What is a good rise time in control system?

For applications in control theory, according to Levine (1996, p. 158), rise time is defined as “the time required for the response to rise from x% to y% of its final value”, with 0% to 100% rise time common for underdamped second order systems, 5% to 95% for critically damped and 10% to 90% for overdamped ones .

Rise time is the time taken for a signal to cross a specified lower voltage threshold followed by a specified upper voltage threshold . This is an important parameter in both digital and analog systems. In digital systems it describes how long a signal spends in the intermediate state between two valid logic levels.

Historically, oscilloscope frequency response tended to approximately follow the rule: Bandwidth x risetime = 0.35 . This corresponds to a 1- or 2-pole filter roll-off in the frequency domain. Today, at the high end, most real-time digital oscilloscopes more closely follow this rule: Bandwidth x rise time = 0.45.

In this equation, Tr is the 10-90% rise time of the signal . The 10-90% rise time is the time interval it takes the signal to go from 10% of its final value to 90% of its final value. For example, if a signal has a rise time of 0.5 ns, its bandwidth will be 700 MHz.10 Eki 2019