PWM drive of IPMC actuators with the consideration of thecapacitive impedance
Kentaro Takagia,b , Naoya Yamaguchia , Kinji Asakac
a Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603 Japan;b RIKEN, Anagahora, Shimoshidami, Moriyama-ku, Nagoya, 463-0003 Japan;
c AIST, Midorigaoka, Ikeda, Osaka, 563-8577 Japan

ABSTRACTThis paper considers driving an Ionic Polymer-Metal Composite (IPMC) actuator using a Pulse Width Modulation (PWM) ampliﬁer, in order to shed light on the characteristics of PWM driving of IPMCs. Generally, it issaid that an eﬃciency of a PWM ampliﬁer is higher than that of a linear ampliﬁer. However, high current ﬂows
across the IPMC in the use of a PWM ampliﬁer, and it is supposed to become the power consumption high. We
solve this problem by putting an inductor between the PWM ampliﬁer and the IPMC. The simulation and theexperiment results demonstrate the eﬀectiveness of the proposed method.
Keywords: Ionic Polymer-Metal Composite, Pulse Width Modulation, Ampliﬁer, Filter

1. INTRODUCTION
Ionic Polymer-Metal Composite (IPMC) is one of the most promising Electro-Active Polymers (EAPs).1 EAPs
can deform easily by external force owing to the inherent compliance like biological muscles, in contrast to
the conventional actuators such as geared electric motors. The EAPs can be used as artiﬁcial muscles forbio-mimetic robots because of the similarities to the biological muscles. Utilizing the advantage that they candrive relatively low voltages (typically a few volts) in contrast to the dielectric polymers (typically thousandsof volts), IPMCs and ionic polymers have been employed as muscle-like actuators for bio-mimetic underwater
robots.2, 3 Unfortunately, IPMCs, ionic polymers or other EAPs have capacitive electrical impedance and thecharging current is relatively high (a few hundreds milliamperes) compared with usual capacitors, therefore
energy consumption in the electrical system could become a serious problem for the battery-powered robots.
For linear ampliﬁers, undesirable high current leads to low energy eﬃciency. On the other hands, Pulse Width
Modulation (PWM) ampliﬁers, which are said to be energy eﬃcient in driving electric actuators, may cause aproblem of highly impulsive current in driving IPMC actuators.
This paper reveals the problem in driving IPMCs with PWM ampliﬁers and proposes a method for solving
the problem caused by the PWM driving. PWM ampliﬁers, also referred as switching ampliﬁers, modulate thecommand signals into high-frequency rectangular pulse signals. PWM ampliﬁers are widely used for driving theelectric motors. Though there have been some studies4 on the reduction of the electrical noise of the PWM
ampliﬁers, the noise or the high-frequency current does not become a serious problem because the electrical
impedance of electro-magnetic actuators increases in high frequency range. However in the experiment we canobserve that high current ﬂows through an IPMC by applying PWM voltage. This is because the electrical
impedance of the IPMC decreases in high frequency range. We solve this problem by putting a ﬁlter circuit withan inductor between the PWM ampliﬁer and the IPMC. Assuming a simple transfer function model of IPMCs,
we investigate characteristics of the frequency response. Simulations in the cases with and without the ﬁlter
circuit are shown in order to estimate the eﬀectiveness. The experimental results validate the eﬀectiveness of
the ﬁlter circuit and demonstrate the reduction of the current and a comparison of energy consumption.
Further author information: (Send correspondence to K.Takagi)
K.Takagi: E-mail: takagi@nuem.nagoya-u.ac.jp, Telephone: +81-52-789-2741, Fax: +81-52-789-2754
N.Yamaguchi: n yamaguchi@nuem.nagoya-u.ac.jp, K.Asaka: asaka-kinji@aist.go.jp

Electroactive Polymer Actuators and Devices (EAPAD) 2011, edited by Yoseph Bar-Cohen, Federico Carpi,
Proc. of SPIE Vol. 7976, 79762L · © 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.880360

