anti-resonance vibration suppression control in full

IEEJ Journal of Industry ApplicationsVol.9 No.3 pp.311–317 DOI: 10.1541/ieejjia.9.311Translated from IEEJ Transactions on Industry Applications, Vol.139 No.10 pp.847–853

Paper(Translation ofIEEJ Trans. IA)

Anti-resonance Vibration Suppression Control in Full-closedControl System

Yasufumi Yoshiura∗ Member, Yusuke Asai∗ Member

Yasuhiko Kaku∗ Senior Member

External position sensors such as linear scales are frequently used in motion control systems of industrial machines,and they form a full-closed position feedback loop for accurate positioning. When the velocity signal calculated withthe position signal from the motor encoder is used for the velocity control loop, resonance is less likely to occur thanwhen using the velocity signal calculated with the position signal from the external encoder. If the position loop gainis increased, vibration is generated at the anti-resonant frequency, even if the velocity loop is stably controlled withrespect to the resonance frequency. Since there is no control method for suppressing the vibration, such as the vibrationcontrol method in semi-closed control, the proportional gain of the position feedback loop cannot be made sufficientlyhigh. In this paper, we propose a full-closed control method that suppresses the vibration at anti-resonance frequencyand confirm its effectiveness through simulation and experiment.

Keywords: anti-resonance, vibration suppression, full-closed control

1. Introduction

In the control system of a general industrial applicationservo driver that drives a linear motion mechanism by a ballscrew etc., it is common to configure a double loop that feedsback the motor angle signal and the motor angular velocitysignal. Servo motors often only have an angle detector suchas a rotary encoder, and the angular velocity is obtained bycalculation from the angle signal of the detector. This kindof control method that configures a closed loop based on themotor rotation angle is called semi-closed control (1)–(3), and isoften used in industrial applications because it can be drivenwith a simple configuration.

Meanwhile, with mechanisms such as semiconductor in-spection equipment, positioning control using full-closedcontrol with an external sensor such as a linear scale may beperformed as the target of inspection becomes smaller. Suchmechanisms start and stop frequently, but the rigidity of themechanism itself is often not ensured in order to reduce costs,and the machine base and ball screw often vibrate due to theexcitation force accompanying the acceleration and deceler-ation of the motor. In the case of ball screw vibration, themotor generates vibration due to resonance, but in the case ofmachine base vibration, the anti-resonance vibration of themachine base vibrates the motor according to the law of ac-tion and reaction.

When mechanical resonance characteristics are included inthe control loop, the control gain is limited to prevent oscilla-tion of the control system. In particular, the proportional gainof the velocity controller is set higher than the proportional

∗ YASKAWA ELECTRIC CORPORATION480, Kamifujisawa, Iruma, Saitama 358-8555, Japan

gain of the position controller for the sake of stability of thecontrol loop, and therefore is significantly affected by reso-nance characteristics.

There are two methods for configuring the velocity controlsystem in fully-closed control: a method that calculates thevelocity signal from the motor encoder signal and a methodthat calculates it from the external position sensor signal. Inthe case of the former, the start-up of the machine can firstbe commenced as a semi-closed control system, and then theposition loop can be switched to an external sensor signalthereafter to improve the position control accuracy of loadposition (4).

When setup a servo drive on the manufacturing site, it isoften the case that the first step is to confirm operation byvelocity control. At that time, the mechanism is often underassembly, so it is often operated by semi-closed control usinga motor encoder. In applications that require high-accuracypositioning after completion of operation confirmation, posi-tion control is performed by switching to full-closed control,but the velocity control system often remains in semi-closedcontrol for the purpose of reducing man-hours.

Examples of measures to stabilize the mechanical reso-nance characteristics in the velocity loop include a methodthat uses a low-pass, notch or other filter; a method that in-puts the same signal as in a normative model into the ac-tual system, processes the output difference between the twoand returns it to the input with the aim of a response sim-ilar to the model (5), and a method of stabilizing the controlsystem by feeding back the state quantity estimated using anobserver (6)–(13).

In the above full-closed control system, after stabilizingthe velocity loop and increasing the gain by such a method,vibration may occur at the anti-resonance frequency of the

c© 2020 The Institute of Electrical Engineers of Japan. 311

Anti-resonance Vibration Suppression Control in Full-closedControl System（Yasufumi Yoshiura et al.）

mechanism when the proportional gain of the position loopis increased (14).

