Optimal PID plus second-order derivative controller design for AVR system using a modified Runge Kutta optimizer and Bode’s ideal reference model

This paper presents the development of a new metaheuristic algorithm by modifying one of the recently proposed optimizers named Runge Kutta optimizer (RUN). The modified RUN (mRUN) algorithm is obtained by integrating a modified opposition-based learning (OBL) mechanism into RUN algorithm. A probability coefficient is employed to provide a good balance between exploration and exploitation stages of the mRUN algorithm. The greater ability of the mRUN algorithm over the original RUN algorithm is shown by performing statistical test and illustrating the convergence profiles. The developed algorithm is then proposed as an efficient tool to tune a proportional-integral-derivative (PID) plus second-order derivative (PIDD²) controller adopted in an automatic voltage regulator (AVR) system. The controlling scheme is further enhanced by integrating the Bode’s ideal reference model and using the performance index of integral of squared error as an objective function. The proposed reference model-based PIDD² controller tuned by mRUN (mRUN-RM-PIDD²) approach is demonstrated to be superior in terms of transient and frequency responses compared to other available and best performing approaches reported in the last 5 years. In that respect, PID, fractional order PID (FOPID), PID acceleration (PIDA) and PIDD² controllers tuned with the most effective algorithms reported in the last 5 years are adopted for comparisons. The comparative study confirms superior performance of the proposed method.