Indirect sliding mode adaptive fractional order nonlinear observer based controller with fractional order single-ended primary inductor converter

Direct Current to Direct Current (DC/DC) converters like the SEPIC (Single-Ended Primary-Inductor Converter) use both passive and active components to control the system via a duty cycle. The SEPIC converter is non-inverting and can both step up and step down the voltage with low ripple current. It is a nonlinear variable structure that uses sliding mode control (SMC) for stable operation. Traditional modeling of the SEPIC and SMC has relied on integer-order calculus, but there is a shift toward fractional calculus to improve dynamic control, introducing fractional-order SMC and an additional modulating variable beyond the duty cycle. However, if only the SMC is fractional while the SEPIC remains integer-order, the advantages of fractional calculus are limited, leaving the system with reduced flexibility and precision. Chattering, an inevitable issue in SMC, occurs when excessive switching between states hampers performance, preventing the system from reaching steady or optimal performance and decreasing efficiency. To address this, we propose a fractional-order sliding mode controller (FOSMC) combined with a fractional-order single-ended primary inductor converter (FOSEPIC). However, chattering persisted in the proposed approach. To mitigate the challenge of chattering, we use a nonlinear observer-based indirect sliding mode adaptive fractional order controller for FOSEPIC. We used the Caputo fractional derivative to develop a mathematical model that solves the average state space equation of the FOSEPIC converter. The Mittag-Leffler function, along with Lyapunov methods, are used to analyze the system’s dynamic stability. The performance of the proposed controller was evaluated using integral time absolute error (ITAE). When ITAE values are compared, the adaptive fractional-order sliding mode control (AFOSMC) with the fractional-order model (FOM), the integer-order sliding mode control (IOSMC) with FOM, and integer-order sliding mode control(IOSMC) with the integer-order model (IOM) achieve ITAE values of 0.09151, 0.1847, and 0.2532, respectively. Thus, the proposed controller has the lowest ITAE. Moreover, simulation results demonstrate that the proposed strategy increases efficiency to 99%. Additionally, with a load variation from 10 Ω to 80 Ω , the controller effectively maintains control with minimal overshoot. The method is flexible, provides a high degree of freedom, offers high accuracy, is non-uniform and nonlocal, and ensures a rapid transient response. • The model of Fractional Order SEPIC Converter is developed • Non-linear observer-based adaptive fractional sliding mode controller is proposed. • Fractional Order Observer (FOB) with its structure and adaptation laws is described. • The effectiveness of the system has been validated in various scenarios.