Abstract
This paper uses a non-isolated DC-DC Cuk converter, models it into a fourth order differential equation. It further concentrates on identifying the transfer function of the DC-DC Cuk converter. The non-isolated model generates a nonlinear dynamics in its characteristics which is linearized by using the average modelling and small signal analysis is done. Thereafter, the work focuses on designing a Fractional order Proportional Integral Derivative (FOPID) controller using the Genetic Algorithm (GA) minimizing the weighted sum of the error specifications i.e. Integral Time Absolute Error (ITAE), Integral Absolute Error (IAE) and Integral Square Error (ISE). The FOPID controller has more parameters giving the controller more degrees of freedom and accuracy than the classical Proportional Integral Derivative Controller (PID). Henceforth, the work implements the designed controller to the model and records various simulation results like step response, current across inductor, voltage across capacitor, response to a disturbance etc., along with setpoint tracking, disturbance rejection and relative stability analysis.