Optimal fractional order pid controller design for non-ideal dc-dc buck converters

This study presents the design of a fractional-order proportional-integral-derivative (FOPID) controller for a non-ideal direct current-to-direct current (DC-DC) buck converter. The gain parameters of the FOPID controller were obtained using a novel metaheuristic algorithm called the opposition-based cooperation search algorithm with Nelder-Mead (OCSANM), which was designed considering disturbance effects and constrained within a desired cutoff frequency range. OCSANM was developed by integrating the Nelder-Mead (NM) algorithm and opposition-based learning (OBL) into the cooperation search algorithm (CSA). OBL was incorporated to enhance the algorithm's exploration capability, while NM was added to improve its exploitation capability. OCSANM, which was first introduced to the literature through this study and its derived publications, was obtained by integrating the Nelder-Mead (NM) algorithm and opposition-based learning (OBL) methods into the cooperation search algorithm (CSA). OBL was incorporated to enhance the algorithm's exploration capability, while NM was added to improve its exploitation capability. In addition, the improved hunger games search (IHGS) and the improved Lévy flight distribution with simulated annealing (LFDSA) algorithms, which were designed without any restrictions for ideal DC-DC buck converter systems with FOPID controllers and were the highest performing algorithms in the literature until the writing of this thesis, were redesigned for the non-ideal DC-DC buck converters by incorporating the crossover frequency constraint for this study and compared with the proposed algorithm. These comparisons consist of analyzes such as box plot analysis, nonparametric statistical tests, benchmark functions analysis and convergence behavior. These comparisons have shown that OCSANM is the superior approach. This study marks the first implementation of OCSANM alongside the redesigned IHGS and LFDSA algorithms in the optimization of FOPID controller parameters for non-ideal DC-DC buck converter systems. The OCSANM-based FOPID controlled non-ideal DC-DC buck converter system was compared with CSA, IHGS, and LFDSA algorithm-based systems, as well as a conventional pole placement (PP) method. This comparison examined transient and frequency responses, objective function values, measurement noise, and robustness analyses. The proposed OCSANM-based system demonstrated rise times that were 25.98%, 36.71%, and 70.63% faster, and settling times that were 14.74%, 20.56%, and 78.58% faster than IHGS, LFDSA, and PP, respectively. Furthermore, the OCSANM-based system exhibited bandwidth increases of 38.59%, 53.68%, and 67.39% compared to the existing approach-based systems, respectively. Additionally, analog circuits using operational amplifiers (Op-Amps) were implemented for non-ideal DC-DC buck converter systems obtained using the optimal FOPID controller parameters provided by OCSANM, CSA, IHGS, and LFDSA algorithms, as well as the filtered PID (FPID) parameters provided by the PP method. These circuits were designed in PSIM software, and transient response, load and input voltage variation effects on output voltage, and frequency response analyses were performed for the four algorithms. Consistent with the comparisons made in MATLAB, the results demonstrated that OCSANM achieved the best performance. These findings validated the effectiveness of the OCSANM algorithm in designing FOPID controllers for non-ideal DC-DC buck converter systems. Finally, the effects of different approximation methods as well as the level of order reduction after the conversion of fractional order to integer order on system performance were analyzed to demonstrate the superiority of the chosen approach.