K¥-Robust Control Systems

Abstract

The article Presents development of the classical control systems with a high gain. In the classical formulation (M. V. Meyerov) these systems found no Proper development. The basis of the proposed approach is the method of Lyapunov functions. As a result of a synthesis "a robust equivalent control" was obtained. A possibility of a limitless increase of the controller gain without violation of the stability of the system makes it possible to suppress the general components of an uncertain model to an arbitrarily small value. This ensures a high precision of the reference trajectory tracking and speed for a wide class of nonlinearities and uncertainties. In the limit the system is described by the equation of the hyperplane for an arbitrary initial state. K_¥-robust system is applied to a nonlinear multidimensional coupled systems with an interval uncertainty. The author managed to solve the problem of autonomy of the direct channels without the use of the cross-channel compensators, which is of important practical significance. The disadvantages of the proposed methodology are absence of the analytical formula for determination of the gain coefficient of the controller, gain of the highfrequency noise having immediate access to the controller, as well as the use of the output derivative for formation of PD controller. Moreover, not every object can achieve a high gain. The theoretical results were proved by solving of the model problems on MATLAB/Simulink.