Analytic approximation of nonlinearities with memory.

This paper considers the problem of analytic approximation of nonlinearities with memory. The mathematical models for nonlinearities with memory used in the paper are differential-based, rate dependent and two-valued, involving the input signal velocity in its description. The nonlinear characteristics, considered in the paper, are the shifted unpolarized relay with hysteresis, relay with hysteresis and dead zone, and relay with hysteresis and saturation. Explicit formulas for their mathematical models are presented, containing the ideal relay as basic element in their description. The analytic approximation for nonlinearities with memory reduces to the problem of rational function approximation of the ideal relay switching behavior. The discontinuous jumps are presented by hyperbolic tangent functions, where the exponential terms are approximated by using the chained fraction method. The error of approximation is reduced by introducing a parameter in the hyperbolic tangent presentation and the corresponding errors of approximation are discussed. [ABSTRACT FROM AUTHOR]