Displacement Measurement System and Control of Ionic Polymer Metal
Composite Actuator
KYRIAKOS TSIAKMAKIS, VASILEIOS DELIMARAS, ARGYRIOS T. HATZOPOULOS,
MARIA S. PAPADOPOULOU
Department of Information and Electronic Engineering
International Hellenic University
Thessaloniki
GREECE
Abstract: - This work presents a study comparing two control methods used in IPMC actuators. The position of the
free end of the actuator is extracted using low-frequency signals, and the driving voltage is limited to ±3 V. This
paper also proposes a new image sensor-based method for measuring displacement, which uses the actuator's route
and applied current to predict the direction and detect the free edge using small areas of interest. The algorithm
detects the area of the moving route, reduces the searching area of the IPMC's free edge, and predicts the edge
direction. An experimental setup was established using a laser sensor and camera system. The results of simple
computer usage reveal that the new technique is 17% faster. The paper also discusses model identification using a
black-box approach. A major objective is to find the optimal control settings for various methods to highlight the
issue of saturation and define the duration in which the IPMC actuator can be controlled.
Key-Words: - displacement measurement, image sensor, laser sensor, control of robotic actuator, PID, MRAC
Received: November 13, 2022. Revised: April 19, 2023. Accepted: May 13, 2023. Published: June 12, 2023.
1 Introduction
Ionic Polymer-Metal Composite (IPMC) is a type of
smart material that exhibits bending deformation
when an electric potential is applied, [1]. These strips
have found applications in various fields, including
biomechanics, automobiles, and robotics, [2].
An application of IPMCs as actuators in the
environment is the development of artificial muscles
for soft robotics. IPMCs can be used as actuators in
soft robots, enabling them to move and manipulate
objects in the environment, [3].
The IPMC actuators have been employed in the
development of water and airflow control systems in
the environment and can be used as pumps and
valves, controlling the flow of fluids and gases. Can
be used in water treatment plants to control the flow
of water and ensure that it is properly treated before
being released back into the environment, [4].
The development of devices that can simulate the
movements of living organisms, such as fish or birds,
is one area of interest for environmental monitoring
and exploration. It is possible to create robotic
machines that can fly or swim in the air or water
using IPMC actuators, [5], [6].
One important aspect of using IPMC strips is the
need for accurate position measurement and control,
[7]. Research in position measurement and control of
IPMC strips has focused on developing techniques
and control algorithms to accurately track and control
the position of the strip. Control methods have also
been developed that use feedback from these sensors
to control the position of the strip. These methods
typically use a proportional-integral-derivative (PID)
controller or an adaptive controller to adjust the
applied electric potential and maintain the desired
position of the strip, [8], [9]. These techniques use
mathematical models of the IPMC strip to predict its
behavior and adjust the applied electric potential in
real-time to achieve the desired position. Overall,
research in position measurement and control of
IPMC strips is an important area of study that has the
potential to advance the use of these smart materials
in various fields, [10]. IPMC strip position
measurement and control research is a rapidly
evolving field with numerous applications in a wide
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DOI: 10.37394/23203.2023.18.15
Kyriakos Tsiakmakis, Vasileios Delimaras,
Argyrios T. Hatzopoulos, Maria S. Papadopoulou
E-ISSN: 2224-2856
144
Volume 18, 2023
range of industries. In the future, the field of IPMC
strips will continue to advance through the
development of new fabrication techniques, control
approaches, and exploration of new applications,
[11].
In this work, two control methods are compared
and presented. Step or low-frequency square signals
are specifically applied to the control systems. Many
researchers extract the position of the free end of the
strip without considering the high increment of the
applied voltage. The driving voltage of the IPMC
actuator is limited to |3 V| due to higher voltage the
plant will be destroyed. In this paper, the simulation
results with and without this saturation are presented.
The study and development of these methods showed
that it is possible to accurately control the position
until the applied voltage does not exceed the
amplitude of ±3 V.
There are several methods for displacement
measurement of Ionic Polymer-Metal Composites
(IPMCs), including using a laser, a camera, or an
integrated sensor. This laser method can provide high
accuracy and resolution, but it requires expensive
equipment and is sensitive to environmental factors
such as temperature and vibration and bigger
displacements, [12].
