## 5 Results  
The primary aim of this study was to develop an ANN-supported open-loop control algorithm for a PAM-based system, which faces challenges in mathematical modeling due to its nonlinear characteristics, and to execute the obtained algorithm on a real-time embedded system. Hence, the design of an ANN-based control algorithm for the PAM model is anticipated to address this gap. In order to test the success of the obtained ANN-based controller in building the system model and to test the generated results by comparing them with actual measurements, 20 different target displacement values were used. The displacement values used during the test were selected from the values not used during ANN training. Thus, we aimed to evaluate the generalization capabilities of the ANN-based controller at interpolation and extrapolation points. The selected target displacement values were used as the input, and the control signals generated by the ANN-based function block were fed to the analog output of the PLC. Figure 13: Test of the control algorithm and fluidic muscle station on two different test specimens: (a) polymer-based test piece; (b) aluminum test piece. The PAM was pressurized with the help of a proportional pressure regulator controlled by the analog output. The displacement of the PAM as a result of the applied pressure input was measured with a linear potentiometer. In order to compare the static force prediction of the ANN-based controller after the displacement, static force values were read with the force-measuring device at the final position. The differences between the measured and targeted displacement values, the resulting static force, and the predicted force were achieved, as shown in Table 2.  
To calculate the absolute errors of the displacement values, the differences between the target displacement and the actual displacement were used. In the same manner, to calculate the static force errors resulting from the displacement, the difference between the force value measured at the final position and the prediction of the ANN-based controller was used. Figure 14 shows the errors produced by the fluidic muscle station actuated with the pressure input controlled by the PLC in response to the target displacement values. It is seen that the greatest displacement error occurs when the obtained displacement is 12.44 mm while the targeted displacement is 15 mm. The desired displacement value is beyond the physical contraction limits of the PAM, but the ANN-based controller still produced an output, so the PAM could not move to the desired position. The point where the largest displacement error occurs also has a greater value than the upper boundary of the ANN training data previously shared in Table 1. When the errors within the boundaries of the training data are analyzed, it is seen that the second largest error occurs when a 7.51 mm displacement is reached at a target displacement value of 7 mm. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Target** & **Predicted** & **Predicted** & **Measured** & **Measured** & **Absolute** & **Absolute** \\
** Displacement** & **Pressure** & **Static Force** & **Displacement** & **Static Force** & **Displacement** & **Static Force** \\
**(mm)** & **(bar)** & **(N)** & **(mm)** & **(N)** & **Error** & **Error** \\ \hline
0.35 & 0.721 & 2.89 & 0.000 & 0.00 & 0.35 & 2.89 \\
1.25 & 1.154 & 4.51 & 1.481 & 5.25 & 0.23  
Similar situations were found for the static force errors shown in Table 2 and Figure 6. The ANN-based control algorithm calculates the force values using the displacement results. Therefore, if the desired displacement exceeds the contraction limits of the PAM, the controller produces results even though the target point cannot be reached. For the reasons mentioned, the largest error between the expected and measured values for static forces was 102.33 N in the scenario where a target displacement of 15 mm outside the contraction limits was used.