Exponentials

Generate a rising and falling exponential signal

 Description The Exponentials component has a real output that is a rising exponential followed by a falling exponential signal.
 Equations $y={y}_{0}+\left\{\begin{array}{cc}0& t<{T}_{0}\\ {y}_{h}\left(1-\mathrm{exp}\left(-\frac{t-{T}_{0}}{{\mathrm{\tau }}_{r}}\right)\right)& {T}_{0}\le t<{T}_{0}+{T}_{r}\\ {y}_{r}\mathrm{exp}\left(-\frac{t-{T}_{0}-{T}_{r}}{{\mathrm{\tau }}_{f}}\right)& \mathrm{otherwise}\end{array}$ ${y}_{r}={y}_{h}\left(1-\mathrm{exp}\left(-\frac{{T}_{r}}{{\mathrm{\tau }}_{r}}\right)\right)$

Connections

 Name Description Modelica ID $y$ Real output signal y

Parameters

 Name Default Units Description Modelica ID ${T}_{0}$ $0$ $s$ Time offset of the signal startTime ${T}_{r}$ $0.5$ $s$ Rise time riseTime ${\mathrm{\tau }}_{r}$ $0.1$ $s$ Rise time constant riseTimeConst ${\mathrm{\tau }}_{f}$ ${\mathrm{taur}}_{r}$ $s$ Fall time constant fallTimeConst ${y}_{0}$ $0$ $1$ Offset of output signal offset ${y}_{h}$ $1$ $1$ Height of output for infinite riseTime outMax

 Modelica Standard Library The component described in this topic is from the Modelica Standard Library. To view the original documentation, which includes author and copyright information, click here.