In the following, the method for calculating the speed fromthe motor encoder signal is defined as P (Position) type full-closed control, and the method for calculating the speed fromthe external position sensor signal is defined as PS (Position-velocity) type full-closed control.

For PS type full-closed control, a method of stabilizingby the differential velocity feedback between the encoder at-tached to the motor and the external sensor (15) and a methodof stabilizing only by the external sensor (16) have been pro-posed. However, none of these methods are intended to sup-press resonance vibration, and are not intended to suppressanti-resonance of the mechanism. Therefore, PS type full-closed control (with an external position sensor) can be ap-plied to P type full-closed control. Detected speed):

In this study, we propose anti-resonance for P type full-closed control.

The structure of this paper is shown below.Section 2 shows the mechanism of anti-resonance vibration

generation in P type full-closed control, and Section 3 ex-plains vibration suppression when the conventional methodis applied. Section 4 explains vibration suppression by theproposed method, and Sections 5 and 6 confirm the effective-ness of the proposed method by simulation and experimentalresults. Finally, the conclusion of this paper is given.

2. Mechanism of Anti-resonance Vibration Gen-eration

Assuming that a motor control system including mechani-cal resonance elements such as ball screws is a 2-inertial res-onance system as shown in Fig. 1, the equations of motionfrom the motor torque to the velocity of the control when op-erating controlled object when operating by full-closed con-trol are Equations (1) and (2) (17).

Jmθ̈m + D(θ̇m − θ̇L) + K(θm − θL) = Tm · · · · · · · · · · · (1)

JLθ̈L + D(θ̇L − θ̇m) + K(θL − θm) = 0 · · · · · · · · · · · · · (2)

Here, J, D, and K represent the moment of inertia, viscousdamping coefficient, and spring constant, respectively. T, θ,and θ̇ represent torque, position, and velocity respectively.Subscripts m and L represent the motor side and load sideconstants, respectively.

When Equations (1) and (2) are made transfer functions byLaplace transform, they become Equations (3) and (4).

P-type full-closed control (detected by motor encoderspeed):

GLp(s) =Θm(s)Tm(s)

s =

(1

JM + JL· 1

s

)

Fig. 1. Control target (2-inertial system)

·⎧⎪⎪⎪⎨⎪⎪⎪⎩

s2+ DJL

s+ KJL

KJL

·(

1Jm+ 1

JL

)K

s2+(

1Jm+ 1

JL

)Ds+

(1Jm+ 1

JL

)K

⎫⎪⎪⎪⎬⎪⎪⎪⎭=

(1

JM + JL· 1

s

)

·(

s2+2ζaωas+ω2a

ω2a

· ω2r

s2+2ζrωr s+ω2r

)· · · · · · (3)

PS type full-closed control (velocity detected by externalencoder):

GLps(s) =ΘL(s)Tm(s)

s =

(1

JM + JL· 1

s

)

·⎧⎪⎪⎪⎨⎪⎪⎪⎩

(1Jm+ 1

JL

)(Ds + K)

s2 +(

1Jm+ 1

JL

)Ds +

(1Jm+ 1

Jm

)K

⎫⎪⎪⎪⎬⎪⎪⎪⎭=

(1

JM+JL· 1

s

)·(

2ζrωr s+ω2r

s2+2ζrωr s + ω2r

)· · · · · (4)

However,ζr: Damping coefficient of resonanceωr: Angular vibration frequency of resonanceζa: Damping coefficient of anti-resonanceωa: Angular frequency of anti-resonanceHere, the first-order term of s in the numerator determines

the characteristics of frequencies higher than the resonancepeak, but the generation of vibration is considered to have noeffect on the study of vibration suppression because of theresonance peak. Therefore, in this study, for simplicity, thefirst order term of s in the numerator is ignored and the PS-type full-closed control is expressed as

GLps(s) =

(1

JM+JL· 1

s

)·(

ω2r

s2 + 2ζrωr s + ω2r

)· · · · (5)

The transfer function from the motor torque to the positionsignal of the external position sensor can also be described asfollows using Equations (3) and (5):.

G(s) =

(1

JM + JL· 1

s2

)

·(

s2 + 2ζaωas + ω2a

ω2a

· ω2r

s2 + 2ζrωr s + ω2r

)

·(

ω2a


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

When describing the control target in Equation (6), theblock diagram of Fig. 2 is obtained in the case the motorvelocity and position signal of the external position locationsensor are fed back.

