Fractional Order Sliding Mode Controller Modelling for Fractional Order SEPIC Converter

DC/DC converters are power electronic devices that utilize passive components such as resistors, capacitors, and inductors, along with transistors to control the system through a duty cycle. Traditionally modeled and controlled using integer-order calculus, these converters are now increasingly examined through the lens of fractional calculus, which introduces a fractional order for the controller, adding a new modulating variable beyond just the duty cycle.However, if only the controller operates in a fractional manner while the plant remains integer-order, the advantages of fractional calculus are limited, leading to challenges in flexibility, degree of freedom, and overall accuracy. To address these limitations, proposing an Indirect Sliding Mode Adaptive Fractional Order Controller (FOSMC) for Fractional Order Systems in Single-Ended Primary Inductor Converters (FOSEPIC).Utilizing the Caputo fractional derivative, mathematical model is develop to resolve the average state space equation of the DC/DC SEPIC converter. The Mittag-Leffler function, along with Lyapunov methods, is employed to analyze the system’s dynamic stability. The performance of the proposed controller is assessed using the Integral Time Absolute Error (ITAE), yielding an ITAE of 0.09151, which is lower than that of the Fractional Order Model (0.1847) and the Integer Order Sliding Mode Controller (0.2532).Simulation results further demonstrate that the proposed strategy enhances efficiency to 98%. Overall, the FOSMC exhibits improved flexibility, a high degree of freedom, and superior accuracy, offering a fast transient response in controlling DC/DC converters.