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This paper presents feedforward, feedback and two-degree-of-freedom control applied to an Ionic Polymer-Metal Composite (IPMC) actuator. It presents a high potential for development of miniature robots and biomedical devices and artificial muscles. We have reported in the last few years that dehydration treatment improves the electrical controllability of bending in Selemion CMV-based IPMCs. We tried to replicate this controllability in Nafion-based IPMC. We found that the displacement of a Nafion-based IPMC was proportional to the total charge imposed, just as in the Selemion-CMV case. This property is the basis of self-sensing controllers for Nafion-based IPMC bending behavior: we perform bending curvature experiments on Nafion-based IPMCs, obtaining the actuator's dynamics and transfer function. From these, we implemented self-sensing controllers using feedforward, feedback and two-degree-of-freedom techniques. All three controllers performed very well with the Nafion-based IPMC actuator.

Ionic Polymer-Metal Composite (IPMC) is a bending mode electroactive polymer actuator. Its supple motion and soft body and electroactive nature make it strikingly similar to animal muscle [

Silver-coated Selemion CMV-based IPMC (hereafter called Selemion IPMC) is another type of IPMC. IPMCs are usually activated in a highly hydrated state even in an aqueous solution, and Selemion IPMC exhibits large bending in response to an applied voltage when in such a state. Its bending controllability was poor like Nafion-based IPMC. However, we found previously that it could be ameliorated greatly by dehydration treatment [

Hoping to capitalize on the similarity between Nafion and Selemion CMV, we fabricated a silver-coated Nafion-based IPMC (hereafter called Nafion IPMC) and investigated its bending controllability in the dehydrated state. Contrary to expectation, we observed only a slight improvement in bending controllability in the dehydrated state. However, we carried out further investigation and found the bending controllability of Nafion-based IPMC improved in the extremely low absolute humidity environment. We observed the linear relationship between the Nafion IPMC bending curvature and the quantity of charge imposed on it like Selemion IPMC. This experimental result indicated that the bending controllability of Nafion-IPMC could be significantly improved in the extremely low humidity environment. Therefore, we attempted to self-sensing control the bending of Nafion-based IPMC by feedback, feedforward and two-degree-of-freedom control techniques [

Nafion based IPMC actuator is formed from a piece of Nafion coated with silver. Its fabrication requires several steps. The surfaces of a Nafion sheet are first crazed and sandblasted to improve silver adhesion [

For clearly explain our research results, firstly, we came to think that it was better to experimentally ascertain the relationship between Nafion IPMC bending behavior and environmental humidity. To do so, following experiment was carried out first.

A dehydrated Nafion IPMC was clamped at one end to a pair of electrodes connected to a power supply as shown in

Experimental setup for measuring the tip displacement of Nafion Ionic Polymer-Metal Composite (IPMC). Illustrations on the left and right respectively show the shape of Nafion IPMC in the OFF and ON stages.

Bending curvature of the Nafion IPMC ^{−3} (^{−3}.

Then we carried out the same experiment even at the lower absolute humidity environment. ^{−3}. We could observe a linear relationship between the curvature and charge about Nafion IPMC like Selemion IPMC in the extremely low humidity environment, and the Nafion IPMC exhibited regular triangular form of curvature as a function of time under the oscillating rectangular voltage (amplitude = 2 V, frequency = 0.05 Hz) as shown in

(^{−3} (

^{−1}. This linearity was all the more surprising because Nafion IPMC was not a precisely structured material. It had a bumpy silver layer as seen in

Top surface of the Nafion IPMC. Notice the bumpy silver layer.

In an extremely low humidity environment, Nafion IPMC bending comes to exhibit well-ordered characteristics as in

Using the experimental data shown in

We employed a system identification technique to derive the transfer function. Among the many applicable techniques, we chose the ARMAX (Auto-Regressive Moving Average exogenous) model. This model is expressed in (1) and its block diagram is shown in

The ARMAX model used in system identification.

The transfer function G(q) and the noise model are given by Equations (2) and (3), respectively.

The ARMAX model works quite well for building noise models and is widely employed in system identification. In this study, we built a model using the System Identification Toolbox in MATLAB. The data set used for the system identification step consists of the rectangular voltage wave shown in

The oscillating rectangular voltage used as input on a Nafion IPMC specimen to obtain the data shown in

We refined our model by making more measurements and doing additional system identifications at various humidities between 7 and 11 gm^{−3}. Despite the observation of unpredictably complex bending behavior of highly hydrated IPMC [^{−3} but the change can be modeled simply by a multiplicative factor m(AH), whose value depends only on the absolute humidity as shown in Equation (5).

To validate the transfer function Equation (4) of the Nafion IPMC, we compared its predicted output in response to an input waveform of 0.17 Hz frequency which is different from the one (0.05 Hz) used to derived the transfer function, although the amplitude was the same as before (2 V).

Time-dependent bending curvature of Nafion IPMC obtained experimentally and computationally.

We attempted to control the bending of dehydrated Nafion IPMC using feedforward, feedback and two-degree-of-freedom techniques. Feedforward control requires an inverse control system using the transfer function of the Nafion IPMC. Thus, we performed a system identification to obtain it. All three control systems were tested in turn by implementing them in Simulink (within Matlab) and using the output to drive an s-BOX (MTT, Tokyo) DSP connected to a Nafion IPMC.

As described already, we tested bending controllability of Nafion IPMC employing feedforward, feedback and two-degree-of-freedom controls. Block diagrams for those three controlling methods were drawn using Simulink of MATLAB. We put in practice those control systems by driving a Simulink-assisted DSP called s-BOX (MTT, Tokyo). All the bending control tests were carried out at the absolute environmental humidity around 7 gm^{−3}.

A diagram of the feedforward control we implemented to control the bending of a Nafion IPMC specimen appears in

(

Bending curvature of the Nafion IPMC ^{−3} under feedforward control. Fine curve: Experimental data Thick curve: Desired ideal curve.

A step disturbance of ^{−1} in the current was introduced at time t = 53 s and kept from then onward, resulting in a disturbance in the curvature. The current was significantly altered at t = 53 s. However, the curvature continued to follow the input wave despite the disturbance. The bending curvature exhibited a tendency to increase with time after t = 53 s, since the current continued to be elevated after the step.

(^{−3} under feedforward control with a disturbance of ^{−1} from t = 53 s onward.

We implemented the self-sensing feedback control system in ^{−1}) described in section 3 was used to estimate the curvature ^{−1} in the current was introduced at time t = 53 s and kept from then onward.

(a) Bending curvature of the Nafion IPMC ^{−3} under self-sensing feedback control with a disturbance of ^{−1} from t = 53 s onward. Fine curve: Experimental data Thick curve: Desired ideal curve.

^{−1} from time t = 53 s onward.

Two-degree-of-freedom control system.

Bending curvature of the Nafion IPMC ^{−3} under the two-degree-of-freedom control with a disturbance of C’ = 0.0005 mm^{−1} from t = 53 s onward. Fine curve: Experimental data Thick curve: Desired ideal curve.

Exploiting the linear relationship of “bending curvature

What we would like to emphasize in this research is not the experimental fact that the three control techniques work well for the bending control of Nafion IPMC. In fact, there have already been a number of publications dealing with the IPMC bending control [

It was found that the dehydrated Nafion IPMC exhibits linear relationship of curvature

The authors would like to express their gratitude to Ministry of Education, Culture, Sports, Science and Technology for the financial support under the Knowledge Cluster Initiative the Second Stage Tokai Region Nanotechnology Manufacturing Cluster and the Grant-in-Aids for Science Research (the research project number 24560291).

The authors declare no conflict of interest.