The camera system involves using a low-cost
camera to capture images of the IPMC and analyze
the displacement based on the image data. This
method is non-contact and can provide high spatial
resolution, but it requires careful calibration and is
sensitive to lighting conditions and camera settings,
[13].
The integrated sensor method involves attaching
a sensor to the IPMC and measuring the displacement
based on the output of the sensor. This method can
provide high accuracy and is relatively simple and
inexpensive, but it requires direct contact with the
IPMC and may not provide high spatial resolution,
[14].
A new image sensor-based method for measuring
displacement is presented. The new algorithm uses
the route of the actuator and the applied current to
predict the direction and detect the free edge using
small areas of interest. The algorithm reduces the
search area by creating small overlapping regions.
Edge detection techniques are applied to these small
areas to locate the free edge of the IPMC.
The algorithm performs gray-scale and clipping,
followed by edge detection and feature edge
detection. It distinguishes the IPMC strip from the
background, determines the edge, and identifies the
region surrounding the edge.
In this work, the problem of saturation in the
applied driving voltage of the IPMC is presented. The
control can hold its position steady for a short time
until the voltage reaches the value |3 V|. One of the
main objectives of the work is to identify the settings
needed by each control method to be able to control
the position of an IPMC with different geometric
characteristics for a longer period of time. Depending
on the time it can be kept in a stable position, IPMC
actuators can be employed in robotic systems for
precise positioning and manipulation tasks. By
implementing position control, IPMC actuators can
be used to control the movement of robotic limbs,
grippers, or other end-effectors. This application is
particularly useful in scenarios where delicate and
precise movements are required, such as in medical
robotics or assembly operations.
2 Measurement Method
An experimental setup was established using a laser
sensor and a camera system, as shown in Fig.1. The
setup was driven with low-frequency voltage signals
(up to 100 mHz) using a computing system and a
current amplifier that generated sinusoidal, square,
and step signals. The captured image of the
movement was then digitized through an image
processing algorithm, which plays a crucial role in
the proposed visual measurement technique. One
IPMC sample was tested in water.
The experimental setup involves the use of a
camera with a frame rate of 60 frames-per-second
and a resolution of 640×480 pixels per frame. The
camera was employed to monitor the movement of
the IPMC (Nafion/Li+) actuator strip of length
2.5 cm.
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DOI: 10.37394/23203.2023.18.15
Kyriakos Tsiakmakis, Vasileios Delimaras,
Argyrios T. Hatzopoulos, Maria S. Papadopoulou
E-ISSN: 2224-2856
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Fig. 1: Experimental setup for measuring the
displacement of IPMC actuators
Accuracy is directly related to the resolution of
the image. Experimental results show 1 pixel
deviation between the marked and real point of
interest. The image resolution of 640×480 pixels
indicates a position error of about ±0.09 mm for this
experimental setup.
A new method for measuring displacement is
presented. The main procedure of the algorithm is the
frame extraction and the calculation of the
displacement from data. The procedure is fully
automated for the detection of the free end edge of
the IPMC actuator in each frame and provides a
graphical display of the points required for the time-
related computations.
The system exports the relevant frames with the
corresponding time-stamps.
Fig. 2: The minimized area of interest and small
regions
One way of determining the correlation between
pixels and the actual size is to utilize a component in
the viewing field as a point of reference, taking into
consideration the camera's resolution and distance
from the actuator.
The camera is placed perpendicular to the
movement of the material and the region of interest is
determined (B), as shown in Fig.2. At the beginning,
the actuator is activated by applying a low-frequency
sinusoidal signal and the algorithm detects the area of
moving route (R). The purpose of this
implementation is to reduce the searching area of the
lower free edge of the IPMC.
Small overlapping areas (C) are created
throughout the route. The goal is to apply edge
detection techniques only to small areas. Then the
algorithm reads the current provided by the external
circuit and predicts the direction of the free edge. It
can detect if the material is moving to the left or to
the right and in the case of the step response (or
control), it is necessary to detect when it holds at a
steady state value.
Using the time and the value of the current value
the algorithm chooses the appropriate small regions
to locate the free edge. The edge detection algorithm
has been described in the paper, [15].
