characteristic evaluation of linear resonant actuator

IEEJ Journal of Industry ApplicationsVol.7 No.2 pp.175–180 DOI: 10.1541/ieejjia.7.175

Paper

Characteristic Evaluation of Linear Resonant Actuator UtilizingElectrical Resonance

Masayuki Kato∗a)Student Member, Katsuhiro Hirata∗ Senior Member

(Manuscript received April 5, 2017, revised Sep. 7, 2017)

Linear resonant actuators (LRAs) have been used in a wide range of applications because they utilize mechanicalresonance and operate at high efficiency. However, the amplitude of LRAs severely decreases when external load isapplied. To solve this problem, we applied PID (Proportional-Integral-Derivative) control to an LRA, and the moveramplitude remained constant against an external load. When a large external load was applied with the target voltageof PID control high, however, input power reached maximum and the amplitude did not follow the target value. Asa solution, it is effective to utilize electrical resonance and generate large current. In this paper, we propose a controlmethod to generate an electrical resonance. The effectiveness of the proposed method was verified through dynamiccharacteristic analysis employing two-dimensional finite element method and measurements.

Keywords: electrical resonance, finite element analysis, linear oscillatory actuators (LOA), linear resonant actuators (LRA), me-chanical resonance, electromagnetic actuators

1. Introduction

Linear oscillatory actuators (LOAs) have been used in awide range of applications (1)–(7) because they have a lot of ad-vantages: simple structure, low mechanical loss, easy con-trol, and so forth. In particular, linear resonant actuators(LRAs), which utilize mechanical resonance consisting of amass and a spring, are able to operate at high efficiency (8)–(10).This advantage enables LRAs to be used as home electronics:electric shaver and tooth brush, and so on. However, the am-plitude of LRAs severely decreases when external loads areapplied. In some applications such as electric shavers and aircompressors, their amplitude need to be able to be arbitrarilycontrolled according to the external load.

We applied PID control to an LRA and the mover ampli-tude remained constant against an external load (11). Further-more, we proposed an external load estimation method usingtwo signals of the back-EMF. As a result, it became possibleto estimate the external load, and to obtain an arbitrary ampli-tude by changing the target voltage of PID control accordingto the estimated load (12) (13).

However, when a large external load is applied with the tar-get voltage high, duty ratio in PWM control reaches 100%.In this case, the amplitude is not controllable as it is required.Meanwhile, LRAs for home electronics applications are op-erated on a battery. To solve the above problem, the batteryvoltage needs to be higher, which results in higher cost andincrease in system size. As a solution, it is effective to utilizeelectrical resonance and generate large current by adding acapacitor to a normal RL circuit of LRA.

a) Correspondence to: Masayuki Kato. E-mail: [email protected]∗ Department of Adaptive Machine Systems, Graduate School of

Engineering, Osaka University2-1, Yamadaoka, Suita, Osaka 565-0871, Japan

In this paper, first, we propose a control method to gener-ate electrical resonance. Second, 2-D finite element analysis(FEA) verifies that electric resonance is successfully coupledwith mechanical resonance and consequently large current isgenerated. Finally, the effectiveness of the proposed controlmethod is verified through measurements.

2. Basic Structure of LRA

The basic structure of the LRA in this study is shown inFig. 1. This actuator mainly consists of two movers, a com-mon stator and resonant springs that support the mover tomaintain the air-gap length (0.36 mm). Two parallelly ar-ranged movers are composed of two opposite pole magnetsfixed on a back yoke. The common stator is composed of anE-shaped laminated yoke with an excitation coil of 68 turnsat its middle pole. The total mass of LRA is 28.6 g.

3. Driving Method Using Electrical Resonance

3.1 Coupling of Mechanical and Electrical ResonanceIn this section, we explain a new control method in which

mechanical resonance is combined with electrical resonance.

