Force control of electro-active polymer actuators using model-free intelligent control

Abstract

In this paper, a model-free control framework is proposed to control the tip force of a cantilevered trilayer CPA and similar cantilevered smart actuators. The proposed control method eliminates the requirement of modeling the CPAs in controller design for each application, and it is based on the online local estimation of the actuator dynamics. Due to the fact that the controller has few parameters to tune, this control method provides a relatively easy design and implementation process for the CPAs as compared to other model-free controllers. Although it is not vital, in order to optimize the controller performance, a meta-heuristic particle swarm optimization (PSO) algorithm, which utilizes an initial baseline model that approximates the CPAs dynamics, is used. The performance of the optimized controller is investigated in simulation and experimentally. Successful results are obtained with the proposed controller in terms of control performance, robustness, and repeatability as compared with a conventional optimized PI controller.

Keywords

Electro-active polymer conducting polymer actuators artificial muscle model-free control force control particle swarm optimization PSO intelligent PID

1. Introduction

Conducting polymer actuators (CPAs) are smart material based actuators that exhibit shape and dimension change when subjected to an electrical stimulus. This mechanical response can be used in positioning and force implementing applications that conventional actuators cannot undertake. Some of the advantages of CPAs such as; suitable to be manufactured as mini/micro-sized actuators, operating in solvent or air, large active strains in response to a driving electrical excitation, biocompatibility, and low cost, make them attractive to use in mini/micro-scale and medical applications such as mechanical stimulation of epithelial cells (Svennersten et al, 2011), a micropump (Fang and Tan, 2010), a bio-inspired compliant robotic fish (El Daou et al., 2012), and a robotic micro-gripper (Alici and Huynh, 2007). These actuators are named artificial muscles because their working mechanism is similar to that of biological muscles (Bar-Cohen and Zhang, 2008; Carpi et al., 2011; Gaihre et al., 2011).

Trilayer bender type CPAs comprise a porous substrate containing electrolyte and two conductive polymer electrodes placed on both surfaces of the substrate to form a sandwiched trilayer structure. The trilayer structure enables CPAs to operate in the air environment and thus provides an advantage in widespread applications compared to the other CPAs. When these actuators are subjected to an electrical voltage stimulation, they generate a bending motion based on an electrochemical redox reaction. Modeling and controlling the CPAs’ mechanical response is vital to understand and improve the capabilities of this class of actuators and broaden their application areas. Initial work on the mechanical response of CPAs concentrated on obtaining their positioning dynamics, including linear and nonlinear models (Alici, 2009; Du et al., 2010; Fang et al., 2007, 2008a; John et al., 2008; Madden, 2000; Nguyen et al., 2012; Shoa et al., 2011; Wang at al., 2009). In addition to modeling their dynamics, a significant amount of work has focused on controlling the CPAs’ position using model-based controllers (Fang et al., 2008b; Itik, 2013; Madden, 2003; Wang et al., 2013). Designing model-based controllers to control the CPAs may not be sufficient as the CPAs represent nonlinear and time-varying dynamics, which often differ from sample to sample. The dynamics of one CPA sample depend on the fabrication process and conditions of the actuator. Therefore, it is always possible to see a dynamic behavior difference between two CPA samples, even if they have identical geometric shapes. They also have some drawbacks such as drift, hysteresis, and degradation in actuation performance due to solvent evaporation, influencing their performance negatively and making their modeling and control insufficient (Yao et al., 2008). As the performance of the model-based controller reduces due to the reasons mentioned above, model-free adaptive controllers are considered as a potential solution instead (Beyhan and Itik, 2016; Druitt and Alici, 2013; Sancak et al., 2019).

Besides controlling the tip displacement of bender-type CPAs, the blocking force generated by their free-end is required to be robustly and accurately controlled in applications such as micro-nano manipulation, cell-injection, etc. Although there are many works in the literature focusing on modeling and control the CPAs’ tip displacement, there is a minimal number of works on the control of blocking force of such actuators (Coskun et al., 2017; Itik et al., 2014). Only quasi-static models (Alici and Huynh, 2006, 2007) are presented to predict the force output of the trilayer CPAs as modeling study which are not convenient to use in applications where the blocking force output of the CPAs needs to be controlled dynamically. Since a dynamic mechanistic model for blocking force dynamics of the CPAs does not exist, one needs to design controllers for the blocking force output of CPAs either by using an empirical model obtained by system identification methods from the input-output behavior of the CPA or by using model-free control methods.