Fig. 3: Proposed block diagram of the process
If the algorithm fails many times to locate the edge,
then an initial process to resize-increase the area of
small regions or redetect the route is performed
again, as shown in Fig.3.
The software then performs grayscale and clipping,
followed by edge detection and feature edge
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Kyriakos Tsiakmakis, Vasileios Delimaras,
Argyrios T. Hatzopoulos, Maria S. Papadopoulou
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detection as the first steps in the extraction process
for each small region. The grey-scale method was
utilized to monitor the end of the strip under varying
light conditions in comparison to the black-white.
The location of the IPMC strip is then distinguished
from the background by utilizing an automated
process that employs an appropriate clipping method
to concentrate on the area where the material is
moving. The edge is then distinctly determined
through surface tracing and edge detection, which
also detects the spots required for calculating the
displacement measurement.
The region surrounding the edge is identified
using an image analysis algorithm. The procedure
then determines the centre point from this region to
correct for any inaccuracies caused by the actuator's
thickness. The accuracy of these calculations is
determined by the magnitude of the displacement.
The procedure is calibrated, and the computer system
automates the process, ensuring a precise relationship
between the pixel difference and real-world
difference. To ensure accurate image capture, the
calibration procedure involves determining and
adjusting the camera's internal properties and
characteristics. This includes factors such as lens
distortion, focal length, sensor size, and other
characteristics that affect how the camera captures
and interprets light. A calibration target or pattern
with a defined size and features is used to calibrate a
camera. Checkerboard patterns and specific
calibration charts are common calibration targets.
These targets serve as reference points throughout the
calibration procedure. The camera's resolution is
equal to 0.09mm when a specified field of view and
distance between the camera and the actuator in mm
are used. The software determines the number of
pixels associated with the actuator and, with the
knowledge of its exact size, calculates the correct
relationship between pixels and actual length units.
The results of the new method showed that the new
technique is 17% faster when using simple computer
usage according to the research, [16].
3 Model Identification
The inherent difficulties of performing experiments
under underwater conditions, combined with the
difficulty in determining the transduction effect of an
IPMC actuator, make obtaining a physical or grey
box model extremely challenging. As a result, this
research takes a black-box approach. The goal of this
method is to estimate the coefficient values of a priori
well-determined transfer function. The coefficients
are calculated empirically by comparing experimental
data to transfer function evaluations.
The IPMC-based cantilever's step response must
be measured first. Fig.4 shows the results of the
experiment. Using the sweep plus step response
signal, the model is estimated and identified
throughout the identification process.
Fig. 4: Step response of IPMC measured by camera-
based system
The estimation process compares the output of the
model to a predetermined set of inputs and
parameters. Using a cost function, the model's output
is compared to the experimental data.
The cost function 𝐹 used is based on the mean
squared error (MSE):
𝐹
∑
𝑦𝑦
(1)
where 𝑦 is the measured value, the 𝑦 is the
corresponding simulated value and the n is the
number of samples. The parameters that minimize the
cost function are determined using a cost function
minimization algorithm. It's critical, to begin with the
appropriate initial settings when using this type of
identification procedure to ensure that the maximum
frequency range is covered. Furthermore, certain
numbers of periods are used in this evaluation for
each of these signals to restrict the influence of noise
sources.
To produce reliable identification results, the
input signal must have sufficient power information
in the frequency region where the model is identified.
The outcome of the identification procedure is a
fourth-order transfer function.
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Kyriakos Tsiakmakis, Vasileios Delimaras,
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The identified fourth-order model is then reduced to a
second-order model in the following function:
𝐻𝑧 . .
.. (2)
The reduction of a fourth-order model to a second-
order model is accomplished by the use of a specific
technique and a related algorithm. Primary phases in
the method include the comparison of poles with
zeros, approximations of equal values, and
adjustment of residual terms, all of which are
necessary. Although a fourth-order model accurately
represents the behavior of IPMC, we must avoid
intricate computations that result in time-consuming
calculations. A simplified approach to system
analysis is achieved by the use of a reduced second-
order model, which provides almost the same
accuracy in the description of the system's behavior
as the original model. The frequency range of interest
is below 1 Hz, which is where the great majority of
underwater robotic applications operate.
