Figure 10. Comparison of Output Voltage for SEPIC and FOSEPIC Converters with FOSMC and IOSMC in Boost Mode Operation

Figure 10 presents a comparison of output voltage for both SEPIC and FOSEPIC converters under boost mode operation, highlighting the performance of different controllers. Panel (a) displays the results for the FOSMC with fractional order model (FOM) in [Red], while panel (b) shows the IOSMC with integer order model (IOM) in [Blue]. Panel (c) illustrates the FOSMC with IOM in [Black], and panel (d) depicts the IOSMC with FOM in [Magenta].

In both Figures 9 and 10, oscillations in the output voltage can be observed during the comparison between FOSMC and traditional SMC. The differentiation order is a critical factor, with integer orders used in IOM systems and fractional orders in FOM systems. This flexibility in fractional orders allows for richer dynamics and better tuning capabilities, making FOM an attractive option for control strategies.

Fractional-order control has emerged as a robust approach, effectively managing system uncertainties and disturbances while incorporating nonlinear dynamics. The combination of fractional-order control with SMC leads to the development of fractional-order sliding mode control (FOSMC), which improves upon traditional integer-order SMC.

This study successfully introduces a Fractional Order Sliding Mode Control (FOSMC) strategy with a simplified sliding surface function tailored for DC-DC FOSEPIC converters. By leveraging the input inductor current error, the proposed control method enables indirect regulation of output voltage, which significantly simplifies both the simulation process and the mathematical modeling involved. Extensive simulations conducted in MATLAB/SIMULINK under various operational conditions validate the performance of the FOSMC, showcasing its superior flexibility and enhanced control compared to traditional integer-order methods.

Additionally, this research pioneers the development of fractional-order models for SEPIC converters, offering a comprehensive framework that accurately captures their operational characteristics. The findings reveal that SEPIC converters equipped with fractional-order inductors and capacitors exhibit markedly improved dynamic performance, characterized by reduced overshoot and shorter regulation times when compared to conventional designs.

Overall, the integration of fractional-order control into sliding mode strategies not only enhances the robustness and performance of power conversion systems but also opens new avenues for future research and application. This innovative approach holds significant promise for advancing the efficiency and reliability of power electronics, particularly in the context of renewable energy systems and electric vehicle technologies. The results underscore the potential of fractional-order control as a key enabler for next-generation power management solutions, paving the way for more adaptive and high-performance systems in the field.