Tuning of PID-controller by genetic algorithm according to multi-criteria objective function for controlling an unstable object

Abstract

The task of adjusting an industrial-type regulator, namely a PID regulator, which has several parameters, namely the coefficients of proportional, integral, and differential links, is considered. In this study, the PID controller is used to control an unstable object with nonlinear dynamics. The task is to track the input signal with minimal overshoot, error, and settling time. At the same time, the problem of the optimal setting of a multi-parameter object to satisfy a multi-criteria objective function arises. Classical approaches to the optimization of several variable functions are faced with the need to find partial derivatives for each variable. At the same time, there are effective heuristic solutions that are based on a genetic algorithm, which creates an initial population, which is then updated by saving the best descendants and searching for new possible options. The article examines such an algorithm for stabilizing an unstable object whose characteristic equation has multiple zero roots. The paper presents the parameters of the algorithm and the results of modeling using modern techniques for modeling automatic control systems in phase space.