An algorithm for modeling smooth hysteresis nonlinearities is proposed, taking into account the slope coefficient k and the saturation level c. The developed model provides accuracy and ease of adjustment while maintaining intuitive physical parameters of the hysteresis loop, which makes it effective for practical application in the tasks of analysis and synthesis of nonlinear control systems.

Keywords: unambiguous nonlinearities, hysteresis, automatic control systems, backlash with saturation, ambiguous nonlinearities, algorithm, modeling of automatic control systems, relay, static characteristic, approximation

The paper proposes a modified method for the parametric synthesis of nonlinear automatic control systems with ambiguous nonlinearities based on the generalized Galerkin method. To eliminate the need to determine switching points, the transient process is approximated by two sections: a polynomial before the time tp and a constant value after it. This allows us to obtain recurrent formulas for Bqi integrals, simplify calculations, and maintain the absolute stability of the system.

Keywords: parametric synthesis, nonlinear automatic control systems, generalized Galerkin method, ambiguous (multi-valued) nonlinearities, hysteresis, switching points, polynomial approximation, impulse automatic control systems, recurrent relations