After obtaining the IPMC actuator's open loop
model, a reference model may be presented to
characterize the system's expected dynamic behavior
in closed loop operation.
The purpose of model reduction is to operate
independently of frequency resonance and to simplify
mathematical computations.
Experiments and simulations have revealed that
the majority of model constraints in the second order,
particularly at low frequencies, are decreased. While
a simplified model without resonance frequency is
simple to create and use in real-time control systems,
it does not accurately represent the model's behavior
and may result in unstable situations, particularly for
long IPMC samples. As a consequence, the strategy
that results in a lower order model and eliminates the
resonance frequency component is best appropriate
for small length samples, and low frequencies where
the influence of resonance is minor.
4 Results
4.1 Simulation Results
According to the specific transfer function of (2), two
position control methods of the IPMC for step
response are presented. The first uses a simple PID
and the second a MRAC control presented in a
previous study, [17].
Fig. 5: PID control for IPMC actuator
The desired final value is achieved when simulated
position control is applied, but a high plant input
voltage is not considered. In this study, the input
voltage, the equation of the discrete transfer function
and the control diagrams are presented. The simple
Discrete PID control is shown in Fig.5. At the system
input, a step function is applied with a voltage
amplitude that determines the controller's setpoint,
denoted as 𝑟𝑛, aiming to achieve the desired
displacement at the plant's output 𝑦𝑛. The error,
denoted as 𝑒𝑛, is then calculated as the difference
between the setpoint and the actual displacement, that
is, 𝑒𝑛𝑟
𝑛𝑦
𝑛. It is important to note that
the output 𝑦𝑛 is multiplied by a suitable factor
𝛼 1000 to scale it to the same order of magnitude
as the amplitude of the input voltage 𝑟𝑛.
Subsequently, using the error 𝑒𝑛, the discrete PID
outputs a signal that controls the plant's input,
denoted as 𝑢𝑛, which is limited to a maximum of ±
3 V before being applied to the IPMC. The
optimization algorithm Taguchi is used to determine
the parameter values 𝛫, 𝛫, and 𝛫, [18].
Fig. 6 and Fig.7 show the simulated response of
the PID control system to a step input signal without
applied voltage saturation for a duration time of 100 s
and 1 s respectively. In the middle part of the figure,
the error computed as the difference between input
voltage and displacement is shown. The output value
remains at a constant value but the applied voltage of
the plant increases to high values. Similar results for
a simulated 100 mHz square signal without applied
voltage saturation are shown in Fig.8.
Fig. 9 shows the simulated response of the PID
control system to a step input signal with applied
voltage saturation for a duration time of 20 s. The
output value remains at a constant value up to 12.3 s.
This saturation prevents the application of low-
frequency signals. The simulated response of PID
control for 100 mHz input square signal with applied
voltage saturation is shown in Fig.10. The frequency
of the input signal is above the lower limit, the output
value remains at a constant value and the applied
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voltage of the plant increases to saturation value
without causing instability.
Fig. 6: PID - Simulation for 100 s - Step response
without applied voltage saturation: displacement,
error and applied voltage
Fig. 7: PID - Simulation for 1 s - Step response
without applied voltage saturation: displacement,
error and applied voltage
Fig. 8: PID - Simulated 100 mHz square signal
without applied voltage saturation: displacement,
error and applied voltage
Fig. 9: PID - Simulation for 20 s - Step response with
applied voltage saturation: displacement, error and
applied voltage
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Fig. 10: PID - Simulated 100 mHz square signal with
applied voltage saturation: displacement, error and
applied voltage
Fig. 11: PID - Simulated 1 Hz sinusoidal signal with
applied voltage saturation: displacement, error and
applied voltage
The simulated response of PID control for 1 Hz
sinusoidal signal with applied voltage saturation is
presented in Fig.11. The saturation problem does not
appear for sinusoidal signals because the voltage at
the input of the plant adapts faster to low values.
Fig. 12: MRAC control for IPMC actuator
The block diagram system of MRAC control for
IPMC actuator is presented in Fig.12. The four
gamma constants (𝛾, 𝛾, 𝛾, and 𝛾) are set by an
optimization algorithm, as reported in a previous
study, [17].