Model-free control methods such as intelligent PID (Fliess and Join, 2009), fuzzy logic (Lee, 1990), or neural networks (Psaltis et al., 1988) are well suited and studied in controlling the position of CPAs since they do not need a precise model of the system in order to design a controller. However, their use in controlling the blocking force output of CPAs is very limited. In our previous work, a linear model obtained by using system identification was used to design a classical PID controller to control the blocking force output of the CPA, which mimics a cell injection process (Coskun et al., 2017). Although the results were successful, the designed controller could not provide the same performance for a long-time working period of the CPA and different CPA sample, due to the dynamic behavior change. Another work of authors shows that a model-free controller also called intelligent PID (i-PID) represents clear performance improvements in controlling the CPAs’ position for long-time usage in air conditions (Sancak et al., 2019). However, there is still room for investigating the proposed controller’s effect on the CPAs’ blocking-force control. Moreover, the proposed model-free controller’s effect on the control performance of different but same-sized CPAs should be investigated.

This paper investigates the effect of a model-free controller on the tip point blocking force control performance of a cantilevered trilayer CPA to eliminate the effects of unmodeled dynamics and disturbances and provide performance repeatability for different same-sized CPA samples. In order to have a fair performance comparison with a model-based PI controller, a PSO algorithm is designed to optimize the controller parameters, which utilizes a model of the CPA obtained by a black box system identification method. We note that this is not required to design the proposed controller since, in general, its parameters are tuned by trial and error (Fliess and Cédric, 2013). Here, we propose that by tuning the parameters of the i-PID controller a priori by using optimization algorithms, a significant performance improvement can be obtained compared to the trial and error method. In order to compare the control performance, a classical PI controller, which is also optimized with the same PSO algorithm, is used. Both controllers are simulated and implemented experimentally to track a step input signal. Moreover, as the CPAs in the same size may represent different dynamics, the repeatability of experiments with the same controller parameters is also investigated on a second CPA sample.

The remainder of this paper is organized as follows. In Section 2, we introduce the details of the CPA. Section 3 includes controller design together with the online estimation of the plant dynamics and optimization of the controllers with the PSO algorithm. In Section 4, simulation and experimental results are given. Finally, concluding remarks are provided.

2. Conducting polymer actuator, its structure and identification

The trilayer structure of the bending-type CPA used in this study is illustrated in Figure 1. There are two polypyrrole (PPy) layers on the outer surface of the actuator. As a separator layer, there is an amorphous, porous, and nonconductive Polyvinylidene Difluoride (PVDF) layer that holds the liquid electrolyte trifluoromethanesulfonimide ( $L i^{+} TFS I^{-}$ ). The thicknesses of PPy and PVDF layers are of 30 and 110 µm, respectively. There are also two thin porous gold layers with a negligible thickness between these layers to provide a conductive surface on which the PPy electrodes can be electrochemically deposited. The fabrication process of the actuator is given in the Appendix 1.

Figure 1.

Actuation mechanism of trilayer CPAs.

The actuation mechanism of CPAs is based on the electrochemical reduction-oxidation (redox) reaction, causing volume expansion and contraction, leading to bending motion like a bilayer cantilever due to electrons and ions passing through layers (Madden, 2000). Applying a sufficient electrical voltage to the actuator starts the reaction, and the PPy layer on the anode side oxidizes, while the layer on the cathode side reduces. The reaction process is also depicted in Figure 1 and can be described as

PPy + TFS I^{-} ⇄_{Reduction}^{Oxidation} PP y^{+} TFS I^{-} + e^{-}

(1)

The positively charged PPy electrode absorbs the $TFS I^{-}$ anions and expands while the anions are expelled from the negatively charged electrode (Alici et al., 2009). When the reduced side of the actuator’s tip point is blocked to move, the actuator applies force on the blocking object due to expansion and contraction of the outside PPy layers. In this study, we focus on controlling the blocking force output generated at the tip point of the actuator, which is a result of the complex electrochemical process. The CPA used in this study has the dimensions of 7 mm (with 2 mm free length) × 5 mm × 0.17 mm. The 5 × 5 mm² area of the actuator from both sides is used to apply electrical voltage, as shown in Figure 2.

