The Laplace transform of the step response of a system is given by
\[
Y(s)=\frac{100}{s(s+100)}
\]
The rise time is defined as the time taken for the response to go from $0.1$ to $0.9$ of its final value. The settling time is defined as the time taken for the response to reach $0.98$ of its final value.
For this system, the rise time $\left(\mathrm{T}_{\mathrm{r}}\right)$, settling time $\left(\mathrm{T}_{\mathrm{s}}\right)$, and time constant $\left(\mathrm{T}_{\mathrm{c}}\right)$, all expressed in seconds, are
- $\mathrm{T}_{\mathrm{r}}=0.022, \mathrm{~T}_{\mathrm{s}}=0.04, \mathrm{~T}_{\mathrm{c}}=0.01$
- $\mathrm{T}_{\mathrm{r}}=0.22, \mathrm{~T}_{\mathrm{s}}=0.404, \mathrm{~T}_{\mathrm{c}}=0.01$
- $\mathrm{T}_{\mathrm{r}}=2.2, \mathrm{~T}_{\mathrm{s}}=4.04, \mathrm{~T}_{\mathrm{c}}=1.01$
- $\mathrm{T}_{\mathrm{r}}=22, \mathrm{~T}_{\mathrm{s}}=40.4, \mathrm{~T}_{\mathrm{c}}=10.1$