Proc. of SPIE Vol. 7976 79762L-1

2. MODELING AND ANALYSIS OF FILTERED PWM DRIVE
2.1 RC Circuit Model
IPMCs are typically fabricated from ion-exchange membranes through electroless plating of noble metals suchas platinum or gold.5 When an IPMC is applied voltage, electric double layers appear at the interface between
the polymer and the electrodes. The electric double layer, which stores charges, can be modeled as a capacitor.
The interface between the polymer and the electrodes of IPMC typically show a complicated shape like fractal
structure6 and electro-chemical reaction arises according to the circumstances, therefore the electrical responseof IPMC exhibits complicated behavior.7–9
In this study, we employ a simple series RC circuit6, 7 shown in Fig. 1 as the simplest electrical model. Let theequivalent series resistance and the equivalent series capacitance be Ripmc and Cipmc respectively. The transfer
function model of the impedance of IPMC, denoted by Zipmc (s), is give by:
Zipmc (s) = Ripmc +1
Cipmc s(1)where s is the complex frequency variable of Laplace transform. Because the model of Eq. (1) cannot cover theactual frequency response of the impedance, we allow the parameters Ripmc and Cipmc to vary with respect tothe frequency in the following sections.

Ripmc

CiprncFigure 1. RC circuit model for the electrical impedance of IPMC

2.2 Fabrication of IPMC and Impedance Measurement
In this study, we employed Naﬁon NE-1110 (DuPont) and carried out electroless gold plating ﬁve times in orderto form the electrode onto the membrane. The fabricated IPMC was cut into some strips. The length and thewidth of a strip are 50[mm] and 5[mm], respectively. The counter ion of the IPMC was exchanged to be sodium
ion by soaking 0.1[mol/l] NaOH solution.
The frequency response of the impedance of the IPMC was measured by an impedance analyzer(3522-50,
Hioki). The measured frequencies are 1[Hz], 10[Hz], 100[Hz] and 20000[Hz]. Table 1 shows the result of themeasurement. In the table, the frequency, the magnitude and the phase are listed in the left three columns.
Equivalent parameters Ripmc and Cipmc are also listed in the right two columns. The results are also shownby Figs.2, 3 and 4. The ﬁgures shows the impedance, the equivalent series resistance Ripmc and the equivalent
series capacitance Cipmc , respectively. From Figs. 3 and 4, we can observe that the equivalent parameters Ripmc
and Cipmc vary with respect to the frequencies. That is to say, the single RC circuit model cannot represent
the response in case the parameters are constant.6, 9 In the following analyses and simulations, the values ofthe equivalent parameters Ripmc and Cipmc will be determined with the consideration of the principle frequency
component of the signal.
Table 1. Measured impedance of the IPMC and its equivalent parameters
Frequency[Hz] Magnitude [Ω] Phase [deg] Ripmc [Ω]Cipmc [F]
1
86.2
−76.1
20.71
1.90 × 10−3
1013.2
−68.644.81
1.30 × 10−3
100
2.82
−38.0
2.22
0.94 × 10−3
20000
1.80
−0.55
1.80
0.46 × 10−3

Proc. of SPIE Vol. 7976 79762L-2

2

[ohm]

10

1

10

0

10
−1
10

0

1

10

10

2

10
[Hz]

10

3

4

5

10

10

[deg]

0

−45

−90
−1

0

10

1

10

10

2

10
[Hz]

10

3

4

5

10

10

Figure 2. Measured impedance of the IPMC
25

2
1.8

20

1.6
1.4
1.2
[mF]

[ohm]

15

10

1
0.8
0.6

5

0.4
0.2

0
−1
10

10

0

1

10

2

10
[Hz]

3

10

4

5

10

10

Figure 3. Equivalent series resistance Ripmc

0
−1
10

0

10

1

10

2

10
[Hz]