Figure 2.

Optical image of the CPA in cantilevered configuration.

2.1. Experimental setup and system identification

The schematic of the experimental setup is illustrated in Figure 3. The force measurement system consists of a Sparkfun mini load cell (TAL221), a load cell amplifier (HX711), and an Arduino-UNO board. The load cell has a maximum capacity of 981 mN with 0.1 mN resolution. The Arduino board is used to communicate between HX711 and PC over the USB port. The force measured at the tip point was used as the output, while the voltage applied via clamps to the actuator was used as the input variable. The clamp was coated with a thin gold film in order to improve conductivity. The input voltage was applied to the CPA actuator via National Instruments (NI) connector block (SC-2345) connected to the NI-6251 PCI data acquisition card located in the target PC. Also, the current passing through the actuator during the activation of the CPA was measured with a DROK Amp to Volt Transmitter module.

Figure 3.

The schematic representation of the experimental setup.

An autoregressive exogenous (ARX) model representing the relationship between the voltage input and force output of the CPA is obtained by system identification on the MATLAB software. A pseudo-random binary sequence (PRBS) signal with a frequency of 1 Hz was applied to the actuator to acquire training data. The output force data was then acquired via the force measurement system with a sampling frequency of 80 Hz. The transfer function model obtained as a result of the system identification process is

G (s) = \frac{8.247 s + 6.09}{s^{2} + 1.842 s + 0.5189}

(2)

The agreement between the model and the experimental training data is determined using a normalized root mean squared error method as 96.76%. The model is also validated with the experimental step response of the CPA, where 95.01% agreement is achieved. The time response comparison of the model and the experimental data is given in Figure 4(a) and (b) for the PRBS and step inputs, respectively. It is possible to validate the system identification results with other sets of data like sine or ramp signals. However, only step response validation is considered sufficient for this study since the desired force control behavior is generally like step response in many applications of CPAs (Alici and Huynh, 2007; Carpi et al., 2011; Coskun et al., 2017). Also, training and validation with PRBS data covers the frequency range up to 1 Hz signals in our experiments which also ensures satisfactory match with sinusoidal test signals. However, since it is omitted here to present all validation results for the sake of conciseness of the paper.

Figure 4.

Comparison of the model and experimental data: (a) PRBS input response and (b) step input response.

3. Controller design and optimization

3.1. Controller design for CPA

In order to control the force output of the CPA, we used a model-free intelligent controller (Fliess and Cédric, 2013) based on continuously updating a local model of the CPA in a small-time interval with only the knowledge of the system input-output behavior. The details of the controller are given in the Appendix 2.

The local blocking force dynamics of the CPA can be represented by a first-order model as follows

\overset{\cdot}{y} = F + α u

(3)

By using a proportional feedback controller as a stabilizing controller, the intelligent controller is of the form of i-P control where the control input of the system becomes:

u (t) = \frac{1}{α} (- F_{e} (t) + {\overset{\cdot}{y}}^{*} - K_{p} (y - y^{*}))

(4)

In the design of the stabilizing controller, integral and derivative terms are not used. That is, because a simple proportional controller is enough to ensure convergence of the error to zero since the local model is first order and the integral effect is included in $F_{e}$ . The derivative term is not preferred because the noisy output measurement signal and force dynamics do not have an oscillatory behavior, causing an overshoot in the step response. Furthermore, ensuring the local stability of the controller is relatively straightforward since it depends on the appropriate tuning of the $K_{p}$ gain. In order to cope with the noisy signal and ensure a good local model estimation, a second-order Butterworth filter with 5 Hz cut-off frequency is designed and implemented on the measurement signal. The schematic representation of the controller is given in Figure 5. Note that, we neglect the derivative of the reference signal in the control input since we use a step signal reference, which results in an infinite slope in the derivation process.

Figure 5.

Block diagram representation of the i-P Controller.

In order to compare the performance of the proposed model-free controller, a classical PI controller is also designed and employed to the CPA. Because using a PI controller, we provide an integral effect to the proportional controller and have the same number of controller parameters with the i-P controller to be optimized. The optimization process of the controller parameters is explained in the next section.

