## 4 Proposed Dual Control Strategy Based on Load Detector and Offset Corrector  
This section introduces the proposed horizon one FCS-MPC controller strategy based on the load detector and offset corrector. The proposed method consists of an FCS-MPC controller only regulating the inductor current and a reference current calculator, involving two sensors, one for measuring the load current (\(i_{Load}\)) and the other one for the output voltage (\(v_{\text{C}}\)). The method is summarized in the block diagram shown in Figure 4.  
Figure 3: Block diagram of the MPC controller with a PI regulator adapting the current reference based on output voltage error [18; 19; 20]. The Ideal Reference Calculator (IRC) block computes the input reference current in an ideal scenario without considering the electrical losses of the switches or other components of the system. Its calculations are based on ensuring that the steady-state power at the input (\(P_{in}=V_{in}\cdot i_{L,ref}\)) equals the power at the output of the boost converter (\(P_{out}=V^{2}_{C,ref}/R\)). Consequently, the reference current is calculated as shown in Equation (6), where \(R\) is the output load resistance. \[i_{L,ref}=\frac{\left(v_{C,ref}\right)^{2}}{R\cdot V_{in}} \tag{6}\]  
By modifying Equation (6) with \(R=v_{C}/i_{Load}\), the final reference current calculation results in Equation (7):  
\[i_{L,ref}=\frac{\left(v_{C,ref}\right)^{2}\cdot i_{Load}}{v_{C}\cdot V_{in}} \tag{7}\]  
The calculated reference current is derived from ideal equations, which do not account for electrical losses and variations in component values due to inaccurate measurements or external factors such as temperature. These losses are especially unpredictable in conventional FCS-MPC, which does not control the switching frequency precisely, making real-time loss prediction challenging. To correct minor steady-state errors in the calculated reference current, the proposed dual control strategy for a DC-DC boost converter includes an offset tuning mechanism. The process begins by measuring the actual output voltage and comparing it with the reference output voltage. The difference between these two values represents the voltage error, which is then fed into a low-speed PI controller. As shown in the flowchart in Figure 5, the control system is designed using a dual-loop configuration. The outer loop features a PI controller, which adjusts an offset based on the accumulated error between the actual and reference output voltages. This offset is added to the ideal reference current generated by the IRC block, which operates under ideal conditions and without delay. This setup ensures that the system compensates for minor deviations not accounted for by (7). The IRC block provides the primary reference current for the FCS-MPC, which can track this reference quickly due to its fast response capabilities. While the FCS-MPC ensures the rapid tracking of the reference current and real-time system adjustments, the IRC block itself is based on ideal conditions. To account for any steady-state errors in the output voltage caused by non-ideal factors, a slower offset tuner, managed by the PI controller, is used. The FCS-MPC handles the direct control of the inductor current by predicting future system states (using Equations (3) and (4)), evaluating possible switching actions (Equation (5)), and selecting the optimal action to minimize the cost function. This approach allows the FCS-MPC to quickly adapt to load changes detected by the IRC block. By decoupling the dynamic regulation from the PI controller, the FCS-MPC is fully responsible for fast real-time adjustments of the inductor current, without being slowed by the PI loop's response. This combination allows the system to maintain fast dynamic responses while ensuring accurate steady-state performance. Figure 4: Block diagram of the proposed FCS-MPC controller with load detector and offset corrector. Since the first loop generates the reference current, the second loop (FCS-MPC) only focuses on controlling the current, not the voltage.