METHOD OF SYNTHESIS OF NONLINEAR SYSTEMS WITH THE APPROXIMATED CONTROL LAWS

Abstract

The article describes the features of synthesis of nonlinear systems in which controls are formed on the basis of approximating functions of state. The current state of the theory and applications of the method of approximating the control by energy facilities and technological objects. It is noted that the use of piecewise linear functions to approximate the nonlinearities has several disadvantages. The main is that unknown combination of linear sections corresponding to the given input signal (voltage, current, etc.). Another disadvantage of the piecewise linear approximation is that the derivatives on the boundaries of parcels have discontinuities, which is undesirable for control of electromechanical systems. It is shown that the wide possibilities that arise in systems with control based on approximating the sigmoid function, due to the lack of discontinuous functions and sliding modes. The synthesis of control systems based on approximation of nonlinear functions by sigmoid function excludes systems with extreme values of control actions, reduces the load on the actuators system and ensures smooth their job. In support of this the results of comparative analysis of the systems with relay and approximating controls.