Second-order Systems Rise Time

Second-order systems Rise Time:

Here the rise time is obtained in terms of . The system is assumed to be underdamped.

Considering the equation,

 

 

we obtain the rise time t_r by letting c(t_r) = 1 or

 

 

We obtain from the above equation, the following equation:

 

 

 

where β is defined in Figure 1.

Fig: 1 Definition of β

 

Clearly, for a small value of t_r,  ω_d must be large.