Fig. 1. Basic structure of the LRA

c© 2018 The Institute of Electrical Engineers of Japan. 175

Characteristic Evaluation of LRA Utilizing Electrical Resonance（Masayuki Kato et al.）

Fig. 2. Schematic diagram of feeback control system

The series circuit equation including an external capacitor isexpressed as follows:

V − RI − 1C

∫Idt − dΨ

dt= 0 · · · · · · · · · · · · · · · · · · · · (1)

where V is the input voltage, R is the resistance, I is the cur-rent, and C is the capacitance. The interlinkage flux of thecoil Ψ is the sum of the flux by permanent magnet Ψmag andthe flux by current excitation ΨI . The interlinkage flux Ψ isdescribed as (2) and (3) is obtained by substituting (2) into(1):

ψ = ψmag + ψI = ψmag + LI · · · · · · · · · · · · · · · · · · · · · (2)

V − RI − 1C

∫Idt − L

dIdt− dΨmag

dt= 0 · · · · · · · · · · (3)

where L is the coil inductance. The fifth term on the left handof (3) is equivalent to the back-EMF induced by motion ofthe mover. When the back-EMF is regarded as a part of in-put voltage, electrical resonant frequency fe is expressed asfollows:

fe =1

2π√

LC

√1 − ξ2 · · · · · · · · · · · · · · · · · · · · · · · · · · (4)

ξ =R2

√CL· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (5)

where ξ is the damping ratio. To generate electrical reso-nance effectively, fe needs to be the same as the frequency ofinput voltage fp. Additionally, the number of the pulse usedin PWM control changed to one for the purpose of simplifiedverification on the proposed driving theory.3.2 Control Method Figure 2 shows the PWM feed-

back control of this actuator. The circuit diagram of this op-erating mode is shown in Fig. 3. First, in interval a, the coildetects the back-EMF V1 after a positive-going zero cross-ing. In interval b, the coil has a delayed time. In interval c,the coil is excited under PWM control according to the dutydetermined by PID control using the back-EMF V1. The cir-cuit diagram of this operating mode is shown in Fig. 3(a). Ininterval d, current circulates through a body diode as shownin Fig. 3(b). Finally, in interval e, the circuit is opened asshown in Fig. 3(c).

4. Dynamic Characteristic Analysis

4.1 Analysis Model and Condition Figure 4 shows

(a) Excitation mode (b) Circulation mode (c) Open mode

Fig. 3. Control circuit

Fig. 4. 2-D FEM model

Table 1. Analysis condition

Fig. 5. Coil inductance of 2-D FEA

the 2-D finite element method (FEM) model. The numberof elements is about 19,000, and the unknown variables areabout 9,500. Table 1 shows the analysis conditions. Theresistance of the circuit for when it is in excitation modeand circulation mode are 700 mΩ and 580 mΩ respectively.The full bridge circuit shown in Fig. 3 is consisted of idealswitches. Therefore, characteristics of MOS-FET are notconsidered except forward voltage of a body diode and on-resistance. The number of step is 20,000, time division is5 μs, and total CPU time is about 3 hours.

Figure 5 shows computed coil inductance obtained from

176 IEEJ Journal IA, Vol.7, No.2, 2018


(a) Capacitance vs. amplitude

(b) Enlarged view

Fig. 6. Optimal capacitance

2-D FEA. The inductance is little dependent on the current.On the other hand, the inductance is dependent on the moverposition. Actually, the coil inductance L in (3) needs tobe treated as a nonlinear function. As shown in Fig. 2, themover is located near the center of oscillation during inter-val c. Therefore, we assumed that nonlinear effect of the coilinductance was tiny because the slope of the coil inductancewith respect to the mover position was relatively small.4.2 Optimal Capacitance As explained in the pre-

vious chapter, electro/mechanical resonance is successfullyachieved if the frequency of the input voltage fp is nearlyequal to electrical resonant frequency fe. However, whenLRA is operated under feedback control, the duty ratiochanges and this results in the change of fp. Then, in this sec-tion, we determine optimal capacitance for generating elec-tro/mechanical resonance.

