The paper introduces a new form of complex fractional order proportional integral derivative (CFOPID) controller of the form D. This latest derivative of has more parameters than any of the Fractional-order PID controller or conventional integer order controller. The paper demonstrates the tuning of this complex fractional order controller using Genetic Algorithm method of tuning. It further relates the results and responses got in the latter tuning method with interior point optimization tuning method (fmincon) of another research paper.

Modeling of a DC-DC converters is usually carried via small-signal approximations with small disturbances taken in account at steady state. Although due to presence of harmonic content or DC offset, the latter’s modeling is restricted to certain range of operation. However, this is limited to a certain range of operation. This paper is a work based on modeling of Dual Active Bridge (DAB) type converters using Generalized Average Modeling. This type of procedure takes into account the harmonic as well as DC effect of the alternating current. After modeling the DAB, it’s open loop transfer function is derived. Thereafter for controlling, parameters of fractional order (FO) controllers namely Fractional order PID and Tilt Integral Derivative (TID) are synthesized using heuristic optimization technique also known as Genetic Algorithm. The use of FO controllers enables more controllability of the plant than classical integer order controllers. The paper then compares the result obtained after simulation of plant controlled by FOPID and TID controllers respectively. It discusses various Power as well as Control results and then concludes the topic by summarizing the procedure and highlighting the importance of FO controllers.

DC-DC converters are generally modeled using small-signal approximations considering small perturbations around a steady-state point. However, this is limited to a certain range of operation which in the presence of harmonic content in addition to dc offset might not provide an accurate result. Generalized Average modeling takes into account the harmonic contents along with the dc values and this can be used for alternating components such as inductor current in a Dual Active Bridge converter. The transfer function is derived which is an open-loop stable system, and in order to establish closed-loop stability, fractional order PI controller is used in this paper. Further, the optimization technique is applied in order to optimize the control variables as the degree of freedom has increased due to the incorporation of fractional powers. These optimized values are used to establish the closed-loop stable operation of a DAB converter and the technique is validated through MATLAB simulations. The entire results are shown in the figures with specifications tabulated and confirm the accurate setpoint tracking with the ripples in range.

Proportional Integral Derivative (PID) controller has been used in feedback mechanism since time immemorial. This work discusses about another hybrid of PID controller of the form PI ^x+i yD ^a+ib also termed as Complex Fractional order PID controller. This variant of PID controller has excess of tuning parameters, more than any of the PID and its other fractional order variant (also known as Fractional order PID controller). Henceforth, this research realizes CFOPID controller and synthesizes all the variants of PID controller’s parameter utilizing Genetic Algorithm (starting from primitive Proportional controller to advanced CFOPID controller) by minimizing the weighted sum of error specifications. It additionally relates the responses of each of the controllers and concludes the superior variant of PID controller.

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.