relative displacement is not precisely mea-surable without additional high-cost displacement sensors.Therefore, we use the MSAFB control to keep the latter rel-ative displacement constant in a steady state and to improve

c© 2018 The Institute of Electrical Engineers of Japan. 15

Relative Vibration Suppression Using Acceleration Feedback Control（Takashi Kai et al.）

the robustness. The acceleration feedback control includingMSAFB is known as a representative vibration suppressionstrategy in a variety of fields (10)–(13). However, few applica-tions are currently used in factory automation (14)–(16). This pa-per presents an MSAFB controller designed specifically fora rocking mode vibration system. We evaluated the effec-tiveness of the proposed MSAFB control via simulations andexperiments.

The rest of this paper is organized as follows. In Section2, we show a mechanical plant of the rocking mode vibrationsystem and the control structure with the proposed part. Sec-tion 3 describes a simulation of the positioning waveformsto determine the effects of suppressing the relative vibrationsand reducing the settling time. Section 4 shows the experi-mental results. The conclusions are given in Section 5.

2. Control Structure

A model of the mechanical plant, a block diagram of thecontrol system, and the design method of MSAFB controllerfor vibration suppression of the relative displacement areshown and described.2.1 Plant Machine The overview of the positioning

machine is shown in Fig. 1. In Fig. 1(a), a linear motor hasbeen horizontally utilized for simplicity of analysis. The sta-tor of the motor is mounted on the top of the machine standwhile the mover is connected to the tip of a positioning ob-ject with a robot hand on the opposite side. The robot handaims to execute a repeated pick-and-place motion, for exam-ple, placing a work on a conveyer belt underneath the ma-chine stand. The work is an object, e.g., a machine part or anelectronic component, which will be picked up by the robothand and be moved to right and left in Fig. 1(a).

When the driving force is given from the motor to themover, its reaction force will cause rocking mode vibrationsin the machine stand due to mutual interference. As is shownin Fig. 1(b), when we drive the motor, the machine stand isvibrated with its swaying motion. Because the vibration am-plitude is different between the top and bottom in the machinestand owing to the inherent flexibility of the columns and theleveling bolts, the installed linear encoder on the top of thestand cannot correctly measure the relative displacement be-tween the robot hand and the work. Hence, the conventionalMSAFB has to be modified for the rocking mode vibrationsystem so as not to interfere with the semi-closed positionand velocity feedback loops that are generally working onpositioning and disturbance attenuation.

Hereafter, we define the relative displacement between thestator and the mover as the motor-side displacement, andalso define the relative displacement between the robot handand the work as machine-side displacement. In Fig. 1(a),the motor-side displacement can be measured by the linearencoder, but the machine-side displacement cannot be mea-sured without using an additional displacement sensor.2.2 Plant Modeling Figure 2 shows a schematic

model of the pick-and-place machine with the rocking modevibration. In this figure, the flexibility of the mover andthe robot hand, namely their rotational modes, are not con-sidered, so suppressing the machine stand vibration is themain focus. When we assume the plant as a simple hori-zontal two degrees-of-freedom (2DOF) vibration system (17),

(a) Overview

(b) Rocking mode vibration

Fig. 1. Pick-and-place machine

Fig. 2. Schematic model of the plant

the equation of motion at any time t is derived as follows:

Mmxm(t) = fdr − Dm (xm − xst) + d, · · · · · · · · · · · · · (1)

Mst xst(t) = fr + Dm (xm − xst) − Dst xst − Kst xst + fext,

· · · · · · · · · · · · · · · · · · · · (2)

where xm is the displacement of the mover, xst is the displace-ment of the top of the machine stand, Mm and Mst are themass of the mover and the machine stand, respectively, fdr

is the driving force generated by the motor, Dm is the frictioncoefficient, d is the disturbance to the mover, fr is the reactionforce that is equal to − fdr, Dst is the viscous damping coeffi-cient of the machine stand, Kst is the stiffness of the machinestand, fext is the external disturbance from the environment tothe machine stand. By using the above symbols, the motor-side displacement x f b and the machine-side displacement xe

can be expressed as follows:

x f b = xm − xst, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (3)

xe = xm − xw. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (4)

In the rocking mode vibration, we assume the displacementof the work xw as

xw(t) = kroxst(t), · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (5)

where kro is a ratio of vibration amplitude between the motor-side and the machine-side displacements. This formulation is

