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.

The structure of the interconnected electric power system and the increasing quality of energy have led to an increased importance of Automatic Generation Control, or AGC. The tie line powers and frequency must be maintained within the permitted standard values. This work applies to Automatic Generation Control in a nonlinear model of an interconnected electric power system using a fractional order sliding mode controller. Three sections of a nonlinear interconnected electric power system are controlled by a fractional order sliding mode controller. The block diagram of the power plant model system considers the nonlinearities that are physical limits, such as governor dead band and generation rate constraints. In the presence of various load changes (sudden load change frequency), parameter uncertainty (variation), and the existence of physical constraints, the control’s goal is to manage the frequency deviation (load frequency error) and tie-line power deviation (tie-line power error) of the interconnected power system. Three sections of an interconnected power system with nonlinearities are used to simulate the fractional order sliding mode controller (FOSMC). These designs display the best performance of the suggested FOSMC controller, with numerical values for tie line power deviation of 2.9765e-5p.u. and frequency deviation of 6.8912e-4Hz. The suggested system has reduced nominal values as compared to SMC for the frequency deviation of 2.0762e-3Hz and tie line power deviation of 1.21754e-3p.u., as well as for PID controller frequency deviation of 3.5918e-3Hz and ti line power deviation of 1.5602e-3p.u. These comparisons further demonstrate that, even in the presence of parameter variation, load changes, and nonlinearities in the system, FOSMC performs the best, with reduced undershoot (5.4823e-4), overshoot (1.5545e-4), rising time (1.00042e-8), and settling time (2.688). MATLAB/Simulink has been used to create and simulate the controllers for the system model.