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Top1. Introduction
One of the most powerful methods for function minimization is known as PSO (particle swarm optimization) proposed by Kennedy and Eberhart (1995). Since then there were hundreds of modifications of the canonical PSO-algorithm. Some of them have quite good searching abilities and allow their applying for a wide range of the real-world problems (Pluhacek, 2018; Wang, 2017; Goudos, 2018). One of such problems is optimal control, particularly tuning of PI or PID-controllers for: quadrotors (Nazaruddin, 2018), active magnetic bearing suspends (Štimac, 2014), variable frequency brushless synchronous generator (Smail, 2018), bioreactors (Latha, 2013), overhead crane (Nur Iffah, 2019), energy conversion system (Atacak, 2017) and many others. Almost all of these works involve following criteria to minimize: Integral Absolute Error (IAE) (Nazaruddin, 2018), Integral of Time-Absolute Error multiplication (ITAE) (Štimac, 2014), overshoot (Smail, 2018; Nur Iffah, 2019; Atacak, 2017), Integral Square Error (ISE) (Latha, 2013), rise time and settling time (Nur Iffah, 2019; Atacak, 2017), steady-state error (Nur Iffah, 2019). However, other ones were ignored: maximal control, Integral Square Control (ISC), Integral Time-Absolute Control (ITAC), etc. Researches in that area are continuing.
The researches aim is to adjust the controller in such a manner, that the most important criteria reduced to a minimum (or, at least, decreased as much as possible) and constraints are met. Nevertheless, constraints are very infrequent in the optimal tuning problems statements. It necessitates the development of such a problem-solving methodology, which might cope with mentioned difficulties.
The efficiency of the problem solving depends on the features of the chosen optimization method (algorithm). For PSO-based class of algorithms, their features depend heavily on their parameters. Appropriate adjusting of the parameters provides good algorithm performance.