3.2. Parameter optimization with PSO algorithm

Particle swarm optimization (PSO) algorithms are well-known population-based meta-heuristic algorithms (Eberhart and Kennedy, 1995a, 1995b) where a flying bird has a position and a velocity, and the birds change his position by adjusting the velocity when searching for food. The velocity changes based on the experience of the bird and the feedbacks received from his neighbor. Each bird in the swarm is called particle, considered as a candidate solution to the optimization problem. The swarm comprises $N$ particles moving around in a D-dimensional search space. Each particle’s position is represented by a set of coordinates that describe a point in the search space. The position and velocity of each particle are calculated using the equations given below (Wang et al., 2018).

V_{i}^{k + 1} = w^{k} V_{i}^{k} + c_{1} r_{1} (P_{best, i}^{k} - X_{i}^{k}) + c_{2} r_{2} (G_{best}^{k} - X_{i}^{k}) i = 1, 2, \dots, N

(5)

X_{i}^{k + 1} = X_{i}^{k} + V_{i}^{k + 1}

(6)

Where $V_{i} = (v_{i 1}, v_{i 2}, \dots, v_{iD})$ and $X_{i} = (x_{i 1}, x_{i 2}, \dots, x_{iD})$ are the velocity and position of the ith particle, k is the iteration number, $r_{1}$ and $r_{2}$ are random numbers distributed in the range of (0,1), $c_{1}$ and $c_{2}$ are two parameters representing the particle’s confidence in itself (cognition) and in the swarm (social behavior), respectively. Also, $w$ is the inertia weight, which is used to control the velocity. During the searching process all the particles preserve their individual best performance called personal best $(P_{best, i} = (p_{i 1}, p_{i 2}, \dots, p_{iD}))$ and also the best performance called global best $(G_{best} = (g_{1}, g_{2}, \dots, g_{D}))$ of their group.

The design parameters used for the initialization of the PSO algorithm are given in Table 1. Typically, $w$ is chosen in the range of 0.4 and 0.9. In this study, $w$ is selected at maximum to obtain global exploration. The acceleration coefficients $c_{1}$ and $c_{2}$ are chosen as 2 in order to make the mean of both stochastic factors in unity. The iteration number and number of particles are selected sufficiently large in order to obtain a balance between computing time and tolerance. The search intervals for the control parameters are determined with trial and error to avoid missing the global best solution, and they are given in Table 2.

Table 1.

PSO parameters for tuning the objective function.

PSO parameters	Values
$c_{1}$	2
$c_{2}$	2
$w$	0.9
Number of particles	20
Iterations	20

Table 2.

Intervals of the controller parameters to be optimized.

Controller parameters		Interval
PI controller	$K_{p}$	[0.001–1]
PI controller	$K_{I}$	[0.001–1]
i-P controller	$K_{p}$	[0.001–50]
i-P controller	$α$	[2–200]

The performance of each particle is evaluated according to the pre-defined objective function, which is related to the problem to be solved. In general, this objective function is considered as integral of squared error (ISE) or integral of absolute error (IAE) because error based objective functions are generally used in the controller design process. However, this objective function can be insufficient in safely controlling the CPA for sensitive application fields because it takes no account of maximum overshoot and control input. Therefore in this study, the maximum overshoot $(M_{p})$ is incorporated into the objective function when overshoot is observed. Furthermore, the magnitude of control signal u is restricted to 1.5 V in order not to damage the actuator by the operation voltage. Hence, the excess control signal $(u_{p})$ is added to the objective function when the control signal exceeds 1.5 V. Settling time and steady-state error are not taken into consideration as they are found to have a limited effect on the performance of the CPA force control. The objective function $f (θ)$ which is used in the PSO algorithm is given below.

f (θ) = w_{1} * M_{p} + w_{2} * u_{p} + w_{3} * ISE

(7)

where $w_{1}$ , $w_{2}$ , and $w_{3}$ are the weighting factors of $M_{p}$ , $u_{p}$ , and $ISE$ , respectively. These factors are directly related to desired specifications such that an increase in a weight factor will result in some improvements in the corresponding feature, while some decline will result in the other features (Zamani et al., 2009). After various trials to set a balance between desired specifications, the weighting factors $w_{1}$ , $w_{2}$ , and $w_{3}$ are determined as 20, 20, and 1, respectively.