16 IEEJ Journal IA, Vol.7, No.1, 2018


Fig. 3. Block diagram of the plant and the controller

because the natural frequency and damping coefficient corre-spond at the top and bottom of the machine stand. So thatmeans the phases of the vibrations are the same, but the am-plitudes are different in the rocking mode vibration system.2.3 Control System In the positioning, residual vi-

brations will occur at both the motor-side and the machine-side displacements due to low stiffness of the Kst. In particu-lar, the ISC strategy is beneficial for simultaneously suppress-ing the vibrations of both displacements. However, becausesuppressing only the vibration at the machine-side displace-ment is sufficient as long as the takt time is reduced in somepractical situations, we utilize the MSAFB to reduce the set-tling time without suppressing the vibrations of the base plat-form.

Figure 3 shows the block diagram of the mechanical plantand the control system. The rocking mode is modeled in themechanical plant, and the framework of the 2DOF controlis utilized. The descriptions of the new symbols are as fol-lows: x∗ is the position command, Flp f (s) is the transfer func-tion of the low pass filter, CIS C(s) is the transfer function ofthe ISC unit, kp is the proportional gain of the position con-troller, Cv(s) is the transfer function of the velocity controller,Cacc(s) is the transfer function of the MSAFB controller, xe

is the machine-side displacement, x f b is the motor-side dis-placement, and ast is the machine stand acceleration.

In Fig. 3, the mechanical plant encircled by the dashed lineis modeled with reference to Eqs. (1) to (5). The rest of thearea of Fig. 3 shows the control structure that consists mainlyof the low pass filter, the ISC unit, the position controller, thevelocity controller, and the MSAFB controller.

The velocity controller is a proportional and integral (PI)controller defined as

Cv(s) = kv

(1 +

1Tvs

), · · · · · · · · · · · · · · · · · · · · · · · · · · · (6)

where kv is the proportional gain and Tv is a time constant.The Flp f (s) and CIS C(s) work as the feedforward con-

troller. The order of Flp f (s) is designed to make a propertransfer function of the feedforward controller. The transferfunctions from position command x∗ to the position, veloc-ity, and torque references (pref , vref , and τref ) are defined asfollows:[

Pref Vref Tref

]T= CIS C(s)Flp f (s)X∗, · · · · · · · · (7)

CIS C(s) =[Fz(s) Fz(s)s Fp(s)Mms2

]T,

Fz(s) =s2 + 2ωzζz s + ω2

z

ω2z

,

Fp(s) =s2 + 2ωpζps + ω2

p

ω2p

,

Flp f (s) =1

ω4s4 + ω3s3 + ω2s2 + ω1s1 + s0,

where Fz(s) and Fp(s) are transfer functions with the samefunction as notch filters, and where ω1, ω2, ω3, and ω4 aretuning parameters that determine command responsiveness.To suppress the residual vibrations, ωz and ωp should be setto anti-resonance and resonance frequencies of the machinestand vibration characteristics, respectively. ζz and ζp shouldbe set to the damping coefficients of the anti-resonance andresonance.2.4 Design of the MSAFB Controller The MSAFB

controller Cacc(s) was designed on the basis of a disturbancelocalization algorithm under the recognition that the reactionforce fr is a kind of disturbance fext.

The transfer function from fext to xe is derived from Fig. 3as

Xe

Fext=

Gn(s)Gdm(s)Gdst(s)+[Cacc(s)−Mm] Mms4

, · · · · · (8)

Gn(s)= [Cacc(s)−Mmkro] s2+[{Dm+Cv(s)} s+kpCv(s)

](1−kro) ,

Gdm(s) = Mms2 + [Dm + Cv(s)] s + kpCv(s),

Gdst(s) = (Mm + Mst) s2 + Dst s + Kst,

where Gn(s) is the transfer function of the numerator polyno-mial whose norm has to be reduced to zero by the MSAFB,Gdm(s) is the mechanical admittance of the mover controlledwith the semi-closed feedback loops, and Gdst(s) is the me-chanical admittance of the machine stand. Substituting kro to1, the mechanical plant is considered to be a simple 2DOFvibration system.

From Eq. (8), Cacc(s) is given so that Gn(s) becomes zeroby

Cacc(s) = Mmkro +

[Dm + Cv(s)

s+

kpCv(s)

s2

](kro − 1) .