The superscripts ref and res indicate reference value andresponse value, respectively. In Fig. 2, the proportional gainof the velocity controller can be made sufficiently larger thanthe proportional gain of the position controller by reducing

Fig. 2. Control block diagram (full-closed control)

312 IEEJ Journal IA, Vol.9, No.3, 2020


the effect of mechanical resonance using filters and variousvibration suppression control methods, so for simplicity, thetransfer function of the velocity control system is made “1”.

At this time, the loop transfer function from the positionerror to the detected position signal is

G(s) =Kp

s· ω2

a

s2 + 2ζaωas + ω2a· · · · · · · · · · · · · · · · · · (7)

Therefore, if the proportional gain of the position controlleris increased, the controller may vibrate at a frequency nearωa. The transfer function from the position reference to theload position is as follows:

G(s) =Kpω

2a

s3 + 2ζaωas2 + ω2as + Kpω2

a· · · · · · · · · · · · · (8)

Substituting s = jω into Equation (7) yields the followingequation:

G( jω) =Kpω

2a

jω(ω2a − ω2) + 2ζaωa

· · · · · · · · · · · · · · · · · (9)

If we rationalize the above equation and find ω with an imag-inary part of 0, we can obtain Equation (10) from ωa > 0.

ω = ωa · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (10)

Equation (10) shows that the vibration frequency in thecase the position control system becomes unstable is the anti-resonance frequency of the mechanism (18). For this reason, amethod for suppressing vibration at the anti-resonance fre-quency is necessary.

3. Vibration Suppression by ConventionalMethod

Figure 4 (15) shows an example of a conventional methodthat feeds back the difference between the motor velocity andthe load velocity calculated from the external position sen-sor. Defining the difference between the motor velocity andthe load velocity calculated from the external position sensoras the differential velocity, the open-loop transfer functionfrom the velocity reference to the differential velocity for thevelocity control system of Fig. 4 is given by the followingequation. However, for simplicity, the integral is excludedand it was made velocity P control, such that Jm + JL = 1.

G(s) =b2s2 + b1s + b0

s3 + a2s2 + a1s + a0

(1 − ω2

a


)

· · · · · · · · · · · · · · · · · · · · · · (11)

=b2s(s + 2ζaωa)

s3 + a2s2 + a1s + a0· · · · · · · · · · · · · · · · · · · · · · · (12)

The coefficients a2 to a0 and b2 to b0 in Equation (11) areas follows:

a2 = 2ζrωr +ω2

r Kvω2

a· · · · · · · · · · · · · · · · · · · · · · · · · · · · (13)

a1 = ω2r +

2ζaω2r Kvωa

· · · · · · · · · · · · · · · · · · · · · · · · · · · (14)

a0 = ω2r Kv · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (15)

b2 =ω2

r Kvω2

a· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (16)

Fig. 3. Comparison of simulation results of conven-tional method and proposed method

Fig. 4. Control block diagram of conventional methodwith vibration suppression control using differential ve-locity feedback

b1 =2ζaω2

r Kvωa

· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (17)

b0 = ω2r Kv · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (18)

The configuration of Equation (12) contains the charac-teristics of the velocity feedback control system, which in-cludes mechanical resonance and anti-resonance character-istics. Since the form of the equation is different from thetransfer function of Equation (7), it is not possible to detectonly the anti-resonance frequency that occurs when the posi-tion control system becomes unstable.

Therefore, it is considered that anti-resonance vibrationcannot be suppressed even if the gain K f is simply appliedto the differential velocity and fed back to the motor torque.Figure 3 shows the simulation results of Fig. 4. In the end,the method of Fig. 4 does not suppress vibration at all.

However, if the transfer function of the velocity controlsystem could be set to “1”, Equation (11) changes as follows:

G(s) =s2 + 2ζaωas

s2 + 2ζaωas + ω2a=

s(s + 2ζaωa)s(s + 2ζaωa) + ω2

a

· · · · · · · · · · · · · · · · · · · (19)

4. Vibration Suppression by the ProposedMethod

With Equation (19), it is possible to detect only the anti-resonance frequency, however in reality, the transfer function



of the velocity control system cannot be set exactly to “1”. Asa countermeasure, if the velocity reference is used instead ofthe motor velocity, the transfer function of the velocity con-trol system can be considered to be exactly “1”. Thereafter,the difference between the velocity reference and the load ve-locity calculated from the external position sensor is used asthe differential velocity.

