Improvisation of artificial hummingbird algorithm through incorporation of chaos theory in intelligent optimization of fractional order PID controller tuning

Artificial hummingbird algorithm (AHA) is one of the recent bio-inspired meta-heuristic algorithms which is based on hummingbirds’ intelligent behaviours. Just like many meta-heuristic algorithms, it also suffers from freezing in local optima and slow convergence speed. In this paper, the authors have proposed a novel chaotic artificial hummingbird algorithm (ChAHA) obtained by incorporating chaos theory in the original AHA with the aim of escaping it from local minima stagnation along with high convergence rate and more precise results. Firstly, detailed studies have been performed on six different unimodal and multimodal constrained benchmark functions by employing ten different chaotic test mappings in order to determine the most enhanced and efficient one. Later, statistical testing and graphical analysis prove that incorporation of chaotic maps (especially tent map) in AHA improves the original AHA by showing promising performance. Finally, the performance of the ChAHA (with tent map) is also validated by finding the optimum gain values of a fractional order proportional-integral-derivative (FOPID) controller, meticulously tailored to meet the specific requirements of DC motor speed control in MATLAB/Simulink. It has been unambiguously affirmed that the closed loop system with the proposed ChAHA-FOPID controller has better performance than certain pre-existing controllers such as grey wolf optimization based FOPID (GWO-FOPID), atom search optimization based FOPID (ASO-FOPID) and manta ray foraging optimization based FOPID (MRFO-FOPID) controllers. Finally, robustness analysis is also carried out with parameter variations of DC motor and the final simulation results validate the superiority of the proposed approach.