Design and application of an optimally tuned PID controller for DC motor speed regulation via a novel hybrid Lévy flight distribution and Nelder–Mead algorithm

This paper deals with the design of an optimally performed proportional–integral–derivative (PID) controller utilized for speed control of a direct current (DC) motor. To do so, a novel hybrid algorithm was proposed which employs a recent metaheuristic approach, named Lévy flight distribution (LFD) algorithm, and a simplex search method known as Nelder–Mead (NM) algorithm. The proposed algorithm (LFDNM) combines both LFD and NM algorithms in such a way that the good explorative behaviour of LFD and excellent local search capability of NM help to form a novel hybridized version that is well balanced in terms of exploration and exploitation. The promise of the proposed structure was observed through employment of a DC motor with PID controller. Optimum values for PID gains were obtained with the aid of an integral of time multiplied absolute error objective function. To verify the effectiveness of the proposed algorithm, comparative simulations were carried out using cuckoo search algorithm, genetic algorithm and original LFD algorithm. The system behaviour was assessed through analysing the results for statistical and non-parametric tests, transient and frequency responses, robustness, load disturbance, energy and maximum control signals. The respective evaluations showed better performance of the proposed approach. In addition, the better performance of the proposed approach was also demonstrated through experimental verification. Further evaluation to demonstrate better capability was performed by comparing the LFDNM-based PID controller with other state-of-the-art algorithms-based PID controllers with the same system parameters, which have also confirmed the superiority of the proposed approach.