Since ζa � 1 frequently occurs, to simplify the explana-tion, in the numerator of Equation (19), at frequencies nearωa, considering s = jωa allows the approximation

s + 2ζaωa ≈ s · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (20)

From Equation (20), Equation (19) can be approximated as

G(s) =s2

s2 + ω2a· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (21)

Since the numerator of the Equation (21) is a 2nd orderequation of s, the signal obtained by integrating the velocitydifference and multiplying by proportional gain K f is neg-atively fed back to the velocity reference. At this time, thetransfer function from the velocity reference to the load ve-locity is as follows:

G(s) =ω2

a

s2 + Kf s + ω2a· · · · · · · · · · · · · · · · · · · · · · · · · (22)

In Equation (22), since the coefficient of the first-orderterm of s of the denominator polynomial can be increasedby the proportional gain K f , an effect equivalent to that ofincreasing the damping coefficient ζa of the controlled objectcan be obtained.

When a full-closed controller that feeds back the positionof the external position sensor is constructed outside the ve-locity control system expressed by the transfer function inEquation (22), the transfer function from the position refer-ence to the load position is as follows:

G(s) =Kpω

2a

s3 + Kf s2 + ω2as + Kpω2

a· · · · · · · · · · · · · · · (23)

Comparing Equations (8) and (23), ζaωa, which cannot bedirectly controlled, is replaced by proportional gain K f , andit the stability of the position control system can be expectedto be restored by increasing K f .

5. Simulation Results

Figure 5 is a control block diagram that assumes a linearmotion mechanism that drives a ball screw with a servo mo-tor. In general, however, the spring element of the mecha-nism is assumed to be a coupling and ball screw nut, how-ever in Fig. 5, the nut alone is assumed to be the spring ele-ment. Figure 7 shows the frequency characteristics from themotor torque to the motor velocity for the control object ofFig. 5. The anti-resonance frequency corresponding to thenatural vibration frequency of the mechanism is about 54 Hz,and the resonance frequency is 300 Hz.

In the case proportional gain of the position controllerKp = 300/s, proportional gain of the velocity controllerKv = 1508/s and integration time Ti = 2.7 ms for semi-closed control, the motor rotation angle and the motor torquebecome as in Fig. 8.

Fig. 5. Control block diagram (semi-closed control)

Fig. 6. Control block diagram (full-closed control withanti-resonance vibration suppression control)

Fig. 7. Frequency characteristics from the torque of thecontrolled object to the motor velocity

Fig. 8. Operating waveform in semi-closed control

Since the motor torque in Fig. 8 oscillates at about 58 Hz,the velocity controller can sufficiently suppress the reso-nance, and it can be considered that only the anti-resonancefrequency is generated.

Consider a full-closed control system with a linear scale orother position sensor attached to the movable table of a linearmotion mechanism.

Regarding full-closed control, we assume a P type full-closed loop control in which only the load position that isused in industrial applications is fed back as shown in Fig. 6,and the velocity is fed back from the motor encoder.



Fig. 9. Operating waveform in full-closed control (with-out anti-resonance vibration suppression control)

Fig. 10. Operating waveform in full-closed control(with anti-resonance vibration suppression control)

Fig. 11. Nyquist diagram without anti-resonance vibra-tion suppression control

First, consider the case where the proposed method is notused (K f = 0). When operating it with the same gain set-ting as in semi-closed control, the load position and motortorque vibrate at approximately 58 Hz as shown in Fig. 9. TheNyquist diagram for the velocity closed loop/position openloop is as shown in Fig. 11, indicating that the control systemis unstable.

When the proposed method is applied to this state with aproportional gain K f = 500, vibration can be suppressed asshown in Fig. 10, and the proportional gain of the positioncontroller can be set to the same level as in semi-closed con-trol. Figure 12 shows the Nyquist diagram of the velocity

Fig. 12. Nyquist diagram with anti-resonance vibrationsuppression control

closed loop/position open loop when the proportional gain ischanged to K f = 200, K f = 300, and K f = 500. In Fig. 12, theproportional gain increases in the order of yellow, blue, andred. As the proportional gain K f is increased, the stabilitygradually recovers.