Fig. 13 shows the simulated response of the
MRAC system to a step input signal without applied
voltage saturation for a duration time 100 s. The
output value remains at a constant value, but the
applied voltage of the plant increases to high values
up to 20 V.
Fig. 13: MRAC - Simulation for 100 s - Step
response without applied voltage saturation:
displacement, error, and applied voltage
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Fig. 14: MRAC - Simulation for 20 s - Step response
with applied voltage saturation: displacement, error
and applied voltage
Fig. 14 shows the simulated response of the
MRAC system to a step input signal with applied
voltage saturation for a duration time of 20 s. The
output value remains at a constant value up to 13.8 s.
It appears that MRAC shows a slight improvement
over PID.
4.2 Experimental Results
In this chapter, the experimental results of the two
controls with the use of voltage saturation for a
simple step response are presented.
Fig. 15: Measuring displacement camera and laser-
based system
In Fig.15 the displacement measured with both
systems, camera and laser-based, when a sinusoidal
input voltage is applied with an amplitude of 0.5 V is
presented. At the operating frequency, the camera
sensor-based measurement system is comparable to
the laser sensor-based measurement system. There is
no significant phase slip observed, nor a significant
difference in the measurement of displacement
between the two methods. However, at the peaks of
the sine wave, an underestimation of the
displacement measurement by the laser sensor is
expected. As the point of interest (i.e., the free end of
the IPMC) moves away, the laser sensor measures
slightly closer to the fixed end of the IPMC, which
exhibits less bending.
Fig. 16 shows the experimental step response
graph produced by the camera-based system when
PID control is applied with voltage saturation. The
output value remains at a constant value up to 12.2 s.
Once this time has elapsed, the output of the PID
reaches a maximum value of 3 V and is unable to
effectively maintain the displacement of the IPMC.
Fig. 16: PID control - Experimental step response
with a camera-based system
The Taguchi-method optimized parameter values 𝛫,
𝛫, and 𝛫 are different from the values set in the
simulation.
This is due to the time required for processing
between the two frames and the input voltage applied
to the actuator through feedback to the PID controller
is dependent on the frame rate.
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Fig. 17: MRAC control - Experimental step response
with a laser-based system
The graph with experimental step response, when
MRAC control is applied with voltage saturation, is
shown in Fig.17. The output value remains at a
constant value up to 13.5 s. The optimized parameters
gamma (𝛾) have been obtained using the same
optimization method as in the case of the PID
controller. The MRAC controller managed to
maintain the displacement of the IPMC for an
additional 1.3 seconds compared to the PID.
Fig. 18 shows the graph with an experimental
100 mHz square signal when PID control is used with
voltage saturation and concludes that the camera
satisfactorily monitors the movement of the actuator.
Fig. 18: PID - Experimental 100 mHz square signal
with applied voltage saturation
5 Conclusion
The research described in the paper aims to find the
optimal settings for different control methods to
highlight this saturation problem and extend the
period during which the IPMC actuator can be
effectively controlled.
The ability to maintain the position of the IPMC
actuator stable for an extended duration is critical for
its use in robotic systems. The IPMC actuator can be
used to precisely control the movement of robotic
grippers by performing position control. To enable
more efficient and reliable positioning and
manipulation in robotic systems, the research's main
objective is to identify the optimums control settings
that enable IPMC actuators to operate reliably and
under control for extended periods of time.
In order to accurately control the position of the
free end of the strip until the applied voltage does not
exceed the amplitude of ±3 V, the study proposed
two control approaches for IPMC actuators using
low-frequency signals.
A new image sensor-based method for measuring
displacement was presented, which involved the use
of an image processing algorithm and a camera
system. For the experimental setup employed, the
proposed technique was 17% faster and had an
accuracy of ±0.09 mm.
The experimental setup, image processing
technique, and control methods presented in this
work contributed to the understanding and
measurement of IPMC actuator displacement, to be
used in robotic applications that require position
control.
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US
WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2023.18.15
Kyriakos Tsiakmakis, Vasileios Delimaras,
Argyrios T. Hatzopoulos, Maria S. Papadopoulou
E-ISSN: 2224-2856
153
Volume 18, 2023
