## 5 Results
### Simulation Results  
Both simulation and experimental tests use the parameters in Table 2 to validate the effectiveness of the proposed method and ensure consistency between the results. A 5 \(\upmu\)s sampling step is used, which is smaller than the state-of-the-art sampling steps. Although the proposed method can achieve even smaller sampling steps, down to 50 ns, the 5 \(\upmu\)s step is selected due to the limitations in the commutation frequency of power electronic switches. Achieving small sampling steps in FCS-MPC is crucial, as it allows for faster and more precise control, improving the dynamic response and stability of the system. Additionally, in high-frequency applications, reaching small sampling steps is necessary to accurately track and respond to rapid changes in the system. Initially, the non-minimum phase issue in a traditional FCS-MPC algorithm is illustrated in Figure 6. In this test, the initial capacitor voltage is set to 40 V, i.e., the same as the input voltage, to focus on the behavior of the controller when it starts to reach an output voltage greater than the input. As can be seen, instead of closing the switch, the controller erroneously opens it (switch \(Q\) is _off_), preventing the output voltage from reaching the desired 60 V reference. This incorrect action is a direct consequence of the non-minimum phase behavior, where the system's immediate response to the control action is opposite to the desired effect. Consequently, the output voltage fails to reach the target of 60 V, as shown in Figure 6. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameters** & **Symbol** & **Value** & **Unit** \\ \hline Input voltage & \(V_{int}\) & 40 & V \\ Output voltage reference & \(v_{C,ref}\) & 60 & V \\ Inductor current reference & \(i_{L,ref}\) & 1.99 & A \\ Load resistance & \(R1\) & 45 & \(\Omega\) \\ Load resistance & \(R2\) & 22.5 & \(\Omega\) \\ Capacitance & \(C\) & 32 & \(\upmu\)F \\ Inductance & \(L\) & 0.5 & mH \\ Sampling time & \(\Delta t\) & 5 & \(\upmu\)s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter values used in the simulation and experimental tests. Figure 7 illustrates the performance of the control strategy presented in Section 3.1 that uses a PI controller to calculate the reference current [18; 19; 20]. This hybrid approach contrasts with the proposal of this paper, highlighting the differences in response and performance. In this approach, the PI controller adjusts the reference current based on the output voltage error, and the FCS-MPC is used to control the inductor current. As shown in the figure, when the load resistance changes from R1 = 45 \(\Omega\) to R2 = 22.5 \(\Omega\) at 0.1 s, there is a noticeable voltage drop up to 25% with a settling time of 20 ms. This drop occurs because the PI controller's slower dynamic response introduces a delay in adjusting the reference current to match the new load conditions. Consequently, the system takes longer to stabilize and return the output voltage to the desired level, affecting the overall speed and efficiency of the control system. The aim of this study is to integrate a PI controller for correcting offset in steady-state performance, along with a sensor to measure load current and adjust the reference current according to Equation (7). To understand the role of the offset corrector block, the first simulation is conducted without incorporating this block, serving as a proof for verification of the IRC block. In this test, the controller updates the reference current without incorporating the offset corrector block. When subjected to a step change in the load, as shown in Figure 8, this method demonstrates an improved dynamic response. The system exhibits a significantly reduced undershoot in the output voltage and a much faster  
Figure 6: Non-minimum phase issue in conventional FCS-MPC for a boost converter. Figure 7: PI-based FCS-MPC response to a step change in load from R1 = 45 \(\Omega\) to R2 = 22.5 \(\Omega\)[18; 19; 20]. settling time compared to previous approaches.