Step response settling time

Question

Vincent 2014-12-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/166160-step-response-settling-time

评论： Bart Nijman 2017-1-14

采纳的回答： Arkadiy Turevskiy

Hi,

The settling is the time required for the response curve to reach and stay within a range of 2% of the final value.

So why in Matalb the two following systems have the same stelling time ? >> Tz = 1

>> Tp = 3

>> SO1 = tf([ 1],[Tp 1])

>> SO2 = tf([Tz 1],[Tp 1])

>> InfoSO1 = stepinfo(SO1);

>> InfoSO2 = stepinfo(SO2);

Theorically (for me) these settling times should be :

tr1 = -Tp*log(0.02)

tr2 = -Tp*log(0.02/(1+Tz/Tp))

Thank's for any answer.

V.

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Answer 1

Arkadiy Turevskiy 2014-12-11

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/166160-step-response-settling-time#answer_162077

If you look at the doc page for stepinfo , you will see that settling time is defined as:

The response has settled when the error y(t) - yfinal becomes smaller than a fraction ST of its peak value. The default value is ST=0.02 (2%).

Changing the value of zero changes the initial output value for the step response, but does not change the time constant of the first order system. stepinfo computes the settling time as a time when the difference between step response and final value (1) is 2% of the difference between initial value and final value.

So that's why the zero does not change the settling time.

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Vincent 2014-12-11

Ok for considering the zero as an inital condition. However, this definition of settling time is for me a little bit strange.

Thank you for your perspicacity

V.

Bart Nijman 2017-1-14

Sorry to bump this old question, but i have a similar problem. I would like to calculate settling time where the error bandwidth is specified as some absolute value rather than a percentage of its peak value. Is there any code,function or adjustment that i could make, so that i could calculate the settling time in that manner?

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