· · · · · · · · · · · · · · · · · · · · (9)

The right of Eq. (9) is for instance implemented in Fig. 4,where Fbp f (s) is the transfer function of a bandpass filterthat works on noise and offset elimination of the detected



Fig. 4. Implementation of the MSAFB controller

machine stand acceleration ast. Owing to the effect of inte-gral compensator in Cv(s), the order of Fbp f (s) should be setover 2, and the integrators in the MSAFB controller have tobe implemented using pseudo-integrators. Because the con-ventional position and velocity controllers are communalizedwith the MSAFB controller, the implementation showed inFig. 4 helps to tune the feedback parameters kp, kv and Tv onthe ground.

In Fig. 4, the transfer function from ast to fdr is derived as

Fdr

Ast=

[k1 +

{k3 + Cv(s)

s+

kpCv(s)

s2

}k2

]Fbp f (s),

· · · · · · · · · · · · · · · · · · · (10)

where k1, k2, and k3 are the tuning parameters of the pro-posed MSAFB controller. Comparing Eq. (10) with Eq. (9),the optimal values of k1, k2, and k3 are given by

[k1 k2 k3

]T=

[Mmkro kro − 1 Dm

]T. · · · · · · (11)

The MSAFB controller consists of four loops. One is a pro-portional feedback loop having k1, another is the second-order integral feedback loop having k2, and the others arefirst-order integral feedback loops having k2 and k3. The con-ventional MSAFB controller has only the proportional feed-back loop, and then the motion of the mover is controlled tofollow the vibration of the top of the machine stand. The con-ventional strategy is basically working to keep the motor-sidedisplacement constant in a steady state by setting k1 = Mm

and k2 = 0, which means kro = 1 in Eq. (9). However, themover has to be controlled in practice to follow the vibrationof the bottom of the machine stand to keep the machine-sidedisplacement constant. In our controller, the integral loopsare essentially working on trajectory formation to eliminatethe interference between the semi-closed feedback loops andthe conventional MSAFB loop. The proposed MSAFB aimsto suppress the vibration of the machine-side displacement.Because the objectives of the conventional and the proposedMSAFB controllers are different, we only show the effects ofthe proposed MSAFB controller in simulations and experi-ments below.

3. Simulations

The effects of suppressing the relative vibrations and of re-ducing the settling time using our MSAFB controller weresimulated to test the working principle.3.1 Positioning Conditions The block diagram

Table 1. Command profiles

shown in Fig. 3 was programmed in MATLAB/Simulink. Be-cause we used a ball-screw driven system and a rotary servomotor in the experimental evaluation described in Section4, the translational states in Fig. 3 were appropriately trans-formed to rotational states with the pitch of the ball-screw at20 mm/rev.

In the simulations, we set the velocity loop response,namely the open-loop gain crossover frequency, to 28 Hz.The cutoff frequency of Flp f (s) was 13 Hz. The plant pa-rameters were selected so that the natural frequency of themachine stand became 12.6 Hz, the motor inertia was 3.2 ×10−6 kg·m2, and the inertia ratio between the motor and theload was set to 5.8.

We executed positioning simulations for three cases byswitching these control configurations:

Case 1: 2DOF control (without vibration suppressionmethod),

Case 2: 2DOF control with ISC,Case 3: 2DOF control with MSAFB.

In Case 1, the inverted mechanical plant modeled by CIS C(s)is regarded as a rigid system by setting Fz(s) = Fp(s) = 1. InCase 2, the ISC is applied by setting the tuning parameters asfollows:[

ωz ωp ζz ζp

]T=

[2π × 11.7 2π × 12.6 0 0

]T.

· · · · · · · · · · · · · · · · · · · (12)

In Case 3, MSAFB was applied by setting the tuning param-eters k1, k2 and k3 as

[k1 k2 k3

]T=

[0 −1 0

]T. · · · · · · · · · · · · · · · · · (13)

Hence, we set kro = 0 and Dm = 0 in the simulations. Thebandwidth of the bandpass filter Fbp f (s) was set from 1.26 to126 Hz, centering on 12.6 Hz in a log scale.

The command profile is summarized in Table 1. The po-sition command x∗ was formulated using an S-shaped curvewith a triangle-shaped profile of the velocity command. Themax speed was 3000 rpm, the acceleration and decelerationtime was 40 ms, and the positioning stroke was 20 mm at thetranslational machine-side displacement.3.2 Simulated Position Error Waveforms Figure 5

shows the simulated position error signals. The position errorsignals regarding the motor-side and the machine-side dis-placements are given in Fig. 3 by (x∗ − x f b) and (x∗ − xe), re-spectively. Figure 5 also shows the used velocity reference tocalculate settling time Ts. As illustrated, Ts is a time framewhere the position error signal regarding the machine-sidedisplacement goes into position threshold 0.5 mm after thedeceleration.

