**Autors:** Perev, K. L.
**Title:** Rational function approximation of the relay with hysteresis nonlinear element
**Keywords:** relay with hysteresis characteristic, hyperbolic tangent function, continued fraction approximation, Pade series approximation**Abstract:** This paper considers the problem of rational function approximation of the relay with hysteresis characteristic. The relay with hysteresis element has differential-based with memory characteristic, which is rate dependent and two-valued, involving the input signal velocity in its description. The presented model includes two ideal relay characteristics, which selection is depending on the input behavior. The rational function description is implemented for analytical approximation of the relay switching behavior. Both relay discontinuous jumps are approximated in terms of hyperbolic tangent functions, which on their own turn are replaced by continued fraction and Pade series expressions. The nearness of approximation is evaluated by using one parameter descriptions for the hyperbolic tangent function. The errors of approximation of the ideal relay characteristic are also discussed.
**References**
- Beebe, N, 1950, “Hyperbolic functions”, in The mathematical function computation handbook, Springer, Volume , pp.
**Issue**
| IFAC PapersOnLine, vol. 54, issue 14, pp. 19 – 24, 2021, Japan, Elsevier |
Copyright IFAC PapersOnLine Full text of the publication |