Vol.:(0123456789) 1 3 Evolutionary Intelligence https://doi.org/10.1007/s12065-019-00290-x RESEARCH PAPER Optimal FOPID/PID controller parameters tuning for the AVR system based on sine–cosine‑algorithm Jailsingh Bhookya 1  · Ravi Kumar Jatoth 1 Received: 15 December 2018 / Revised: 15 May 2019 / Accepted: 5 September 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract To enhance the controller performance, an advanced sine–cosine-algorithm (SCA) is employed for Fractional order PID (FOPID) controller tuning in this paper. The SCA-FOPID controller is based on model-based controller design method of physical systems to get better performance. The FOPID controller is designed by SCA optimization technique using the time domain objective function for AVR system. The SCA technique is responsible to optimize fve parameters of FOPID controller based on minimum value of objective function of the controller design. The proposed SCA-FOPID controller is design at a global optimum of objective function is acheived. Then, the AVR system has good regulation of terminal volt- age at the output to meet desired performance. The proposed method has a good reference tracking ability and frequency responses. This method is compared with the PID and FOPID controller designs of AVR system in the recent years, the proposed SCA-FOPID controller gives an excellent performance from the extensive simulations studies. Keywords Sine cosine algorithm · Optimal control · Optimization methods · FOPID controller · PID controller · AVR system · Optimal control applications 1 Introduction In the power generation plants, the yield of a turbine at syn- chronous generator will oscillate at the equilibrium state that provides output voltage fuctuations by an external distur- bances, those are change in load variation [1, 2], oscillations in the output and so on. These oscillations are adverse in an electromechanical system, this will degrade the power qual- ity and lead to instability of power systems. So, to improve the power system stability and to enhance the power qual- ity, plenty of existing generators are prepared with excita- tions, which are controlled by an automatic voltage regulator (AVR) [2–4]. The power system stabilizer (PSS) is to keep voltage across the terminal without variations, such a key regulation to the exciting of the system. The AVR system is mainly designed to regulate the voltage across the terminal of generator, to a desired voltage level for any of the load conditions at any instant. Signifcant requisites of AVR systems are, it should be stabilized and it can be regulate desired terminal voltage des- ignated by load variations, even though avoiding oscillations in transient performance. Hence, to get a better response of the AVR system should design carefully. There are sev- eral advanced progressive control methods which have been developed in the recent years. To control the AVR system terminal voltage, the choice of excellent primary control- ler is Proportional–Integral–Derivative (PID) controllers due to its easy/simple structure and robustness [5, 6] . The PID controller parameters are tune with conventional and advanced methods has been available to get good response in the literature. As the class of conventional methods for PID parameter tuning are Ziegler Nichols (ZN), Cohen-Coon methods [3], etc. The other class of advanced methods are random search techniques, those are genetic algorithm (GA), simulated annealing (SA), and plenty of evolutionary algorithms. The GA has recognized excessive attention in the feld of con- trol systems to exploration in optimality of PID controller gain parameters. Even though GA has widely applicable to several control system applications, the evolutionary optimi- zation algorithms are in use to overcome the computational complexity. Such evolutionary optimization algorithms are * Jailsingh Bhookya jailsingh@student.nitw.ac.in 1 Department of ECE, NIT Warangal, Hanamkonda, Telangana, India