With 2DOF control (see Fig. 5 top), the residual vibra-tion of the motor-side displacement was almost completely



Fig. 5. Simulated position error signals

suppressed by the position and velocity feedback controller,while that of the machine-side displacement clearly rose uparound 12 Hz. By settingωz, ωp, ζz, and ζp shown in Eq. (12),when the ISC was utilized in addition to the 2DOF control,both of the residual vibrations were suppressed, and the vi-brations were not excited in the entire machine (see Fig. 5middle). However, the settling time takes 43.1 ms in Case2. When our MSAFB controller was utilized with the 2DOFcontrol setting Fz(s) = Fp(s) = 1, the residual vibration atthe machine-side displacement was almost completely sup-pressed, while that at the motor-side displacement becameactivated (see Fig. 5 bottom). This is because the positioningobject was actively moved to follow the vibration motion ofthe bottom of the machine stand. The settling time was re-duced to 31.9 ms in Case 3. The settling time was estimatedfrom the simulations to be reduced by around 25% by theMSAFB.

4. Experimental Results

The experimental results are shown herein, along with thetest of the robustness against plant variation.4.1 Experimental Setup and Conditions Figure 6

shows a picture of the experimental setup. The system con-figuration is detailed in Fig. 7. The bottom of the machinestand was designed as a surface plate on which the top ofthe machine stand was suspended by leaf springs to limitthe fundamental rocking mode vibration to about 12 Hz. Theball screw driven system controlled by the rotary servo mo-tor (HF-KP13, Mitsubishi Electric Corp.) was mounted onthe top of the machine stand. The pitch of the ball-screw was20 mm/rev. The motor inertia was 3.2×10−6 kg·m2, and massof the mover, which did not include a ball screw nut, was0.93 kg. The motor was driven by a rapid prototype controlsystem (dSPACE DS1005) on a trial basis.

Three sensors were installed in the experimental system:one was the rotary encoder for detecting the angular positionof the motor, another was the accelerometer (Bandwidth from0.8 to 3000 Hz) located at the right-hand side of the machinestand to measure the machine stand vibration horizontally,and the other was a laser displacement sensor mounted on

Fig. 6. Experimental setup

Fig. 7. System configuration in the experiments

Fig. 8. Frequency response of the mechanical character-istic

the bottom of the machine stand. The last one was utilized toevaluate the residual vibration of the machine-side displace-ment, and it was not used for implementing feedback control.

In the experiments, the implemented values of the tuningparameters in the ISC and the MSAFB were the same asEqs. (12) and (13). To improve the offset and noise elimi-nation ability, the bandwidth of the bandpass filter was setnarrow from 2.2 to 71.6 Hz, centering on 12.6 Hz in the logscale. The command profiles used in experiments were thesame as those in the simulations. Their details have alreadybeen shown in Table 1.

Figure 8 shows the frequency response from the motortorque to the motor angular velocity. Both resonance andanti-resonance were detected around 12 Hz due to flexibilityof the leaf springs for the machine stand vibration. The iner-tia ratio between the motor and the load was approximately5.8.



Fig. 9. Measured position error signals

Fig. 10. Measured torque signals

4.2 Positioning Results Along with the simulated re-sults, the measured position error signals are shown in Fig. 9.The waveforms in Fig. 9 correspond almost exactly to thosein Fig. 5. However, because the measurement range of theused laser displacement sensor is 10 mm, the transient stateof the machine- side displacement was not measured.

The residual vibration amplitude Vp−p was specifically2.28 mm in Case 1, but Vp−p was reduced to 0.14 and0.21 mm in Cases 2 and 3, respectively. The residual vi-bration was suppressed to less than 10% by using ISC orMSAFB. Moreover, the settling time Ts was 44.8 ms in Case2, but the Ts was reduced to 32.9 ms in Case 3. Therefore, thesetting time was reduced by over 25% by the MSAFB. Theseresults demonstrate that our MSAFB controller is superior tothe ISC strategy for reducing the settling time.4.3 Torque Waveforms Figure 10 shows the mea-

sured torque signals depicted by fdr in Fig. 3. In the verticalaxis, the typical torque output was 0.32 Nm as set 100% forreference. Because the velocity references used in Fig. 10have the same profiles as those in Fig. 9, we show the veloc-ity reference at the top only.