3

10

4

10

5

10

Figure 4. Equivalent series capacitance Cipmc

2.3 Filter Circuit with an Inductor
In this paper, we propose a method for reducing the ﬂowing current by connecting an appropriate ﬁlter circuit
between a PWM ampliﬁer and the IPMC.
For the ﬁlter circuit design, the high-frequency carrier component of the PWM signal should be reduced. As
the ﬁrst requirement, it is desired that the current ﬂowing in the IPMC is small. As the second, it is desiredthat the command voltage and the terminal voltage of the IPMC have both identical wave forms in the relatively
low frequencies at which the IPMC can mechanically respond. The required conditions for the ﬁlter circuit aresummarized as follows.
• In the high frequency range, or around the PWM carrier frequency, the gain of the transfer function fromthe PWM voltage to the current ﬂowed across the IPMC should be suﬃciently small.
• In the low frequency range, or under the mechanical cut-oﬀ frequency, the gain of the transfer function
from the PWM voltage to the terminal voltage of the IPMC should be 1 (one).
For satisfying the requirements, networks with inductors will be suitable because the impedance of an inductor
is monotonically increasing function with respect to the frequency. Therefore, we consider a series connection of
an inductor as the simplest ﬁlter circuit. Fig.5 shows the connection of a PWM ampliﬁer, the ﬁlter circuit withan inductor, and an IPMC. The inductor has the inductance L and the series resistance RL , which are constants.
vpwm and ipwm are the voltage and the current of the PWM ampliﬁer, and va and ia (= ipwm ) are the voltage
and the current across the IPMC, respectively.

2.4 Analysis using Transfer Functions
Let the transfer function from the PWM voltage vpwm to the terminal voltage va be Gva . In a similar fashion,deﬁne Gia as the transfer function from vpwm to ia . As shown in Sec. 2.1, the model of the impedance is theseries RC circuit. The impedance of the inductor, denoted by ZL , is given by:
ZL (s) = Ls + RL .

Proc. of SPIE Vol. 7976 79762L-3(2)

ipWin

I

IR.i

Va

Vpwin

PWIVI amplifier

IPMC

filter circuit

Figure 5. PWM driving circuit with a ﬁlter
Table 2. Parameters of the inductor

RL [Ω]
2.6

L [H]
10.1 × 10−3

From Fig. 5, and with use of Eqs. (1) and (2), we obtain the transfer functions Gva and Gia .
Gva (s) =Ripmc Cipmc s + 1
Zipmc (s)=Zipmc (s) + ZL (s)LCipmc s2 + (Ripmc + RL )Cipmc s + 1(3)

Gia (s) =Cipmc s1=
Zipmc (s) + ZL (s)LCipmc s2 + (Ripmc + RL )Cipmc s + 1(4)

Figs. 6 and 7 are bode diagrams of Eqs. (3) and (4), respectively. The sold lines and dashed lines correspondto the cases with the ﬁlter and without the ﬁlter (ZL ≡ 0), respectively. The parameters used in Figs. 6 and 7
are shown in Tables 1 and 2. Table 2 shows the parameters of the inductor. As shown in Fig. 6, the gain of Gva
under 100[Hz] is suﬃciently close to 1. The gain diagram of Gia in Fig. 7 shows that the solid line over 20[kHz]is suﬃciently smaller than the dashed line. Therefore, we can conﬁrm that the proposed ﬁlter circuit with an
inductor satisﬁes the conditions in Sec. 2.3.

0

0

−20

−20

[dB]

[dB]

Because the equivalent parameters Ripmc and Cipmc of Zipmc vary with respect to the frequency, Gva and
Gia have variations. Figs. 8 and 9 show bode diagrams of Eqs. (3) and (4) for some variations of Ripmc andCipmc as shown in Table 1. From the bode diagram of Gva , the condition of gain of 1 under 10[Hz] is satisﬁed
even though the responses over 10[Hz] depend on the equivalent parameters. In contrast to Fig. 8, the responses
over 1000[Hz] in Fig. 9 are almost identical, that is, the condition of decreasing gain in the higher frequencies issatisﬁed. Therefore, the model of Zipmc can be used for qualitative analysis of the ﬁltering properties although
the simple RC circuit model has parametric uncertainties. The eﬀectiveness of the ﬁlter circuit is demonstrated
by simulations and experiments in the following sections.