6. Experimental Results

Since the effectiveness of the proposed method was con-firmed by simulation, experiments were performed on twotypes of mechanisms to confirm its effectiveness. Experi-ments were conducted using two mechanisms: A rotary two-inertial system using a low stiffness spring coupling and HEI-DENHAIN K.K. rotary encoder, and a linear motion systemconnecting a THK CO., LTD. ball screw slider (lead 20 mm)to a HEIDENHAIN K.K. linear scale (measurement resolu-tion 0.1 μm).

Figures 13 and 16 show the appearance of the experimentalapparatus, and Figs. 14 and 17 show the respective frequencycharacteristics.

Table 1 shows the servo parameters applied during the ex-periment and the load moment of inertia of the experimentalequipment.

In the rotary two-inertial mechanism shown in Fig. 13,three couplings are connected. Couplings 2 and 3 exhibitspring characteristics at a frequency much higher than thefrequency range of the controller used in Table 1. This re-sults in the two-inertial characteristics of Coupling 1 only asin the frequency characteristics of Fig. 14.

Meanwhile, in the ball screw mechanism of the linear mo-tion system of Fig. 16, the resonance characteristic of Cou-pling 1 exists near 1300 Hz, and the resonance characteristicof the ball screw nut exists near 200 Hz. Furthermore, be-cause it is a linear motion system, the natural vibration ofthe machine base exists in the frequency characteristics as ananti-resonance characteristic of about 30 Hz. Resonance gen-erated at 1300 Hz when the proportional gain of the velocitycontroller is increased is suppressed by a notch filter.

When the proposed method is not applied, the two-inertialmechanism in Fig. 13 generates 8.2 Hz vibration in the posi-tion error and motor torque as shown in Fig. 15, and the ballscrew mechanism in Fig. 16 generates 31 Hz vibration in theposition error and motor torque shown in Fig. 18.



Fig. 13. Experimental device: 2-inertial mechanism

Fig. 14. Frequency characteristic: 2-inertial mechanism

Fig. 15. Experimental result: 2-inertial mechanism

Fig. 16. Experimental device: Ball screw mechanism

Since all the vibrations that occur are almost the sameas the anti-resonance frequency of the mechanism, theyare found to be generated by the natural vibration of the

Fig. 17. Frequency characteristic: Ball screw mecha-nism

Table 1. Experiment parameters

Parameters Physical quantity 2-inertial mechanism Ball screw mechanismSetting value Setting value

KpPosition controller

proportional gain[1/s] 10 105

KvVelocity controller

proportional gain[1/s] 63 660

Ti

Velocity controllerintegral time[ms] 30.00 7.62

JL/JMMoment of

inertia ratio[%] 3872 1032

K f

Vibration suppressiongain[%] 1000 1600

Fig. 18. Experimental result: Ball screw mechanism

mechanism. In particular, when looking at the position errorgraph, the vibration damping time is long, so the position-ing time of the mechanism is long, which is a problem forindustrial use.

When the proposed method is applied to a state in whichvibration occurs, the results are as shown in Figs. 15 and 18,respectively.

In all cases, the vibration was clearly reduced, and the ef-fectiveness of the proposed method in industrial applicationswas confirmed.



7. Conclusion

Simulations and experiments demonstrated that the methodof suppressing vibration by feeding back the difference be-tween the velocity reference and the velocity calculated fromthe external sensor position is effective against vibrationcaused by the natural vibration of a mechanism that occursduring full-closed control.

The proposed method is considered to be effective for in-dustrial applications because the configuration and adjust-ment of the control system are simple.

References

( 1 ) K. Seki, H. Matsuura, M. Iwasaki, H. Hirai, and S. Tohyama: “High-Precision Positioning of Galvano Scanners by Structural Design Using Nodeof Vibration Modes”, IEEJ Trans. PE, Vol.131, No.3, pp.275–282 (2011) (inJapanese)

( 2 ) N. Hirose, M. Kawafuku, M. Iwasaki, and H. Hirai: “Initial Value Compensa-tion Using Additional Input for Semi-Closed Control Systems”, IEEJ Trans.PE, Vol.127, No.10, pp.1081–1089 (2007) (in Japanese)

( 3 ) K. Yuki, T. Murakami, and K. Ohnishi: “Vibration Control of a 2 Mass Res-onant System by the Resonance Ratio Control”, IEEJ Trans. PE, Vol.113,No.10, pp.1162–1169 (1993) (in Japanese)

( 4 ) T. Kai, H. Sekiguchi, and H. Ikeda: “Relative Vibration Suppression in a Po-sitioning Machine Using Acceleration Feedback Control”, IEEJ Journal ofIA, Vol.7, No.1, pp.15–21 (2018)

