Designing fractional-order (PID mu)-D-lambda controller using differential harmony search algorithm

Harmony Search (HS) has recently emerged as an efficient metaheuristic algorithm that draws inspiration from the music improvisation process. This article describes the design of fractional-order proportional-integral-derivative (FOND) controllers, using a newly developed variant of HS, known as differential harmony search (DHS). Design of FOPID controllers is more complex than that of conventional integer-order PID controller since the latter involves only three parameters while the former involves five parameters to tune. Controller synthesis is based on user specifications like peak overshoot and, rise time; which are used to formulate a single objective optimisation problem. Tustin operator-based continuous fraction expansion (CFE) scheme was used to digitally realise fractional-order closed loop transfer function of the designed plant-controller setup. Experimental results of comparison between DHS and a few established optimisation techniques [particle swami optimisation (PSO) and genetic algorithm (GA)] over different instantiations of the design problem reflect the superiority of the proposed methodology.