Principles of constructing multi-mode control based on S-shaped sigma functions

Abstract

For a wide class of multi-mode control objects operating under uncertainty, the principles of synthesis of control actions based on S-shaped sigma functions approximating combinations of single-valued typical nonlinearities have been developed. The use of these functions made it possible to ensure, with a decrease in deviations of the controlled variables from the specified influences, a smooth change of control levels without jumps, which does not require setting the switching times to the ranges of change of the implemented controls, as well as to exclude frequent maximum effects on the actuator and to limit their amplitude when changing the modes of operation of the system, which leads to an increase in performance in transient modes and a decrease in overshoot in steady-state modes. In addition, with practical implementation, a favorable operation of the executive mechanism is ensured. Based on the analysis of the obtained transient processes in systems with relay control and in systems with approximating control, the features of the application of the principles for multi-mode systems operating in transient and steady-state modes are shown.