The evaluated objective functions are compared and $P_{best}$ is set to the best solution if it is better than the current solution. The best solution among the $P_{best}$ is denoted as $G_{best}$ . Finally, all particles update their position and velocity by using equations (5) and (6). If the stop condition or the maximum number of generations is satisfied, then the solution is found. Otherwise, the loop continues.

Both the i-P and PI controllers have two parameters ( $K_{p}$ and $α$ for i-P controller, $K_{p}$ and $K_{I}$ for PI controller) to be optimized. Therefore, the same algorithm, which is designed for the i-P controller is also used for optimizing the PI controller parameters.

With the given design parameters, the fitness function equation (7) is calculated using the linear time-invariant (LTI) model of the CPA. The noise in the experimental measurement is added as white noise with 10⁻⁴ noise power. Then, the noise is filtered with the same filter that is used in the experiments. Also, a time delay due to experimental measurement is added to the simulation as 0.09 s. As a reference signal to be tracked, a unit step input with an amplitude of 5 mN is considered to obtain linear dynamics from the CPA actuator. The total simulation is performed for 5 s in each iteration, and the fitness function is calculated at this time. The optimization process is repeated many times, and the change of fitness functions for both i-P and PI controllers are shown in Figure 6 for some trials. The optimization results for the best trials, where the fitness function cost is the lowest, are given in Table 3 together with the simulation results of the controllers in terms of maximum overshoot $(M_{p})$ , rise time ( $T_{r}$ ), settling time $(T_{s})$ , and maximum value of control signal (CS).

Table 3.

Optimized values of the PI and i-P controller.

Algorithms	Controller parameters			Performance results
Algorithms	$K_{p}$	$K_{I}$	$α$	$f (θ)$	$M_{p}$ (%)	$T_{r}$ (s)	$T_{s}$ (s)	CS
PI	0.29	0.11	—	16.2389	1.9420	1.9827	3.5163	1.5322
i-P	2.59	—	155.4	12.9759	2.5506	0.4665	0.8013	1.5544

Figure 6.

Fitness functions of i-P and PI controller for some trials.

As shown in Figure 6, the PSO algorithm converged to an optimal solution on average in the eighth iteration for both controllers. Although the PSO algorithm is used to tune the controllers with the same number of optimization and design parameters, the i-P controller provides better cost values than the PI controller. This implies that the optimized i-P controller improves the transient response of CPA since the evaluated 5-s simulation time mostly encapsulates the transient response.

4. Simulation and experimental results

In force control applications such as micromanipulation, the desired control accuracy is generally under mili-Newton levels. As an example, one possible area of use of CPAs is the biological cell-injection process (Coskun et al., 2017). The time-varying dynamics or slow transient response of the CPAs can be a problem for the work on a living cell. The force applied to the cell should be robustly and accurately controlled to prevent harming the cell. For this kind of application, it is vital to keep the blocking-force in a constant value that corresponds to a step reference signal. Therefore, we used only step references in our simulations and experiments. Nevertheless, the same procedure may be applied for different test signals such as ramp or sinus. However, for the sake of conciseness, we limit our simulations and experiments with step reference.

The LTI model of the CPA is used to simulate the dynamics in the optimization and control simulations. The optimized controller parameters are used to perform simulations, and the results are given in Figures 7 and 8 with the experimental results for PI and proposed i-P controllers, respectively. The simulations and experiments are performed for 20 s, and a unit step input with 5 mN amplitude is used as a reference signal. Before starting the experiments, the actuator was soaked in the electrolyte $L i^{+} TFS I^{-}$ to enable the actuator to perform in the air environment.

Figure 7.

Experimental and simulation results of actuator force $(mN)$ and control signal $(u)$ for optimized PI controller (left) with zoomed versions (right).

Figure 8.

Experimental and simulation results of actuator force $(mN)$ and control signal $(u)$ for optimized i-P controller (left) with zoomed versions (right).