( 5 ) T. Hasegawa, R. Kurosawa, H. Hosoda, and K. Abe: “A Microcomputer-Based Motor Drive System with Simulator Following Control”, IEEE-IECON, p.41 (1986)

( 6 ) Y. Urakawa: “Experiment of High Gain Servo System for Optical DiscDrives”, 47th Proceedings of the Japan Joint Automatic Control Conference,Session ID801 (2005)

( 7 ) Y. Urakawa: “Parameter Design for a Digital Control System with Calcu-lation Delay Using a Limited Pole Placement Method”, IEEJ Trans. PE,Vol.133, No.3, pp.272–281 (2013) (in Japanese)

( 8 ) S. Kawahara, T. Yoshioka, K. Ohishi, H. Nguyen, T. Miyazaki, and Y.Yokokura: “Vibration Suppression Control Method using Extended State Ob-server for Angular Transmission Error in Cycloid Gear”, IEEJ Trans. PE,Vol.134, No.3, pp.241–251 (2014) (in Japanese)

( 9 ) K. Ohishi, T. Myoui, K. Ohnishi, and K. Miyachi: “One Approach to SpeedControl of dc Motor Having two Inertia Resonant System”, IEEJ Trans. PE,Vol.106, No.2, pp.31–38 (1986)

(10) M. Koyama: “Design of a motor control system for driving a low-rigidityload machine using a reference model”, Proceedings of IEE-Japan IndustryApplications Society Conference, pp.451–456 (1987)

(11) Y. Hori: “Comparison of Vibration Suppression Control Strategies in 2-MassSystems including a Novel Two-Degrees-Of-Freedom H∞ Controller”, Proc.IEEE AMC’92, Nagoya, pp.409–416 (1992)

(12) Y. Chen, K. Fujikawa, and H. Kobayashi: “Observer based torsionaltorque control of vibration systems”, Proceedings of IEE-Japan IndustryApplications Society Conference (1993)

(13) T. Yoshioka, A. Yabuki, Y. Yokokura, K. Ohishi, T. Miyazaki, and T.T.Phuong: “Stable force Control of Industrial Robot Based on Spring Ratioand Instantaneous State Observer”, IEEJ Journal of Industry Applications,Vol.5, No.2, pp.132–140 (2016)

(14) Y. Yoshiura and Y. Kaku: “A Study on Vibration Suppression in Full-ClosedControl System”, Technical Meeting on Mechatronics Control, MEC-17-015(2017)

(15) H. Sugimoto, M. Koyama, and S. Tamai: “Theory and Design Practice of ACServo System”, Sogo Electronics Press, pp.162–168 (1990)

(16) S. Yamada, H. Fujimoto, and Y. Hori: “Vibration Suppression Controlof Two-Inertia System without Using Drive-Side Information by Apply-ing High-Resolution Encoder”, IEEJ Trans. PE, Vol.135, No.3, pp.212–219(2015) (in Japanese)

(17) A. Sueoka, Y. Kanemitsu, and T. Kondou: “Mechanical vibrations”, AsakuraPublishing Co. Ltd., pp.12–13, 43–44 (2000)

(18) F. Golnaraghi and B.C. Kuo: “AUTOMATIC CONTROL SYSTEMS 10thEdition”, McGrawHill Education, pp.616–617, pp.641–642

Yasufumi Yoshiura (Member) received the B.Sc. and M.Sc. degreesfrom Kyushu University, Fukuoka, Japan, in 2000.The same year, he joined YASKAWA ELECTRICCORPORATION, Japan. He has been engaged in de-veloping technology of mechatronics-system.

Yusuke Asai (Member) received B.Sc. and M.Sc. degrees from Na-gaoka University of Technology, Niigata, Japan in2014 and 2016. In 2016, he joined YASKAWAELECTRIC CORPORATION, Japan. He has beenengaged in developing and designing of servo ampli-fier.

Yasuhiko Kaku (Senior Member) received the M.Sc. degree fromKyushu Institute of Technology, Fukuoka, Japan, in1982. The same year, he joined YASKAWA ELEC-TRIC CORPORATION, Japan. And he received thePh.D. from Chiba University, Chiba, Japan, in 1988.He has been engaged in developing technology ofmechatronics-system.


anti-resonance vibration suppression control in full

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