Fig. 11. Measured machine stand acceleration signals

The top of Fig. 10 shows that the torque signal residu-ally vibrated around 12 Hz after the deceleration. Thus, thesemi-closed feedback loops were working to keep the po-sition error of the motor-side displacement zero. The mid-dle of Fig. 10 shows that the use of the ISC method enabledtorque peaks to appear during the positioning. These peaksincreased as the cut-off frequency of Flp f (s) was set higher toreduce the settling time. The ISC strategy has problems withtorque saturation, so reducing the settling time is difficult.The bottom of Fig. 10 shows that the shape of the torque sig-nal in Case 3 almost correspond exactly to that in Case 1, butthe torque signal actively vibrated due to the feedback torqueof the MSAFB after the deceleration because the referencetrajectory was compensated.4.4 Machine Stand Acceleration WaveformsFigure 11 shows the measured acceleration signals of the

machine stand depicted by ast in Fig. 3. The velocity refer-ences used in Fig. 11 have the same profiles as those in Figs. 9and 10.

In addition, Fig. 11 shows the machine stand vibration oc-curred in Cases 1 and 3, but the vibration was almost com-pletely suppressed by the ISC after the deceleration in Case2.4.5 Evaluation Tests of Robustness To determine

the robustness against variation in the mechanical character-istics, we carried out positioning tests by shifting the identi-fied value of the natural frequency of the rocking mode vi-bration.

Figure 12 shows the measured position error signals inCases 2 and 3. Although the true value of the natural fre-quency, basically the resonance and the anti-resonance, ismeasurable from Fig. 8, ωz and ωp of the ISC and the centralfrequency of the bandpass filter Fbp f (s) were shifted to 15 Hzin this evaluation. In detail, we set ωz = ωp = 2π × 15 rad/s,and the bandwidth of the bandpass filter was set from 2.23to 101 Hz centering on 15 Hz in the log scale. In Fig. 12, theVp−p was reduced from 1.0 mm in Case 2 to 0.4 mm in Case3. Compared to the ISC method, the amplitude of the resid-ual vibration was reduced by 60%. Therefore, the MSAFBwas superior to the ISC in terms of robustness against the



Fig. 12. Evaluation results of robustness

variation in the mechanical characteristics, even when thebandwidth of Fbp f (s) was not ideally expanded.

5. Conclusions

In this paper, an MSAFB controller was designed to sup-press the vibration of the relative displacement in the rockingmode vibration system. The results can be summarized asfollows:

1) The positioning machine and its base platform werestructurally modeled. A vibration ratio kro was usedfor the description of the rocking mode vibration sys-tem because the vibration amplitudes were differentbetween the top and bottom of the base platform.

2) The MSAFB controller was designed on the basis ofthe disturbance localization algorithm. The MSAFBconsists of the proportional feedback loop, the first-order integral feedback loop, and the second-order in-tegral feedback loop.

3) The positioning waveforms were simulated. Thesettling time was estimated to be reduced by around25% compared to the ISC method.

4) The effectiveness of the proposed MSAFB wasdemonstrated experimentally. Compared to the ISCmethod, the settling time was reduced by over 25%and the robustness against variation in the mechanicalcharacteristics was improved by 60%.

References

( 1 ) Mitsubishi Electric Corporation: “Mitsubishi Servo System Family Catalog”,L(NA) 03055ENG-B 1310 (2013)

( 2 ) B. Babakhani and T.J.A. de Vries: “Active damping of the 1D rocking mode”,in the Proceedings of the 2010 IEEE International Conference on Mechatron-ics and Automation, Xian, pp.1370–1375 (2010)

( 3 ) K. Mori, D. Kono, I. Yamaji, and A. Matsubara: “Vibration reduction of ma-chine tool using viscoelastic damper support”, Science Direct Procedia CIRP,Vol.46, pp.448–451 (2016)

( 4 ) L.Y. Pao: “Multi-input shaping design for vibration reduction”, Automatica,Vol.35, pp.81–89 (1999).