As shown in Figures 7 and 8, both force output and control voltage input of the experimental and simulation results of the controllers are quite close to each other. This implies that the LTI model obtained by the system identification process was quite sufficient in the parameter optimization process of the controller for the early stages of the experiments. Although the PI and i-P controllers are optimized with the same PSO algorithm for the same number of optimization parameters, the i-P controller improves the actuator’s transient response compared to the PI controller. The transient response improvement in the experiments is 84% for rise time and 85% for settling time. No significant overshoot was observed for both controllers except noise. The performances of the controllers are compared in Table 4. Here, the steady-state error of the i-P controller is slightly larger than that of the PI controller due to the fact that we mostly focused on the transient response in the optimization process, but this can be solved by only tuning the $α$ parameter. The steady-state error declines for large $α$ values, but larger values could cause degradation in transient response. Moreover, the current passing through the CPA during the control processes is given in Figure 9 to show the actuator’s current characteristics. In the next section, the i-P controller and PI controller are implemented on another CPA sample with the same geometrical dimensions to show the controllers’ repeatability.

Figure 9.

Current passing through the CPA during control processes.

Table 4.

Performance results.

Controller/performance criteria	PI controller	i-P controller
$T_{r}$ (s)	1.6601	0.3779
$T_{s}$ (s)	7.4351	1.1372
$M_{p}$ (%)	1.8642	4.3884
Steady-state RMSE	1.4630	2.0837

4.1. Repeatability

The performance of the CPAs substantially depends on the fabrication process and air conditions of the environment that the actuator operates. A small difference in the polymer structure, solvent amount, or air conditions cause a change in the CPA dynamics. Thus, it is difficult to obtain identical mathematical models for different CPA samples with the same geometry. As a result, the control performance of model-based controllers varies from sample to sample. In this section, we employed the proposed model-free controller, which was designed for the first sample, on a second CPA sample to prove the repeatability of the experiments and robustness of the designed controller for the CPA samples. In Figure 10, the force control responses of first and second CPA samples are compared. The PI controller is also implemented with the same controller parameters to the second sample, and results are given in Figure 11.

Figure 10.

Comparison of sample 1 and sample 2 results of actuator force $(mN)$ and control signal $(u)$ for optimized i-P controller (left) with zoomed versions (right).

Figure 11.

Comparison of sample 1 and sample 2 results of actuator force $(mN)$ and control signal $(u)$ for optimized PI controller (left) with zoomed versions (right).

The same trend was obtained in the control results of the second sample with the proposed model-free controller. However, the PI controller showed performance degradation for the second sample, as shown in Figure 11. According to the PI controller performance, the second sample of the CPA has slower dynamics in rise time and settling time. Also, the voltage input for the second sample increased by the controllers to hold the CPA at 5 mN reference value. Although the dynamic behavior change was observed in the second CPA sample, the i-P controller showed almost the same control performance as it did in the first sample. This proves the robustness of the i-P control for different but same sized CPA samples. For a better comparison, the performance results of the controllers for the second CPA sample are given in Table 5.

Table 5.

Performance results for second CPA sample.

Controller/performance criteria	PI controller	i-P controller
$T_{r}$ (s)	4.7359	0.6413
$T_{s}$ (s)	14.8924	0.9702
$M_{p}$ (%)	1.3862	4.8180
Steady-state RMSE	2.4948	1.4736

5. Conclusion

In this study, a model-free controller was employed in simulation and experimentally to control the blocking force output of a trilayer conducting polymer actuator with PPy electrodes. The controller parameters were optimized by a designed PSO algorithm to achieve the desired performance characteristics with the controller. A classical PI controller, which was also optimized using the same performance index and algorithm, was used for comparison purposes. Although it is not necessary, utilizing a base-line model in order to optimize the controllers for the force control of the CPA provides better performance compared to the trial-error tuning methods used for intelligent controllers. The results demonstrated that the i-P controller with optimized parameters considerably improved the transient force response of the CPA for step reference tracking as compared to the PI controller. The designed controllers were also implemented on another CPA sample with the same dimensions to show the robustness of the controller under model uncertainties of different CPA samples. The i-P controller performed almost similar performance as it showed on the first sample, while the performance of the PI controller reduced due to the dynamic behavior difference between the two actuators. This shows the robustness and repeatability of the proposed i-P controller and the advantage of using the model-free controller framework in controlling the force output of the CPAs. Our work shows that model-free i-P control is quite promising to control the force dynamics of CPAs since the complete mechanism behind the actuation dynamics of the CPAs is not yet fully understood. As a relatively simple and effective method, the proposed controller can be used to control the dynamics of similar actuators.

Footnotes

Appendix 1

Appendix 2 Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Mehmet Itik

Gürsel Alici

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