## 4 Results and Discussion
### Expert System Adaptive Control Evaluation  
Building an adaptive control system integrated within expert system for a hydraulic press is challenging, but the knowledge-based approach taken with the data-driven model proves to be beneficial. The accuracy of the regression model and the effectiveness of the PR-MPC mechanism integrated into the expert system were investigated to evaluate the capability of objective condition recognition and adaptation. In addition, regression modeling is used to replicate the condition changes due to external disturbances on the hydraulic press in the experimental environment. In addition, the expert system is used in the expert system to analyze the improvement of the adaptive control integrated into the control mechanism. To evaluate the actual effectiveness of the control mechanism, an adaptive control is performed on the existing observation area of the hydraulic press working area to confirm its effectiveness. In addition, the validation area of the hydraulic press is tested to validate the ability of the control mechanism to adapt to external disturbances in various conditions. The results shown in Figure 11 demonstrate the beneficial impact of integrating the PR-MPC mechanism into the expert system within the observation area. Hydraulic press cycles 1 and 2 are used to illustrate the adaptive capabilities of the algorithms in real-time control. In the holding phase, the consistent response error \(\Delta X_{\text{C}}\) of the hydraulic press is observed in both cycles, while \(\Delta X_{\text{C}}\) with adaptive control is significantly reduced and approaches the reference displacement of the hydraulic cylinder. Hydraulic press cycle 1 \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **RMSE** & \(R^{2}\) & **SSE** \\ \hline Case (a) & 0.02126 & 0.9999 & 5.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation metrics of regression models for the movement phase. Figure 10: Prediction surface of the movement phase: experimental result, initial and changed friction conditions. shows higher hydraulic cylinder velocity during fast forward movement (\(v_{C}=40\) mm/s) in comparison to hydraulic press cycle 2, where \(v_{C}=25\) mm/s. Consequently, the response error \(\Delta X_{C}\) of the hydraulic press for cycle 1 is higher compared to cycle 2. However, the PR-MPC mechanism integrated into the expert system is capable of significantly reducing the response error \(\Delta X_{C}\), thus improving the accuracy of the hydraulic cylinder's movement during fast movement in hydraulic press cycles 1 and 2. In the bending phase, hydraulic press cycles 1 and 2 maintain hydraulic cylinder velocities \(v_{C}\) at 15 mm/s and 25 mm/s, while the hydraulic press is subjected to higher intensities of the bending process. A sudden change is noticeable when the die tool touches the workpiece and begins to deform it, which leads to an increase in response error \(\Delta X_{C}\), while the initial control system is active without the PR-MPC mechanism integrated into the expert system. In the case of hydraulic press cycle 1, the response error \(\Delta X_{C}\) is lower, as the velocity of the hydraulic cylinder's movement is lower (\(v_{C}=15\) mm/s). Compared to cycle 2, the response error \(\Delta X_{C}\) is higher as the velocity of the hydraulic cylinder movement during the bending process is higher (\(v_{C}=25\) mm/s). Meanwhile, the improved control system with the PR-MPC mechanism can recognize the sudden changes and reduce the response error \(\Delta X_{C}\). With the enhanced control system, the hydraulic cylinder movement has been optimized to achieve a satisfactory range of response error \(\Delta X_{C}=\pm 0.2\) mm relative to the reference displacement. Observing the leveling phase, the initial control system exhibits a response error \(\Delta X_{C}\) that shows a similar deviation from the reference displacement of the hydraulic cylinder in both hydraulic press cycles 1 and 2.