In this paper, atom search optimization (ASO) algorithm and a novel chaotic version of it [chaotic ASO (ChASO)] are proposed to determine the optimal parameters of the fractional-order propor-tional+integral+derivative (FOPID) controller for dc motor speed control. The ASO algorithm is simple and easy to implement, which mathematically models and mimics the atomic motion model in nature, and is developed to address a diverse set of optimization problems. The proposed ChASO algorithm, on the other hand, is based on logistic map chaotic sequences, which makes the original algorithm be able to escape from local minima stagnation and improve its convergence rate and resulting precision. First, the proposed ChASO algorithm is applied to six unimodal and multimodal benchmark optimization problems and the results are compared with other algorithms. Second, the proposed ChASO-FOPID, ASO-FOPID, and ASO-PID controllers are compared with GWO-FOPID, GWO-PID, IWO-PID, and SFS-PID controllers using the integral of time multiplied absolute error (ITAE) objective function for a fair comparison. Comparisons were also made for the integral of time multiplied squared error (ITSE) and Zwe-Lee Gaing's (ZLG) objective function as the most commonly used objective functions in the literature. Transient response analysis, frequency response (Bode) analysis, and robustness analysis were all carried out. The simulation results are promising and validate the effectiveness of the proposed approaches. The numerical simulations of the proposed ChASO-FOPID and ASO-FOPID controllers for the dc motor speed control system demonstrated the superior performance of both the chaotic ASO and the original ASO, respectively. INDEX TERMS DC motor speed control, fractional order PID controller, chaotic atom search optimization algorithm, robustness analysis, transient response.

This paper proposes a novel tuning design of proportional integral derivative (PID) controller via an improved kidney-inspired algorithm (IKA) with a new objective function. The main objective of the proposed approach is to optimize the transient response of the AVR system by minimizing the maximum overshoot, settling time, rise time and peak time values of the terminal voltage, and eliminating the steady state error. After obtaining the optimal values of the three gains of the PID controller (K P , K I , and K D ) with the proposed approach, the transient response analysis was performed and compared with some of the current heuristic algorithms-based approaches in literature to show the superiority of the optimized PID controller. In order to evaluate the stability of the automatic voltage regulator (AVR) system tuned by IKA method, the pole/zero map analysis and Bode analysis are performed. Finally, the robustness analysis of the proposed approach has been carried out with variations in the parameters of the AVR system. The numerical simulation results demonstrated that the proposed IKA tuned PID controller has better control performances compared to the other existing approaches. The essence of the presented study points out that the proposed approach may successfully be applied for the AVR system.INDEX TERMS Automatic voltage regulator, improved kidney-inspired algorithm, PID tuning, robustness analysis, transient response. I. INTRODUCTION A. RESEARCH BACKGROUNDAutomatic voltage regulator (AVR) is essential equipment that is used in power system utilities. As its name implies, the main objective of AVR is to control the terminal voltage of synchronous generator by adjusting its exciter voltage. Due to the high inductance of the generator field windings and load variations, stable and fast response of the regulator is difficult to achieve [1]. Therefore, it is important to improve the AVR performance and ensure stable and efficient response to transient changes in terminal voltage. So far, different control techniques have been proposed by researchers to analyze the AVR system with an aim to gain better dynamic response. However, among these controllers the classical proportional plus integral plus derivative (PID) is the most preferable controller because of its simple design structure and robustness to variations of the system parameters [2]. B. LITERATURE SURVEYThe optimal tuning of the gain parameters (K P , K I and K D ) of the PID controller is a very difficult problem.The associate editor coordinating the review of this manuscript and approving it for publication was Fangfei Li.

A novel design method, sine-cosine algorithm (SCA) is presented in this paper to determine optimum proportional-integral-derivative (PID) controller parameters of an automatic voltage regulator (AVR) system. The proposed approach is a simple yet effective algorithm that has balanced exploration and exploitation capabilities to search the solutions space effectively to find the best result. The simplicity of the algorithm provides fast and high-quality tuning of optimum PID controller parameters. The proposed SCA-PID controller is validated by using a time domain performance index. The proposed method was found efficient and robust in improving the transient response of AVR system compared with the PID controllers based on Ziegler-Nichols (ZN), differential evolution (DE), artificial bee colony (ABC) and bio-geography-based optimization (BBO) tuning methods.

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