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 considers the solution of the problem of synthesis of a multiconnected nonlinear system with polynomial and piecewise linear approximations. The generalized Galerkin method is used as a mathematical apparatus. The synthesis results and advantages of each of the approximations are presented.

Keywords: multivariable automatic control systems, parametric synthesis, nonlinear automatic control systems, generalized Galerkin method, polynomial approximation, piecewise-linear approximation, saturation, minimization, objective function, recurrent relations