( 5 ) J.R. Huey, K.L. Sorensen, and W.E. Singhose, “Useful applications of closed-loop signal shaping controllers”, Control Engineering Practice, Vol.16,pp.836–846 (2008)

( 6 ) H. Sekiguchi and H. Ikeda: “Vibration Suppression Control for Two- fre-quency Vibrations with Automatic Adjustment”, in the Proceedings of the39th Annual Conference of the IEEE, Vienna, pp.6575–6580 (2013)

( 7 ) S. Wakui: “Recognition of Base-Plate Acceleration Feedback Embedded inStage Positioning Control System”, the Journal of the Japan Society for Pre-cision Engineering, Vol.64, No.7, pp.1017–1021 (1998) (in Japanese)

( 8 ) Y. Tsuchimoto, K. Seki, and M. Iwasaki: “Robust Vibration Control Using

Machine Stand Acceleration Signal in Linear-Motor-Driven Table Systems”,The Papers of the Joint Technical Meeting on Industrial Instrumentation andControl, Vol.95, pp.91–96 (2011) (in Japanese)

( 9 ) M. Wali, Y. Nakamura, and S. Wakui: “A Method Using the Base PlateJerk Feedback to Control the Positioning of a Pneumatic Stage”, in the Pro-ceedings of the 2011 8th Asian Control Conference, Kaohsiung, pp.629–634(2013)

(10) S. Futami, N. Kyura, and S. Hara: “Vibration Absorption Control of Indus-trial Robots by Acceleration Feedback”, The IEEE Transactions of IndustrialElectronics, Vol.IE-30, No.3, pp.299–305 (1983)

(11) O. Zirn and C. Jaeger: “Vibration Damping for Machine Tool Servo Drivesby Load Acceleration Feedback”, in the Proceedings of the 2010 IEEE Inter-national Symposium on Industrial Electronics (ISIE), pp.3264–3269 (2010)

(12) M. Rios-Gutierrez and G. Silva-Navarro: “Suppression of Mechanical Vibra-tions in a Building Like Structure by Means of a Piezoelectric Patch Actuatorand Positive Acceleration Feedback”, in the Proceedings of the 2010 7th In-ternational Conference on Electrical Engineering, Computing Science andAutomatic Control (CCE2010), Chiapas, pp.452–457 (2010)

(13) M.M.Z. Shahadat, T. Mizuno, Y. Ishino, and M. Takasaki: “Improvementof Vibration Isolation Characteristics by Kalman-Filter Estimated Accelera-tion Feedback”, in the Proceedings of the 2015 European Control Conference(ECC), Linz, pp.1106–1111 (2015)

(14) Y. Yoshiura and Y. Kaku: “Vibration Suppression Control by AccelerationSensors Feedback”, IEEJ Journal of IA, Vol.134, No.9, pp.801–806 (2014)(in Japanese)

(15) G. Ellis and R.D. Lorenz: “Resonant Load Control Methods for IndustrialServo Drives”, Conference Record of the 2000 IEEE Industry ApplicationsConference, pp.1438–1445 (2000)

(16) Y. Marushita, H. Ikeda, and H. Sugie: “Vibration Suppression Control usingthe Load-side Acceleration Feedback”, in the Proceedings of the 33rd AnnualConference of the IEEE (IECON2007), Taipei, pp.810–815 (2007)

(17) V. Shilpiekandula, S.A. Bortoff, J.C. Barnwell, III, and K. El Rifai: “LoadPositioning in the Presence of Base Vibration”, in the Proceedings of the2012 American Control Conference, Montreal, pp.6282–6287 (2012)

Takashi Kai (Member) received his B.E., M.E., and Ph.D. degreesfrom the Tokyo University of Agriculture and Tech-nology, Tokyo, Japan, in 2008, 2010, and 2013. From2011 to 2013, he was a Research Fellow of the JapanSociety for the Promotion of Science. Since 2013, hehas been with the Advanced Technology R&D Cen-ter, Mitsubishi Electric Corp. He is a member ofJSME and JSPE. His research interest includes mo-tion control, sensor application, and model-based de-sign.

Hiroyuki Sekiguchi (Member) received his B.E., and M.E. degreesfrom the Tokyo Institute of Technology, Tokyo,Japan, in 2005, and 2007. Since 2007, he has beenwith the Advanced Technology R&D Center, Mit-subishi Electric Corp. He is a member of IEEJ. Hisresearch interest includes motion control.

Hidetoshi Ikeda (Member) received his B.E. and M.E. degrees inelectrical engineering from Kyoto University, Kyoto,Japan, in 1989, and 1991, respectively. In 1991,he joined Mitsubishi Electric Corporation, where heis currently engaged in research on motion controland its industrial application in Advanced Technol-ogy R&D Center. He is a member of the IEEJ, SICE,ISCIE and IEEE.


Documents

Relative Vibration Suppression in a Positioning Machine