−40−60−80 −110

with filter
w/o filter
10

0

−40
−60

10

1

2

3

10

10

4

10

5

10

−80 −110

610with filter
w/o filter
10

0

10

1

2

10

4

10

5

10

6

100

0

50

−40

[deg]

[deg]

10
[Hz]

−20

−60

0
−50

−80
−100 −1
10

3

10

[Hz]

10

0

10

1

2

3

10

10

4

10

5

10

6

10

−100
−1
10

10

0

10

1

2

3

10

10

10

4

10

5

10

6

[Hz]

[Hz]

Figure 6. Bode diagram of Gva without (dashed)
and with (solid) the ﬁlter

Figure 7. Bode diagram of Gia without (dashed)
and with (solid) the ﬁlter

Proc. of SPIE Vol. 7976 79762L-4

with the parameter at 1Hz
with the parameter at 10Hz
with the parameter at 100Hzwith the parameter at 20kHz

0

0

−40

with the parameter at 1Hz
with the parameter at 10Hz
with the parameter at 100Hzwith the parameter at 20kHz

−20
[dB]

[dB]

−20

−40
−60

−60
−80 −1
10

0

10

1

10

10

2

3

10

4

10

5

−80 −1
10

6

10

10

10

0

10

1

2

10

10

3

4

10

10

5

6

10

[Hz]

[Hz]

100

0

50
[deg]

[deg]

−50

−100

0
−50

−150
−1
10

0

10

1

10

10

2

3

10

4

10

5

6

10

10

−100
−1
10

10

0

10

[Hz]

1

2

10

10

3

4

10

10

5

6

10

[Hz]

Figure 8. Bode diagram of Gva for some variations of Zipmc

Figure 9. Bode diagram of Gia for some variations of Zipmc

3. SIMULATION
3.1 Method
We used MATLAB and Simulink (MathWorks) for the simulation of PWM drive of IPMC. The PWM signal
vpwm (t) is calculated from the command signal which is sine wave with 1[V] amplitude and 1[Hz] frequency.
vpwm (t) has three values of −6[V], 0[V] and 6[V], and has the carrier frequency of 20[kHz]. We also calculate va
and ia from vpwm (t) by using Eqs. (3) and (4). We use circuit parameters of 1[Hz] in Table 1 and Table 2. The
sampling frequency for numerical integration is 100[MHz] and the simulation interval is 2[s].

3.2 Results
The time response of va , which is the voltage across the IPMC, is shown in Fig. 10. We indicate the result withthe ﬁlter circuit at the right and without at the left. Without the ﬁlter circuit, va is square wave of 20[kHz],
while with the ﬁlter circuit, the wave form of va is nearly sine wave of 1[V] and of 1[Hz]. This is because the ﬁlter
circuit cuts high-frequency harmonic components of vpwm , therefore the voltage applied to the IPMC becomesclose to the sinusoidal command signal.
Similarly, the time response of ia which is the current through IPMC is shown in Fig. 11. The result with theﬁlter circuit is indicated at the right and without the ﬁlter is at the left. The peak of ia without the ﬁlter circuit
is about 0.3[A], while the wave form of ia with the ﬁlter circuit is nearly sine wave with 0.013[A] amplitude.
With regard to the current peak, the result with the ﬁlter circuit is less than one-tenth as large as the result
without the ﬁlter circuit. The wave form with ﬁlter circuit gives close agreement with the sine wave response of
IPMC. From the simulation results, we can observe that the ﬁlter circuit can suppress the harmonic components
and can keep the current through IPMC small.
v ipmc

1.5

4

1

2

0.5

[V]

[V]

pwm

6

0

0

−2

−0.5

−4

−1

−6

0

0.5

1
[s]

1.5

2

−1.5

0

0.5

1
[s]

1.5

Figure 10. Simulated voltage va without (left) and with (right) the ﬁlter circuit

Proc. of SPIE Vol. 7976 79762L-52

i ipmc

0.4

0.015

0.3

0.01

0.2
0.005

[A]

[A]

0.1
0
−0.1

0

−0.005

−0.2
−0.01

−0.3
−0.4
0

0.5

1
[s]

1.5

2

−0.015

0

0.5

1
[s]

1.5

2

Figure 11. Simulated current ia without (left) and with (right) the ﬁlter circuit