Figure 6 shows the relationship between capacitance andamplitude when input voltage and its duty ratio are 2.5 V and100% respectively. Figure 6(b) indicates the amplitude be-comes maximum when capacitance is approximately 230 μF.When capacitance is less than 50 μF, the amplitude is tinyand the value is approximately one third of the maximumamplitude. When capacitance is more than 50 μF and lessthan 230 μF, the amplitude inclines according to capacitance.When capacitance is more than 230 μF, the amplitude slightlydecrease according to capacitance.

Figures 7, 8, 9, and 10 show the dynamic characteristics re-sults in case of (a), (b), (c), and (d), respectively. From Figs. 7and 8, the low amplitude results from an opposite current di-rection and this phenomenon is caused because fe is higherthan fp. In Fig. 9, current waveform is sinusoidal and elec-tro mechanical resonance is successfully achieved. In caseof (d), the current waveform is similar to sinusoid and the

Fig. 7. Dynamic characteristics in case of (a) (9.5 μF)

Fig. 8. Dynamic characteristics in case of (b) (95μF)

Fig. 9. Dynamic characteristics in case of (c) (228μF)

current direction is correct. Therefore, if fe is lower than fp,electrical resonance is generated even when fe is not equal tofp.4.3 Performance Comparison with Conventional

PWM Control Figure 11 shows the analyzed results ofmover position, input voltage, and current when capacitor isintroduced into the normal RL circuit. The capacitance is de-termined to 228 μF from the results described in the previoussection. These results suggest that the current waveform issinusoidal when the circuit is operated in excitation mode.Moreover, the phase in voltage and current is the same. Themover amplitude is 2.13 mm and average current in intervalc is 1.96 A. From these results, electrical resonance is suc-cessfully achieved on the basis of the theory explained in theprevious chapter.



Fig. 10. Dynamic characteristics in case of (d) (4760μF)

Fig. 11. Dynamic analysis results under the proposedcontrol (0.6 N load)

Fig. 12. Dynamic analysis results under the normal con-trol (0.6 N load)

Figure 12 shows the analyzed results of mover position,input voltage, and current when the LRA is driven by thenormal control method. In this result, duty ratio is 100% andthe excitation time is the same length as that in the proposedcontrol. The mover amplitude is 1.72 mm and average cur-rent in interval c is 1.72 A. From the characteristics compar-ison between the two control methods, we conclude that theproposed control method is able to generate large current be-cause of smaller circuit impedance and consequently obtainlarge mover amplitude.4.4 Load and Efficiency Characteristic In this sec-

tion, we compare load characteristics with and without elec-tro/mechanical resonance. Figure 13 shows amplitude andefficiency characteristics under feedback control. Even whenelectric resonance is employed, the duty ratio is controlled byPID control. When external load is more than 0.6 N, ampli-tude decrease depending on the load under both the two driv-ing methods. However, in this range, electro/mechanical res-onance is successfully able to obtain large amplitude. From

Fig. 13. Computed amplitude and efficiency character-istics

Fig. 14. Computed amplitude and efficiency character-istics

this result, we are able to conclude that electro/mechanicalresonance improves the amplitude characteristic particularlyat large load range.

With respect to the efficiency characteristics, when the loadis large, the superiority of electro/mechanical resonance isconfirmed. On the other hand, when the load is small, higherefficiency is achieved under the conventional control. Thisis because LRA is able to operate with small input power byutilizing long circulation time, as shown in Fig. 14. In thiscase, the duty ratio was about 0.66.

5. Experimental Verification

5.1 Measurement Setup Figure 15 shows a sche-matic diagram of a load device and a dynamic characteristicsmeasuring system. This load device consists of two actua-tors and two connection bars. The two LRAs are connectedby the rigid connection bars and their vibrations are synchro-nized. A mechanical resonant frequency is maintained evenwhen the LRAs are connected because they have the samemechanical and electrical properties.

Figure 16 shows a capacitor used in measurement. Apolypropylene film capacitor is chosen because non-polarityand large capacitance are required for this experiment. Thespecification of the capacitor is shown in Table 2. A mea-sured values of coil inductance and capacitance are 302 μHand 200 μF, respectively.5.2 Experimental Results and Discussion Figure 17

shows the measured results of mover position, input voltage,and current when a capacitor is introduced into the normalRL circuit. These results suggest that the current waveformis sinusoidal when the circuit is operated in excitation mode.



