A novel improved arithmetic optimization algorithm for optimal design of PID controlled and Bode’s ideal transfer function based automobile cruise control system

Abstract

This paper considers the development of a novel hybrid metaheuristic algorithm which is proposed to achieve an optimum design for automobile cruise control (ACC) system by using a proportional-integral-derivative (PID) controller based on Bode’s ideal transfer function. The developed algorithm (AOA-NM) adopts one of the recently published metaheuristic algorithms named the arithmetic optimization algorithm (AOA) to perform explorative task whereas another well-known local search method known as Nelder–Mead (NM) simplex search to perform exploitative task. The developed hybrid algorithm was initially tested on well-known benchmark functions by comparing the results with only its original version since AOA has already been shown to be better than other state-of-the-art algorithms. The statistical results obtained from benchmark functions have demonstrated better capability of AOA-NM. Furthermore, a PID controller based on Bode’s ideal transfer function was adopted to regulate an ACC system optimally. Statistical, convergence rate, time domain and frequency domain analyses were performed by comparing the performance of AOA-NM with AOA. The respective analyses have shown better capability of the proposed hybrid algorithm. Moreover, the capability of the proposed AOA-NM based PID control scheme was compared with other available approaches in the literature by using time domain analysis. The latter case has also confirmed enhanced capability of the proposed approach for regulating an ACC system which further verified the ability of the proposed AOA-NM algorithm. Lastly, other recently reported and effective metaheuristic algorithms were also used to assess the performance of the proposed approach. The obtained comparative results further confirmed the AOA-NM to be a greater tool to achieve more successful results for ACC system. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.