4. EXPERIMENT
4.1 Experimental Setup and Method
The experimental setup is shown in Fig. 12. As mentioned in Sec. 2.1, we use a beam-shaped IPMC that is of
50[mm] long and 5[mm] wide and is clamped by a gold-plated Kelvin clip. We also give the IPMC deionizedwater during the experiment, in order not to dry the IPMC.
The inductor used in the ﬁlter circuit is a radial lead inductor of 25.5[mm] tall, 20.8[mm] in diameter and26[g] weight. The parameter of the inductor has been indicated in Table 2. In the experiment, we use acommercial PWM ampliﬁer (ZDCMD-1C3008, ZUCO). We give the PWM ampliﬁer 6.0[V] power-supply, andhas conﬁrmed that the amplitude of the PWM signal is almost equal to the power-supply voltage. The carrier
frequency of the PWM signal is 18.6[kHz]. The command voltage applied to the PWM ampliﬁer takes 0[V] to
5[V] corresponding to negative and positive output signals. We apply the sine wave of 0.42[V] amplitude and1[Hz] frequency with 2.5[V] biased voltage as the command signal in order to output the modulated sine wave of
1[V] and 1[Hz] frequency. The command voltage output by a function generator is applied to the PWM ampliﬁer.
Unfortunately, there exists a dead zone of the PWM ampliﬁer used in this experiment. The dead zone means
small interval within which the output keeps 0[V] even the input voltage is applied to the ampliﬁer. The deadzone of the command voltage of this PWM ampliﬁer was about 2.5±0.1[V].
The measurement and the data acquisition is done by a oscilloscope (TDS2004B, Tektronix). The applied
voltage va is measured and the current ia is estimated from the terminal voltage of the shunt resistor shown in
Fig. 12. The shunt voltage is ampliﬁed by an instrumentation ampliﬁer with the magnitude of 97.4 becauseof the small resistance that is 93.3[mΩ]. The consumed energy in the resistive elements of the IPMC and theinductor is also calculated from the estimated current ia .

Figure 12. Experimental setup

4.2 Results and Discussions
Figures 13 and 14 show time histories of the applied va and the current ia , respectively. The discontinuous partsaround 0[V] or 0[A] are due to the dead zone of the PWM ampliﬁer. Although the low sampling frequency

Proc. of SPIE Vol. 7976 79762L-6

Table 3. Averaged power consumption

Pc [W] (without the ﬁlter)
365.4 × 10−3

Pc [W] (with the ﬁlter)
2.9 × 10−3

(2.5[kHz]) relative to the PWM frequency (18.6[kHz]) causes aliasing, we can observe the diﬀerence of the wave
forms of the cases without and with the ﬁlter circuit. As shown in Fig. 13, the wave form of the voltage va
becomes sine wave by the ﬁlter circuit. The peak of the current ia dramatically decreased, from 1.6[A] to
0.04[A], as shown in Fig. 14. Due to the saturation of the instrumentation ampliﬁer, the peak of the current in
the case without the ﬁlter is over 1.6[A]. The reduction ratio of the peak current is under 1/50.
The instantaneous consumed power, denoted by pc , is shown in Fig.15. The instantaneous consumed powerpc is calculated by:pc (t)
pc (t)==

Ripmc i2a (t)(without ﬁlter circuit)2(Ripmc + RL ) ia (t)(with ﬁlter circuit)

(5)
(6)

where Ripmc and RL are the resistances of the IPMC and the inductor. Averaged consumed power, denoted by
Pc , is given by:1 T
pc (t) dt
(7)
Pc =
T 0
where T is the period of the command signal. In the computation of Eq. (7), the resistance of the IPMC ischosen by the dominant frequency component. In the case without ﬁlter, Ripmc = 1.80[Ω] because the PWM
frequency is about 20[kHz]. In the case with ﬁlter, Ripmc = 20.71[Ω] because the principle frequency is 1[Hz].
The estimated Pc by the computation is shown in Table 3. The consumed energy can be reduced under 1/100
by the ﬁlter circuit.
In summary, the results have shown that the power consumption in addition to the current through the IPMC
could be reduced dramatically by the ﬁlter circuit.
1

6
4

0.5

[V]

[V]

2
0

0

−2

−0.5
−4
−6
−0.5

−0.25

0
[s]

0.25

0.5

−1
−0.5

−0.25

0
[s]

