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 .

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How is bandwidth and rise time related?

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.

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