Analysis of Methods of Design of Robust Control Systems with High Gain Coefficient

Abstract

This work is not an overview paper and doesn't cover history of evolution of design methods of robust control systems with high gain coefficient. According to the chronology of the development there are discussed theoretical foundations and practical features of the main methods of this class allowing to control dynamic objects with functional uncertainties. The subject of the research is methods of "localization of motion", "robust correction" and a method based on Lyapunov functions, presented as "K_¥ - robust control systems". The first two methods lead to a two-loop scheme, and the second to a single-loop with robust controller. Despite the compensation of uncertainties and the ghosting of the system in a linear form, the regulators of the first two methods are not robust in relation to the reference trajectory and external disturbances. Therefore, when changing them, it is necessary to perform a structural-parametric change in the regulator in real time. Implementation of this concept in practice leads to the use of a complex adaptive system with a perturbation identifier. The advantages and disadvantages of the methods are analysed. The use of a high gain coefficient for suppressing uncertainties has a dialectical basis - the inverse proportionality of the static error to the open-loop gain. This feature led to a simple and universal engineering method of synthesis, which does not require the use of a special mathematical device. The main disadvantage of the first two methods is that there are prevailing heuristic reasonings while synthesis, mainly in the search for a structure that allows an unlimited increase in the gain without breaking stability. The results of computer simulation in the Matlab/Simulink software environment are presented.