0.25

0.5

Figure 13. Measured voltage va without (left) and with (right) the ﬁlter circuit

5. CONCLUSION
This paper has pointed out the problem that large current ﬂowed across an IPMC when was driven by a PWM
ampliﬁer. In order to solve the problem, we have proposed a method using a ﬁlter circuit. For the analysis andthe design of the ﬁlter circuit, a simple equivalent series RC circuit model has been introduced. The proposedﬁlter circuit, inserted between the IPMC and the PWM ampliﬁer, simply consists of one inductor for ﬁltering
the high frequency component of the PWM signal. Analysis using the transfer functions, from the input PWM
voltage to the output voltage/the output current, has shown that the ﬁlter circuit did not aﬀect the low-frequency
gain and could reduce the high-frequency gain to cut the high-frequency current. Simulation results have shownthat the wave form of the voltage or the current with the use of the ﬁlter circuit became similar to that in theProc. of SPIE Vol. 7976 79762L-7

0.03

1

0.02

0.5

0.01

[A]

0.04

[A]

2
1.5

0

0

−0.5

−0.01

−1

−0.02

−1.5

−0.03

−2
−0.5

−0.25

0
[s]

0.25

−0.04
−0.5

0.5

−0.25

0
[s]

0.25

0.5

6

0.03

5

0.025

4

0.02

[W]

[W]

Figure 14. Measured current ia without (left) and with (right) the ﬁlter circuit

3

0.015

2

0.01

1

0.005

0
−0.5

0
[s]

0.5

0
−0.5

−0.25

0
[s]

0.25

0.5

Figure 15. Estimated power consumption pc without (left) and with (right) the ﬁlter circuit

case of the sinusoidal input. Experimental results have demonstrated that the ﬁlter circuit could dramaticallyreduce the spike current, in addition to the electrical energy consumption of the IPMC.
Because the ﬁlter circuit has the capability of the reducing the current of IPMCs or other EAPs for the useof PWM ampliﬁer, it is expected that the proposed method can be employed for energy-eﬃcient PWM driving
for any capacitive EAPs.

REFERENCES[1] Bar-Cohen, Y., ed., [Electroactive Polymer (EAP) Actuators as Artificial Muscles: Reality, Potential, andChallenges ], SPIE Press, Washington, 2nd ed. (2004).
[2] Takagi, K., Yamamura, M., Luo, Z.-W., Onishi, M., Hirano, S., Asaka, K., and Hayakawa, Y., “Developmentof a rajiform swimming robot using ionic polymer artiﬁcial muscles,” IEEE/RSJ International Conferenceon Intelligent Robots and Systems , 1861–1866 (2006).
[3] Aureli, M., Kopman, V., and Porﬁri, M., “Free-locomotion of underwater vehicles actuated by ionic polymer
metal composites,” IEEE/ASME Transactions on Mechatronics 15, 603–614 (2010).
[4] Sozer, Y., Trrey, D. A., and Reva, S., “New inverter output ﬁlter topology for PWM motor drives,” IEEE
Transactions on Power Electronics 15(6), 1007–1017 (2000).
[5] Shahinpoor, M. and Kim, K. J., “Ionic polymer-metal composites: I. fundamentals,” Smart Materials andStructures 10, 819–833 (2001).
[6] Bao, X., Bar-Cohen, Y., and Lih, S., “Measurements and macro models of ionomeric polymer-metal composites,” Proc. SPIE 4695, 220–227 (2002).
[7] Onishi, K., Sewa, S., Asaka, K., Fujiwara, N., and Oguro, K., “The eﬀects of counter ions on characterizationand performance of a solid polymer electrolyte actuator,” Electrochimica Acta 46, 1233–1241 (2001).
[8] Farinholt, K. and Leo, D., “Electrical impedance modeling of ionic polymer transducers,” Proc. SPIE 5761,
69–80 (2005).
[9] Takagi, K., Nakabo, Y., Luo, Z.-W., and Asaka, K., “On a distributed parameter model for electrical
impedance of ionic polymer,” Proc. SPIE 6524 (2007).

Proc. of SPIE Vol. 7976 79762L-8