## 2 Methodology
### Load Variation Test  
To evaluate the performance of the proposed Enhanced Error-Adaptive Extended-State Kalman Filter Model Predictive Control (EEA-ESKF-MPC) against baseline controllers, a load variation test was conducted across an extensive operating range from 70 MW to 320 MW. This range simulates the wide load fluctuations encountered in supercritical power plants, providing a rigorous evaluation of the controllers' setpoint tracking capabilities under dynamic conditions. The simulation results, depicted in Figure 5 and summarized in Table 2, compare the EEA-ESKF-MPC against the standard ESKF-MPC, EA-ESKF-MPC, and traditional MPC through a Kalman Filter, focusing on the control of pressure, load, and intermediate point temperature. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Controller** & **IAE1** & **IAE2** & **IAE3** & **ME1 (MPa)** & **ME2 (MW)** & **ME3 (\({}^{\circ}\)C)** \\ \hline ESKF-MPC & 118.045 & 1703.785 & 3810.075 & 0.283 & 4.809 & 6.242 \\ EEA-ESKF-MPC & 118.548 & 1651.894 & 3716.664 & 0.285 & 4.754 & 6.099 \\ EA-ESKF-MPC & 151.675 & 3004.522 & 3583.273 & 0.322 & 6.555 & 5.769 \\ MPC & 125.830 & 1752.969 & 3859.232 & 0.336 & 5.808 & 6.327 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of control results of different controllers. Figure 4: Identification results of the identification model in the test set. (**a**) Neural network; (**b**) transfer function. Figure 5: Comparison of control results for controllers. (**a**) Pressure; (**b**) load; (**c**) temperature. Figure 5 illustrates the dynamic responses of the process outputs under varying load conditions. In Figure 5a, the pressure response of the EEA-ESKF-MPC shows a slightly slower rise time compared to the ESKF-MPC, but it avoids the pronounced overshoot observed in the EA-ESKF-MPC, suggesting improved stability during transients. Figure 5b highlights the load tracking performance, where the EEA-ESKF-MPC closely follows the setpoint with minimal deviation, outperforming the EA-ESKF-MPC, which exhibits significant oscillations. Similarly, Figure 5c demonstrates that the EEA-ESKF-MPC maintains tighter temperature control compared to the baseline controllers, reducing fluctuations around the setpoint. The quantitative metrics in Table 2 further elucidate these observations. For pressure control, the EEA-ESKF-MPC yields an IAE1 of 118.548, a marginal increase of 0.43% over the ESKF-MPC's 118.045, and an ME1 of 0.285 MPa, slightly higher than the ESKF-MPC's 0.283 MPa. This indicates a minor trade-off in pressure control precision, likely due to the prioritization of load and temperature tracking in the adaptive mechanism. In contrast, the load control performance is notably enhanced, with an IAE2 of 1651.894 (a 3.05% reduction from the ESKF-MPC's 1703.785) and an ME2 of 4.754 MW (a 1.41% reduction over 4.809 MW), reflecting superior tracking accuracy and stability. For temperature control, the EEA-ESKF-MPC achieves an IAE3 of 3716.664, a 2.46% reduction from the ESKF-MPC's 3810.075, and an ME3 of 6.099 \({}^{\circ}\)C, reduced by 2.23% from 6.242 \({}^{\circ}\)C, underscoring its effectiveness in minimizing temperature deviations. Compared to the EA-ESKF-MPC and traditional MPC, the EEA-ESKF-MPC consistently outperforms across most metrics. The EA-ESKF-MPC, despite a lower IAE3 (3583.273), suffers from a significantly higher IAE1 (151.675) and IAE2 (3004.522), indicating poor handling of pressure and load under wide-ranging conditions. The traditional MPC, with IAE1, IAE2, and IAE3 values of 125.830, 1752.969, and 3859.232, respectively, lags behind in all aspects, highlighting the limitations of fixed-parameter approaches. These results demonstrate that the EEA-ESKF-MPC, with its multiple dynamic error compensation and adaptive weighting (Equations (32) and (33)), effectively balances the trade-offs among pressure, load, and temperature control.