Fig. 15. Experimental setup

Fig. 16. Polypropylene film capacitor

Table 2. Specification of film capacitor

Fig. 17. Measured results under the proposed control(0.6 N load)

Fig. 18. Reverse current flow under the proposed con-trol

The mover amplitude is 2.18 mm and average current in in-terval c is 2.09 A. From the measured results, electrical reso-nance is also achieved on experiment. Meanwhile, after thecurrent excitation mode, unexpected current flows in the op-posite direction. The reason is described below. A voltageacross the capacitor occurs by storing electric charge and thevoltage is higher than the sum of the input voltage and thediode forward voltage. In this case, current flows back intopower supply through body diodes as shown in Fig. 18.

Figure 19 shows the measured results of mover position,

Fig. 19. Measured results under the normal control(0.6 N load)

Fig. 20. Measured load and efficiency characteristics

input voltage, and current when the LRA is driven by thenormal control method. In this result, duty ratio is 100%and the input time is the same length as that in the analy-sis. The mover amplitude is 1.81 mm and average current ininterval c is 1.87 A. From the measured characteristics com-parison between the two control methods, we conclude thatthe proposed control method is able to generate large currentbecause of smaller circuit impedance and consequently ob-tain large mover amplitude also on experiment. Additionally,although opposite current in the proposed control is undesir-able, the effectiveness of electrical resonance is sufficient.

Figure 20 compares two measured load characteristics un-der PID control. When the load is more than 0.6 N, ampli-tude decreases depending on the load under the normal con-trol. However, in this range, the proposed control is success-fully able to obtain larger amplitude. From the above results,we are able to conclude that the proposed control is effectivemethod to improve the mechanical output at high load rangewithout changing the input voltage or its input time. Withrespect to the efficiency, when the load is large, the superi-ority of electro/mechanical resonance is also confirmed onexperiment. On the other hand, when the load is small, theconventional control is effective because the LRA is able toutilize long circulation time.

6. Conclusion

This paper proposed a new control method in which electri-cal resonance was coupled with mechanical resonance. First,the control method was explained on the basis of a circuitequation of a RLC series circuit. Second, 2-D finite elementanalysis was implemented and the proposed control was suc-cessfully able to generate large current because of smallercircuit impedance and consequently obtain larger amplitude



than that of the normal control without increasing input volt-age or excitation time. Finally, dynamic characteristics mea-surement was conducted to verify the proposed control. Al-though opposite current flowed through body diodes due tothe voltage across the capacitor, the effectiveness of the pro-posed control was verified through the measured characteris-tics comparison between two control methods.

However, opposite current phenomenon was unexpected inthis measurement and there was no consideration of this phe-nomenon in the present analysis method. In the near future,we will implement dynamic analysis in which behavior ofreal FETs is considered.

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Masayuki Kato (Student Member) received the B.E. degree from Os-aka University in 2014 and M.E. degree in 2016. Heis currently a student in the Department of AdaptiveMachine System, Graduate School of Engineering, atOsaka University. His current research interest is onlinear resonant actuators. He received Paper Awardfrom IEEJ in 2013.

Katsuhiro Hirata (Senior Member) received the B.E. degree fromOsaka University in 1982 and D.E. degree fromDoshisha University in 1996. He was a researcherat the R&D lab., Matsushita Electric works Ltd. from1982 to 2005. He joined Osaka University in 2005.He is presently a professor in the Department ofAdaptive Machine Systems, Graduate School of En-gineering at Osaka University. He has been engagedin research of electromagnetic applied actuators andsensors. He has received Ministry Award of Educa-

tion, Science & Technology (Ministry of Education, Culture, Sports, Scienceand Technology-Japan) in 2003, IEEE member. He has received OHM Tech-nology Award (Promotion Foundation for Electrical Science and Engineer-ing) in 2004. He received Advanced Technology Award and Paper Award(IEEJ) in 2007, 2009.


characteristic evaluation of linear resonant actuator

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