## 6 Discussion  
In this study, a fully data-driven-based open-loop controller design has been implemented for PAM-actuated systems that have nonlinear characteristics and have differences between the proposed mathematical models and experimental test results. The controller, which is embedded in a PLC (Siemens S7-1200), one of the control devices frequently used in field applications due to its reliability, is designed with input variable pressure value and the output force and displacement responses instead of analyzing the sub-components of the system one by one. Utilizing the gathered data, two distinct artificial neural networks were trained to delineate the relationships between displacement and pressure, as well as pressure and force. Subsequently, a cascade controller was formulated, wherein the pressure signal, derived from the artificial neural network estimating the displacement-pressure model from the two discrete models, serves as input to another artificial neural network defining the pressure-force relationship. Consequently, by inputting the desired position of the pressing unit, the cascade controller generates the requisite control signal for the proportional control regulator, facilitating the regulation of pressure. Additionally, the static force exerted on the PAM due to displacement is acquired as an additional output. A comparison of the experimental results obtained in our study with those from the literature [11] that uses DMSP-20 reveals notable differences in the modeling approaches and error magnitudes. Our experimental setup involved the utilization of a PAM actuator in combination with pre-tensioning springs and an aluminum block, constituting a more  
Figure 14: Displacement and force prediction errors of the controller. comprehensive system than the focus on the PAM alone in previous studies. While previous studies have primarily focused on modeling the PAM's behavior, our approach aimed to capture the model of the entire system through a data-driven approach. Despite the differences in system composition, we compared the errors of various force models from the literature to assess the efficacy of our approach. Table 3 presents the percentage errors of these force models computed based on (9) with the measured and predicted force values [11]. \[Error\;\%=\;100\cdot max(F_{Measured}\;-\;F_{Predicted}\;)/F_{Measured} \tag{9}\]  
The fact that the analytical models proposed for the calculation of the force to be produced by the contraction of the DMSP-20 PAM used in the fluidic muscle station also perform calculations with margins of error is a consequence of the nonlinear characteristics of the system. In the [PERSON], Andrikopoulos, and Wickramatunge model, the difference between the experimental results and the results produced by the system model is more than 8%, while the errors are reduced in the models proposed by [PERSON], [PERSON], and [PERSON]. The results produced by the ANN-based controller proposed in this study were observed to produce acceptable results with an error rate of 7.72%, despite the fact that other components of the system, in addition to the DMSP-20 PAM, increased the nonlinearity of the model. The calculated error rate of 7.72% occurred when the system produced a static force of 34.85 N, although the PAM was predicted to produce a force of 37.55 N in the case where a displacement of 10.25 mm was required. However, it should be noted that the error calculation was performed by considering only the values of the points where the system can move within the physical limits from the results produced by the ANN-based controller. When a displacement outside the contraction limits of the PAM is desired, the controller will still calculate a force value, but since the PAM cannot reach the desired point anyway, it will not be possible to reach the predicted force.