Sigmoid

Chemical Reactor Design Toolbox Reference Manual

function y = Sigmoid(x,c,xnom)

The function approximates a unit step,

$\begin{equation*} y = \left\{ \begin{array}{lcl} 1 & \text{for} & x > c \\ 0 & \text{for} & x < c \end{array} \right. \end{equation*}$

by a continuous and a differentiable sigmoidal function.

$\begin{equation*} y = \frac{1}{\left(1 + \exp\left\{-\frac{a \, \left(x-c\right)}{x_{small}}} \right\}\right)} \end{equation*}$

Note: The nominal value $xnom$ is needed to adjust the slope of the exponential function.

Example

$\begin{equation*} c = 0 \, bar \qquad a = 500 \qquad xnom = 1.0 \times 10^{-5} \, bar \end{equation*}$