## 4 Results and Discussion
### Expert System Adaptive Control Evaluation
However, the improved control system, which integrates the PR-MPC mechanism into the expert system, consistently adapts to the response error \(\Delta X_{C}\), leading to a noticeable improvement in the hydraulic press response. In the fast backward movement, the adaptability of the hydraulic cylinder demonstrates results like those observed in the fast forward movement, further confirming the effectiveness of the adaptive control mechanism in maintaining consistent performance across movement phases. Table 5 shows the absolute error of the residuals for various phases (1) holding, (2) fast forward movement, (3) bending, (4) leveling, (5) fast backward movement comparing the initial and improved responses. The values show the reduction in hydraulic press response error \(\Delta X_{C}\) after control system is improved by PR-MPC mechanism. Figure 11: Improvement of adaptive control mechanisms in the observation area. In the (1) holding phase, a significant reduction in response error \(\Delta X_{C}\) is evident between the initial and improved responses for both hydraulic press cycles 1 and 2. In case of hydraulic press cycle 1, the response error \(\Delta X_{C}\) is improved by 98.4% from an initial value of 0.993 mm to a minimized value of 0.016 mm. In the case of hydraulic press cycle 2, the response error \(\Delta X_{C}\) is improved by 98.7% from an initial value of 1.215 mm to 0.016 mm. This indicates a substantial improvement in accuracy. In the (2) fast forward movement, the integrated PR-MPC mechanism in the expert system shows a decrease in response error \(\Delta X_{C}\) for both hydraulic press cycles 1 and 2. In the case of hydraulic press cycle 1, the response error \(\Delta X_{C}\) decreases from 2.038 mm to 0.192 mm, showcasing a 90.6% improvement. Moreover, in hydraulic press cycle 2, the response error \(\Delta X_{C}\) decreases by 97.3% from 3.089 mm to 0.083 mm. These reductions indicate that the improved response significantly enhances the system performance during fast forward movements. In the (3) bending phase, the initial response error \(\Delta X_{C}\) in the case of hydraulic press cycles 1 and 2 is reduced after the advanced control system with the integrated PR-MPC mechanism is introduced. In hydraulic press cycle 1, the response error \(\Delta X_{C}\) decreases by 92.7% from 3.142 mm to 0.231 mm. Moreover, in the case of hydraulic press cycle 2, response error \(\Delta X_{C}\) is decreased from 2.431 mm to 0.221 mm, showcasing a 90.9% improvement in response error \(\Delta X_{C}\). This shows that the adaptive control system is effective in minimizing response errors \(\Delta X_{C}\) even under high loads, where higher bending process intensity is applied. In the (5) leveling phase, the initial absolute response error \(\Delta X_{C}\) is lower compared to phases (1), (2), (3), and (4). In the case of hydraulic press cycle 1, the PR-MPC mechanism integrated into the expert system reduces the absolute response error \(\Delta X_{C}\) from 1.082 mm to 0.055 mm, showcasing a 94.2% improvement. Moreover, in hydraulic press cycle 2, the response error \(\Delta X_{C}\) is effectively improved by 93.4% from an initial absolute response error \(\Delta X_{C}\) of 1.099 mm to an improved absolute response error \(\Delta X_{C}\) 0.073 mm. These values show that the integrated PR-MPC mechanism in the expert system is effective in minimizing errors during the leveling phase. Overall, Table 5 shows a quantitative validation of the proposed PR-MPC mechanism as the improvement in the response error \(\Delta X_{C}\) is significantly reduced. The decrease in response error \(\Delta X_{C}\) is particularly evident in the bending (3) and fast movement phases (2) and (5), as well as in hydraulic press cycles 1 and 2, showcasing the effectiveness of the enhanced control system in improving accuracy across various operating conditions.