Time Delay of An Underdamped Second Order System

Transient response for a second-order system.

A student asked me how to find the time delay, t_d  for a second-order system by applying mathematical equation.

Let c_{final} denote the final value of the waveform. Then, the rise time t_r will be the time duration between 0.1c_{final} to 0.9c_{final} .

Since the time delay t_d equals to the time for the waveform to reach 0.5c_{final}. My rough idea for the mathematical equation is:
t_d \approx 1.25 * t_r / 2 .

Just an approximation as the waveform between 0.1c_{final} to 0.9c_{final} is not a linear line.

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Author: zkchong

I have been teaching in university for 7 years and currently a data science engineer at Axiata Digital Advertising, Malaysia. Like to do research.

2 thoughts on “Time Delay of An Underdamped Second Order System”

  1. For an under-damped system, the rise time is the time it takes for the system to go from 0 to 100% of the final value

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