Sigmoids superposition for signals approximation with a deadband for sweep in a sequence of quasi-rectangular pulses

In this article, we show how a specially constructed combination of smooth, monotonic non-linear functions and affine transformations can approximate dead-zone-looking one-dimensional signals, previously represented, as a rule, in a piecewise-linear form. Our results can help solve some open questions in analyzing systems with dead-zone-looking nonlinearities. In particular, in the study of such systems in which there are mechanical gaps, or the development of pulse-phase control systems. They can be well approximated by superposition of two symmetric or asymmetrical sigmoidal functions. Finally, numerical experiments show that the resulting formulas describe deadband-looking signals with a high degree of accuracy. This method is simple, because requires a minimum set of input parameters.